gwm17/catima
1
0
Fork 0
mirror of https://github.com/gwm17/catima.git synced 2024-11-22 10:18:50 -05:00
Code Issues Projects Releases Wiki Activity

initial

Browse Source
This commit is contained in:
hrocho 2017-07-25 18:19:11 +02:00
commit 56f2b07e4e
53 changed files with 10371 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

37
.gitignore vendored Normal file
View File

@ -0,0 +1,37 @@
# Object files
*.o
*.ko
*.obj
*.elf
# Precompiled Headers
*.gch
*.pch
# Libraries
*.lib
*.a
*.la
*.lo
# Shared objects (inc. Windows DLLs)
*.dll
*.so
*.so.*
*.dylib
# Executables
*.exe
*.out
*.app
*.i*86
*.x86_64
*.hex
# Debug files
*.dSYM/
*.su
ana/*
benchmark/*
build/*

148
CMakeLists.txt Normal file
View File

@ -0,0 +1,148 @@
cmake_minimum_required(VERSION 3.2.0)
project(catima)
############ options #############
#option(THREADS "Use multi-threading" ON)
option(CATIMA_PYTHON "compile the Catima python module(requires numpy and cython installed)" OFF)
option(TESTS "build tests" OFF)
option(EXAMPLES "build examples" ON)
option(GENERATE_DATA "make data tables generator" OFF)
option(THIN_TARGET_APPROXIMATION "thin target approximation" ON)
option(DOCS "build documentation (requires doxygen)" OFF)
######## build type ############
#set(CMAKE_BUILD_TYPE Release)
set(CMAKE_BUILD_TYPE Debug)
set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -g")
################################
######### compiler flags ###########
set(CMAKE_CXX_EXTENSIONS OFF)
set(CMAKE_CXX_STANDARD 14)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
if ("${CMAKE_CXX_COMPILER_ID}" STREQUAL "GNU" OR
"${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
set(warnings "-Wall -Wextra -Werror")
endif()
############# Requirements ##################
find_package(GSL REQUIRED)
#if(THREADS)
# find_package(Threads REQUIRED)
# set (EXTRA_LIBS ${EXTRA_LIBS} ${CMAKE_THREAD_LIBS_INIT})
# set (USE_THREADS ON)
# MESSAGE(STATUS "Nurex will use threads")
#endif(THREADS)
find_package(PythonInterp)
if(PYTHONINTERP_FOUND)
message("-- Python found: ${PYTHON_EXECUTABLE}")
endif()
configure_file(
"${PROJECT_SOURCE_DIR}/build_config.in"
"${PROJECT_BINARY_DIR}/include/catima/build_config.h"
)
configure_file("${PROJECT_SOURCE_DIR}/init.sh.in"
"${PROJECT_BINARY_DIR}/init.sh"
)
############### main build ###########################
file(GLOB SOURCES *.cpp)
file(GLOB HEADERS *.h)
add_library(catima SHARED ${SOURCES})
add_library(catima_static STATIC ${SOURCES})
set_target_properties(catima_static PROPERTIES OUTPUT_NAME catima POSITION_INDEPENDENT_CODE ON)
target_link_libraries(catima ${EXTRA_LIBS} ${GSL_LIBRARIES} )
FILE(COPY ${HEADERS} DESTINATION ${PROJECT_BINARY_DIR}/include/catima)
# the compiler used for C++ files
MESSAGE( STATUS "CMAKE_CXX_COMPILER: " ${CMAKE_CXX_COMPILER} )
# the compiler flags for compiling C++ sources
MESSAGE( STATUS "CMAKE_CXX_FLAGS: " ${CMAKE_CXX_FLAGS_RELEASE} )
######## for python module
if(CATIMA_PYTHON)
if(NOT PYTHONINTERP_FOUND)
MESSAGE(SEND_ERROR "Python is required to build nurex python modules")
endif(NOT PYTHONINTERP_FOUND)
find_program(CYTHON_EXECUTABLE
NAMES cython cython2 cython3 cython.bat
DOC "path to the cython executable"
)
if(NOT CYTHON_EXECUTABLE)
MESSAGE(SEND_ERROR "Cython not found, it is required to build nurex python modules")
endif(NOT CYTHON_EXECUTABLE)
MESSAGE(STATUS "Cython found: " ${CYTHON_EXECUTABLE})
### build libraries string
foreach(entry ${EXTRA_LIBS} ${GSL_LIBRARIES} catima)
LIST (APPEND EXTRA_PYTHON_LIBS \"${entry}\")
endforeach(entry ${EXTRA_LIBS} ${GSL_LIBRARIES} catima)
string (REPLACE ";" "," EXTRA_PYTHON_LIBS "${EXTRA_PYTHON_LIBS}")
# if(THREADS)
# set (CYTHON_DEFINES "-DUSE_THREADS=1")
# endif(THREADS)
### insert libraries string and create setup.py
FILE(COPY catimac.pxd catima.pyx DESTINATION ${PROJECT_BINARY_DIR})
set(CATIMA_LIB ${CMAKE_SHARED_LIBRARY_PREFIX}catima${CMAKE_SHARED_LIBRARY_SUFFIX})
configure_file(${CMAKE_CURRENT_SOURCE_DIR}/setup.py.in ${PROJECT_BINARY_DIR}/setup.py)
add_custom_target(target_python ALL DEPENDS catima)
add_custom_command(TARGET target_python
COMMAND ${PYTHON_EXECUTABLE} ${PROJECT_BINARY_DIR}/setup.py build_ext ${CYTHON_DEFINES} -i
)
endif(CATIMA_PYTHON )
########## Sub Directories ###########
include_directories(${CMAKE_CURRENT_SOURCE_DIR})
include_directories("${PROJECT_BINARY_DIR}/include")
if(EXAMPLES)
file(GLOB EXAMPLES examples/*.cpp)
FILE(COPY ${EXAMPLES} DESTINATION ${PROJECT_BINARY_DIR}/examples)
FILE(COPY examples/makefile DESTINATION ${PROJECT_BINARY_DIR}/examples)
#add_subdirectory("examples")
endif(EXAMPLES)
if(TESTS)
add_subdirectory("tests")
endif(TESTS)
########## data generator ########
if(GENERATE_DATA)
add_executable(generate_ls_coeff utils/generator.cpp)
target_link_libraries(generate_ls_coeff catima)
#add_custom_command(
# OUTPUT ${CMAKE_CURRENT_BINARY_DIR/include/generated_LS_coeff.h}
# COMMAND
#)
endif(GENERATE_DATA)
####### DOCS generation #########
if(DOCS)
find_package(Doxygen REQUIRED)
if(DOXYGEN_FOUND)
configure_file(${CMAKE_CURRENT_SOURCE_DIR}/doxygen.in ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile @ONLY)
add_custom_target(docs
COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile COMMENT "Generating API documentation with Doxygen" VERBATIM )
endif(DOXYGEN_FOUND)
endif(DOCS)
####### install part #######
FILE(GLOB headers "*.h")
install (TARGETS catima catima_static
LIBRARY DESTINATION lib
ARCHIVE DESTINATION lib)
install (FILES ${headers} DESTINATION include/catima)
###### packaging #######
set(CPACK_PACKAGE_NAME "catima")
set(CPACK_PACKAGE_VENDOR "A. Prochazka")
set(CPACK_PACKAGE_DESCRIPTION_SUMMARY "")
set(CPACK_PACKAGE_VERSION "1.0.0")
set(CPACK_PACKAGE_VERSION_MAJOR "1")
set(CPACK_PACKAGE_VERSION_MINOR "0")
set(CPACK_PACKAGE_VERSION_PATCH "0")
set(CPACK_PACKAGE_INSTALL_DIRECTORY "catima")
include(CPack)

10
CREDITS Normal file
View File

@ -0,0 +1,10 @@
Credits and References
======================
Physics references:
ATIMA
------
https://web-docs.gsi.de/~weick/atima/
B.A.Wealer et. al, Energy loss of relativistic heavy ions im matter, NIM B187(2002)

661
LICENSE Normal file
View File

@ -0,0 +1,661 @@
GNU AFFERO GENERAL PUBLIC LICENSE
Version 3, 19 November 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The GNU Affero General Public License is a free, copyleft license for
software and other kinds of works, specifically designed to ensure
cooperation with the community in the case of network server software.
The licenses for most software and other practical works are designed
to take away your freedom to share and change the works. By contrast,
our General Public Licenses are intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.
Developers that use our General Public Licenses protect your rights
with two steps: (1) assert copyright on the software, and (2) offer
you this License which gives you legal permission to copy, distribute
and/or modify the software.
A secondary benefit of defending all users' freedom is that
improvements made in alternate versions of the program, if they
receive widespread use, become available for other developers to
incorporate. Many developers of free software are heartened and
encouraged by the resulting cooperation. However, in the case of
software used on network servers, this result may fail to come about.
The GNU General Public License permits making a modified version and
letting the public access it on a server without ever releasing its
source code to the public.
The GNU Affero General Public License is designed specifically to
ensure that, in such cases, the modified source code becomes available
to the community. It requires the operator of a network server to
provide the source code of the modified version running there to the
users of that server. Therefore, public use of a modified version, on
a publicly accessible server, gives the public access to the source
code of the modified version.
An older license, called the Affero General Public License and
published by Affero, was designed to accomplish similar goals. This is
a different license, not a version of the Affero GPL, but Affero has
released a new version of the Affero GPL which permits relicensing under
this license.
The precise terms and conditions for copying, distribution and
modification follow.
TERMS AND CONDITIONS
0. Definitions.
"This License" refers to version 3 of the GNU Affero General Public License.
"Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.
"The Program" refers to any copyrightable work licensed under this
License. Each licensee is addressed as "you". "Licensees" and
"recipients" may be individuals or organizations.
To "modify" a work means to copy from or adapt all or part of the work
in a fashion requiring copyright permission, other than the making of an
exact copy. The resulting work is called a "modified version" of the
earlier work or a work "based on" the earlier work.
A "covered work" means either the unmodified Program or a work based
on the Program.
To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
computer or modifying a private copy. Propagation includes copying,
distribution (with or without modification), making available to the
public, and in some countries other activities as well.
To "convey" a work means any kind of propagation that enables other
parties to make or receive copies. Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.
An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License. If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.
1. Source Code.
The "source code" for a work means the preferred form of the work
for making modifications to it. "Object code" means any non-source
form of a work.
A "Standard Interface" means an interface that either is an official
standard defined by a recognized standards body, or, in the case of
interfaces specified for a particular programming language, one that
is widely used among developers working in that language.
The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
packaging a Major Component, but which is not part of that Major
Component, and (b) serves only to enable use of the work with that
Major Component, or to implement a Standard Interface for which an
implementation is available to the public in source code form. A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
(if any) on which the executable work runs, or a compiler used to
produce the work, or an object code interpreter used to run it.
The "Corresponding Source" for a work in object code form means all
the source code needed to generate, install, and (for an executable
work) run the object code and to modify the work, including scripts to
control those activities. However, it does not include the work's
System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work. For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,
such as by intimate data communication or control flow between those
subprograms and other parts of the work.
The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.
The Corresponding Source for a work in source code form is that
same work.
2. Basic Permissions.
All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met. This License explicitly affirms your unlimited
permission to run the unmodified Program. The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work. This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.
You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force. You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright. Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.
Conveying under any other circumstances is permitted solely under
the conditions stated below. Sublicensing is not allowed; section 10
makes it unnecessary.
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.
When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.
4. Conveying Verbatim Copies.
You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.
You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.
5. Conveying Modified Source Versions.
You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:
a) The work must carry prominent notices stating that you modified
it, and giving a relevant date.
b) The work must carry prominent notices stating that it is
released under this License and any conditions added under section
7. This requirement modifies the requirement in section 4 to
"keep intact all notices".
c) You must license the entire work, as a whole, under this
License to anyone who comes into possession of a copy. This
License will therefore apply, along with any applicable section 7
additional terms, to the whole of the work, and all its parts,
regardless of how they are packaged. This License gives no
permission to license the work in any other way, but it does not
invalidate such permission if you have separately received it.
d) If the work has interactive user interfaces, each must display
Appropriate Legal Notices; however, if the Program has interactive
interfaces that do not display Appropriate Legal Notices, your
work need not make them do so.
A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit. Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.
6. Conveying Non-Source Forms.
You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:
a) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by the
Corresponding Source fixed on a durable physical medium
customarily used for software interchange.
b) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by a
written offer, valid for at least three years and valid for as
long as you offer spare parts or customer support for that product
model, to give anyone who possesses the object code either (1) a
copy of the Corresponding Source for all the software in the
product that is covered by this License, on a durable physical
medium customarily used for software interchange, for a price no
more than your reasonable cost of physically performing this
conveying of source, or (2) access to copy the
Corresponding Source from a network server at no charge.
c) Convey individual copies of the object code with a copy of the
written offer to provide the Corresponding Source. This
alternative is allowed only occasionally and noncommercially, and
only if you received the object code with such an offer, in accord
with subsection 6b.
d) Convey the object code by offering access from a designated
place (gratis or for a charge), and offer equivalent access to the
Corresponding Source in the same way through the same place at no
further charge. You need not require recipients to copy the
Corresponding Source along with the object code. If the place to
copy the object code is a network server, the Corresponding Source
may be on a different server (operated by you or a third party)
that supports equivalent copying facilities, provided you maintain
clear directions next to the object code saying where to find the
Corresponding Source. Regardless of what server hosts the
Corresponding Source, you remain obligated to ensure that it is
available for as long as needed to satisfy these requirements.
e) Convey the object code using peer-to-peer transmission, provided
you inform other peers where the object code and Corresponding
Source of the work are being offered to the general public at no
charge under subsection 6d.
A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.
A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling. In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage. For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product. A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.
"Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source. The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.
If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information. But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).
The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed. Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.
Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.
7. Additional Terms.
"Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law. If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.
When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it. (Additional permissions may be written to require their own
removal in certain cases when you modify the work.) You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.
Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:
a) Disclaiming warranty or limiting liability differently from the
terms of sections 15 and 16 of this License; or
b) Requiring preservation of specified reasonable legal notices or
author attributions in that material or in the Appropriate Legal
Notices displayed by works containing it; or
c) Prohibiting misrepresentation of the origin of that material, or
requiring that modified versions of such material be marked in
reasonable ways as different from the original version; or
d) Limiting the use for publicity purposes of names of licensors or
authors of the material; or
e) Declining to grant rights under trademark law for use of some
trade names, trademarks, or service marks; or
f) Requiring indemnification of licensors and authors of that
material by anyone who conveys the material (or modified versions of
it) with contractual assumptions of liability to the recipient, for
any liability that these contractual assumptions directly impose on
those licensors and authors.
All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10. If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term. If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.
If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.
Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.
8. Termination.
You may not propagate or modify a covered work except as expressly
provided under this License. Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).
However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.
Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License. If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.
9. Acceptance Not Required for Having Copies.
You are not required to accept this License in order to receive or
run a copy of the Program. Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance. However,
nothing other than this License grants you permission to propagate or
modify any covered work. These actions infringe copyright if you do
not accept this License. Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.
10. Automatic Licensing of Downstream Recipients.
Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License. You are not responsible
for enforcing compliance by third parties with this License.
An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations. If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.
You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.
11. Patents.
A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based. The
work thus licensed is called the contributor's "contributor version".
A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version. For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.
Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.
In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement). To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.
If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients. "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.
If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.
A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License. You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.
Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.
12. No Surrender of Others' Freedom.
If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all. For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.
13. Remote Network Interaction; Use with the GNU General Public License.
Notwithstanding any other provision of this License, if you modify the
Program, your modified version must prominently offer all users
interacting with it remotely through a computer network (if your version
supports such interaction) an opportunity to receive the Corresponding
Source of your version by providing access to the Corresponding Source
from a network server at no charge, through some standard or customary
means of facilitating copying of software. This Corresponding Source
shall include the Corresponding Source for any work covered by version 3
of the GNU General Public License that is incorporated pursuant to the
following paragraph.
Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU General Public License into a single
combined work, and to convey the resulting work. The terms of this
License will continue to apply to the part which is the covered work,
but the work with which it is combined will remain governed by version
3 of the GNU General Public License.
14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of
the GNU Affero General Public License from time to time. Such new versions
will be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the
Program specifies that a certain numbered version of the GNU Affero General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation. If the Program does not specify a version number of the
GNU Affero General Public License, you may choose any version ever published
by the Free Software Foundation.
If the Program specifies that a proxy can decide which future
versions of the GNU Affero General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.
Later license versions may give you additional or different
permissions. However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.
15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
16. Limitation of Liability.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published
by the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If your software can interact with users remotely through a computer
network, you should also make sure that it provides a way for users to
get its source. For example, if your program is a web application, its
interface could display a "Source" link that leads users to an archive
of the code. There are many ways you could offer source, and different
solutions will be better for different programs; see section 13 for the
specific requirements.
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU AGPL, see
<http://www.gnu.org/licenses/>.

39
README.md Normal file
View File

@ -0,0 +1,39 @@
CATima
=======
C++ library for caclulalaton of energy loss, range, angular scattering and time of flight of the particle passing through matter.
The library is based on physics used in the ATIMA code,however its not 100% copy of ATIMA physics.
see CREDITS for more details.
Installation
------------
CMake is used to build the library. For default build use:
```
> mkdir build
> cd build
> cmake ../
> make
```
cmake options
-------------
compile options, enable or disable with cmake:
> cmake ../ -D[OPTION]
available options:
* CATIMA_PYTHON - enable/disable building of the python bindigs, cython and numpy are required to build the catima python module, default OFF
* TESTS - build tests
* EXAMPLES - build examples
* DOCS - prepare doxygen documentation (after cmake, __make docs__ needs to be executed)
ie:
> cmake -DCATIMA_PYTHON=ON -DEXAMPLES=ON ../
after the compilation the libraries and headers must be either installed system-wide by make install or PATH and LD_LIBRARY_PATH must be adjusted to point to headers and library files.
The default install path can be change, ie: cmake -DCMAKE_INSTALL_PREFIX=/opt/catima
the option to system-wide installation is to adjust library path and include paths.
This can be done sourcing the init.sh file, which is generated in the build directory:
> source init.sh

6
build_config.in Normal file
View File

@ -0,0 +1,6 @@
#ifndef BUILD_CONFIG_H
#define BUILD_CONFIG_H
#cmakedefine THIN_TARGET_APPROXIMATION
#endif

758
calculations.cpp Normal file
View File

@ -0,0 +1,758 @@
#include <math.h>
#include <algorithm>
#include <cassert>
#include "catima/calculations.h"
#include "catima/constants.h"
#include "catima/data_ionisation_potential.h"
#include "catima/data_atima.h"
#include "catima/generated_LS_coeff.h"
#include "catima/nucdata.h"
#include "catima/storage.h"
namespace catima{
double dedx_e(Projectile &p, const Target &t, const Config &c){
double se = -1;
if(p.T<=10){
se = sezi_dedx_e(p,t);
}
else if(p.T>10 && p.T<30){
double factor = 0.05 * ( p.T - 10.0 );
se = (1-factor)*sezi_dedx_e(p,t) + factor*bethek_dedx_e(p,t);
}
else {
se = bethek_dedx_e(p,t);
}
return se;
}
double dedx(Projectile &p, const Target &t, const Config &c){
return dedx_e(p,t) + dedx_n(p,t);
}
double reduced_energy_loss_unit(const Projectile &p, const Target &t){
double zpowers = pow(p.Z,0.23)+pow(t.Z,0.23);
double asum = p.A + t.A;
return 32.53*t.A*1000*p.T*p.A/(p.Z*t.Z*asum*zpowers); //projectile energy is converted from MeV/u to keV
}
double dedx_n(const Projectile &p, const Target &t){
double zpowers = pow(p.Z,0.23)+pow(t.Z,0.23);
double asum = p.A + t.A;
double epsilon = 32.53*t.A*1000*p.T*p.A/(p.Z*t.Z*asum*zpowers); //projectile energy is converted from MeV/u to keV
double sn=0;
if(epsilon<=30){
sn = log(1+(1.1383*epsilon))/ (2*(epsilon + 0.01321*pow(epsilon,0.21226) + 0.19593*pow(epsilon,0.5)));
}
else{
sn = log(epsilon)/(2*epsilon);
}
sn = 100*8.4621*p.Z*t.Z*p.A*sn*Avogadro/(asum*zpowers*t.A);
return sn;
}
double bethek_dedx_e(Projectile &p, const Target &t, const Config &c){
assert(t.Z>0 && p.Z>0);
assert(t.A>0 && p.A>0);
if(p.T==0)return 0.0;
double gamma=1.0 + p.T/atomic_mass_unit;
double beta2=1.0-1.0/(gamma*gamma);
assert(beta2>=0);
double beta = sqrt(beta2);
assert(beta>=0 && beta<1);
//double zeta = 1.0-exp(-130.0*beta/pow(p.Z,2.0/3.0));
//assert(zeta>=0);
//double zp_eff = p.Z*zeta;
double zp_eff = z_effective(p,t,c);
assert(zp_eff>=0);
double Ipot = ipot(t.Z);
assert(Ipot>0);
double f1 = dedx_constant*pow(zp_eff,2.0)*t.Z/(beta2*t.A);
assert(f1>=0);
double f2 = log(2.0*electron_mass*1000000*beta2/Ipot);
double eta = beta*gamma;
if(!(c.dedx&corrections::no_shell_correction) && eta>=0.13){ //shell corrections
double c = (+0.422377*pow(eta,-2)
+0.0304043*pow(eta,-4)
-0.00038106*pow(eta,-6))*1e-6*pow(Ipot,2)
+(+3.858019*pow(eta,-2)
-0.1667989*(pow(eta,-4))
+0.00157955*(pow(eta,-6)))*1.0e-9*pow(Ipot,3);
f2 = f2 -c/t.Z;
}
f2+=2*log(gamma) -beta2;
double barkas=1.0;
if(!(c.dedx&corrections::no_barkas)){
barkas = bethek_barkas(zp_eff,eta,t.Z);
}
double delta = bethek_density_effect(beta, t.Z);
double LS = 0.0;
if(!(c.dedx&corrections::no_lindhard)){
//double LS = bethek_lindhard(p);
LS = precalculated_lindhard(p);
}
double result = (f2)*barkas + LS - delta/2.;
result *=f1;
return result;
}
double bethek_barkas(double zp_eff,double eta, double zt){
double V2FVA[4]={0.33,0.30,0.26,0.23};
double VA[4]={1.,2.,3.,4.};
double v1 = eta/(fine_structure*sqrt(zt));
double v2fv;
if(v1 >= 4){
v2fv = 0.45 / sqrt(v1);
}
else if((v1 >= 1) && v1 < 4){//VALUES FROM THE JACKSON MC CARTHY FUNCTION //PHYS. REV. B 6 4131 P4136
int i;
for(i=1; i<4; i++){
if( VA[i] >= v1) break;
}
v2fv = V2FVA[i-1]+(v1-VA[i-1])*(V2FVA[i]-V2FVA[i-1])/(VA[i]-VA[i-1]);
}
else{
v2fv=0;
}
return 1.0+2.0 * zp_eff * v2fv /(v1*v1*sqrt(zt));
}
double bethek_density_effect(double beta, int zt){
double gamma = 1/sqrt(1-(beta*beta));
double x = log(beta * gamma) / 2.302585;
int i = zt-1;
double del = 0;
if (x < density_effect::x0[i] ){
if(density_effect::del_0[i] > 0.)del = density_effect::del_0[i] * pow(10.0,(2.*(x-density_effect::x0[i])));
}
else {
del = 4.6052 * x - density_effect::c[i];
if ( density_effect::x0[i]<= x && x <= density_effect::x1[i] ) del += density_effect::a[i] * pow((density_effect::x1[i] - x),density_effect::m[i]);
}
return del;
}
double bethek_lindhard(const Projectile &p){
const double compton=3.05573356675e-3; // 1.18 fm / Compton wavelength
double rho = exp(log(p.A)/3.0)*compton;
double gamma=1.0 + p.T/atomic_mass_unit;
double beta2=1.0-1.0/(gamma*gamma);
double beta = sqrt(beta2);
double eta = p.Z*fine_structure/beta;
double beta_gamma_R = beta*gamma*rho;
double sum = 0;
int n=1;
if(gamma < 10.0/rho){
double dk[3];
double dmk = 0;
double dkm1 = 0;
while(n<100){
double k0 = n;
int max = (n==1)?3:2;
for(int i=0;i<max;i++){
double k;
if(i==0)k=k0;
if(i==1)k=-k0 - 1.0;
if(i==2)k=-k0;
double l = (k>0)?k:-k-1.0;
double signk = (k>0)?1:((k<0)?-1:0);
double sk = sqrt(k*k-fine_structure*fine_structure*p.Z*p.Z);
std::complex<double> cexir_n (k,-eta/gamma);
std::complex<double> cexir_den (sk,-eta);
std::complex<double> cexir = std::sqrt(cexir_n/cexir_den);
std::complex<double> csketa (sk + 1.0, eta);
std::complex<double> cpiske(0.0,(M_PI*(l-sk)/2.0) - lngamma(csketa).imag());
std::complex<double> cedr = cexir*std::exp(cpiske);
double H=0;
//std::complex<double> ceds(0.0,0.0);
// finite struct part
std::complex<double> cmsketa (-sk + 1.0, eta);
std::complex<double> cexis_den (-sk,-eta);
std::complex<double> cexis = std::sqrt(cexir_n/cexis_den);
std::complex<double> cpimske(0.0,(M_PI*(l+sk)/2.0) - lngamma(cmsketa).imag());
std::complex<double> ceds = cexir*std::exp(cpimske);
std::complex<double> cmbeta_gamma_R(0,-beta_gamma_R);
std::complex<double> c2beta_gamma_R(0,2.0*beta_gamma_R);
std::complex<double> c2sk_1 (2.0*sk+1,0);
std::complex<double> cm2sk_1 (-2.0*sk+1,0);
std::complex<double> clambda_r = cexir*std::exp(cmbeta_gamma_R)*hyperg(csketa,c2sk_1,c2beta_gamma_R);
std::complex<double> clambda_s = cexis*std::exp(cmbeta_gamma_R)*hyperg(cmsketa,cm2sk_1,c2beta_gamma_R);
std::complex<double> cGrGs = lngamma(cm2sk_1);
double GrGs = clambda_r.imag()/clambda_s.imag();
GrGs *= exp( lngamma(csketa).real()
- lngamma(cmsketa).real()
- lngamma(c2sk_1).real()
+ cGrGs.real()
+ 2.0*sk*log(2.0*beta_gamma_R));
if(cos(cGrGs.imag()) < 1.0)GrGs*=-1;
if(fabs(GrGs)>1.0e-9){
double FrGr = sqrt((gamma-1)/(gamma+1)) * clambda_r.real()/clambda_r.imag();
double FsGs = sqrt((gamma-1)/(gamma+1)) * clambda_s.real()/clambda_s.imag();
double gz = -1.0*signk*(rho*gamma + 1.5*p.Z*fine_structure);
double z1 = -1.0*signk*p.Z;
double b0 = 1.0;
double a0 = (1.0 + 2.0*fabs(k))*b0/(rho-gz);
double a1 = 0.5*(gz+rho)*b0;
double an = a1;
double anm1 = a0;
double bnm1 = b0;
double asum = a0;
double bsum = b0;
double nn = 1.0;
while(fabs(anm1/asum)>1e-6 && fabs(anm1/asum)>1e-6){
double bn = ((rho-gz)*an + fine_structure*z1*anm1/2.0)/(2.0*nn+2.0*fabs(k)+1.0);
double anp1 = ((gz+rho)*bn - fine_structure*z1*bnm1/2.0)/(2.0*nn + 2.0);
asum += an;
bsum += bn;
nn += 1.0;
anm1 = an;
an = anp1;
bnm1 = bn;
}
double figi= (k>0) ? asum/bsum : bsum/asum;
H = (FrGr - figi)/(figi-FsGs)* GrGs;
}
else
H = 0;
dk[i] = std::arg(cedr + H*ceds);
}
if(n>1)dk[2] = dmk;
double sdm2 = sin(dk[2]-dk[1]);
double term1 = k0*(k0+1.0)*sdm2*sdm2/(eta*eta*(2.0*k0 + 1.0));
if(n>1){
double sd2 = sin(dk[0]-dkm1);
term1 += k0*(k0-1.0)*sd2*sd2/(eta*eta*(2.0*k0 - 1.0));
}
double sdd = sin(dk[0]-dk[2]);
double term2 = k0*sdd*sdd/(eta*eta*(4.0*k0*k0 - 1.0));
double term3 = term1 - 1.0/k0;
sum += term2 + term3;
n += 1;
dmk = dk[1];
dkm1 = dk[0];
}// end of while n<100
}
else{ // ultrarelativistic limit
sum = -log(beta_gamma_R) - 0.2;
}
return sum + (0.5*beta2);
}
double bethek_lindhard_X(const Projectile &p){
const double compton=3.05573356675e-3; // 1.18 fm / Compton wavelength
double rho = exp(log(p.A)/3.0)*compton;
double gamma=1.0 + p.T/atomic_mass_unit;
double beta2=1.0-1.0/(gamma*gamma);
double beta = sqrt(beta2);
double eta = p.Z*fine_structure/beta;
double beta_gamma_R = beta*gamma*rho;
double sum = 0;
int n=1;
if(1){
double dk[4];
double dmk = 0;
double dmkp1 = 0;
double dkm1 = 0;
double dkm2 = 0;
while(n<200){
double k0 = n;
//int max = (n==1)?4:2;
int max = 4;
for(int i=0;i<max;i++){
double k;
if(i==0)k=k0;
if(i==1)k=-k0 - 1.0;
if(i==2 && n==1)k=-k0;
if(i==3)k=-k0 - 2.0;
double l = (k>0)?k:-k-1.0;
double signk = (k>0)?1:((k<0)?-1:0);
double sk = sqrt(k*k-fine_structure*fine_structure*p.Z*p.Z);
std::complex<double> cexir_n (k,-eta/gamma);
std::complex<double> cexir_den (sk,-eta);
std::complex<double> cexir = std::sqrt(cexir_n/cexir_den);
std::complex<double> csketa (sk + 1.0, eta);
std::complex<double> cpiske(0.0,(M_PI*(l-sk)/2.0) - lngamma(csketa).imag());
std::complex<double> cedr = cexir*std::exp(cpiske);
double H=0;
//std::complex<double> ceds(0.0,0.0);
// finite struct part
std::complex<double> cmsketa (-sk + 1.0, eta);
std::complex<double> cexis_den (-sk,-eta);
std::complex<double> cexis = std::sqrt(cexir_n/cexis_den);
std::complex<double> cpimske(0.0,(M_PI*(l+sk)/2.0) - lngamma(cmsketa).imag());
std::complex<double> ceds = cexir*std::exp(cpimske);
std::complex<double> cmbeta_gamma_R(0,-beta_gamma_R);
std::complex<double> c2beta_gamma_R(0,2.0*beta_gamma_R);
std::complex<double> c2sk_1 (2.0*sk+1,0);
std::complex<double> cm2sk_1 (-2.0*sk+1,0);
std::complex<double> clambda_r = cexir*std::exp(cmbeta_gamma_R)*hyperg(csketa,c2sk_1,c2beta_gamma_R);
std::complex<double> clambda_s = cexis*std::exp(cmbeta_gamma_R)*hyperg(cmsketa,cm2sk_1,c2beta_gamma_R);
std::complex<double> cGrGs = lngamma(cm2sk_1);
double GrGs = clambda_r.imag()/clambda_s.imag();
GrGs *= exp( lngamma(csketa).real()
- lngamma(cmsketa).real()
- lngamma(c2sk_1).real()
+ cGrGs.real()
+ 2.0*sk*log(2.0*beta_gamma_R));
if(cos(cGrGs.imag()) < 1.0)GrGs*=-1;
if(fabs(GrGs)>1.0e-9){
double FrGr = sqrt((gamma-1)/(gamma+1)) * clambda_r.real()/clambda_r.imag();
double FsGs = sqrt((gamma-1)/(gamma+1)) * clambda_s.real()/clambda_s.imag();
double gz = -1.0*signk*(rho*gamma + 1.5*p.Z*fine_structure);
double z1 = -1.0*signk*p.Z;
double b0 = 1.0;
double a0 = (1.0 + 2.0*fabs(k))*b0/(rho-gz);
double a1 = 0.5*(gz+rho)*b0;
double an = a1;
double anm1 = a0;
double bnm1 = b0;
double asum = a0;
double bsum = b0;
double nn = 1.0;
while(fabs(anm1/asum)>1e-6 && fabs(anm1/asum)>1e-6){
double bn = ((rho-gz)*an + fine_structure*z1*anm1/2.0)/(2.0*nn+2.0*fabs(k)+1.0);
double anp1 = ((gz+rho)*bn - fine_structure*z1*bnm1/2.0)/(2.0*nn + 2.0);
asum += an;
bsum += bn;
nn += 1.0;
anm1 = an;
an = anp1;
bnm1 = bn;
}
double figi= (k>0) ? asum/bsum : bsum/asum;
H = (FrGr - figi)/(figi-FsGs)* GrGs;
}
else
H = 0;
dk[i] = std::arg(cedr + H*ceds);
}
if(n>1)dk[2] = dmk;
double strterm1p = 0;
double strterm1n = 0;
double strterm2 = 0;
double strterm3 = 0;
double eta2 = eta*eta;
double sdm2 = sin(dk[0]-dkm2);
if(n>2){
strterm1p = sdm2*sdm2*(k0-1)*(k0-2)/((2.0*k0 - 1.0)*(2.0*k0-3.0));
}
sdm2 = sin(dk[2]-dk[3]);
strterm1n = sdm2*sdm2*(-k0-1)*(-k0-2)/((-2.0*k0 - 1.0)*(-2.0*k0-3.0));
if(n>1){
double sd2 = sin(dk[0]-dmkp1);
strterm2 += (k0-1.0)*sd2*sd2/((2.0*k0 - 3.0)*(4.0*k0*k0 - 1.0));
}
double sdd = sin(dk[0]-dk[1]);
strterm3 = sdd*sdd*(k0+1.0)*((1/(4.0*k0*k0 -1.0))+(1/(4*(k0+1.0)*(k0+1.0) - 1.0)))/(2.0*k0 + 1.0);
//sum += k0*(strterm1p + strterm1n + (strterm2*2) + strterm3)/eta2;
sum += k0*(strterm1p + strterm1n + (strterm2*2) + strterm3)/eta2;
sum += - (2.0/k0);
//std::cout<<n<<" "<<strterm1p<<" "<<strterm1n<<" "<<strterm2<<" "<<strterm3<<" "<<sum<<std::endl;
n += 1;
dmk = dk[1];
dkm2 = dkm1;
dkm1 = dk[0];
dmkp1 = dk[2];
}// end of while n<100
}
else{ // ultrarelativistic limit
}
return 2*bethek_lindhard(p) - sum - beta2;
//return sum;
}
double sezi_p_se(double energy,const Target &t){
double sp = -1;
double e = 1000*energy; //e in keV/u
int i = t.Z - 1;
if(e<=25)e=25;
//double sl = (proton_stopping_coef[i][0]*pow(e,proton_stopping_coef[i][1])) + (proton_stopping_coef[i][2]*pow(e,proton_stopping_coef[i][3]));
//double sh = proton_stopping_coef[i][4]/pow(e,proton_stopping_coef[i][5]) * log( (proton_stopping_coef[i][6]/e) + (proton_stopping_coef[i][7]*e));
double sl = (proton_stopping_coef[i][0]*catima::power(e,proton_stopping_coef[i][1])) + (proton_stopping_coef[i][2]*catima::power(e,proton_stopping_coef[i][3]));
double sh = proton_stopping_coef[i][4]/catima::power(e,proton_stopping_coef[i][5]) * log( (proton_stopping_coef[i][6]/e) + (proton_stopping_coef[i][7]*e));
sp = sl*sh/(sl+sh);
e=1000*energy;
if(e<=25){
//sp *=(t.Z>6)?pow(e/25,0.45):pow(e/25,0.25);
sp *=(t.Z>6)?catima::power(e/25,0.45):catima::power(e/25,0.25);
}
return 100*sp*Avogadro/t.A;
}
double sezi_dedx_e(const Projectile &p, const Target &t){
double e=p.T*1000; // e in keV/u
double se = 0;
if(p.Z==1){
return sezi_p_se(p.T,t);
}
else if(p.Z == 2){
double a=0;
double b=0;
//double zeta = 0;
if(e<=1)e=1;
// He Zeff
b = log(e);
a = 0.2865 + b*(0.1266+ b*(-0.001429+ b*(0.02402 + b*(-0.01135 + b*0.001475))));
double heh = 1.0 - exp(-std::min(30.,a));
b = 7.6 - std::max(0., b);
a = (1.0 + (0.007 + 0.00005*t.Z)*exp(- b*b ));
heh *= a*a;
//zeta = sqrt(heh);
se = sezi_p_se(p.T,t)*heh*4.0; //scale proton stopping
if(e==1)se*= sqrt(p.T*1000.0); //vel proportional
return se;
}
else{ // heavy ion
double h1,h2,h3,h4;
double a,q,b;
double l1,l0,l;
double YRmin = 0.130; // YRmin = VR / ZP**0.67 <= 0.13 OR VR <= 1.0
double VRmin = 1.0;
double v=0;
double vfermi = atima_vfermi[(int)t.Z-1];
double yr=0;
double zeta = 0;
double se;
v = sqrt(e/25.0)/vfermi;
double v2=v*v;
double vr = (v >= 1)? v*vfermi*(1.+ 1./(5.*v2)) : 3.0*vfermi/4.0*(1.0+v2*(2.0/3.0-v2/15.0));
h1= 1./catima::power(p.Z,0.6667);
yr = std::max(YRmin,vr*h1);
yr = std::max(yr, VRmin*h1);
//-- CALCULATE ZEFF
a = -0.803*catima::power(yr,0.3) + 1.3167*catima::power(yr,0.6) + 0.38157*yr + 0.008983*yr*yr;
q = std::min(1.0, std::max(0.0 , (1.0 - exp(-std::min(a, 50.0))))); //-- Q = IONIZATION LEVEL OF THE ION AT RELATIVE VELOCITY YR
//-- IONIZATION LEVEL TO EFFECTIVE CHARGE
h1 = 1./ catima::power(p.Z,0.3333);
b = (std::min(0.43, std::max(0.32,0.12 + 0.025*p.Z)))*h1;
l0 = (.8 - q * std::min(1.2,0.6 +p.Z/30.0))*h1;
if(q < 0.2){
l1 = 0;
}
else{
if (q < std::max(0.0,0.9-0.025*p.Z)){
l1 = b*(q-0.2)/fabs(std::max(0.0,0.9-0.025*p.Z)-0.2000001);
}
else{
if(q < std::max(0.0,1.0 - 0.025*std::min(16.,p.Z))) l1 = b;
else l1 = b*(1.0 - q)/(0.025*std::min(16.,p.Z));
}
}
// calculate screening
l = std::max(l1,l0*atima_lambda_screening[(int)p.Z-1]);
h1 =4.0*l*vfermi/1.919;
zeta = q + (1./(2.*(vfermi*vfermi)))*(1. - q)* log(1. + h1*h1);
// ZP**3 EFFECT AS IN REF. 779?
a = 7.6 - std::max(0.0, log(e));
zeta = zeta*(1. + (1./(p.Z*p.Z))*(0.18 + .0015*t.Z)*exp(-a*a));
h1= 1./catima::power(p.Z,0.6667);
if (yr <= ( std::max(YRmin, VRmin*h1))){
VRmin=std::max(VRmin, YRmin/h1);
//--C ..CALCULATE VELOCITY STOPPING FOR YR < YRmin
double vmin =.5*(VRmin + sqrt(std::max(0.0,VRmin*VRmin - .8*vfermi*vfermi)));
double eee = 25.0*vmin*vmin;
double eval = 1;
if((t.Z == 6) || (((t.Z == 14) || (t.Z == 32)) && (p.Z <= 19))) eval = 0.35;
else eval = 0.5;
h1 = zeta *p.Z;
h4 = catima::power(e / eee,eval);
se = sezi_p_se(eee*0.001,t) * h1*h1*h4;
return se;
}
else {
se = sezi_p_se(p.T,t)*catima::power(zeta*p.Z,2.0);
return se;
}
return 0;
}
};
double gamma_from_T(double T){
return 1.0 + T/atomic_mass_unit;
};
double beta_from_T(double T){
double gamma = gamma_from_T(T);
return sqrt(1.0-1.0/(gamma*gamma));
}
double energy_straggling_firsov(double z1,double energy, double z2, double m2){
double gamma = gamma_from_T(energy);
double beta2=1.0-1.0/(gamma*gamma);
double factor=4.8184E-3*pow(z1+z2,8.0/3.0)/m2;
return factor*beta2/fine_structure/fine_structure;
}
double angular_scattering_variance(Projectile &p, Target &t){
if(p.T<=0)return 0.0;
double e=p.T;
double _p = sqrt(e*(e+2*atomic_mass_unit))*p.A;
double beta = _p/((e+atomic_mass_unit)*p.A);
double lr = radiation_length(t.Z,t.A);
return 198.81 * pow(p.Z,2)/(lr*pow(_p*beta,2));
}
/// radioation lengths are taken frm Particle Data Group 2014
double radiation_length(int z, int m){
double lr = 0;
if(z==1){return 63.04;}
if(z==2){return 94.32;}
if(z==3){return 82.78;}
if(z==4){return 65.19;}
if(z==6){return 42.7;}
if(z==7){return 37.99;}
if(z==8){return 34.24;}
if(z==9){return 32.93;}
if(z==10){return 28.94;}
if(z==13){return 24.01;}
if(z==14){return 21.82;}
if(z==17){return 19.28;}
if(z==18){return 19.55;}
if(z==22){return 16.16;}
if(z==26){return 13.84;}
if(z==29){return 12.86;}
if(z==32){return 12.25;}
if(z==50){return 8.82;}
if(z==54){return 8.48;}
if(z==74){return 6.76;}
if(z==78){return 6.54;}
if(z==79){return 6.46;}
if(z==82){return 6.37;}
if(z==92){return 6.00;}
double z2 = z*z;
double z_13 = 1.0/pow(z,1./3.);
double z_23 = z_13*z_13;
double a2 = fine_structure*fine_structure*z2;
double a4 = a2*a2;
double a6 = a4*a2;
lr= 716.405*m/(z2* (log(184.15*z_13) + log(1194.0*z_23)/z - -1.202*a2 + 1.0369*a4 - 1.008*a6/(1+a2) ) );
return lr;
}
double precalculated_lindhard(const Projectile &p){
double T = p.T;
int z = (int)p.Z ;
if(z>LS_MAX_Z)z=LS_MAX_Z;
//if(p.T<ls_coefficients::ls_energy_points[0])T=ls_coefficients::ls_energy_points[0];
if(p.T<ls_coefficients::ls_energy_table(0))T=ls_coefficients::ls_energy_table(0);
double da = (p.A - element_atomic_weight(z))/element_atomic_weight(z);
z = z-1;
//catima::Interpolator ls_a(ls_coefficients::ls_energy_points,ls_coefficients::ls_coefficients_a[z],LS_NUM_ENERGY_POINTS,interpolation_t::linear);
//catima::Interpolator ls_ahi(ls_coefficients::ls_energy_points,ls_coefficients::ls_coefficients_ahi[z],LS_NUM_ENERGY_POINTS,interpolation_t::linear);
//catima::Interpolator ls_a(ls_coefficients::ls_energy_table.values,ls_coefficients::ls_coefficients_a[z],LS_NUM_ENERGY_POINTS,interpolation_t::cspline);
//catima::Interpolator ls_ahi(ls_coefficients::ls_energy_table.values,ls_coefficients::ls_coefficients_ahi[z],LS_NUM_ENERGY_POINTS,interpolation_t::cspline);
double v1 = EnergyTable_interpolate(ls_coefficients::ls_energy_table,T,ls_coefficients::ls_coefficients_a[z]);
double v2 = EnergyTable_interpolate(ls_coefficients::ls_energy_table,T,ls_coefficients::ls_coefficients_ahi[z]);
//double dif = ls_ahi(T) - ls_a(T);
//return ls_a(T)+(dif*da/ls_coefficients::a_rel_increase);
double dif = v2 - v1;
return v1+(dif*da/ls_coefficients::a_rel_increase);
}
double precalculated_lindhard_X(const Projectile &p){
double T = p.T;
int z = (int)p.Z ;
if(z>LS_MAX_Z)z=LS_MAX_Z;
//if(p.T<ls_coefficients::ls_energy_points[0])T=ls_coefficients::ls_energy_points[0];
if(p.T<ls_coefficients::ls_energy_table(0))T=ls_coefficients::ls_energy_table(0);
double da = (p.A - element_atomic_weight(z))/element_atomic_weight(z);
z = z-1;
//catima::Interpolator ls_X_a(ls_coefficients::ls_energy_table.values,ls_coefficients::ls_X_coefficients_a[z],LS_NUM_ENERGY_POINTS,interpolation_t::linear);
//catima::Interpolator ls_X_ahi(ls_coefficients::ls_energy_table.values,ls_coefficients::ls_X_coefficients_ahi[z],LS_NUM_ENERGY_POINTS,interpolation_t::linear);
double v1 = EnergyTable_interpolate(ls_coefficients::ls_energy_table,T,ls_coefficients::ls_X_coefficients_a[z]);
double v2 = EnergyTable_interpolate(ls_coefficients::ls_energy_table,T,ls_coefficients::ls_X_coefficients_ahi[z]);
//double dif = ls_X_ahi(T) - ls_X_a(T);
//return ls_X_a(T)+(dif*da/ls_coefficients::a_rel_increase);
double dif = v2 - v1;
return v1+(dif*da/ls_coefficients::a_rel_increase);
}
double dedx_rms(Projectile &p, Target &t, const Config &c){
double zp_eff = z_effective(p,t,c);
double gamma = gamma_from_T(p.T);
double f = domega2dx_constant*pow(zp_eff,2)*t.Z*gamma*gamma;
//double X = bethek_lindhard_X(p);
double X = precalculated_lindhard_X(p);
return f*X/t.A;
}
double z_effective(const Projectile &p,const Target &t, const Config &c){
if(c.z_effective == z_eff_type::none){
return p.Q;
}
double gamma=1.0 + p.T/atomic_mass_unit;
double beta = sqrt(1.0-1.0/(gamma*gamma));
if(c.z_effective == z_eff_type::pierce_blann){
return z_eff_Pierce_Blann(p.Z, beta);
}
if(c.z_effective == z_eff_type::anthony_landorf){
return z_eff_Anthony_Landford(p.Z, beta, t.Z);
}
if(c.z_effective == z_eff_type::hubert){
return z_eff_Hubert(p.Z, p.T, t.Z);
}
return 0.0;
}
double z_eff_Pierce_Blann(double z, double beta){
return z*(1.0-exp(-130.1842*beta/pow(z,2.0/3.0)));
}
double z_eff_Anthony_Landford(double pz, double beta, double tz){
double B = 1.18-tz*(7.5e-03 - 4.53e-05*tz);
double A = 1.16-tz*(1.91e-03 - 1.26e-05*tz);
return pz*(1.0-exp(-137.035999139*B*beta/pow(pz,2.0/3.0))*A);
}
double z_eff_Hubert(double pz, double E, double tz){
double lntz = log(tz);
double x1,x2,x3,x4;
if(tz == 4){
x1 = 2.045 + 2.0*exp(-0.04369*pz);
x2 = 7.0;
x3 = 0.2643;
x4 = 0.4171;
}
else if(tz==6){
x1 = 2.584 + 1.91*exp(-0.03958*pz);
x2 = 6.933;
x3 = 0.2433;
x4 = 0.3969;
}
else{
x1 = (1.164 + 0.2319*exp(-0.004302*tz)) + 1.658*exp(-0.0517*pz);
x2 = 8.144 + 0.09876*lntz;
x3 = 0.314 + 0.01072*lntz;
x4 = 0.5218 + 0.02521*lntz;
}
return pz*(1-x1*exp(-x2*catima::power(E,x3)*catima::power(pz,-x4)));
}
std::complex<double> hyperg(const std::complex<double> &a,
const std::complex<double> &b,
const std::complex<double> &z){
double dm = 0.0;
std::complex<double> term(1.0, 0.0);
std::complex<double> sumterm(1.0, 0.0);
std::complex<double> previousterm;
do {
previousterm = term;
dm += 1.0;
std::complex<double> Cm(dm-1.0, 0.0);
term = previousterm * ((a + Cm)/(b + Cm)) * (z/dm);
sumterm += term;
} while( std::abs(term) > 1.0e-6 && std::abs(previousterm) > 1.0e-6 );
return(sumterm);
}
std::complex<double> lngamma( const std::complex<double> &z )
{
const static double coeff[6] = {76.18009172947146,
-86.50532032941677,
24.01409824083091,
-1.231739572450155,
0.1208650973866179e-2,
-0.5395239384953e-5};
double x, y;
if(z.real() > 0) {
x=z.real()-1.0;
y=z.imag();
} else {
x=-z.real();
y=-z.imag();
}
double r = sqrt((x+5.5)*(x+5.5)+y*y);
double aterm1=y*log(r);
double aterm2=(x+0.5)*atan2(y,(x+5.5))-y;
double lterm1=(x+0.5)*log(r);
double lterm2=-y*atan2(y,(x+5.5)) - (x+5.5) + 0.5*log(2.0*M_PI);
double num=0.0;
double denom=1.000000000190015;
for(int j=1;j<7;j++){
double fj=(double)j;
double cterm=coeff[j-1]/((x+fj)*(x+fj)+y*y);
num+=cterm;
denom+=(x+fj)*cterm;
}
num*=-y;
double aterm3=atan2(num,denom);
double lterm3 = 0.5*log(num*num + denom*denom);
std::complex<double> result(lterm1+lterm2+lterm3,aterm1+aterm2+aterm3);
if(z.real() < 0){
std::complex<double> lpi(log(M_PI), 0.0);
result = lpi - (result + std::log(std::sin(M_PI*z)));
}
return(result);
}
}

137
calculations.h Normal file
View File

@ -0,0 +1,137 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/// \file calculations.h
#ifndef CALCULATIONS_H
#define CALCULATIONS_H
#include <complex>
#include "catima/structures.h"
#include "catima/config.h"
namespace catima{
/**
* returns nuclear stopping power for projectile-target combination
*/
double dedx_n(const Projectile &p, const Target &t);
/**
* returns electronic stopping power for projectile-target combination
*/
double dedx_e(Projectile &p, const Target &t, const Config &c=default_config);
/**
* returns total stopping power for projectile-target combination
*/
double dedx(Projectile &p, const Target &t, const Config &c=default_config);
/**
* returns energy loss straggling
*/
double dedx_rms(Projectile &p, Target &t, const Config &c=default_config);
/**
* returns reduced energy loss unit for projectile-target combination
*/
double reduced_energy_loss_unit(const Projectile &p, const Target &t);
double bethek_dedx_e(Projectile &p,const Target &t, const Config &c=default_config);
double bethek_barkas(double zp_eff,double eta, double zt);
double bethek_density_effect(double beta, int zt);
/**
* calculates lindhard correction for energy loss calculation
*/
double bethek_lindhard(const Projectile &p);
/**
* calculates lindhard correction for energy loss straggling calculation
*/
double bethek_lindhard_X(const Projectile &p);
/**
* returns linhard correction (L) calulated from tabulated precalculated data
*/
double precalculated_lindhard(const Projectile &p);
/**
* returns linhard energy loss straggling correction (X) calulated from tabulated precalculated data
*/
double precalculated_lindhard_X(const Projectile &p);
double energy_straggling_firsov(double z1,double energy, double z2, double m2);
double sezi_dedx_e(const Projectile &p, const Target &t);
double sezi_p_se(double energy,const Target &t);
double angular_scattering_variance(Projectile &p, Target &t);
/**
* returns radiation length of the (M,Z) material
* for certain z the radiation length is tabulated, otherwise calculated
* @param z - proton number of material
* @return radiation length in g/cm^2
*/
double radiation_length(int z, int m);
/** returns effective Z of the projectile
* @param c - Configuration, the z effective will be calculated according to c.z_effective value
* @return - z effective
*/
double z_effective(const Projectile &p, const Target &t, const Config &c=default_config);
/**
* calculates effective charge
* @param z - proton number of projectile
* @param beta - velocity of projectile
* @return effective charge
*/
double z_eff_Pierce_Blann(double z, double beta);
/**
* calculates effective charge
* @param pz - proton number of projectile
* @param beta - velocity of projectile
* @param tz - proton number of target material
* @return effective charge
*/
double z_eff_Anthony_Landford(double pz, double beta, double tz);
/**
* calculates effective charge
* @param pz - proton number of projectile
* @param beta - velocity of projectile
* @param tz - proton number of target material
* @return effective charge
*/
double z_eff_Hubert(double pz, double E, double tz);
//helper
double gamma_from_T(double T);
double beta_from_T(double T);
std::complex<double> lngamma( const std::complex<double> &z );
std::complex<double> hyperg(const std::complex<double> &a,
const std::complex<double> &b,
const std::complex<double> &z);
inline double power(double x, double y){
return exp(log(x)*y);
}
}
#endif

388
catima.cpp Normal file
View File

@ -0,0 +1,388 @@
#include <iostream>
#include <math.h>
#include <algorithm>
#include "catima/catima.h"
#include "catima/constants.h"
#include "catima/data_ionisation_potential.h"
#include "catima/data_atima.h"
#include "catima/integrator.h"
#include "catima/storage.h"
#include "catima/nucdata.h"
#include "catima/calculations.h"
namespace catima{
Config default_config;
bool operator==(const Config &a, const Config&b){
if(std::memcmp(&a,&b,sizeof(Config)) == 0){
return true;
}
else
return false;
}
double dedx(Projectile &p, double T, const Material &mat, const Config &c){
double sum = 0;
Target t;
double w=0;
if(T<=0)return 0.0;
for(int i=0;i<mat.ncomponents();i++){
auto res = mat.get_element(i);
t = res.first; //struct of target
w = res.second; //number of atoms of the element
p.T = T;
sum += t.A*w*dedx(p,t);
}
return sum/mat.M();
}
double domega2dx(Projectile &p, double T, const Material &mat, const Config &c){
double sum = 0;
Target t;
double w=0;
for(int i=0;i<mat.ncomponents();i++){
auto res = mat.get_element(i);
t = res.first; //struct of target
w = res.second; //number of atoms of the element
p.T = T;
sum += t.A*w*dedx_rms(p,t);
}
return sum/mat.M();
}
double da2dx(Projectile &p, double T, const Material &mat, const Config &c){
double sum = 0;
Target t;
double w=0;
for(int i=0;i<mat.ncomponents();i++){
auto res = mat.get_element(i);
t = res.first; //struct of target
w = res.second; //number of atoms of the element
p.T = T;
sum += t.A*w*angular_scattering_variance(p,t);
}
return sum/mat.M();
}
double range(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
return range_spline(T);
}
double dedx_from_range(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
return p.A/range_spline.derivative(T);
}
double range_straggling(Projectile &p, double T, const Material &t, const Config &c){
double r=0;
auto data = _storage.Get(p,t,c);
Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
return sqrt(range_straggling_spline(T));
}
double range_variance(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
return range_straggling_spline(T);
}
double domega2de(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
return range_straggling_spline.derivative(T);
}
double da2de(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
return angular_variance_spline.derivative(T);
}
double angular_straggling_from_E(Projectile &p, double T, double Tout, const Material &t, const Config &c){
double r=0;
auto data = _storage.Get(p,t,c);
Interpolator angular_straggling_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
return sqrt(angular_straggling_spline(T) - angular_straggling_spline(Tout));
}
double energy_straggling_from_E(Projectile &p, double T, double Tout,const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
double dEdxo = p.A/range_spline.derivative(Tout);
return dEdxo*sqrt(range_straggling_spline(T) - range_straggling_spline(Tout))/p.A;
}
double energy_out(double T, double thickness, Interpolator &range_spline){
constexpr double epsilon = 1E-5;
int counter = 0;
double lo=0,hi=T;
double range;
double dedx;
double e,r;
double step;
range = range_spline(T);
dedx = 1.0/range_spline.derivative(T);
if(range<= thickness) return 0.0;
e = T - (thickness*dedx);
while(1){
r = range - range_spline(e) - thickness;
if(fabs(r)<epsilon)return e;
step = -r*dedx;
e = e-step;
if(e<Ezero)return 0.0;
dedx = 1.0/range_spline.derivative(T);
counter++;
if(counter>100){printf("too many iterations finding Eout");return -1;}
}
return -1;
}
double energy_out(Projectile &p, double T, const Material &t, const Config &c){
auto data = _storage.Get(p,t,c);
Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
return energy_out(T,t.thickness(),range_spline);
}
Result calculate(Projectile &p, const Material &t, const Config &c){
Result res;
double T = p.T;
auto data = _storage.Get(p,t,c);
Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
res.Ein = T;
res.range = range_spline(T);
res.dEdxi = p.A/range_spline.derivative(T);
res.Eout = energy_out(T,t.thickness(),range_spline);
Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
if(res.Eout<Ezero){
res.dEdxo = 0.0;
res.sigma_a = 0.0;
res.tof = 0.0;
res.sigma_E = 0.0;
}
else{
res.dEdxo = p.A/range_spline.derivative(res.Eout);
#ifdef THIN_TARGET_APPROXIMATION
if(thin_target_limit*res.Ein<res.Eout){
double edif = (res.Ein-res.Eout);
double s1 = range_straggling_spline.derivative(T);
double s2 = range_straggling_spline.derivative(res.Eout);
res.sigma_E = res.dEdxo*sqrt(edif*0.5*(s1+s2))/p.A;
Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
s1 = angular_variance_spline.derivative(T);
s2 = angular_variance_spline.derivative(res.Eout);
res.sigma_a = sqrt(0.5*(s1+s2)*edif);
}
else{
res.sigma_E = res.dEdxo*sqrt(range_straggling_spline(T) - range_straggling_spline(res.Eout))/p.A;
Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));
}
#else
res.sigma_E = res.dEdxo*sqrt(range_straggling_spline(T) - range_straggling_spline(res.Eout))/p.A;
Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));
#endif
if( !(c.skip&skip_tof) && t.thickness()>0){
//auto tofdata = calculate_tof(p,t,c);
//Interpolator tof_spline(energy_table.values, tofdata.data(), energy_table.num,interpolation_t::linear);
//res.tof = tof_spline(res.Ein) - tof_spline(res.Eout);
res.tof = calculate_tof_from_E(p,res.Eout,t);
}
}
res.sigma_r = sqrt(range_straggling_spline(T));
res.Eloss = (res.Ein - res.Eout)*p.A;
return res;
}
MultiResult calculate(Projectile &p, const Layers &layers, const Config &c){
MultiResult res;
double e = p.T;
res.total_result.Ein = e;
res.results.reserve(layers.num());
for(auto&m:layers.get_materials()){
Result r = calculate(p,m,e,c);
e = r.Eout;
res.total_result.sigma_a += r.sigma_a*r.sigma_a;
res.total_result.Eloss += r.Eloss;
res.total_result.sigma_E += r.sigma_E*r.sigma_E;
res.total_result.tof += r.tof;
res.total_result.Eout = r.Eout;
res.results.push_back(r);
}
if(e>Ezero){
res.total_result.sigma_a = sqrt(res.total_result.sigma_a);
res.total_result.sigma_E = sqrt(res.total_result.sigma_E);
}
else{
res.total_result.sigma_a = 0.0;
res.total_result.sigma_E = 0.0;
}
return res;
}
Result calculate(double pa, int pz, double T, double ta, double tz, double thickness, double density){
Projectile p(pa,pz);
Material m(ta,tz,density,thickness);
return calculate(p(T),m);
}
std::vector<double> calculate_range(Projectile p, const Material &t, const Config &c){
double res;
std::vector<double>values;
values.reserve(max_datapoints);
auto fdedx = [&](double x)->double{return 1.0/dedx(p,x,t);};
//calculate 1st point to have i-1 element ready for loop
res = integratorGSL.Integrate(fdedx,Ezero,energy_table(0),int_eps_range,false);
res = p.A*res;
values.push_back(res);
for(int i=1;i<max_datapoints;i++){
res = integratorGSL.Integrate(fdedx,energy_table(i-1),energy_table(i),int_eps_range,false);
res = p.A*res;
res += values[i-1];
values.push_back(res);
}
return values;
}
std::vector<double> calculate_range_straggling(Projectile p, const Material &t, const Config &c){
double res;
std::vector<double>values;
values.reserve(max_datapoints);
auto function = [&](double x)->double{return 1.0*domega2dx(p,x,t)/pow(dedx(p,x,t),3);};
//auto function = [&](double x)->double{
//double de = dedx(p,x,t);
//return 1.0*domega2dx(p,x,t)/(de*de*de);
//};
//calculate 1st point to have i-1 element ready for loop
res = integratorGSL.Integrate(function,Ezero,energy_table(0),int_eps_range_str,false);
res = p.A*res;
values.push_back(res);
for(int i=1;i<max_datapoints;i++){
res = integratorGSL.Integrate(function,energy_table(i-1),energy_table(i),int_eps_range_str,false);
res = p.A*res;
res += values[i-1];
values.push_back(res);
}
return values;
}
std::vector<double> calculate_da2dx(Projectile p, const Material &t, const Config &c){
double res;
std::vector<double>values;
values.reserve(max_datapoints);
//auto function = [&](double x)->double{return p.A*da2dx(p,x,t)/dedx(p,x,t);};
auto function = [&](double x)->double{return 1.0/dedx(p,x,t);};
res = integratorGSL.Integrate(function,Ezero,energy_table(0),int_eps_ang_str,false);
res = p.A*da2dx(p,energy_table(0),t)*res;
values.push_back(res);
for(int i=1;i<max_datapoints;i++){
res = integratorGSL.Integrate(function,energy_table(i-1),energy_table(i),int_eps_ang_str,false);
res = p.A*da2dx(p,energy_table(i),t)*res;
res += values[i-1];
values.push_back(res);
}
return values;
}
std::vector<double> calculate_tof(Projectile p, const Material &t, const Config &c){
double res;
std::vector<double> values;
values.reserve(max_datapoints);
auto function = [&](double x)->double{return 1.0/(dedx(p,x,t)*beta_from_T(x));};
res = integratorGSL.Integrate(function,Ezero,energy_table(0),int_eps_tof,false);
res = res*10.0*p.A/(c_light*t.density());
values.push_back(res);
for(int i=1;i<max_datapoints;i++){
res = integratorGSL.Integrate(function,energy_table(i-1),energy_table(i),int_eps_tof,false);
res = res*10.0*p.A/(c_light*t.density());
res += values[i-1];
values.push_back(res);
}
return values;
}
DataPoint calculate_DataPoint(Projectile p, const Material &t, const Config &c){
DataPoint dp(p,t,c);
std::vector<double>range_values;
range_values.reserve(max_datapoints);
std::vector<double>range_straggling_values;
range_straggling_values.reserve(max_datapoints);
std::vector<double>angular_straggling_values;
angular_straggling_values.reserve(max_datapoints);
double dedxval;
auto fdedx = [&](double x)->double{
return 1.0/dedx(p,x,t);
};
auto fomega = [&](double x)->double{
//return 1.0*domega2dx(p,x,t)/pow(dedx(p,x,t),3);
return domega2dx(p,x,t)/catima::power(dedx(p,x,t),3);
};
double res;
//calculate 1st point to have i-1 element ready for loop
res = integratorGSL.Integrate(fdedx,Ezero,energy_table(0),int_eps_range,false);
res = p.A*res;
range_values.push_back(res);
res = da2dx(p,energy_table(0),t)*res;
angular_straggling_values.push_back(res);
res = integratorGSL.Integrate(fomega,Ezero,energy_table(0),int_eps_range_str,false);
res = p.A*res;
range_straggling_values.push_back(res);
for(int i=1;i<max_datapoints;i++){
res = p.A*integratorGSL.Integrate(fdedx,energy_table(i-1),energy_table(i),int_eps_range,false);
range_values.push_back(res + range_values[i-1]);
res = da2dx(p,energy_table(i),t)*res;
angular_straggling_values.push_back(res + angular_straggling_values[i-1]);
res = integratorGSL.Integrate(fomega,energy_table(i-1),energy_table(i),int_eps_range_str,false);
res = p.A*res;
res += range_straggling_values[i-1];
range_straggling_values.push_back(res);
}
dp.range = range_values;
dp.range_straggling = range_straggling_values;
dp.angular_variance = angular_straggling_values;
return dp;
}
double calculate_tof_from_E(Projectile p, double Eout, const Material &t, const Config &c){
double res;
//double beta_in = beta_from_T(p.T);
//double beta_out = beta_from_T(Eout);
auto function = [&](double x)->double{return 1.0/(dedx(p,x,t)*beta_from_T(x));};
res = integratorGSL.Integrate(function,Eout,p.T,int_eps_tof,false);
res = res*10.0*p.A/(c_light*t.density());
return res;
}
} // end of atima namespace

204
catima.h Normal file
View File

@ -0,0 +1,204 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef CPPATIMA_H
#define CPPATIMA_H
#include <utility>
// #define NDEBUG
#include "catima/build_config.h"
#include "catima/config.h"
#include "catima/constants.h"
#include "catima/structures.h"
#include "catima/calculations.h"
#include "catima/material_database.h"
namespace catima{
class Interpolator;
/**
* calculate dEdx for projectile-Material combination
* @param p - Projectile
* @param mat - Material
* @return dEdx
*/
double dedx(Projectile &p, double T, const Material &mat, const Config &c=default_config);
/**
* calculate energy loss straggling variance for projectile-Material combination
* @param p - Projectile
* @param mat - Material
* @return dOmega^2/dx
*/
double domega2dx(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* calculates variance of angular scattering of Projectile p on Material m
*/
double da2dx(Projectile &p, double T, const Material &m, const Config &c=default_config);
/**
* returns the range of the Projectile in Material calculated from range spline
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return range
*/
double range(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* returns the dEdx calculated from range spline as derivative
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return range
*/
double dedx_from_range(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* returns the range straggling of the Projectile in Material from spline
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return range straggling
*/
double range_straggling(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* returns the range variance of the Projectile in Material from spline
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return range straggling
*/
double range_variance(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* returns the range variance per dE, calculated as derivative of range variance spline
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return range variance / dE
*/
double domega2de(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* returns the angular variance per dE, calculated as derivative of angular variance spline
* @param p - Projectile
* @param T - energy in MeV/u
* @param mat - Material
* @return angular variance / dE
*/
double da2de(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* calculates angular scattering in the material from difference of incoming a nd outgoing energies
* @param p - Projectile
* @param T - incoming energy
* @param Tout - outcoming energy
* @param mat - Material
* @return angular straggling
*/
double angular_straggling_from_E(Projectile &p, double T, double Tout,const Material &t, const Config &c=default_config);
/**
* calculates Energy straggling in the material from difference of incoming a nd outgoing energies
* @param p - Projectile
* @param T - incoming energy
* @param Tout - outcoming energy
* @param mat - Material
* @return angular straggling
*/
double energy_straggling_from_E(Projectile &p, double T, double Tout,const Material &t, const Config &c=default_config);
/**
* calculates outcoming energy from range spline
* @param T - incoming energy
* @thickness - thicnkess of the target in g/cm2
* @range_spline - precaclulated range spline for material
* @return outcoming energy after the thickness in Mev/u
*/
double energy_out(double T, double thickness, Interpolator &range_spline);
/**
* calculates outcoming energy
* @p - Projectile
* @t - Material
* @param T - incoming energy
* @return outcoming energy after the material in Mev/u
*/
double energy_out(Projectile &p, double T, const Material &t, const Config &c=default_config);
/**
* calculates all observables for projectile passing material
* @param p - Projectile
* @param mat - Material
* @return structure of Result
*/
Result calculate(Projectile &p, const Material &t, const Config &c=default_config);
inline Result calculate(Projectile &p, const Material &t, double T, const Config &c=default_config){
p.T = T;
return calculate(p, t, c);
}
/**
* wrapper to other calculate function with simplified arguments
* @param p - Projectile
* @param mat - Material
* @return structure of Result
*/
Result calculate(double pa, int pz, double T, double ta, double tz, double thickness, double density);
/**
* calculate observables for multiple layers of material defined by Layers
* @return results stored in MultiResult structure
*
*/
MultiResult calculate(Projectile &p, const Layers &layers, const Config &c=default_config);
inline MultiResult calculate(Projectile &p, double T, const Layers &layers, const Config &c=default_config){
p.T = T;
return calculate(p, layers, c);
}
/// the following functions are used to calculates array of data points for whole range of energies
/// usually used to construct splines
std::vector<double> calculate_range(Projectile p, const Material &t, const Config &c=default_config);
std::vector<double> calculate_range_straggling(Projectile p, const Material &t, const Config &c=default_config);
std::vector<double> calculate_angular_variance(Projectile p, const Material &t, const Config &c=default_config);
std::vector<double> calculate_tof(Projectile p, const Material &t, const Config &c=default_config);
/**
* calculates TOF of the Projectile in Material
* this is used instead of precalculated TOF spline
* @return TOF in ns
*/
double calculate_tof_from_E(Projectile p, double Eout, const Material &t, const Config &c=default_config);
class DataPoint;
/**
* calculates DataPoint for Projectile Material combinatino
* it substitute series of calls to calculate_* functions
* they are all combined here in 1 single function
* it has a perfomance gain to call this function if all splines are to be caclulated
*/
DataPoint calculate_DataPoint(Projectile p, const Material &t, const Config &c=default_config);
bool operator==(const Config &a, const Config&b);
}
#endif

243
catima.pyx Normal file
View File

@ -0,0 +1,243 @@
cimport catimac
from enum import IntEnum
import numpy
cdef class Material:
cdef catimac.Material cbase
def __cinit__(self, elements):
self.cbase = catimac.Material()
if(elements and isinstance(elements[0],int)):
self.cbase.add_element(elements[0],elements[1],elements[2])
if(elements and isinstance(elements[0],list)):
for e in elements:
self.cbase.add_element(e[0],e[1],e[2])
def add_element(self, a, z , s):
self.cbase.add_element(a, z, s)
def ncomponents(self):
return self.cbase.ncomponents()
def molar_mass(self):
return self.cbase.M()
def M(self):
return self.cbase.M()
def density(self, val=None):
if(val is None):
return self.cbase.density()
else:
return self.cbase.density(val)
def thickness(self, val=None):
if(val is None):
return self.cbase.thickness()
else:
return self.cbase.thickness(val)
cdef class Target:
cdef catimac.Target cbase
def __cinit__(self,a,z):
self.cbase.A = a
self.cbase.Z = z
def A(self):
return self.cbase.A
def Z(self):
return self.cbase.Z
cdef class Layers:
cdef catimac.Layers cbase
def __cinit__(self):
self.cbase = catimac.Layers()
self.materials = []
def add(self,Material m):
self.cbase.add(m.cbase)
self.materials.append(m)
def num(self):
return self.cbase.num()
def __getitem__(self, key):
if(isinstance(key,int)):
return self.materials[key]
cdef class Projectile:
cdef catimac.Projectile cbase
def __cinit__(self, a, z, t=None,q=None):
self.cbase.A = a
self.cbase.Z = z
self.cbase.Q = z
if(q):
self.cbase.Q = q
if(t):
self.cbase.T = t
def T(self,val):
self.cbase.T = val;
def __call__(self,val=None):
if(val is None):
return self.cbase.T
else:
self.T(val)
return self
def A(self):
return self.cbase.A
def Z(self):
return self.cbase.Z
cdef class Result:
cdef public double Ein
cdef public double Eout
cdef public double Eloss
cdef public double range
cdef public double dEdxi
cdef public double dEdxo
cdef public double sigma_E
cdef public double sigma_a
cdef public double sigma_r
cdef public double tof
def __init__(self):
self.Ein=0.0
self.Eout=0.0
self.Eloss=0.0
self.range=0.0
self.dEdxi=0.0
self.dEdxo=0.0
self.sigma_E=0.0
self.sigma_a=0.0
self.sigma_r=0.0
self.tof=0.0
cdef setc(self,catimac.Result &val):
self.Ein=val.Ein
self.Eout=val.Eout
self.Eloss=val.Eloss
self.range=val.range
self.dEdxi=val.dEdxi
self.dEdxo=val.dEdxo
self.sigma_E=val.sigma_E
self.sigma_a=val.sigma_a
self.sigma_r=val.sigma_r
self.tof=val.tof
class z_eff_type(IntEnum):
none = 0,
atima = 1
pierce_blann = 1
anthony_landorf = 2
hubert = 3
class skip_calculation(IntEnum):
skip_none = 0
skip_tof = 1
skip_sigma_a = 2
skip_sigma_r = 4
class corrections(IntEnum):
no_barkas = 1
no_lindhard = 2
no_shell_correction = 4
cdef class Config:
cdef catimac.Config cbase
def __cinit__(self):
#self.cbase = catimac.Config()
self.cbase.z_effective = z_eff_type.atima
self.cbase.skip = skip_calculation.skip_none
self.cbase.dedx = skip_calculation.skip_none
def z_effective(self, val=None):
if(val is None):
return self.cbase.z_effective
else:
self.cbase.z_effective = val
def skip_calculation(self, val=None):
if(val is None):
return self.cbase.skip
else:
self.cbase.skip = val
def dedx(self, val=None):
if(val is None):
return self.cbase.dedx
else:
self.cbase.dedx = val
default_config = Config()
def calculate(Projectile projectile, Material material, energy = None, Config config = default_config):
if(not energy is None):
projectile.T(energy)
cdef catimac.Result cres = catimac.calculate(projectile.cbase,material.cbase,config.cbase)
res = Result()
res.setc(cres)
return res
def range(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.range(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.range(projectile.cbase, energy, material.cbase, config.cbase);
def dedx_from_range(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.dedx_from_range(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.dedx_from_range(projectile.cbase, energy, material.cbase, config.cbase);
def domega2de(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.domega2de(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.domega2de(projectile.cbase, energy, material.cbase, config.cbase);
def da2de(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.da2de(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.da2de(projectile.cbase, energy, material.cbase, config.cbase);
def dedx(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.dedx(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.dedx(projectile.cbase, energy, material.cbase, config.cbase)
def energy_out(Projectile projectile, Material material, energy = None, Config config = default_config):
if(isinstance(energy,numpy.ndarray)):
res = numpy.empty(energy.size)
for i,e in enumerate(energy):
res[i] = catimac.energy_out(projectile.cbase, e, material.cbase, config.cbase)
return res
if(energy is None):
energy = projectile.T()
return catimac.energy_out(projectile.cbase, energy, material.cbase, config.cbase)
def z_effective(Projectile p, Target t, Config c = default_config):
return catimac.z_effective(p.cbase, t.cbase, c.cbase)
def z_eff_Pierce_Blann(double z, double beta):
return catimac.z_eff_Pierce_Blann(z,beta)

81
catimac.pxd Normal file
View File

@ -0,0 +1,81 @@
from libcpp.pair cimport pair
from libcpp.vector cimport vector
cdef extern from "catima/structures.h" namespace "catima":
cdef struct Target:
double A
int Z
cdef struct Projectile:
double A
double Z
double Q
double T
cdef struct Result:
double Ein
double Eout
double Eloss
double range
double dEdxi
double dEdxo
double sigma_E
double sigma_a
double sigma_r
double tof
cdef cppclass MultiResult
cdef cppclass Material:
Material() except +
void add_element(double , int , double )
pair[Target,double] getElement(int)
int ncomponents()
double M()
double density()
void density(double val)
double thickness()
void thickness(double val)
cdef cppclass Layers:
Layers() except +
const vector[Material]& get_materials() const
void add(Material m)
int num()const
Material& operator[](int i)
Layers& operator=(const Layers& other)
cdef extern from "catima/config.h" namespace "catima":
cdef struct Config:
char z_effective;
char skip;
char dedx;
cdef extern from "catima/catima.h" namespace "catima":
cdef double dedx(Projectile &p, double T, const Material &t,const Config &c)
cdef double range(Projectile &p, double T, const Material &t, const Config &c);
cdef double dedx_from_range(Projectile &p, double T, const Material &t, const Config &c);
cdef double energy_out(Projectile &p, double T, const Material &t, const Config &c);
cdef double domega2de(Projectile &p, double T, const Material &t, const Config &c);
cdef double da2de(Projectile &p, double T, const Material &t, const Config &c);
cdef double range_straggling(Projectile &p, double T, const Material &t, const Config &c);
cdef double da2dx(Projectile &p, double T, const Material &t, const Config &c);
cdef double dedx_rms(Projectile &p, Target &t, const Config &c);
cdef double angular_variance(Projectile &p, double T, const Material &t, const Config& c);
cdef Result calculate(Projectile &p, const Material &t, const Config &c);
cdef MultiResult calculate(Projectile &p, const Layers &layers, const Config &c);
cdef extern from "catima/calculations.h" namespace "catima":
cdef double z_effective(const Projectile &p, const Target &t, const Config &c);
cdef double z_eff_Pierce_Blann(double z, double beta);
cdef extern from "catima/constants.h" namespace "catima":
cdef int max_datapoints;
cdef extern from "catima/storage.h" namespace "catima":
cdef cppclass Interpolator:
double eval(double)
double derivative(double)

56
config.h Normal file
View File

@ -0,0 +1,56 @@
/// \file config.h
#ifndef CONFIG
#define CONFIG
#include <cstring>
namespace catima{
/**
* \enum z_eff_type
* enum to select formulat to calculate effective charge of the Projectile
*/
enum z_eff_type:char {
none = 0,
atima = 1, // the same as Pierce Blann
pierce_blann = 1,
anthony_landorf = 2,
hubert = 3
};
/**
* enum to select which calculation to skip
*/
enum skip_calculation:char{
skip_none = 0,
skip_tof = 1,
skip_sigma_a = 2,
skip_sigma_r = 4
};
/**
* enum to select which dEdx correction to skip
*/
enum corrections:char{
no_barkas = 1,
no_lindhard = 2,
no_shell_correction = 4
};
/**
* structure to store calculation configuration
* each group of options are grouped and enum are suppose to use
* see catima::z_eff_type, catima::skip_calculation, catima::corrections
*
* check catima::z_effective()
*
*/
struct Config{
char z_effective=z_eff_type::atima;
char skip=skip_none;
char dedx = 0;
};
extern Config default_config;
}
#endif

45
constants.h Normal file
View File

@ -0,0 +1,45 @@
#ifndef CONSTANTS_H
#define CONSTANTS_H
namespace catima {
constexpr double Ezero = 9E-4; // lowest E to calculate, below taken as 0
constexpr double logEmin = -3; // log of minimum energy
constexpr double logEmax = 4.5; // log of max energy
constexpr int max_datapoints = 500; // how many datapoints between logEmin and logEmax
constexpr int max_storage_data = 50; // number of datapoints which can be stored in cache
/// required integration precision (relative units)
constexpr double int_eps_range = 0.01;
constexpr double int_eps_range_str = 0.01;
constexpr double int_eps_ang_str = 0.01;
constexpr double int_eps_tof = 0.01;
constexpr double thin_target_limit = 1 - 1e-3;
constexpr double Avogadro = 6.022140857; // 10^23
constexpr double electron_mass = 0.510998928; // MeV/c^2
constexpr double atomic_mass_unit = 931.4940954; // MeV/c^2
constexpr double classical_electron_radius = 2.8179403227; //fm
constexpr double fine_structure = 1/137.035999139;
constexpr double c_light = 299.792458; //Mm/s
constexpr double dedx_constant = 0.3070749187; //4*pi*Na*me*c^2*r_e^2 //MeV cm^2
constexpr double domega2dx_constant = dedx_constant*electron_mass; //4*pi*Na*me*c^2*r_e^2 //MeV^2 cm^2
// units //
namespace units{
constexpr double g = 1.0;
constexpr double mg = 1000.0;
constexpr double cm3 = 1.0;
constexpr double cm = 1.0;
constexpr double mm = 10.;
constexpr double keV = 1000.0;
constexpr double ns = 1.0;
}
}
#endif

52
cwrapper.cpp Normal file
View File

@ -0,0 +1,52 @@
#include "catima/cwrapper.h"
#include "catima/catima.h"
#include "catima/material_database.h"
#include <cstring>
extern "C" {
CatimaResult catima_calculate(double pa, int pz, double T, double ta, double tz, double thickness, double density){
catima::default_config.z_effective = catima_defaults.z_effective;
catima::default_config.skip = catima_defaults.skip;
catima::Material mat;
catima::Projectile p(pa,pz);
if(tz>200){
mat = catima::get_material(tz);
}
else{
mat.add_element(ta,tz,1.0);
}
mat.density(density).thickness(thickness);
catima::Result r = catima::calculate(p(T),mat);
CatimaResult res;
std::memcpy(&res,&r,sizeof(res));
return res;
}
double catima_angular_straggling_from_E(double pa, int pz, double Tin, double Tout,double ta, double tz){
catima::Projectile p(pa,pz);
catima::Material mat;
if(tz>200){
mat = catima::get_material(tz);
}
else{
mat.add_element(ta,tz,1.0);
}
catima::angular_straggling_from_E(p,Tin,Tout,mat);
}
double catima_energy_straggling_from_E(double pa, int pz, double Tin, double Tout,double ta, double tz){
catima::Projectile p(pa,pz);
catima::Material mat;
if(tz>200){
mat = catima::get_material(tz);
}
else{
mat.add_element(ta,tz,1.0);
}
catima::energy_straggling_from_E(p,Tin,Tout,mat);
}
}

52
cwrapper.h Normal file
View File

@ -0,0 +1,52 @@
#ifndef CATIMA_CWRAPPER
#define CATIMA_CWRAPPER
#ifdef __cplusplus
extern "C" {
#endif
struct CatimaResult{
double Ein;
double Eout;
double Eloss;
double range;
double dEdxi;
double dEdxo;
double sigma_E;
double sigma_a;
double sigma_r;
double tof;
};
enum z_eff_type {
none = 0,
atima = 1
};
enum skip_calculation{
skip_none = 0,
skip_tof = 1,
skip_sigma_a = 2,
skip_sigma_r = 4
};
struct CatimaConfig {
char z_effective;
char skip;
};
struct CatimaConfig catima_defaults = {none,skip_none};
typedef struct CatimaResult CatimaResult;
CatimaResult catima_calculate(double pa, int pz, double T, double ta, double tz, double thickness, double density);
double catima_angular_straggling_from_E(double pa, int pz, double Tin, double Tout,double ta, double tz);
double catima_energy_straggling_from_E(double pa, int pz, double Tin, double Tout,double ta, double tz);
#ifdef __cplusplus
}
#endif
#endif

368
data_atima.h Normal file
View File

@ -0,0 +1,368 @@
#ifndef ATIMA_DATA
#define ATIMA_DATA
// this is taken from atima
namespace catima{
constexpr double proton_stopping_coef[92][8] = { // proton in material stopping coefficient
{ .0091827, .0053496, .69741, .48493, 316.07,1.0143, 9329.3, .0539890}, //H
{ .11393, .0051984, 1.0822, .39252, 1081.0, 1.0645, 4068.5, .0176990}, //He
{ .85837, .0050147, 1.6044, .38844, 1337.3, 1.0470, 2659.2, .01898},
{ .8781, .0051049, 5.4232, .2032, 1200.6, 1.0211, 1401.8, .0385290},
{ 1.4608, .0048836, 2.338, .44249, 1801.3, 1.0352, 1784.1, .02024},
{ 3.2579, .0049148, 2.7156, .36473, 2092.2, 1.0291, 2643.6, .0182370}, //C
{ .59674, .0050837, 4.2073, .30612, 2394.2, 1.0255, 4892.1, .0160060},
{ .75253, .0050314, 4.0824, .30067, 2455.8, 1.0181, 5069.7, .0174260}, //O
{ 1.226, .0051385, 3.2246, .32703, 2525.0, 1.0142, 7563.6, .0194690},
{ 1.0332, .0051645, 3.004, .33889, 2338.6, .99997, 6991.2, .0217990}, //Ne
{ 6.0972, .0044292, 3.1929, .45763, 1363.3, .95182, 2380.6, .0818350},
{14.013, .0043646, 2.2641, .36326, 2187.4, .99098, 6264.8, .0462},
{ .039001, .0045415, 5.5463, .39562, 1589.2, .95316, 816.16, .0474840},
{ 2.072, .0044516, 3.5585, .53933, 1515.2, .93161, 1790.3, .0351980},
{17.575, .0038346, .078694, 1.2388,2806.0, .97284, 1037.6, .0128790},
{16.126, .0038315, .054164, 1.3104,2813.3, .96587, 1251.4, .0118470},
{ 3.217, .0044579, 3.6696, .5091, 2734.6, .96253, 2187.5, .0169070},
{ 2.0379, .0044775, 3.0743, .54773, 3505.0, .97575, 1714.00, .0117010},
{ .74171, .0043051, 1.1515, .95083, 917.21, .8782, 389.93, .18926},
{ 9.1316, .0043809, 5.4611, .31327, 3891.8, .97933, 6267.9, .0151960}, //Ca
{ 7.2247, .0043718, 6.1017, .37511, 2829.2, .95218, 6376.1, .0203980},
{ .147, .0048456, 6.3485, .41057, 2164.1, .94028, 5292.6, .0502630},
{ 5.0611, .0039867, 2.6174, .57957, 2218.9, .92361, 6323.00, .0256690},
{ .53267, .0042968, .39005, 1.2725, 1872.7, .90776, 64.166, .0301070},
{ .47697, .0043038, .31452, 1.3289, 1920.5, .90649, 45.576, .0274690},
{ .027426, .0035443, .031563, 2.1755, 1919.5, .90099, 23.902, .0253630},
{ .16383, .0043042, .073454, 1.8592, 1918.4, .89678, 27.61, .0231840},
{ 4.2562, .0043737, 1.5606, .72067, 1546.8, .87958, 302.02, .0409440}, //Ni
{ 2.3508, .0043237, 2.882, .50113, 1837.7, .89992, 2377.00, .04965},
{ 3.1095, .0038455, .11477, 1.5037, 2184.7, .89309, 67.306, .0165880},
{15.322, .0040306, .65391, .67668, 3001.7, .92484, 3344.2, .0163660},
{ 3.6932, .0044813, 8.608, .27638, 2982.7, .9276, 3166.6, .0308740},
{ 7.1373, .0043134, 9.4247, .27937, 2725.8, .91597, 3166.1, .0250080},
{ 4.8979, .0042937, 3.7793, .50004, 2824.5, .91028, 1282.4, .0170610},
{ 1.3683, .0043024, 2.5679, .60822, 6907.8, .9817, 628.01, .0068055},
{ 1.8301, .0042983, 2.9057, .6038, 4744.6, .94722, 936.64, .0092242},
{ .42056, .0041169, .01695, 2.3616, 2252.7, .89192, 39.752, .0277570},
{30.78, .0037736, .55813, .76816, 7113.2, .97697, 1604.4, .0065268},
{11.576, .0042119, 7.0244, .37764, 4713.5, .94264, 2493.2, .01127},
{ 6.2406, .0041916, 5.2701, .49453, 4234.6, .93232, 2063.9, .0118440},
{ .33073, .0041243, 1.7246, 1.1062, 1930.2, .86907, 27.416, .0382080},
{ .017747, .0041715, .14586, 1.7305,1803.6, .86315, 29.669, .0321230},
{ 3.7229, .0041768, 4.6286, .56769, 1678.0, .86202, 3094.00, .06244},
{ .13998, .0041329, .25573, 1.4241, 1919.3, .86326, 72.797, .0322350},
{ .2859, .0041386, .31301, 1.3424, 1954.8, .86175, 115.18, .0293420},
{ .76, .0042179, 3.386, .76285, 1867.4, .85805, 69.994, .0364480},
{ 6.3957, .0041935, 5.4689, .41378, 1712.6, .85397,18493.00, .0564710},
{ 3.4717, .0041344, 3.2337, .63788, 1116.4, .81959, 4766.0, .1179},
{ 2.5265, .0042282, 4.532, .53562, 1030.8, .81652,16252.0, .19722},
{ 7.3683, .0041007, 4.6791, .51428, 1160.0, .82454,17965.0, .13316},
{ 7.7197, .004388, 3.242, .68434, 1428.1, .83398, 1786.7, .0665120},
{16.78, .0041918, 9.3198, .29568, 3370.9, .90289, 7431.7, .02616},
{ 4.2132, .0042098, 4.6753, .57945, 3503.9, .89261, 1468.9, .0143590},
{ 4.0818, .004214, 4.4425, .58393, 3945.3, .90281, 1340.5, .0134140}, //Xe
{.18517, .0036215, .00058788,3.5315, 2931.3, .88936, 26.18, .0263930},
{ 4.8248, .0041458, 6.0934, .57026, 2300.1, .86359, 2980.7, .0386790},
{ .49857, .0041054, 1.9775, .95877, 786.55, .78509, 806.6, .40882},
{ 3.2754, .0042177, 5.768, .54054, 6631.3, .94282, 744.07, .0083026},
{ 2.9978, .0040901, 4.5299, .62025, 2161.2, .85669, 1268.6, .0430310},
{ 2.8701, .004096, 4.2568, .6138, 2130.4, .85235, 1704.1, .0393850},
{10.853, .0041149, 5.8907, .46834, 2857.2, .8755, 3654.2, .0299550},
{ 3.6407, .0041782, 4.8742, .57861, 1267.7, .82211, 3508.2, .24174},
{17.645, .0040992, 6.5855, .32734, 3931.3, .90754, 5156.7, .0362780},
{ 7.5309, .0040814, 4.9389, .50679, 2519.7, .85819, 3314.6, .0305140},
{ 5.4742, .0040829, 4.897, .51113, 2340.1, .85296, 2342.7, .0356620},
{ 4.2661, .0040667, 4.5032, .55257, 2076.4, .84151, 1666.6, .0408010},
{ 6.8313, .0040486, 4.3987, .51675, 2003.0, .83437, 1410.4, .03478},
{ 1.2707, .0040553, 4.6295, .57428, 1626.3, .81858, 995.68, .0553190},
{ 5.7561, .0040491, 4.357, .52496, 2207.3, .83796, 1579.5, .0271650},
{14.127, .0040596, 5.8304, .37755, 3645.9, .87823, 3411.8, .0163920},
{ 6.6948, .0040603, 4.9361, .47961, 2719.0, .85249, 1885.8, .0197130},
{ 3.0619, .0040511, 3.5803, .59082, 2346.1, .83713, 1222.0, .0200720},
{10.811, .0033008, 1.3767, .76512, 2003.7, .82269, 1110.6, .0249580},
{ 2.7101, .0040961, 1.2289, .98598, 1232.4, .79066, 155.42, .0472940},
{ .52345, .0040244, 1.4038, .8551, 1461.4, .79677, 503.34, .0367890},
{ .4616, .0040203, 1.3014, .87043, 1473.5, .79687, 443.09, .0363010},
{ .97814, .0040374, 2.0127, .7225, 1890.8, .81747, 930.7, .02769},
{ 3.2086, .004051, 3.6658, .53618, 3091.2, .85602, 1508.1, .0154010},
{ 2.0035, .0040431, 7.4882, .3561, 4464.3, .88836, 3966.5, .0128390},
{15.43, .0039432, 1.1237, .70703, 4595.7, .88437, 1576.5, .0088534},
{ 3.1512, .0040524, 4.0996, .5425, 3246.3, .85772, 1691.8, .0150580},
{ 7.1896, .0040588, 8.6927, .35842, 4760.6, .88833, 2888.3, .0110290}, //Pb
{ 9.3209, .004054, 11.543, .32027, 4866.2, .89124, 3213.4, .0119350},
{29.242, .0036195, .16864, 1.1226, 5688.0, .89812, 1033.3, .0071303},
{ 1.8522, .0039973, 3.1556, .65096, 3755.0, .86383, 1602.0, .0120420},
{ 3.222, .0040041, 5.9024, .52678, 4040.2, .86804, 1658.4, .0117470},
{ 9.3412, .0039661, 7.921, .42977, 5180.9, .88773, 2173.2, .0092007},
{36.183, .0036003, .58341, .86747, 6990.2, .91082, 1417.1, .0062187},
{ 5.9284, .0039695, 6.4082, .52122, 4619.5, .88083, 2323.5, .0116270},
{ 5.2454, .0039744, 6.7969, .48542, 4586.3, .87794, 2481.5, .0112820},
{33.702, .0036901, .47257, .89235, 5295.7, .8893, 2053.3, .0091908},
{2.7589, .0039806, 3.2092, .66122, 2505.4, .82863, 2065.1, .0228160} //U
};
const double atima_vfermi[92] = {
1.0309,
0.15976,
0.59782,
1.0781,
1.0486,
1.00,
1.058,
0.93942,
0.74562,
0.3424,
0.45259,
0.71074,
0.90519,
0.97411,
0.97184,
0.89852,
0.70827,
0.39816,
0.36552,
0.62712,
0.81707,
0.9943,
1.1423,
1.2381,
1.1222,
0.92705,
1.0047,
1.2,
1.0661,
0.97411,
0.84912,
0.95,
1.0903,
1.0429,
0.49715,
0.37755,
0.35211,
0.57801,
0.77773,
1.0207,
1.029,
1.2542,
1.122,
1.1241,
1.0882,
1.2709,
1.2542,
0.90094,
0.74093,
0.86054,
0.93155,
1.0047,
0.55379,
0.43289,
0.32636,
0.5131,
0.6950,
0.72591,
0.71202,
0.67413,
0.71418,
0.71453,
0.5911,
0.70263,
0.68049,
0.68203,
0.68121,
0.68532,
0.68715,
0.61884,
0.71801,
0.83048,
1.1222,
1.2381,
1.045,
1.0733,
1.0953,
1.2381,
1.2879,
0.78654,
0.66401,
0.84912,
0.88433,
0.80746,
0.43357,
0.41923,
0.43638,
0.51464,
0.73087,
0.81065,
1.9578,
1.0257};
const double atima_lambda_screening[92]= {
1.00,
1.00,
1.10,
1.06,
1.01,
1.03,
1.04,
0.99,
0.95,
0.90,
0.82,
0.81,
0.83,
0.88,
1.00,
0.95,
0.97,
0.99,
0.98,
0.97,
0.98,
0.97,
0.96,
0.93,
0.91,
0.9,
0.88,
0.9,
0.9,
0.9,
0.9,
0.85,
0.9,
0.9,
0.91,
0.92,
0.9,
0.9,
0.9,
0.9,
0.9,
0.88,
0.9,
0.88,
0.88,
0.9,
0.9,
0.88,
0.9,
0.9,
0.9,
0.9,
0.96,
1.2,
0.9,
0.88,
0.88,
0.85,
0.90,
0.90,
0.92,
0.95,
0.99,
1.03,
1.05,
1.07,
1.08,
1.10,
1.08,
1.08,
1.08,
1.08,
1.09,
1.09,
1.10,
1.11,
1.12,
1.13,
1.14,
1.15,
1.17,
1.20,
1.18,
1.17,
1.17,
1.16,
1.16,
1.16,
1.16,
1.16,
1.16,
1.16};
}
namespace density_effect{
const double x0[92]= {
1.8639, 2.2017, 0.1304, 0.0592, 0.0305, -.0178, 1.7378, 1.7541, 1.8433, 2.0735,
0.2880, 0.1499, 0.1708, 0.2014, 0.1696, 0.1580, 1.5555, 1.7635, 0.3851, 0.3228,
0.1640, 0.0957, 0.0691, 0.0340, 0.0447, -.0012, -.0187, -.0566, -.0254, 0.0049,
0.2267, 0.3376, 0.1767, 0.2258, 1.5262, 1.7158, 0.5737, 0.4585, 0.3608, 0.2957,
0.1785, 0.2267, 0.0949, 0.0599, 0.0576, 0.0563, 0.0657, 0.1281, 0.2406, 0.2879,
0.3189, 0.3296, 0.0549, 1.5630, 0.5473, 0.4190, 0.3161, 0.2713, 0.2333, 0.1984,
0.1627, 0.1520, 0.1888, 0.1058, 0.0947, 0.0822, 0.0761, 0.0648, 0.0812, 0.1199,
0.1560, 0.1965, 0.2117, 0.2167, 0.0559, 0.0891, 0.0819, 0.1484, 0.2021, 0.2756,
0.3491, 0.3776, 0.4152, 0.4267, 0.4300, 1.5368, 0.6000, 0.5991, 0.4559, 0.4202,
0.3144, 0.2260 };
const double x1[92]= {
3.2718, 3.6122, 1.6397, 1.6922, 1.9688, 2.3415, 4.1323, 4.3213, 4.4096, 4.6421,
3.1962, 3.0668, 3.0127, 2.8715, 2.7815, 2.7159, 4.2994, 4.4855, 3.1724, 3.1191,
3.0593, 3.0386, 3.0322, 3.0451, 3.1074, 3.1531, 3.1790, 3.1851, 3.2792, 3.3668,
3.5434, 3.6096, 3.5702, 3.6264, 4.9899, 5.0748, 3.7995, 3.6778, 3.5542, 3.4890,
3.2201, 3.2784, 3.1253, 3.0834, 3.1069, 3.0555, 3.1074, 3.1667, 3.2032, 3.2959,
3.3489, 3.4418, 3.2596, 4.7371, 3.5914, 3.4547, 3.3293, 3.3432, 3.2773, 3.3063,
3.3199, 3.3460, 3.4633, 3.3932, 3.4224, 3.4474, 3.4782, 3.4922, 3.5085, 3.6246,
3.5218, 3.4337, 3.4805, 3.4960, 3.4845, 3.5414, 3.5480, 3.6212, 3.6979, 3.7275,
3.8044, 3.8073, 3.8248, 3.8293, 4.0000, 4.9889, 4.0000, 3.9428, 3.7966, 3.7681,
3.5079, 3.3721 };
const double a[92]= {
0.14092, 0.13443, 0.95136, 0.80392, 0.56224, 0.26142, 0.15349, 0.11778, 0.11083, .08064,
0.07772, 0.08163, 0.08024, 0.14921, 0.23610, 0.33992, 0.19849, 0.19714, 0.19827, .15643,
0.15754, 0.15662, 0.15436, 0.15419, 0.14973, 0.14680, 0.14474, 0.16496, 0.14339, .14714,
0.09440, 0.07188, 0.06633, 0.06568, 0.06335, 0.07446, 0.07261, 0.07165, 0.07138, .07177,
0.13883, 0.10525, 0.16572, 0.19342, 0.19205, 0.24178, 0.24585, 0.24609, 0.23879, .18689,
0.16652, 0.13815, 0.23766, 0.23314, 0.18233, 0.18268, 0.18591, 0.18885, 0.23265, .23530,
0.24280, 0.24698, 0.24448, 0.25109, 0.24453, 0.24665, 0.24638, 0.24823, 0.24889, .25295,
0.24033, 0.22918, 0.17798, 0.15509, 0.15184, 0.12751, 0.12690, 0.11128, 0.09756, .11014,
0.09455, 0.09359, 0.09410, 0.09282, 0.09000, 0.20798, 0.08000, 0.08804, 0.08567, 0.08655,
0.14770, 0.19677 };
const double c[92]= {
9.5835, 11.1393, 3.1221, 2.7847, 2.8477, 2.8680, 10.5400, 10.7004, 10.9653, 11.9041,
5.0526, 4.5297, 4.2395, 4.4351, 4.5214, 4.6659, 11.1421, 11.9480, 5.6423, 5.0396,
4.6949, 4.4450, 4.2659, 4.1781, 4.2702, 4.2911, 4.2601, 4.3115, 4.4190, 4.6906,
4.9353, 5.1411, 5.0510, 5.3210, 11.7307,12.5115,6.4776, 5.9867, 5.4801 , 5.1774,
5.0141, 4.8793, 4.7769, 4.7694, 4.8008, 4.9358, 5.0630, 5.2727, 5.5211, 5.5340,
5.6241, 5.7131, 5.9488, 12.7281, 6.9135, 6.3153, 5.7850, 5.7837, 5.8096, 5.8290,
5.8224, 5.8597, 6.2278, 5.8738, 5.9045, 5.9183, 5.9587, 5.9521, 5.9677, 6.3325,
5.9785, 5.7139, 5.5262, 5.4059, 5.3445, 5.3083, 5.3418, 5.4732, 5.5747, 5.9605,
6.1365, 6.2018, 6.3505, 6.4003, 6.4, 13.2839, 7., 7.0452, 6.3742, 6.2473,
6.0327, 5.8694 };
const double m[92]= {
5.7273, 5.8347, 2.4993, 2.4339, 2.4512, 2.8697, 3.2125, 3.2913, 3.2962, 3.5771,
3.6452, 3.6166, 3.6345, 3.2546, 2.9158, 2.6456, 2.9702, 2.9618, 2.9233, 3.0745,
3.0517, 3.0302, 3.0163, 2.9896, 2.9796, 2.9632, 2.9502, 2.8430, 2.9044, 2.8652,
3.1314, 3.3306, 3.4176, 3.4317, 3.4670, 3.4051, 3.4177, 3.4435, 3.4585, 3.4533,
3.0930, 3.2549, 2.9738, 2.8707, 2.8633, 2.7239, 2.6899, 2.6772, 2.7144, 2.8576,
2.9319, 3.0354, 2.7276, 2.7414, 2.8866, 2.8906, 2.8828, 2.8592, 2.7331, 2.7050,
2.6674, 2.6403, 2.6245, 2.5977, 2.6056, 2.5849, 2.5726, 2.5573, 2.5469, 2.5141,
2.5643, 2.6155, 2.7623, 2.8447, 2.8627, 2.9608, 2.9658, 3.0417, 3.1101, 3.0519,
3.1450, 3.1608, 3.1671, 3.1830, 1.1111, 2.7409, 1.1111, 3.2454, 3.2683, 3.2610,
2.9845, 2.8171 };
const double del_0[92]= {
0.0, 0.00, 0.14, 0.14, 0.14, 0.12, 0.00, 0.00, 0.00, 0.00,
0.08, 0.08, 0.12, 0.14, 0.14, 0.14, 0.00, 0.00, 0.10, 0.14,
0.10, 0.12, 0.14, 0.14, 0.14, 0.12, 0.12, 0.10, 0.08, 0.08,
0.14, 0.14, 0.08, 0.10, 0.00, 0.00, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14, 0.00, 0.00, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14, 0.14,
0.14, 0.14, 0.14, 0.14, 0.08, 0.10, 0.10, 0.12, 0.14, 0.14,
0.14, 0.14, 0.14, 0.14, 0.00, 0.00, 0.00, 0.14, 0.14, 0.14,
0.14, 0.14 };
}
#endif

155
data_ionisation_potential.h Normal file
View File

@ -0,0 +1,155 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef IONISATION_POTENTIALS_H
#define IONISATION_POTENTIALS_H
#define IPOT_ZMAX 120
namespace catima{
const double ionisation_potentials_z[IPOT_ZMAX+1] = {
9999999, // 0
19.2, // H
41.8, // He
40.0,
63.7,
76.0,
78.0, // C
82.0,
95.0,
115.0,
137.0,
149.0,
156.0,
166.0,
173.0,
173.0,
180.0,
174.0,
188.0,
190.0,
191.0, //Ca (20)
216.0,
233.0,
245.0,
257.0,
272.0,
286.0, //Fe 26
297.0,
311.0,
322.0,
330.0,
334.0,
350.0,
347.0,
348.0,
343.0,
352.0,
363.0,
366.0,
379.0,
393.0,
417.0,
424.0,
428.0,
441.0,
449.0,
470.0,
470.0,
469.0,
488.0,
488.0, //Sn 50
487.0,
485.0,
491.0,
482.0, // Xe 54
488.0,
491.0,
501.0,
523.0,
535.0,
546.0,
560.0,
574.0,
580.0,
591.0,
614.0,
628.0,
650.0,
658.0,
674.0,
684.0,
694.0,
705.0,
718.0,
727.0,
736.0,
746.0,
757.0,
790.0,
790.0, // Au 79
800.0,
810.0,
823.0, //Pb 82
823.0,
830.0,
825.0,
794.0,
827.0,
826.0,
841.0,
847.0,
878.0,
890.0, // U 92
900.0,
910.0,
920.0,
930.0,
940.0,
950.0,
960.0,
970.0,
980.0,
990.0,
1000.0,
1010.0,
1020.0,
1030.0,
1040.0,
1050.0,
1060.0,
1070.0,
1080.0,
1090.0,
1100.0,
1110.0,
1120.0,
1130.0,
1140.0,
1150.0,
1160.0,
1170.0,
};
inline double ipot(int z){
if(z<1 || z>IPOT_ZMAX){
return 0.0;
}
return ionisation_potentials_z[z];
}
}
#endif

288
data_srim.h Normal file
View File

@ -0,0 +1,288 @@
#ifndef SRIM_DATA
#define SRIM_DATA
// this is take from atima
constexpr double proton_stopping_coef[92][8] = { // proton in material stopping coefficient
{ .0091827, .0053496, .69741, .48493, 316.07,1.0143, 9329.3, .0539890}, //H
{ .11393, .0051984, 1.0822, .39252, 1081.0, 1.0645, 4068.5, .0176990}, //He
{ .85837, .0050147, 1.6044, .38844, 1337.3, 1.0470, 2659.2, .01898},
{ .8781, .0051049, 5.4232, .2032, 1200.6, 1.0211, 1401.8, .0385290},
{ 1.4608, .0048836, 2.338, .44249, 1801.3, 1.0352, 1784.1, .02024},
{ 3.2579, .0049148, 2.7156, .36473, 2092.2, 1.0291, 2643.6, .0182370}, //C
{ .59674, .0050837, 4.2073, .30612, 2394.2, 1.0255, 4892.1, .0160060},
{ .75253, .0050314, 4.0824, .30067, 2455.8, 1.0181, 5069.7, .0174260}, //O
{ 1.226, .0051385, 3.2246, .32703, 2525.0, 1.0142, 7563.6, .0194690},
{ 1.0332, .0051645, 3.004, .33889, 2338.6, .99997, 6991.2, .0217990}, //Ne
{ 6.0972, .0044292, 3.1929, .45763, 1363.3, .95182, 2380.6, .0818350},
{14.013, .0043646, 2.2641, .36326, 2187.4, .99098, 6264.8, .0462},
{ .039001, .0045415, 5.5463, .39562, 1589.2, .95316, 816.16, .0474840},
{ 2.072, .0044516, 3.5585, .53933, 1515.2, .93161, 1790.3, .0351980},
{17.575, .0038346, .078694, 1.2388,2806.0, .97284, 1037.6, .0128790},
{16.126, .0038315, .054164, 1.3104,2813.3, .96587, 1251.4, .0118470},
{ 3.217, .0044579, 3.6696, .5091, 2734.6, .96253, 2187.5, .0169070},
{ 2.0379, .0044775, 3.0743, .54773, 3505.0, .97575, 1714.00, .0117010},
{ .74171, .0043051, 1.1515, .95083, 917.21, .8782, 389.93, .18926},
{ 9.1316, .0043809, 5.4611, .31327, 3891.8, .97933, 6267.9, .0151960}, //Ca
{ 7.2247, .0043718, 6.1017, .37511, 2829.2, .95218, 6376.1, .0203980},
{ .147, .0048456, 6.3485, .41057, 2164.1, .94028, 5292.6, .0502630},
{ 5.0611, .0039867, 2.6174, .57957, 2218.9, .92361, 6323.00, .0256690},
{ .53267, .0042968, .39005, 1.2725, 1872.7, .90776, 64.166, .0301070},
{ .47697, .0043038, .31452, 1.3289, 1920.5, .90649, 45.576, .0274690},
{ .027426, .0035443, .031563, 2.1755, 1919.5, .90099, 23.902, .0253630},
{ .16383, .0043042, .073454, 1.8592, 1918.4, .89678, 27.61, .0231840},
{ 4.2562, .0043737, 1.5606, .72067, 1546.8, .87958, 302.02, .0409440}, //Ni
{ 2.3508, .0043237, 2.882, .50113, 1837.7, .89992, 2377.00, .04965},
{ 3.1095, .0038455, .11477, 1.5037, 2184.7, .89309, 67.306, .0165880},
{15.322, .0040306, .65391, .67668, 3001.7, .92484, 3344.2, .0163660},
{ 3.6932, .0044813, 8.608, .27638, 2982.7, .9276, 3166.6, .0308740},
{ 7.1373, .0043134, 9.4247, .27937, 2725.8, .91597, 3166.1, .0250080},
{ 4.8979, .0042937, 3.7793, .50004, 2824.5, .91028, 1282.4, .0170610},
{ 1.3683, .0043024, 2.5679, .60822, 6907.8, .9817, 628.01, .0068055},
{ 1.8301, .0042983, 2.9057, .6038, 4744.6, .94722, 936.64, .0092242},
{ .42056, .0041169, .01695, 2.3616, 2252.7, .89192, 39.752, .0277570},
{30.78, .0037736, .55813, .76816, 7113.2, .97697, 1604.4, .0065268},
{11.576, .0042119, 7.0244, .37764, 4713.5, .94264, 2493.2, .01127},
{ 6.2406, .0041916, 5.2701, .49453, 4234.6, .93232, 2063.9, .0118440},
{ .33073, .0041243, 1.7246, 1.1062, 1930.2, .86907, 27.416, .0382080},
{ .017747, .0041715, .14586, 1.7305,1803.6, .86315, 29.669, .0321230},
{ 3.7229, .0041768, 4.6286, .56769, 1678.0, .86202, 3094.00, .06244},
{ .13998, .0041329, .25573, 1.4241, 1919.3, .86326, 72.797, .0322350},
{ .2859, .0041386, .31301, 1.3424, 1954.8, .86175, 115.18, .0293420},
{ .76, .0042179, 3.386, .76285, 1867.4, .85805, 69.994, .0364480},
{ 6.3957, .0041935, 5.4689, .41378, 1712.6, .85397,18493.00, .0564710},
{ 3.4717, .0041344, 3.2337, .63788, 1116.4, .81959, 4766.0, .1179},
{ 2.5265, .0042282, 4.532, .53562, 1030.8, .81652,16252.0, .19722},
{ 7.3683, .0041007, 4.6791, .51428, 1160.0, .82454,17965.0, .13316},
{ 7.7197, .004388, 3.242, .68434, 1428.1, .83398, 1786.7, .0665120},
{16.78, .0041918, 9.3198, .29568, 3370.9, .90289, 7431.7, .02616},
{ 4.2132, .0042098, 4.6753, .57945, 3503.9, .89261, 1468.9, .0143590},
{ 4.0818, .004214, 4.4425, .58393, 3945.3, .90281, 1340.5, .0134140}, //Xe
{.18517, .0036215, .00058788,3.5315, 2931.3, .88936, 26.18, .0263930},
{ 4.8248, .0041458, 6.0934, .57026, 2300.1, .86359, 2980.7, .0386790},
{ .49857, .0041054, 1.9775, .95877, 786.55, .78509, 806.6, .40882},
{ 3.2754, .0042177, 5.768, .54054, 6631.3, .94282, 744.07, .0083026},
{ 2.9978, .0040901, 4.5299, .62025, 2161.2, .85669, 1268.6, .0430310},
{ 2.8701, .004096, 4.2568, .6138, 2130.4, .85235, 1704.1, .0393850},
{10.853, .0041149, 5.8907, .46834, 2857.2, .8755, 3654.2, .0299550},
{ 3.6407, .0041782, 4.8742, .57861, 1267.7, .82211, 3508.2, .24174},
{17.645, .0040992, 6.5855, .32734, 3931.3, .90754, 5156.7, .0362780},
{ 7.5309, .0040814, 4.9389, .50679, 2519.7, .85819, 3314.6, .0305140},
{ 5.4742, .0040829, 4.897, .51113, 2340.1, .85296, 2342.7, .0356620},
{ 4.2661, .0040667, 4.5032, .55257, 2076.4, .84151, 1666.6, .0408010},
{ 6.8313, .0040486, 4.3987, .51675, 2003.0, .83437, 1410.4, .03478},
{ 1.2707, .0040553, 4.6295, .57428, 1626.3, .81858, 995.68, .0553190},
{ 5.7561, .0040491, 4.357, .52496, 2207.3, .83796, 1579.5, .0271650},
{14.127, .0040596, 5.8304, .37755, 3645.9, .87823, 3411.8, .0163920},
{ 6.6948, .0040603, 4.9361, .47961, 2719.0, .85249, 1885.8, .0197130},
{ 3.0619, .0040511, 3.5803, .59082, 2346.1, .83713, 1222.0, .0200720},
{10.811, .0033008, 1.3767, .76512, 2003.7, .82269, 1110.6, .0249580},
{ 2.7101, .0040961, 1.2289, .98598, 1232.4, .79066, 155.42, .0472940},
{ .52345, .0040244, 1.4038, .8551, 1461.4, .79677, 503.34, .0367890},
{ .4616, .0040203, 1.3014, .87043, 1473.5, .79687, 443.09, .0363010},
{ .97814, .0040374, 2.0127, .7225, 1890.8, .81747, 930.7, .02769},
{ 3.2086, .004051, 3.6658, .53618, 3091.2, .85602, 1508.1, .0154010},
{ 2.0035, .0040431, 7.4882, .3561, 4464.3, .88836, 3966.5, .0128390},
{15.43, .0039432, 1.1237, .70703, 4595.7, .88437, 1576.5, .0088534},
{ 3.1512, .0040524, 4.0996, .5425, 3246.3, .85772, 1691.8, .0150580},
{ 7.1896, .0040588, 8.6927, .35842, 4760.6, .88833, 2888.3, .0110290}, //Pb
{ 9.3209, .004054, 11.543, .32027, 4866.2, .89124, 3213.4, .0119350},
{29.242, .0036195, .16864, 1.1226, 5688.0, .89812, 1033.3, .0071303},
{ 1.8522, .0039973, 3.1556, .65096, 3755.0, .86383, 1602.0, .0120420},
{ 3.222, .0040041, 5.9024, .52678, 4040.2, .86804, 1658.4, .0117470},
{ 9.3412, .0039661, 7.921, .42977, 5180.9, .88773, 2173.2, .0092007},
{36.183, .0036003, .58341, .86747, 6990.2, .91082, 1417.1, .0062187},
{ 5.9284, .0039695, 6.4082, .52122, 4619.5, .88083, 2323.5, .0116270},
{ 5.2454, .0039744, 6.7969, .48542, 4586.3, .87794, 2481.5, .0112820},
{33.702, .0036901, .47257, .89235, 5295.7, .8893, 2053.3, .0091908},
{2.7589, .0039806, 3.2092, .66122, 2505.4, .82863, 2065.1, .0228160} //U
};
const double srim_vfermi[92] = {
1.0309,
0.15976,
0.59782,
1.0781,
1.0486,
1.00,
1.058,
0.93942,
0.74562,
0.3424,
0.45259,
0.71074,
0.90519,
0.97411,
0.97184,
0.89852,
0.70827,
0.39816,
0.36552,
0.62712,
0.81707,
0.9943,
1.1423,
1.2381,
1.1222,
0.92705,
1.0047,
1.2,
1.0661,
0.97411,
0.84912,
0.95,
1.0903,
1.0429,
0.49715,
0.37755,
0.35211,
0.57801,
0.77773,
1.0207,
1.029,
1.2542,
1.122,
1.1241,
1.0882,
1.2709,
1.2542,
0.90094,
0.74093,
0.86054,
0.93155,
1.0047,
0.55379,
0.43289,
0.32636,
0.5131,
0.6950,
0.72591,
0.71202,
0.67413,
0.71418,
0.71453,
0.5911,
0.70263,
0.68049,
0.68203,
0.68121,
0.68532,
0.68715,
0.61884,
0.71801,
0.83048,
1.1222,
1.2381,
1.045,
1.0733,
1.0953,
1.2381,
1.2879,
0.78654,
0.66401,
0.84912,
0.88433,
0.80746,
0.43357,
0.41923,
0.43638,
0.51464,
0.73087,
0.81065,
1.9578,
1.0257};
double srim_lambda_screening[92]= {
1.00,
1.00,
1.10,
1.06,
1.01,
1.03,
1.04,
0.99,
0.95,
0.90,
0.82,
0.81,
0.83,
0.88,
1.00,
0.95,
0.97,
0.99,
0.98,
0.97,
0.98,
0.97,
0.96,
0.93,
0.91,
0.9,
0.88,
0.9,
0.9,
0.9,
0.9,
0.85,
0.9,
0.9,
0.91,
0.92,
0.9,
0.9,
0.9,
0.9,
0.9,
0.88,
0.9,
0.88,
0.88,
0.9,
0.9,
0.88,
0.9,
0.9,
0.9,
0.9,
0.96,
1.2,
0.9,
0.88,
0.88,
0.85,
0.90,
0.90,
0.92,
0.95,
0.99,
1.03,
1.05,
1.07,
1.08,
1.10,
1.08,
1.08,
1.08,
1.08,
1.09,
1.09,
1.10,
1.11,
1.12,
1.13,
1.14,
1.15,
1.17,
1.20,
1.18,
1.17,
1.17,
1.16,
1.16,
1.16,
1.16,
1.16,
1.16,
1.16};
#endif

39
docs/calculations.tex Normal file
View File

@ -0,0 +1,39 @@
\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\begin{document}
\section{splines caclulations}
Splines data points are calculated at fixed energies. The energy points are uniformly distributed in logarithmic range.
The number of points and logarithmic limits are defined in \textit{constants.h}.
The number of points is \textit{max\_datapoints}, log limits are \textit{logEmin} and \textit{logEmax}.
The energy points are stored in \textit{EnergyTable} class and precalculated values are stored in \textit{energy\_table} variable.
the double array can be accessed as energy\_table.values.
The integration is done using GSL numerical integration library.
\subsection{range spline precision}
The range spline precision is checked via calculating dE/dx from inverse derivative of range spline and compared to directly calculated dE/dx.
\begin{figure}[h]
\centering
\includegraphics[width=6.5cm]{plots/dedx_difs_n500.png}
\includegraphics[width=6.5cm]{plots/dedx_difs_n400.png}
\includegraphics[width=6.5cm]{plots/dedx_difs_n300.png}
\includegraphics[width=6.5cm]{plots/dedx_difs_n200.png}
\caption{Relative difference of dE/dx calculated directly and from range spline, number of range spline datapoints = 500(top left), 400(top right), 300(bottom left), 200(bottom right)}
\end{figure}
\section{Benchmarks}
\subsection{Thin Target Approximation}
test: projectile: 238U@700MeV/u - 30GeV/u, material: C(1mg/cm2), 30000 calculation in loop.
reults: with thin target pproximation: 2.4s, without: 2.4s
\end{document}

231
docs/catima_manual.md Normal file
View File

@ -0,0 +1,231 @@
CATima library manual {#mainpage}
=====================
Compiling and Instalation
-------------------------
See [README.md](README.md) for details.
Units
------
The following units are used for input and outputs:
* projectile energy - MeV/u
* density - g/cm^3
* material thickness - g/cm^2
* material length - cm
* angle - rad
* time of flight - ns
Projectile
----------
The __Projectile__ class is used to store projectile data.
Each projectile must provide A,Z combination, additionally charge state can be set as well.
The example of projectile definition:
~~~~~~~~~~~~~~~~~~~{.cpp}
catima::Projectile p1(12,6); //12C projectile
catima::Projectile p2(12,6,5); //12C(5+) projectile
~~~~~~~~~~~~~~~~~~~
to set the energy of the projectile in MeV/u units:
```cpp
p1.T = 1000.0;
p2(1000.0);
```
Material Definition
-------------------
The material is defined and stored in __Material__ class.
The class stores the atom constituents, thickness and density of the material etc.
There are 2 ways to define materials: specifying all elements in constructor or using `add_element(double, int, double)` function.
The example of water definition:
```cpp
catima::Material water1({
{1,1,2}, // 2 atoms of 1H
{16,8,1} // 1 atom of 16O
});
water1.density(1.0);
water1.thickness(2.0);
catima::Material water2;
water2.add_element(1,1,2);
water2.add_element(16,8,1);
water2.density(1.0).thickness(2.0);
```
If mass number is equal to 0, the mass number of the element is taken as atomic weight of the element with provided Z
Other methods which can be used for Material:
```cpp
double den = water2.density(); //den equals 1.0
double th = water2.thickness(); //th equals 2.0
double molar_mass = water2.M(); // get molar mass of water
int ncomp = water2.ncomponents(); // ncomp equals 2
```
### predefined materials ###
If the library is compiled with predefined materials database, the Material can be retrieved from the database as:
```cpp
using namespace catimal
Material water = get_material(material::WATER);
Material graphite = get_material(6);
```
currently all meterial up to Z=98 are predefined plus compounds from MOCADI:
```
enum material{
PLASTIC = 201,
AIR = 202,
CH2,
LH2,
LD2,
WATER,
DIAMOND,
GLASS,
ALMG3,
ARCO2_30,
CF4,
ISOBUTANE,
KAPTON,
MYLAR,
NAF,
P10,
POLYOLEFIN,
CMO2,
SUPRASIL,
HAVAR
};
```
Calculation
-----------
To calculate all observable following function can be used:
```cpp
Result calculate(Projectile &p, const Material &t, double T, Config c)
Result calculate(Projectile &p, const Material &t, Config c)
```
Both function returns structure ___Result___ which contains all calculated variables.
```cpp
struct Result{
double Ein=0.0;
double Eout=0.0;
double Eloss = 0.0;
double range=0.0;
double dEdxi=0.0;
double dEdxo=0.0;
double sigma_E=0.0;
double sigma_a=0.0;
double sigma_r=0.0;
double tof=0.0;
};
```
If one is interested only in one of the variable, the following function can be used:
```cpp
double dedx(Projectile &p, double T, const Material &t, Config c=default_config);
double domega2dx(Projectile &p, double T, const Material &t, Config c=default_config);
double range(Projectile &p, double T, const Material &t, Config c=default_config);
double range_straggling(Projectile &p, double T, const Material &t, Config c=default_config);
double angular_straggling(Projectile &p, double T, const Material &t, Config c=default_config);
\end{verbatim}
```
Example calculation:
```cpp
...
double T=1000;
auto result = catima::calculate(p1(1000),water1);
cout<<"T "<<T<<", dEdx = "<<result.dEdxi<<" MeV/g/cm2"<<", range = "<<result.range<<" g/cm2"<<endl;
```
Multilayer Material
-------------------
The layers of __Materials__ are stored in __catima::Layers__ class.
There are following ways to define Layers from catima::Material classes:
```cpp
catima::Material graphite({12,6,1});
catima::Material nitrogen({14,7,1});
...
catima::Layers matter1;
matter1.add(graphite);
matter1.add(nitrogen);
matter1.add(graphite);
cout<<"number of layers = "<<matter1.num()<<"\n"; // 3
```
Layers can be copied from existing Layes:
```cpp
catima::Layers matter2;
matter2 = matter1; //matter2 contain 3 layers
matter2.add(nitrogen);
matter2.add(graphite); //matter2 contains 5 layers now
```
Layers can be created as a combination of another Layers:
```cpp
catima::Layers matter3 = matter1 + matter2;
```
Config
------
The calculation configuration is set via catima::Config class. The dafault configuration is predefined in __catima::default_config__ variable.
This __default_config__ is supplied as default argument to functions like catima::calculate. If custom config is needed another configuration can be provided.
the structure Config is defined as:
```cpp
struct Config{
char z_effective=z_eff_type::atima;
char skip=skip_none;
char dedx = 0;
};
```
### effective charge calculation###
the following effective charge calculations are buit in:
```
enum z_eff_type:char {
none = 0,
atima = 1,
pierce_blann = 1,
anthony_landorf = 2,
hubert = 3
};
```
* z_eff_type::none - the provided Projectile Q is used as a charge
* z_eff_type::pierce_blann - Pierce Blann formula, using function: z_eff_Pierce_Blann()
* z_eff_type::anthony_landorf - function: z_eff_Anthony_Landorf()
* z_eff_type::huber - function: z_eff_Huber()
All available switches are defined in __config.h__ file.
Using the library
=================
the include direcotry and LD_LIBRARY_PATH must be properly adjusted.
The app must be linked against catima library.
For example check examples directory and makefile inside to see how to link.
All functions and classes are inside __catima namespace__
Normally including main file is enough:
```cppp
#include "catima/catima.h"
```
Using with C
-------------
the C wrapper is provided in cwapper.h, this file can be included in C app. The C app must be then linked against catima library.
It provides only basic interface.

BIN
docs/catima_manual.pdf Normal file
View File

Binary file not shown.

BIN
docs/plots/dedx_difs_n200.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 26 KiB

BIN
docs/plots/dedx_difs_n300.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 20 KiB

BIN
docs/plots/dedx_difs_n400.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 28 KiB

BIN
docs/plots/dedx_difs_n500.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 27 KiB

2428
doxygen.in Normal file
View File

File diff suppressed because it is too large Load Diff

31
examples/example2.cpp Normal file
View File

@ -0,0 +1,31 @@
#include "catima/catima.h"
#include <iostream>
using std::cout;
using std::endl;
int main(){
catima::Material graphite;
graphite.add_element(12,6,1); // arguments are A,Z, stoichiometric number
graphite.density(1.8); // density in g/cm3
graphite.thickness(2.0); // thickness in g/cm2
catima::Material water({ // material with 2 atoms
{1,1,2}, // 1H - two atoms
{16,8,1} // 16O - 1 atom
});
water.density(1.0).thickness(2.0);
catima::Projectile p(12,6); // define projectile, ie 12C
catima::Layers layer1; // create layers from materials defined above
layer1.add(graphite);
layer1.add(water);
layer1.add(graphite);
auto results = catima::calculate(p(1000),layer1); //calculate rtansport through layers with initial energy 1000 MeV/u
return 0;
}

16
examples/makefile Normal file
View File

@ -0,0 +1,16 @@
PROGRAMS=simple example2 materials
GCC=g++ -Wall -std=c++14
INCDIR=-I$(CATIMAPATH)/include
LIBDIR=-L$(CATIMAPATH)
LIBS=-lcatima
all: $(PROGRAMS)
%: %.cpp
$(GCC) $< $(INCDIR) $(LIBDIR) $(LIBS) -o $@
clean:
rm $(PROGRAMS)

21
examples/materials.cpp Normal file
View File

@ -0,0 +1,21 @@
#include "catima/catima.h"
#include <iostream>
using std::cout;
using std::endl;
int main(){
catima::Material graphite = catima::get_material(6);
catima::Material water = catima::get_material(catima::material::WATER);
cout<<"Material info"<<endl;
cout<<"Molar Mass = "<<graphite.M()<<endl;
cout<<"density = "<<graphite.density()<<endl;
cout<<"Material info"<<endl;
cout<<"Molar Mass = "<<water.M()<<endl;
cout<<"density = "<<water.density()<<endl;
return 0;
}

35
examples/simple.cpp Normal file
View File

@ -0,0 +1,35 @@
#include "catima/catima.h"
#include <iostream>
using std::cout;
using std::endl;
int main(){
catima::Material graphite;
graphite.add_element(12,6,1); // arguments are A,Z, stoichiometric number
graphite.density(1.8); // density in g/cm3
graphite.thickness(2.0); // thickness in g/cm2
catima::Material water({ // material with 2 atoms
{1,1,2}, // 1H - two atoms
{16,8,1} // 16O - 1 atom
});
water.density(1.0).thickness(2.0);
catima::Projectile p(12,6); // define projectile, ie 12C
cout<<"C->C\n";
for(double T:{20,50,100,600,1000}){
auto result = catima::calculate(p(T),graphite);
cout<<"T "<<T<<", dEdx = "<<result.dEdxi<<" MeV/g/cm2"<<", range = "<<result.range<<" g/cm2"<<endl;
}
cout<<"C->H2O\n";
for(double T:{20,50,100,600,1000}){
auto result = catima::calculate(p,water,T);
cout<<"T "<<T<<", dEdx = "<<result.dEdxi<<" MeV/g/cm2"<<", range = "<<result.range<<" g/cm2"<<endl;
}
return 0;
}

476
generated_LS_coeff.h Normal file
View File

@ -0,0 +1,476 @@
//LS precalculated LS coefficients
#include "catima/storage.h"
#define LS_NUM_ENERGY_POINTS 200
#define LS_MAX_Z 110
namespace catima{
namespace ls_coefficients{
// relative difference of mass number for 2nd mass point ls_coefficients_ahi
constexpr double a_rel_increase=0.05;
constexpr double logEmin = 0;
constexpr double logEmax = 4.5;
// energy points array in MeV/u
constexpr EnergyTable<200> ls_energy_table(0,4.5);
//arrays dimensions are [z][energy], z=1 starts from index=0
//LS coefficient for A=atomic weight
double ls_coefficients_a[][200]=
{
{-0.0286505,-0.0271861,-0.0257923,-0.0244655,-0.0232028,-0.022001,-0.0208572,-0.0197686,-0.0187325,-0.0177465,-0.016808,-0.0159148,-0.0150646,-0.0142554,-0.013485,-0.0127516,-0.0120534,-0.0113885,-0.0107554,-0.0101523,-0.00957792,-0.00903066,-0.00850919,-0.00801218,-0.00753838,-0.00708661,-0.00665573,-0.00624466,-0.00585237,-0.00547787,-0.00512024,-0.00477858,-0.00445205,-0.00413984,-0.00384118,-0.00355535,-0.00328163,-0.00301938,-0.00276796,-0.00252676,-0.00229522,-0.00207279,-0.00185895,-0.00165319,-0.00145507,-0.00126411,-0.00107989,-0.000902012,-0.000730078,-0.00056372,-0.000402582,-0.00024633,-9.4641e-05,5.27904e-05,0.000196256,0.000336035,0.000472391,0.000605578,0.000735837,0.000863397,0.000988477,0.00111129,0.00123202,0.00135088,0.00146802,0.00158364,0.00169788,0.00181091,0.00192287,0.00203389,0.00214412,0.00225366,0.00236264,0.00247117,0.00257935,0.00268727,0.00279503,0.00290269,0.00301035,0.00311806,0.00322588,0.00333387,0.00344208,0.00355055,0.0036593,0.00376837,0.00387777,0.00398751,0.00409759,0.00420802,0.00431877,0.00442982,0.00454115,0.00465271,0.00476446,0.00487633,0.00498827,0.0051002,0.00521203,0.00532366,0.005435,0.00554591,0.00565628,0.00576597,0.00587483,0.0059827,0.00608941,0.00619478,0.0062986,0.00640068,0.0065008,0.00659873,0.00669422,0.00678703,0.00687688,0.00696349,0.00704656,0.0071258,0.00720088,0.00727145,0.00733716,0.00739765,0.00745252,0.00750136,0.00754374,0.0075792,0.00760726,0.00762741,0.0076391,0.00764175,0.00763475,0.00761743,0.00758908,0.00754892,0.00749612,0.00742978,0.00734891,0.00725244,0.00713921,0.00700793,0.0068572,0.00668547,0.00649106,0.0062721,0.00602654,0.0057521,0.0054463,0.00510637,0.00472927,0.00431163,0.00384972,0.00333945,0.00277627,0.00215514,0.00147053,0.000716299,-0.000114344,-0.00102889,-0.00203562,-0.00314368,-0.00436318,-0.00570527,-0.00718226,-0.00880776,-0.0105968,-0.0125658,-0.014733,-0.0171186,-0.0197446,-0.0226353,-0.0258175,-0.0293205,-0.0331766,-0.0374211,-0.0420926,-0.0472336,-0.0528901,-0.0591125,-0.0659555,-0.0734784,-0.0817456,-0.0908262,-0.100795,-0.111733,-0.123722,-0.136852,-0.151217,-0.166915,-0.184045,-0.202707,-0.223,-0.245019,-0.268851,-0.294567,-0.32222,-0.351833,-0.383389,-0.416816,-0.451971,-0.488617},
{-0.10874,-0.103545,-0.0985745,-0.0938197,-0.0892728,-0.0849261,-0.0807717,-0.0768023,-0.0730105,-0.0693891,-0.0659313,-0.0626302,-0.0594793,-0.0564723,-0.0536031,-0.0508656,-0.0482542,-0.0457633,-0.0433876,-0.0411219,-0.0389612,-0.0369008,-0.0349361,-0.0330626,-0.0312761,-0.0295725,-0.027948,-0.0263987,-0.0249211,-0.0235117,-0.0221673,-0.0208846,-0.0196606,-0.0184925,-0.0173775,-0.0163129,-0.0152962,-0.014325,-0.013397,-0.0125099,-0.0116617,-0.0108504,-0.0100739,-0.00933059,-0.00861859,-0.00793625,-0.00728198,-0.00665427,-0.00605165,-0.00547275,-0.00491625,-0.00438088,-0.00386545,-0.0033688,-0.00288985,-0.00242755,-0.00198092,-0.001549,-0.0011309,-0.000725754,-0.000332741,4.8917e-05,0.000419963,0.000781106,0.00113302,0.00147634,0.00181169,0.00213963,0.00246073,0.0027755,0.00308444,0.00338802,0.0036867,0.00398087,0.00427096,0.00455732,0.00484032,0.00512028,0.00539751,0.0056723,0.00594492,0.00621562,0.00648462,0.00675213,0.00701834,0.00728341,0.00754751,0.00781074,0.00807323,0.00833506,0.00859631,0.00885702,0.00911723,0.00937694,0.00963615,0.00989482,0.0101529,0.0104103,0.010667,0.0109229,0.0111777,0.0114314,0.0116838,0.0119346,0.0121838,0.0124309,0.0126759,0.0129183,0.0131579,0.0133944,0.0136275,0.0138567,0.0140817,0.0143021,0.0145175,0.0147275,0.0149316,0.0151293,0.0153202,0.0155037,0.0156793,0.0158465,0.0160046,0.0161532,0.0162916,0.0164191,0.0165351,0.0166389,0.0167297,0.0168068,0.0168694,0.0169166,0.0169475,0.0169611,0.0169563,0.016932,0.016887,0.01682,0.0167294,0.0166138,0.0164713,0.0163001,0.0160982,0.0158631,0.0155925,0.0152834,0.0149328,0.0145374,0.0140934,0.0135965,0.0130423,0.0124256,0.0117408,0.0109817,0.0101415,0.00921236,0.00818604,0.00705318,0.0058035,0.00442564,0.00290704,0.00123385,-0.000609226,-0.00263905,-0.00487421,-0.00733519,-0.0100446,-0.0130271,-0.0163102,-0.0199237,-0.0239005,-0.0282767,-0.0330917,-0.0383894,-0.0442157,-0.0506223,-0.0576651,-0.0654045,-0.0739058,-0.0832394,-0.093481,-0.104711,-0.117016,-0.130486,-0.145215,-0.161302,-0.178848,-0.197952,-0.218713,-0.241226,-0.265576,-0.291831,-0.320042,-0.350224,-0.382353,-0.416347,-0.452048,-0.489195,-0.5274,-0.566104},
{-0.223931,-0.214126,-0.204675,-0.195569,-0.186802,-0.178365,-0.170251,-0.16245,-0.154954,-0.147756,-0.140845,-0.134214,-0.127854,-0.121756,-0.115912,-0.110312,-0.104949,-0.0998141,-0.0948989,-0.0901955,-0.0856958,-0.081392,-0.0772765,-0.0733418,-0.0695808,-0.0659862,-0.0625513,-0.0592692,-0.0561336,-0.0531382,-0.0502768,-0.0475436,-0.0449328,-0.0424391,-0.0400571,-0.0377816,-0.0356079,-0.0335311,-0.0315467,-0.0296503,-0.0278377,-0.0261049,-0.0244481,-0.0228633,-0.0213473,-0.0198964,-0.0185074,-0.0171772,-0.0159029,-0.0146814,-0.0135101,-0.0123863,-0.0113076,-0.0102715,-0.00927566,-0.00831798,-0.00739631,-0.00650866,-0.00565312,-0.00482785,-0.00403112,-0.00326125,-0.00251667,-0.00179586,-0.00109737,-0.000419834,0.000238064,0.000877569,0.00149987,0.0021061,0.00269732,0.00327457,0.0038388,0.00439094,0.00493185,0.00546237,0.00598326,0.00649527,0.00699909,0.00749536,0.00798469,0.00846766,0.00894479,0.00941658,0.00988348,0.0103459,0.0108043,0.0112589,0.01171,0.0121581,0.0126032,0.0130456,0.0134854,0.0139229,0.014358,0.0147909,0.0152217,0.0156502,0.0160765,0.0165005,0.0169221,0.0173411,0.0177575,0.018171,0.0185814,0.0189883,0.0193917,0.019791,0.020186,0.0205763,0.0209615,0.0213411,0.0217148,0.022082,0.0224422,0.0227949,0.0231395,0.0234756,0.0238025,0.0241196,0.0244264,0.0247221,0.0250061,0.0252778,0.0255365,0.0257814,0.0260119,0.0262272,0.0264266,0.0266091,0.0267741,0.0269206,0.0270477,0.0271545,0.0272399,0.0273029,0.0273422,0.0273566,0.0273447,0.0273051,0.0272361,0.027136,0.0270028,0.0268343,0.0266283,0.026382,0.0260927,0.0257571,0.0253718,0.0249327,0.0244355,0.0238755,0.0232472,0.0225449,0.0217619,0.0208909,0.019924,0.0188522,0.0176657,0.0163536,0.0149037,0.0133029,0.0115363,0.00958772,0.00743925,0.00507109,0.00246146,-0.000413632,-0.00358058,-0.00706871,-0.0109094,-0.0151377,-0.0197921,-0.0249144,-0.0305504,-0.0367501,-0.0435676,-0.051062,-0.0592972,-0.0683421,-0.0782707,-0.0891625,-0.101102,-0.114179,-0.128486,-0.144123,-0.16119,-0.179788,-0.200019,-0.221982,-0.245765,-0.271448,-0.299092,-0.328728,-0.360352,-0.39391,-0.429278,-0.466242,-0.504462,-0.543468},
{-0.35636,-0.342263,-0.328567,-0.315271,-0.302374,-0.289872,-0.277763,-0.266042,-0.254705,-0.243746,-0.233159,-0.22294,-0.21308,-0.203573,-0.194412,-0.185589,-0.177096,-0.168924,-0.161066,-0.153513,-0.146256,-0.139287,-0.132597,-0.126178,-0.12002,-0.114115,-0.108454,-0.103029,-0.0978315,-0.0928531,-0.0880857,-0.0835212,-0.0791519,-0.07497,-0.0709681,-0.0671388,-0.063475,-0.0599698,-0.0566164,-0.0534083,-0.0503393,-0.0474031,-0.0445937,-0.0419056,-0.0393332,-0.036871,-0.034514,-0.0322572,-0.0300958,-0.0280253,-0.0260411,-0.0241391,-0.0223152,-0.0205654,-0.018886,-0.0172734,-0.0157242,-0.0142349,-0.0128025,-0.011424,-0.0100963,-0.00881674,-0.00758266,-0.0063915,-0.00524084,-0.00412835,-0.00305182,-0.00200913,-0.000998272,-1.73198e-05,0.000935557,0.0018621,0.00276397,0.00364274,0.00449992,0.00533691,0.00615507,0.00695568,0.00773993,0.00850898,0.00926388,0.0100056,0.0107352,0.0114535,0.0121613,0.0128594,0.0135485,0.0142292,0.0149021,0.0155679,0.0162269,0.0168797,0.0175265,0.0181677,0.0188037,0.0194345,0.0200605,0.0206817,0.0212982,0.0219101,0.0225173,0.0231198,0.0237174,0.0243101,0.0248975,0.0254796,0.0260559,0.0266262,0.0271901,0.0277473,0.0282972,0.0288394,0.0293735,0.0298989,0.0304151,0.0309214,0.0314173,0.0319022,0.0323754,0.0328363,0.0332842,0.0337184,0.0341383,0.0345431,0.0349321,0.0353046,0.0356599,0.0359972,0.0363157,0.0366148,0.0368935,0.0371511,0.0373868,0.0375996,0.0377886,0.037953,0.0380916,0.0382033,0.038287,0.0383414,0.0383652,0.0383567,0.0383144,0.0382365,0.0381208,0.0379652,0.0377673,0.0375242,0.037233,0.0368902,0.0364921,0.0360344,0.0355126,0.0349214,0.0342551,0.0335073,0.0326708,0.0317379,0.0306997,0.0295465,0.0282677,0.0268513,0.0252841,0.0235517,0.0216379,0.0195249,0.0171933,0.0146211,0.011785,0.00865844,0.00521274,0.00141617,-0.00276602,-0.00737193,-0.0124433,-0.0180257,-0.0241688,-0.0309269,-0.0383587,-0.046528,-0.0555036,-0.0653597,-0.0761757,-0.0880362,-0.101031,-0.115255,-0.130806,-0.147787,-0.1663,-0.186448,-0.208332,-0.232046,-0.257671,-0.285274,-0.314892,-0.346531,-0.38014,-0.415616,-0.452758,-0.491254},
{-0.492363,-0.474856,-0.457727,-0.440983,-0.424627,-0.408665,-0.393099,-0.377932,-0.363165,-0.3488,-0.334835,-0.321271,-0.308106,-0.295337,-0.282962,-0.270976,-0.259377,-0.248157,-0.237314,-0.226839,-0.216727,-0.206972,-0.197565,-0.1885,-0.179768,-0.171362,-0.163273,-0.155493,-0.148013,-0.140825,-0.133919,-0.127288,-0.120922,-0.114813,-0.108951,-0.103329,-0.0979381,-0.0927695,-0.0878151,-0.0830668,-0.0785166,-0.0741567,-0.0699795,-0.0659775,-0.0621434,-0.0584701,-0.0549509,-0.0515789,-0.0483477,-0.0452511,-0.0422829,-0.0394373,-0.0367086,-0.0340912,-0.03158,-0.0291697,-0.0268556,-0.0246327,-0.0224967,-0.0204431,-0.0184677,-0.0165666,-0.0147357,-0.0129714,-0.0112702,-0.00962862,-0.00804341,-0.00651145,-0.00502976,-0.00359548,-0.00220589,-0.000858379,0.000449523,0.00172018,0.00295585,0.00415867,0.00533067,0.00647378,0.00758984,0.00868058,0.00974764,0.0107926,0.0118168,0.0128217,0.0138087,0.0147787,0.0157331,0.0166728,0.0175988,0.018512,0.0194132,0.020303,0.0211822,0.0220514,0.0229111,0.0237616,0.0246035,0.0254369,0.0262622,0.0270795,0.0278889,0.0286906,0.0294844,0.0302702,0.0310481,0.0318177,0.0325789,0.0333314,0.0340748,0.0348087,0.0355327,0.0362463,0.036949,0.0376403,0.0383196,0.0389862,0.0396396,0.0402791,0.0409039,0.0415135,0.042107,0.0426839,0.0432433,0.0437845,0.0443068,0.0448095,0.0452917,0.0457529,0.0461921,0.0466087,0.047002,0.0473711,0.0477152,0.0480337,0.0483256,0.0485901,0.0488263,0.0490333,0.04921,0.0493554,0.0494683,0.0495474,0.0495913,0.0495985,0.0495672,0.0494956,0.0493815,0.0492225,0.0490161,0.0487593,0.0484488,0.0480809,0.0476516,0.0471563,0.0465898,0.0459466,0.0452203,0.0444037,0.0434892,0.042468,0.0413305,0.0400659,0.0386624,0.0371068,0.0353845,0.0334795,0.0313739,0.0290481,0.0264805,0.0236471,0.0205216,0.0170751,0.0132757,0.00908846,0.00447514,-0.000606252,-0.00620156,-0.0123608,-0.0191386,-0.026594,-0.0347913,-0.0437999,-0.0536943,-0.0645548,-0.0764666,-0.0895203,-0.103812,-0.11944,-0.136508,-0.15512,-0.175382,-0.197394,-0.221253,-0.247043,-0.274832,-0.304656,-0.336531,-0.37041,-0.406188,-0.44367},
{-0.623829,-0.603849,-0.58419,-0.564861,-0.54587,-0.527229,-0.508943,-0.491022,-0.473473,-0.456302,-0.439513,-0.423114,-0.407106,-0.391494,-0.37628,-0.361466,-0.347052,-0.333038,-0.319423,-0.306207,-0.293386,-0.280958,-0.268919,-0.257264,-0.245989,-0.235089,-0.224557,-0.214386,-0.204571,-0.195104,-0.185976,-0.177182,-0.168711,-0.160557,-0.15271,-0.145162,-0.137905,-0.130929,-0.124226,-0.117787,-0.111603,-0.105665,-0.0999657,-0.0944955,-0.0892463,-0.0842096,-0.0793774,-0.0747416,-0.0702943,-0.066028,-0.0619351,-0.0580083,-0.0542405,-0.0506247,-0.0471543,-0.0438227,-0.0406237,-0.037551,-0.0345989,-0.0317615,-0.0290334,-0.0264092,-0.0238839,-0.0214524,-0.0191101,-0.0168523,-0.0146747,-0.0125731,-0.0105435,-0.00858186,-0.00668461,-0.00484816,-0.00306914,-0.00134428,0.00032951,0.00195517,0.00353553,0.00507326,0.0065709,0.00803087,0.00945547,0.0108469,0.0122071,0.0135381,0.0148417,0.0161197,0.0173735,0.0186047,0.0198148,0.0210049,0.0221763,0.02333,0.0244671,0.0255885,0.0266949,0.0277871,0.0288657,0.0299312,0.0309841,0.0320248,0.0330535,0.0340704,0.0350757,0.0360694,0.0370516,0.038022,0.0389805,0.0399269,0.040861,0.0417823,0.0426904,0.043585,0.0444654,0.0453312,0.0461817,0.0470164,0.0478345,0.0486354,0.0494184,0.0501828,0.0509279,0.0516528,0.0523569,0.0530394,0.0536997,0.0543368,0.0549501,0.055539,0.0561025,0.0566401,0.0571511,0.0576347,0.0580902,0.0585169,0.0589141,0.0592811,0.0596172,0.0599214,0.0601931,0.0604312,0.0606349,0.0608031,0.0609347,0.0610283,0.0610826,0.061096,0.0610668,0.0609929,0.0608722,0.0607022,0.06048,0.0602026,0.0598664,0.0594675,0.0590014,0.0584632,0.0578473,0.0571476,0.0563571,0.0554682,0.0544722,0.0533597,0.05212,0.0507415,0.049211,0.0475141,0.045635,0.0435559,0.0412573,0.0387177,0.0359132,0.0328178,0.0294026,0.0256358,0.0214828,0.0169053,0.0118616,0.00630583,0.000188151,-0.00654585,-0.0139553,-0.0221043,-0.0310623,-0.0409038,-0.0517091,-0.0635637,-0.0765585,-0.0907894,-0.106357,-0.123364,-0.141917,-0.162121,-0.184082,-0.207897,-0.23365,-0.261419,-0.291248,-0.323153,-0.357099,-0.392991},
{-0.746999,-0.725309,-0.703874,-0.682704,-0.661811,-0.641207,-0.620901,-0.600904,-0.581228,-0.561881,-0.542873,-0.524213,-0.50591,-0.487971,-0.470403,-0.453212,-0.436405,-0.419985,-0.403956,-0.388323,-0.373087,-0.358249,-0.343811,-0.329772,-0.316131,-0.302887,-0.290038,-0.277579,-0.265509,-0.253821,-0.242512,-0.231576,-0.221006,-0.210796,-0.200939,-0.191429,-0.182257,-0.173415,-0.164896,-0.156691,-0.148791,-0.141188,-0.133873,-0.126837,-0.120072,-0.113569,-0.107319,-0.101312,-0.0955417,-0.0899979,-0.0846726,-0.0795574,-0.0746441,-0.0699248,-0.0653915,-0.0610365,-0.0568524,-0.0528318,-0.0489676,-0.0452528,-0.0416807,-0.0382449,-0.0349389,-0.0317566,-0.0286923,-0.02574,-0.0228944,-0.0201501,-0.0175019,-0.0149451,-0.0124748,-0.0100866,-0.00777597,-0.00553886,-0.00337125,-0.0012693,0.000770633,0.00275203,0.00467822,0.00655237,0.00837748,0.0101564,0.0118919,0.0135864,0.0152425,0.0168623,0.0184481,0.0200019,0.0215254,0.0230206,0.0244889,0.0259319,0.027351,0.0287475,0.0301224,0.0314769,0.0328118,0.0341279,0.035426,0.0367066,0.0379703,0.0392174,0.0404482,0.0416629,0.0428616,0.0440444,0.0452112,0.0463618,0.0474961,0.0486137,0.0497142,0.0507974,0.0518625,0.0529093,0.053937,0.054945,0.0559327,0.0568993,0.0578443,0.0587667,0.059666,0.0605413,0.0613918,0.0622169,0.0630156,0.0637874,0.0645314,0.065247,0.0659334,0.0665899,0.0672158,0.0678106,0.0683734,0.0689037,0.0694008,0.0698641,0.0702929,0.0706864,0.0710441,0.071365,0.0716485,0.0718935,0.0720991,0.0722642,0.0723876,0.0724679,0.0725036,0.0724928,0.0724337,0.072324,0.0721612,0.0719423,0.0716643,0.0713234,0.0709155,0.0704361,0.06988,0.0692414,0.0685139,0.0676901,0.0667621,0.0657208,0.0645562,0.0632573,0.0618115,0.0602053,0.0584234,0.0564491,0.0542637,0.0518466,0.0491753,0.0462246,0.042967,0.0393723,0.0354069,0.0310344,0.0262147,0.0209038,0.0150536,0.00861196,0.00152173,-0.00627895,-0.0148572,-0.0242852,-0.034641,-0.0460079,-0.0584747,-0.0721355,-0.0870891,-0.103438,-0.121289,-0.14075,-0.161925,-0.184917,-0.209824,-0.236728,-0.26569,-0.296747,-0.329894,-0.365072},
{-0.86075,-0.837895,-0.815236,-0.792784,-0.770551,-0.748546,-0.726782,-0.70527,-0.684021,-0.663046,-0.642357,-0.621965,-0.601879,-0.582111,-0.562671,-0.543568,-0.52481,-0.506407,-0.488366,-0.470694,-0.453398,-0.436483,-0.419954,-0.403815,-0.38807,-0.372721,-0.357769,-0.343215,-0.329059,-0.315301,-0.301938,-0.28897,-0.276391,-0.2642,-0.252391,-0.24096,-0.229901,-0.219208,-0.208874,-0.198894,-0.189259,-0.179962,-0.170995,-0.162349,-0.154018,-0.145991,-0.138261,-0.130819,-0.123655,-0.116761,-0.110128,-0.103748,-0.0976107,-0.0917084,-0.0860323,-0.0805738,-0.0753246,-0.0702764,-0.0654211,-0.0607508,-0.0562578,-0.0519344,-0.0477735,-0.0437676,-0.03991,-0.0361938,-0.0326124,-0.0291595,-0.025829,-0.022615,-0.0195116,-0.0165134,-0.013615,-0.0108114,-0.00809756,-0.00546887,-0.00292077,-0.000448947,0.00195075,0.00428226,0.00654936,0.00875563,0.0109045,0.0129991,0.0150427,0.017038,0.0189879,0.0208948,0.0227612,0.0245894,0.0263815,0.0281394,0.029865,0.0315598,0.0332255,0.0348634,0.0364748,0.0380608,0.0396224,0.0411604,0.0426756,0.0441686,0.0456398,0.0470898,0.0485187,0.0499268,0.051314,0.0526804,0.0540259,0.0553502,0.056653,0.0579341,0.0591928,0.0604289,0.0616416,0.0628305,0.0639947,0.0651338,0.0662469,0.0673333,0.0683923,0.069423,0.0704248,0.0713969,0.0723384,0.0732487,0.0741271,0.0749727,0.075785,0.0765632,0.0773067,0.0780148,0.078687,0.0793227,0.0799213,0.0804822,0.0810047,0.0814885,0.0819327,0.0823368,0.0827001,0.0830218,0.0833011,0.0835371,0.0837287,0.0838746,0.0839737,0.0840242,0.0840245,0.0839726,0.0838661,0.0837025,0.0834789,0.0831917,0.0828373,0.0824114,0.0819091,0.0813251,0.0806531,0.0798864,0.0790174,0.0780374,0.0769371,0.0757056,0.0743313,0.0728011,0.0711005,0.0692132,0.0671215,0.0648057,0.062244,0.0594123,0.056284,0.0528301,0.0490184,0.0448135,0.0401769,0.035066,0.0294345,0.0232318,0.0164026,0.00888679,0.000619429,-0.00846994,-0.0184572,-0.0294237,-0.0414565,-0.0546479,-0.0690956,-0.0849013,-0.102171,-0.121012,-0.141531,-0.163838,-0.188032,-0.214202,-0.242425,-0.27275,-0.305194,-0.339729},
{-0.96529,-0.941636,-0.918132,-0.894787,-0.871612,-0.848616,-0.82581,-0.803204,-0.780809,-0.758637,-0.736698,-0.715004,-0.693565,-0.672395,-0.651503,-0.6309,-0.610598,-0.590608,-0.570938,-0.551599,-0.532601,-0.513951,-0.495658,-0.47773,-0.460173,-0.442993,-0.426195,-0.409785,-0.393765,-0.378139,-0.362908,-0.348074,-0.333636,-0.319596,-0.305951,-0.2927,-0.279839,-0.267366,-0.255277,-0.243566,-0.232229,-0.22126,-0.210653,-0.2004,-0.190496,-0.180932,-0.1717,-0.162793,-0.154203,-0.14592,-0.137936,-0.130243,-0.122832,-0.115693,-0.108818,-0.102199,-0.0958251,-0.0896889,-0.0837813,-0.0780939,-0.0726181,-0.0673455,-0.062268,-0.0573776,-0.0526664,-0.0481267,-0.0437511,-0.0395323,-0.0354631,-0.0315368,-0.0277466,-0.0240862,-0.0205492,-0.0171297,-0.0138218,-0.01062,-0.00751891,-0.00451331,-0.00159826,0.00123097,0.00397894,0.00664996,0.00924819,0.0117776,0.0142418,0.0166445,0.0189889,0.0212783,0.0235157,0.0257037,0.0278452,0.0299425,0.0319979,0.0340134,0.0359912,0.0379329,0.0398401,0.0417143,0.0435569,0.045369,0.0471515,0.0489055,0.0506315,0.0523302,0.0540021,0.0556475,0.0572667,0.0588597,0.0604265,0.0619671,0.0634812,0.0649686,0.0664289,0.0678616,0.0692663,0.0706423,0.0719891,0.073306,0.0745922,0.0758471,0.0770699,0.0782598,0.0794161,0.080538,0.0816248,0.0826756,0.0836898,0.0846667,0.0856056,0.0865058,0.0873667,0.0881877,0.0889682,0.0897077,0.0904057,0.0910616,0.0916749,0.0922451,0.0927716,0.0932539,0.0936914,0.0940834,0.0944292,0.0947279,0.0949786,0.0951802,0.0953316,0.0954311,0.0954773,0.0954681,0.0954016,0.095275,0.0950857,0.0948303,0.0945052,0.0941061,0.0936284,0.0930668,0.0924151,0.0916667,0.0908141,0.0898486,0.0887609,0.0875404,0.0861755,0.084653,0.0829584,0.0810757,0.0789871,0.0766729,0.0741112,0.0712782,0.0681471,0.0646889,0.0608714,0.0566593,0.0520138,0.0468926,0.0412491,0.0350326,0.0281878,0.0206547,0.0123679,0.003257,-0.00675409,-0.017747,-0.029809,-0.0430327,-0.0575161,-0.0733616,-0.0906755,-0.109565,-0.130141,-0.152511,-0.176777,-0.203031,-0.231349,-0.261787,-0.294364,-0.329055},
{-1.06138,-1.03717,-1.01307,-0.989094,-0.965251,-0.941547,-0.917992,-0.894595,-0.871366,-0.848314,-0.825451,-0.802786,-0.78033,-0.758095,-0.736092,-0.714331,-0.692825,-0.671585,-0.650622,-0.629946,-0.609569,-0.589502,-0.569754,-0.550335,-0.531255,-0.512521,-0.494144,-0.476129,-0.458483,-0.441214,-0.424325,-0.407822,-0.391708,-0.375985,-0.360657,-0.345725,-0.331188,-0.317046,-0.303298,-0.289943,-0.276977,-0.264398,-0.252201,-0.240381,-0.228934,-0.217854,-0.207134,-0.196767,-0.186747,-0.177067,-0.167717,-0.158691,-0.14998,-0.141575,-0.133468,-0.12565,-0.118112,-0.110846,-0.103842,-0.097091,-0.090585,-0.0843147,-0.0782716,-0.0724469,-0.0668321,-0.061419,-0.0561992,-0.0511648,-0.0463079,-0.0416208,-0.0370961,-0.0327264,-0.0285047,-0.0244242,-0.0204781,-0.0166602,-0.0129641,-0.00938389,-0.00591385,-0.00254844,0.000717651,0.00388952,0.00697202,0.00996981,0.0128873,0.0157287,0.0184981,0.0211991,0.0238354,0.0264104,0.0289273,0.0313889,0.0337982,0.0361576,0.0384695,0.0407362,0.0429597,0.0451418,0.0472842,0.0493884,0.0514556,0.0534871,0.0554838,0.0574466,0.0593761,0.0612729,0.0631375,0.0649701,0.0667708,0.0685397,0.0702767,0.0719816,0.0736541,0.0752939,0.0769006,0.0784736,0.0800123,0.0815161,0.0829844,0.0844165,0.0858116,0.0871691,0.0884881,0.089768,0.091008,0.0922073,0.0933654,0.0944815,0.095555,0.0965853,0.0975719,0.0985142,0.0994117,0.100264,0.10107,0.101831,0.102545,0.103212,0.103832,0.104404,0.104928,0.105403,0.105829,0.106205,0.106531,0.106806,0.107028,0.107196,0.10731,0.107367,0.107365,0.107303,0.107178,0.106987,0.106727,0.106394,0.105983,0.10549,0.10491,0.104235,0.10346,0.102575,0.101574,0.100444,0.099177,0.0977589,0.0961768,0.0944153,0.092458,0.0902861,0.0878793,0.0852148,0.0822676,0.0790102,0.0754121,0.0714399,0.067057,0.0622231,0.056894,0.0510216,0.0445532,0.0374316,0.0295944,0.0209741,0.0114978,0.00108699,-0.0103425,-0.0228805,-0.0366222,-0.0516681,-0.0681228,-0.0860929,-0.105691,-0.127026,-0.150205,-0.175329,-0.202487,-0.231751,-0.263165,-0.296738},
{-1.14994,-1.12533,-1.1008,-1.07637,-1.05204,-1.02783,-1.00373,-0.97975,-0.955907,-0.932205,-0.908654,-0.885263,-0.862042,-0.839,-0.816149,-0.793499,-0.77106,-0.748845,-0.726864,-0.705128,-0.683649,-0.662438,-0.641506,-0.620865,-0.600525,-0.580496,-0.560788,-0.541412,-0.522376,-0.503688,-0.485357,-0.46739,-0.449793,-0.432572,-0.415733,-0.399278,-0.383213,-0.367539,-0.352258,-0.337371,-0.322878,-0.308779,-0.295072,-0.281755,-0.268825,-0.256279,-0.244111,-0.232318,-0.220894,-0.209832,-0.199127,-0.188772,-0.178759,-0.169081,-0.159729,-0.150697,-0.141974,-0.133553,-0.125426,-0.117582,-0.110013,-0.102711,-0.0956665,-0.0888702,-0.0823136,-0.0759878,-0.0698841,-0.0639939,-0.0583089,-0.0528206,-0.047521,-0.0424021,-0.037456,-0.0326754,-0.0280526,-0.0235807,-0.0192525,-0.0150615,-0.0110011,-0.00706504,-0.00324726,0.000458032,0.00405642,0.00755324,0.0109536,0.0142624,0.0174842,0.0206235,0.0236845,0.026671,0.0295869,0.0324357,0.0352206,0.0379447,0.0406109,0.0432218,0.0457798,0.0482872,0.0507461,0.0531582,0.0555252,0.0578486,0.0601296,0.0623694,0.0645688,0.0667287,0.0688497,0.0709322,0.0729766,0.0749829,0.0769514,0.0788819,0.0807742,0.0826281,0.0844432,0.0862191,0.0879552,0.0896511,0.091306,0.0929193,0.0944904,0.0960185,0.097503,0.098943,0.100338,0.101687,0.10299,0.104246,0.105454,0.106614,0.107725,0.108787,0.109799,0.110761,0.111673,0.112534,0.113343,0.114102,0.114809,0.115464,0.116066,0.116616,0.117112,0.117555,0.117944,0.118278,0.118556,0.118777,0.11894,0.119043,0.119085,0.119064,0.118977,0.118821,0.118594,0.118292,0.11791,0.117444,0.116888,0.116237,0.115483,0.114618,0.113635,0.112524,0.111272,0.10987,0.108302,0.106554,0.10461,0.10245,0.100055,0.0974019,0.094466,0.0912198,0.0876329,0.0836721,0.0793009,0.0744791,0.0691627,0.0633038,0.0568497,0.0497435,0.0419229,0.0333205,0.0238636,0.0134738,0.00206697,-0.0104467,-0.0241625,-0.0391809,-0.0556057,-0.0735473,-0.0931156,-0.114422,-0.137574,-0.162676,-0.189818,-0.219076,-0.250499,-0.284102},
{-1.23188,-1.20696,-1.18212,-1.15735,-1.13267,-1.10807,-1.08356,-1.05915,-1.03485,-1.01066,-0.986592,-0.962653,-0.93885,-0.915194,-0.891693,-0.868357,-0.845196,-0.82222,-0.79944,-0.776867,-0.754511,-0.732384,-0.710497,-0.688862,-0.667489,-0.646391,-0.625577,-0.60506,-0.584849,-0.564954,-0.545385,-0.526153,-0.507264,-0.488728,-0.470552,-0.452743,-0.435306,-0.418247,-0.401571,-0.385281,-0.36938,-0.353871,-0.338753,-0.324028,-0.309695,-0.295754,-0.282202,-0.269036,-0.256253,-0.243849,-0.231819,-0.220159,-0.208862,-0.197922,-0.187332,-0.177085,-0.167174,-0.15759,-0.148326,-0.139373,-0.130724,-0.122368,-0.114297,-0.106503,-0.0989759,-0.0917076,-0.0846888,-0.0779107,-0.0713644,-0.0650413,-0.0589327,-0.0530301,-0.0473252,-0.0418099,-0.0364762,-0.0313161,-0.0263222,-0.0214871,-0.0168036,-0.0122646,-0.00786361,-0.00359401,0.000550413,0.00457567,0.00848753,0.0122915,0.0159929,0.0195967,0.0231077,0.0265304,0.0298691,0.033128,0.0363107,0.0394209,0.042462,0.0454369,0.0483486,0.0511998,0.0539928,0.0567299,0.0594131,0.0620441,0.0646245,0.0671558,0.0696392,0.0720755,0.0744658,0.0768105,0.0791104,0.0813656,0.0835765,0.085743,0.0878652,0.0899429,0.0919758,0.0939637,0.0959059,0.0978022,0.0996518,0.101454,0.103209,0.104915,0.106572,0.10818,0.109736,0.111242,0.112696,0.114098,0.115448,0.116743,0.117986,0.119174,0.120307,0.121386,0.12241,0.123378,0.124291,0.125149,0.12595,0.126696,0.127385,0.128019,0.128595,0.129115,0.129577,0.129982,0.130328,0.130614,0.130841,0.131006,0.131108,0.131145,0.131115,0.131016,0.130845,0.130598,0.130272,0.129862,0.129364,0.128771,0.128078,0.127276,0.126358,0.125315,0.124136,0.12281,0.121324,0.119664,0.117814,0.115756,0.113471,0.110938,0.108131,0.105027,0.101594,0.0978016,0.0936145,0.0889941,0.083898,0.0782801,0.0720898,0.0652721,0.0577668,0.049509,0.0404282,0.0304482,0.0194873,0.00745814,-0.00573259,-0.0201834,-0.0359967,-0.053282,-0.0721492,-0.0927103,-0.115076,-0.139355,-0.165645,-0.194032,-0.224581,-0.257328},
{-1.30799,-1.28285,-1.25776,-1.23274,-1.20778,-1.18289,-1.15807,-1.13334,-1.10868,-1.08412,-1.05966,-1.0353,-1.01105,-0.986921,-0.962918,-0.939049,-0.915325,-0.891753,-0.868344,-0.845108,-0.822055,-0.799195,-0.776539,-0.754099,-0.731885,-0.709909,-0.688182,-0.666715,-0.645519,-0.624607,-0.603987,-0.583672,-0.563671,-0.543994,-0.524651,-0.505649,-0.486998,-0.468704,-0.450775,-0.433217,-0.416035,-0.399233,-0.382816,-0.366786,-0.351145,-0.335894,-0.321035,-0.306567,-0.292488,-0.278796,-0.26549,-0.252565,-0.240018,-0.227843,-0.216037,-0.204592,-0.193503,-0.182763,-0.172365,-0.162301,-0.152564,-0.143145,-0.134036,-0.125228,-0.116714,-0.108483,-0.100527,-0.0928377,-0.0854055,-0.0782216,-0.0712771,-0.0645633,-0.0580715,-0.0517929,-0.0457193,-0.0398423,-0.0341537,-0.0286456,-0.0233103,-0.0181402,-0.013128,-0.00826658,-0.00354911,0.00103105,0.00548027,0.00980469,0.0140102,0.0181024,0.0220866,0.025968,0.0297514,0.0334414,0.0370423,0.0405583,0.0439931,0.0473502,0.0506331,0.0538448,0.0569881,0.0600656,0.0630797,0.0660325,0.0689259,0.0717616,0.0745411,0.0772656,0.0799362,0.0825538,0.0851192,0.0876327,0.090095,0.0925061,0.0948661,0.0971751,0.0994329,0.101639,0.103794,0.105896,0.107946,0.109942,0.111885,0.113773,0.115607,0.117385,0.119106,0.120771,0.122379,0.123928,0.12542,0.126853,0.128226,0.129541,0.130795,0.13199,0.133124,0.134199,0.135212,0.136166,0.137059,0.137892,0.138663,0.139375,0.140025,0.140615,0.141143,0.14161,0.142015,0.142357,0.142635,0.142849,0.142996,0.143076,0.143086,0.143025,0.142889,0.142675,0.142379,0.141998,0.141527,0.140959,0.140289,0.139509,0.138612,0.137589,0.136428,0.13512,0.133651,0.132007,0.130173,0.12813,0.12586,0.123342,0.120551,0.117462,0.114045,0.110269,0.1061,0.101498,0.0964212,0.0908244,0.084657,0.0778641,0.0703858,0.0621575,0.0531088,0.0431639,0.0322414,0.0202539,0.00710842,-0.00729271,-0.0230544,-0.0402839,-0.0590924,-0.0795925,-0.101897,-0.126113,-0.152344,-0.180678,-0.211183,-0.243901},
{-1.37898,-1.35366,-1.32839,-1.30317,-1.27799,-1.25288,-1.22782,-1.20283,-1.1779,-1.15305,-1.12828,-1.10359,-1.079,-1.0545,-1.0301,-1.00581,-0.981643,-0.957601,-0.933694,-0.90993,-0.88632,-0.862871,-0.839596,-0.816503,-0.793603,-0.770908,-0.748428,-0.726174,-0.704158,-0.682392,-0.660885,-0.63965,-0.618698,-0.598039,-0.577684,-0.557643,-0.537925,-0.518541,-0.499499,-0.480806,-0.46247,-0.444498,-0.426896,-0.409669,-0.392821,-0.376357,-0.360278,-0.344587,-0.329286,-0.314373,-0.29985,-0.285713,-0.271963,-0.258595,-0.245606,-0.232992,-0.220749,-0.208871,-0.197352,-0.186186,-0.175366,-0.164885,-0.154735,-0.144908,-0.135397,-0.126192,-0.117286,-0.108669,-0.100333,-0.0922692,-0.0844681,-0.0769211,-0.0696192,-0.0625537,-0.0557158,-0.0490967,-0.0426882,-0.0364816,-0.0304689,-0.024642,-0.018993,-0.0135144,-0.00819872,-0.00303882,0.00197225,0.00684117,0.0115744,0.0161781,0.0206581,0.0250203,0.0292698,0.0334119,0.0374513,0.0413927,0.0452403,0.0489983,0.0526703,0.0562598,0.0597702,0.0632043,0.0665649,0.0698545,0.0730753,0.0762294,0.0793184,0.082344,0.0853074,0.0882099,0.0910522,0.0938353,0.0965595,0.0992254,0.101833,0.104383,0.106875,0.109309,0.111684,0.114001,0.116258,0.118456,0.120594,0.122672,0.124689,0.126644,0.128537,0.130368,0.132135,0.133839,0.135479,0.137055,0.138566,0.140013,0.141395,0.142711,0.143963,0.145149,0.146271,0.147327,0.148318,0.149245,0.150107,0.150904,0.151637,0.152306,0.152909,0.153448,0.153922,0.154331,0.154673,0.154949,0.155156,0.155294,0.155361,0.155355,0.155274,0.155114,0.154872,0.154545,0.154128,0.153616,0.153003,0.152281,0.151445,0.150484,0.14939,0.148152,0.146757,0.145193,0.143443,0.141492,0.139321,0.13691,0.134235,0.131272,0.127993,0.124368,0.120362,0.11594,0.11106,0.105678,0.0997464,0.093211,0.0860145,0.0780943,0.0693822,0.0598047,0.0492825,0.0377305,0.025058,0.0111692,-0.00403906,-0.0206728,-0.0388424,-0.0586609,-0.080242,-0.103697,-0.129134,-0.156647,-0.186319,-0.218206},
{-1.44545,-1.41999,-1.39457,-1.36919,-1.34385,-1.31855,-1.2933,-1.26811,-1.24297,-1.21789,-1.19287,-1.16792,-1.14305,-1.11825,-1.09354,-1.06892,-1.0444,-1.01998,-0.995678,-0.971491,-0.947431,-0.923508,-0.89973,-0.876106,-0.852646,-0.829361,-0.80626,-0.783355,-0.760655,-0.738174,-0.715921,-0.693907,-0.672145,-0.650645,-0.629419,-0.608478,-0.587832,-0.567491,-0.547466,-0.527766,-0.508401,-0.489378,-0.470706,-0.452392,-0.434442,-0.416861,-0.399656,-0.38283,-0.366386,-0.350327,-0.334654,-0.319369,-0.304472,-0.289961,-0.275835,-0.262091,-0.248728,-0.23574,-0.223125,-0.210876,-0.198988,-0.187456,-0.176272,-0.16543,-0.154922,-0.144741,-0.134878,-0.125326,-0.116077,-0.10712,-0.0984484,-0.0900526,-0.0819239,-0.0740533,-0.0664319,-0.0590511,-0.0519019,-0.0449758,-0.0382642,-0.0317588,-0.0254512,-0.0193334,-0.0133976,-0.00763621,-0.00204169,0.0033931,0.0086751,0.013811,0.0188072,0.0236699,0.028405,0.033018,0.0375144,0.0418991,0.046177,0.0503525,0.0544298,0.0584129,0.0623053,0.0661106,0.0698317,0.0734716,0.0770327,0.0805175,0.0839279,0.0872658,0.0905328,0.0937303,0.0968594,0.0999212,0.102916,0.105845,0.108709,0.111507,0.114239,0.116907,0.119509,0.122046,0.124516,0.126921,0.129259,0.13153,0.133734,0.135869,0.137937,0.139935,0.141865,0.143724,0.145514,0.147234,0.148883,0.150462,0.15197,0.153408,0.154775,0.156072,0.157298,0.158454,0.15954,0.160557,0.161504,0.162382,0.163191,0.163931,0.164602,0.165204,0.165737,0.166201,0.166595,0.166919,0.167172,0.167351,0.167457,0.167486,0.167437,0.167308,0.167093,0.166791,0.166396,0.165904,0.165308,0.164603,0.16378,0.162831,0.161746,0.160516,0.159127,0.157566,0.155819,0.153869,0.151697,0.149283,0.146603,0.143634,0.140347,0.136712,0.132695,0.12826,0.123365,0.117966,0.112016,0.10546,0.0982405,0.0902956,0.0815567,0.0719501,0.0613965,0.0498107,0.0371024,0.0231737,0.00792315,-0.0087563,-0.0269755,-0.0468479,-0.0684879,-0.0920083,-0.117517,-0.145111,-0.174875,-0.206867},
{-1.50792,-1.48235,-1.4568,-1.43129,-1.40581,-1.38037,-1.35497,-1.32961,-1.30429,-1.27903,-1.25381,-1.22866,-1.20356,-1.17853,-1.15356,-1.12867,-1.10387,-1.07914,-1.05451,-1.02998,-1.00556,-0.981248,-0.95706,-0.933001,-0.909081,-0.885309,-0.861695,-0.838249,-0.81498,-0.791899,-0.769017,-0.746346,-0.723896,-0.701678,-0.679704,-0.657985,-0.636533,-0.615358,-0.594471,-0.573883,-0.553604,-0.533644,-0.514012,-0.494716,-0.475766,-0.457168,-0.43893,-0.421057,-0.403554,-0.386427,-0.369679,-0.353313,-0.337331,-0.321734,-0.306522,-0.291696,-0.277254,-0.263194,-0.249514,-0.236209,-0.223277,-0.210712,-0.198509,-0.186662,-0.175165,-0.164012,-0.153195,-0.142706,-0.132538,-0.122683,-0.113132,-0.103877,-0.094909,-0.0862197,-0.0778,-0.0696412,-0.0617345,-0.0540709,-0.0466419,-0.0394388,-0.0324531,-0.0256764,-0.0191005,-0.0127174,-0.00651921,-0.000498434,0.00535236,0.0110403,0.0165723,0.0219549,0.0271946,0.0322973,0.0372689,0.0421149,0.0468405,0.0514506,0.0559498,0.0603426,0.064633,0.0688246,0.0729211,0.0769255,0.0808408,0.0846697,0.0884144,0.0920773,0.09566,0.0991642,0.102591,0.105943,0.109219,0.112421,0.11555,0.118606,0.121588,0.124499,0.127336,0.130101,0.132793,0.135411,0.137957,0.140428,0.142826,0.145149,0.147397,0.14957,0.151668,0.15369,0.155636,0.157506,0.159299,0.161017,0.162658,0.164223,0.165712,0.167125,0.168463,0.169726,0.170914,0.172028,0.173067,0.174034,0.174927,0.175747,0.176495,0.17717,0.177774,0.178304,0.178763,0.179148,0.179459,0.179696,0.179856,0.179939,0.179943,0.179864,0.1797,0.179448,0.179103,0.178661,0.178116,0.177462,0.176692,0.175798,0.17477,0.173599,0.172273,0.17078,0.169104,0.167229,0.165139,0.162813,0.16023,0.157364,0.15419,0.150678,0.146795,0.142506,0.137771,0.132548,0.12679,0.120444,0.113455,0.105762,0.0972983,0.0879925,0.0777672,0.0665389,0.0542195,0.0407129,0.0259191,0.00973268,-0.0079565,-0.0272617,-0.0482978,-0.0711796,-0.0960178,-0.122917,-0.151967,-0.183241},
{-1.56681,-1.54115,-1.5155,-1.48989,-1.4643,-1.43873,-1.41321,-1.38771,-1.36225,-1.33683,-1.31146,-1.28613,-1.26085,-1.23562,-1.21045,-1.18534,-1.1603,-1.13532,-1.11043,-1.08562,-1.06089,-1.03626,-1.01174,-0.987319,-0.963019,-0.938844,-0.914803,-0.890905,-0.867159,-0.843575,-0.820164,-0.796936,-0.773901,-0.75107,-0.728455,-0.706067,-0.683917,-0.662016,-0.640376,-0.619007,-0.597921,-0.577129,-0.55664,-0.536465,-0.516612,-0.497092,-0.477912,-0.459081,-0.440604,-0.422489,-0.404741,-0.387366,-0.370366,-0.353745,-0.337505,-0.321649,-0.306176,-0.291087,-0.27638,-0.262055,-0.248108,-0.234536,-0.221336,-0.208503,-0.196032,-0.183917,-0.172153,-0.160733,-0.149649,-0.138895,-0.128462,-0.118343,-0.10853,-0.0990135,-0.0897857,-0.0808377,-0.0721608,-0.0637463,-0.0555854,-0.0476695,-0.0399898,-0.0325378,-0.025305,-0.0182832,-0.0114642,-0.00484015,0.0015968,0.00785412,0.0139391,0.0198587,0.0256198,0.0312288,0.0366919,0.0420151,0.047204,0.052264,0.0572001,0.062017,0.0667192,0.0713108,0.0757956,0.0801773,0.084459,0.0886436,0.092734,0.0967325,0.100641,0.104462,0.108197,0.111847,0.115413,0.118896,0.122298,0.125618,0.128858,0.132017,0.135096,0.138094,0.141012,0.14385,0.146607,0.149283,0.151878,0.154392,0.156824,0.159174,0.161441,0.163627,0.16573,0.167751,0.169689,0.171544,0.173318,0.175009,0.176618,0.178146,0.179592,0.180958,0.182244,0.18345,0.184578,0.185626,0.186597,0.18749,0.188306,0.189045,0.189707,0.190293,0.190802,0.191235,0.191589,0.191865,0.192061,0.192176,0.192209,0.192155,0.192013,0.19178,0.191451,0.191021,0.190486,0.189838,0.189071,0.188177,0.187147,0.185969,0.184634,0.183127,0.181434,0.17954,0.177426,0.175072,0.172456,0.169554,0.166338,0.162779,0.158845,0.154498,0.1497,0.144407,0.138572,0.132141,0.12506,0.117266,0.108693,0.0992673,0.0889119,0.0775432,0.0650707,0.0513991,0.0364272,0.0200489,0.00215334,-0.0173733,-0.0386466,-0.0617818,-0.0868902,-0.114076,-0.143431,-0.175026},
{-1.62251,-1.59677,-1.57104,-1.54533,-1.51965,-1.49399,-1.46835,-1.44274,-1.41717,-1.39162,-1.36611,-1.34064,-1.3152,-1.28981,-1.26447,-1.23918,-1.21394,-1.18876,-1.16365,-1.1386,-1.11363,-1.08873,-1.06393,-1.03921,-1.01459,-0.990078,-0.96568,-0.941403,-0.917256,-0.893248,-0.869389,-0.845688,-0.822155,-0.798801,-0.775636,-0.752671,-0.729917,-0.707385,-0.685087,-0.663035,-0.641238,-0.619709,-0.598458,-0.577497,-0.556835,-0.536482,-0.516449,-0.496744,-0.477376,-0.458352,-0.43968,-0.421366,-0.403417,-0.385836,-0.368629,-0.351798,-0.335347,-0.319276,-0.303587,-0.288279,-0.273353,-0.258806,-0.244636,-0.230841,-0.217416,-0.204357,-0.191659,-0.179318,-0.167326,-0.155677,-0.144365,-0.133382,-0.122721,-0.112374,-0.102332,-0.0925869,-0.083131,-0.0739554,-0.0650514,-0.0564103,-0.0480235,-0.0398823,-0.0319783,-0.0243028,-0.0168477,-0.0096047,-0.0025658,0.0042768,0.0109307,0.0174033,0.0237016,0.0298326,0.0358029,0.0416187,0.0472861,0.0528107,0.0581981,0.0634534,0.0685812,0.0735862,0.0784726,0.0832441,0.0879045,0.0924569,0.0969044,0.10125,0.105495,0.109643,0.113695,0.117652,0.121518,0.125291,0.128974,0.132567,0.136071,0.139486,0.142813,0.146052,0.149202,0.152265,0.155239,0.158124,0.160922,0.16363,0.16625,0.168781,0.171222,0.173575,0.175838,0.178012,0.180097,0.182093,0.184,0.185819,0.18755,0.189193,0.190749,0.192219,0.193602,0.194901,0.196115,0.197245,0.198292,0.199256,0.200138,0.200938,0.201657,0.202294,0.20285,0.203325,0.203717,0.204027,0.204253,0.204393,0.204446,0.204409,0.20428,0.204055,0.20373,0.203299,0.202759,0.202102,0.201321,0.200408,0.199353,0.198146,0.196775,0.195227,0.193487,0.191539,0.189363,0.18694,0.184247,0.181259,0.177948,0.174283,0.170232,0.165757,0.160817,0.155368,0.149361,0.142743,0.135457,0.12744,0.118622,0.108931,0.0982865,0.0866035,0.0737904,0.0597503,0.0443804,0.0275732,0.00921668,-0.010804,-0.032605,-0.0563013,-0.0820043,-0.109816,-0.139826,-0.172102},
{-1.67533,-1.64952,-1.62372,-1.59794,-1.57218,-1.54643,-1.52071,-1.495,-1.46932,-1.44367,-1.41805,-1.39245,-1.36689,-1.34136,-1.31588,-1.29043,-1.26503,-1.23968,-1.21438,-1.18913,-1.16395,-1.13883,-1.11379,-1.08882,-1.06393,-1.03914,-1.01444,-0.989841,-0.965354,-0.940987,-0.916746,-0.892642,-0.868684,-0.84488,-0.821242,-0.797779,-0.774503,-0.751423,-0.728551,-0.705899,-0.683477,-0.661297,-0.63937,-0.617708,-0.596321,-0.575219,-0.554415,-0.533917,-0.513735,-0.493879,-0.474356,-0.455176,-0.436344,-0.417869,-0.399754,-0.382007,-0.36463,-0.347628,-0.331003,-0.314756,-0.298889,-0.283402,-0.268294,-0.253563,-0.239208,-0.225226,-0.211613,-0.198364,-0.185476,-0.172942,-0.160757,-0.148914,-0.137406,-0.126226,-0.115368,-0.104822,-0.0945806,-0.0846362,-0.07498,-0.0656037,-0.0564985,-0.0476561,-0.0390679,-0.0307252,-0.0226198,-0.0147432,-0.00708738,0.000355809,0.00759417,0.0146353,0.0214867,0.0281555,0.0346486,0.0409727,0.047134,0.0531388,0.0589927,0.0647012,0.0702695,0.0757024,0.0810045,0.0861799,0.0912326,0.0961662,0.100984,0.105689,0.110283,0.11477,0.119151,0.123429,0.127604,0.131679,0.135654,0.13953,0.143309,0.146991,0.150576,0.154064,0.157457,0.160754,0.163954,0.167059,0.170068,0.172981,0.175798,0.178519,0.181144,0.183673,0.186106,0.188443,0.190685,0.192832,0.194884,0.196841,0.198705,0.200476,0.202154,0.203741,0.205236,0.206642,0.207959,0.209187,0.210328,0.211383,0.212351,0.213235,0.214034,0.214749,0.215381,0.215928,0.216392,0.216771,0.217066,0.217274,0.217394,0.217425,0.217364,0.217207,0.216952,0.216594,0.216128,0.215549,0.214849,0.214022,0.213057,0.211947,0.210679,0.209242,0.207622,0.205802,0.203766,0.201495,0.198967,0.196159,0.193044,0.189594,0.185778,0.18156,0.176901,0.171761,0.166092,0.159844,0.152963,0.145388,0.137055,0.127893,0.117826,0.106771,0.0946425,0.0813451,0.0667797,0.0508415,0.0334207,0.0144037,-0.00632579,-0.0288845,-0.0533876,-0.0799448,-0.108656,-0.139604},
{-1.72555,-1.69968,-1.67382,-1.64797,-1.62214,-1.59633,-1.57052,-1.54474,-1.51898,-1.49323,-1.46751,-1.44181,-1.41614,-1.3905,-1.36489,-1.33931,-1.31377,-1.28827,-1.26281,-1.2374,-1.21204,-1.18673,-1.16149,-1.13631,-1.11119,-1.08616,-1.0612,-1.03633,-1.01155,-0.986878,-0.962312,-0.937863,-0.913539,-0.889349,-0.865303,-0.841409,-0.817679,-0.794122,-0.770749,-0.747572,-0.7246,-0.701845,-0.679319,-0.657033,-0.634998,-0.613225,-0.591726,-0.57051,-0.549589,-0.528973,-0.508671,-0.488692,-0.469045,-0.449738,-0.430779,-0.412173,-0.393927,-0.376045,-0.358532,-0.341392,-0.324626,-0.308238,-0.292227,-0.276593,-0.261338,-0.246457,-0.231951,-0.217815,-0.204046,-0.19064,-0.177593,-0.164898,-0.15255,-0.140542,-0.128868,-0.117521,-0.106493,-0.0957764,-0.0853632,-0.0752453,-0.0654144,-0.0558623,-0.0465804,-0.0375604,-0.0287937,-0.0202722,-0.0119874,-0.00393128,0.0039042,0.0115269,0.0189443,0.026164,0.0331931,0.0400386,0.046707,0.0532048,0.059538,0.0657124,0.0717336,0.0776065,0.0833362,0.0889271,0.0943834,0.099709,0.104907,0.109982,0.114936,0.119771,0.124491,0.129097,0.133591,0.137975,0.14225,0.146417,0.150478,0.154432,0.158281,0.162026,0.165666,0.169202,0.172634,0.175963,0.179187,0.182308,0.185326,0.18824,0.191051,0.193759,0.196364,0.198866,0.201266,0.203564,0.205761,0.207858,0.209854,0.211752,0.213551,0.215253,0.216858,0.218369,0.219785,0.221107,0.222338,0.223478,0.224528,0.225488,0.226361,0.227145,0.227842,0.228453,0.228977,0.229413,0.229762,0.230023,0.230194,0.230274,0.23026,0.23015,0.22994,0.229627,0.229206,0.228671,0.228016,0.227235,0.226317,0.225255,0.224038,0.222654,0.221088,0.219328,0.217354,0.21515,0.212694,0.209964,0.206934,0.203576,0.199859,0.19575,0.191211,0.1862,0.180674,0.174582,0.167872,0.160485,0.152356,0.143419,0.133597,0.122811,0.110975,0.0979957,0.0837762,0.0682127,0.0511965,0.0326148,0.0123514,-0.00971093,-0.0336891,-0.0596958,-0.0878356,-0.1182},
{-1.7734,-1.74748,-1.72157,-1.69567,-1.66978,-1.6439,-1.61804,-1.59218,-1.56634,-1.54052,-1.51471,-1.48893,-1.46316,-1.43742,-1.4117,-1.38601,-1.36035,-1.33473,-1.30913,-1.28358,-1.25807,-1.2326,-1.20718,-1.18181,-1.15651,-1.13126,-1.10608,-1.08098,-1.05595,-1.03102,-1.00617,-0.981422,-0.956783,-0.932259,-0.907859,-0.883592,-0.859467,-0.835494,-0.811683,-0.788045,-0.764589,-0.741327,-0.71827,-0.695429,-0.672815,-0.650441,-0.628316,-0.606453,-0.584862,-0.563554,-0.542539,-0.521828,-0.50143,-0.481354,-0.461609,-0.442202,-0.423142,-0.404433,-0.386083,-0.368096,-0.350476,-0.333227,-0.316351,-0.29985,-0.283724,-0.267975,-0.252601,-0.2376,-0.222972,-0.208711,-0.194816,-0.181281,-0.168102,-0.155274,-0.142791,-0.130645,-0.118832,-0.107343,-0.0961704,-0.0853077,-0.0747465,-0.0644789,-0.0544966,-0.0447913,-0.0353549,-0.0261791,-0.0172555,-0.00857599,-0.000132553,0.00808277,0.0160778,0.02386,0.0314369,0.0388155,0.0460028,0.0530053,0.0598295,0.0664814,0.0729668,0.079291,0.0854592,0.0914762,0.0973465,0.103074,0.108663,0.114117,0.119439,0.124632,0.129699,0.134641,0.139462,0.144162,0.148744,0.153208,0.157557,0.16179,0.165909,0.169915,0.173807,0.177587,0.181254,0.18481,0.188253,0.191585,0.194805,0.197914,0.200912,0.203799,0.206577,0.209244,0.211801,0.21425,0.216591,0.218824,0.22095,0.222971,0.224887,0.226699,0.228409,0.230017,0.231525,0.232935,0.234246,0.235461,0.236581,0.237606,0.238537,0.239376,0.240122,0.240777,0.24134,0.241811,0.24219,0.242476,0.242668,0.242764,0.242761,0.242658,0.242451,0.242135,0.241706,0.241158,0.240486,0.23968,0.238734,0.237637,0.236378,0.234946,0.233325,0.231501,0.229457,0.227174,0.224629,0.2218,0.21866,0.21518,0.21133,0.207073,0.202371,0.197182,0.19146,0.185155,0.17821,0.170567,0.16216,0.152918,0.142766,0.131621,0.119395,0.105994,0.0913181,0.0752628,0.0577175,0.038568,0.0176975,-0.00501208,-0.0296771,-0.0564091,-0.0853104,-0.116468},
{-1.81909,-1.79313,-1.76718,-1.74123,-1.71529,-1.68936,-1.66343,-1.63752,-1.61162,-1.58573,-1.55985,-1.53399,-1.50814,-1.48231,-1.4565,-1.43071,-1.40495,-1.37921,-1.3535,-1.32782,-1.30218,-1.27657,-1.251,-1.22548,-1.2,-1.17458,-1.14921,-1.1239,-1.09866,-1.07349,-1.0484,-1.0234,-0.998486,-0.973672,-0.948964,-0.924371,-0.899901,-0.875564,-0.851368,-0.827324,-0.803441,-0.77973,-0.756202,-0.732867,-0.709737,-0.686823,-0.664136,-0.641689,-0.619491,-0.597554,-0.575889,-0.554507,-0.533418,-0.512632,-0.492159,-0.472008,-0.452186,-0.432703,-0.413565,-0.394778,-0.376348,-0.35828,-0.340578,-0.323245,-0.306284,-0.289696,-0.273482,-0.257642,-0.242175,-0.22708,-0.212354,-0.197994,-0.183997,-0.170357,-0.157072,-0.144134,-0.131538,-0.119278,-0.107347,-0.0957384,-0.084444,-0.0734566,-0.0627684,-0.0523715,-0.0422579,-0.0324194,-0.0228479,-0.0135354,-0.00447374,0.004345,0.0129286,0.0212849,0.0294212,0.0373449,0.0450631,0.0525825,0.0599098,0.0670513,0.0740129,0.0808003,0.0874189,0.0938737,0.10017,0.106311,0.112302,0.118146,0.123847,0.129407,0.134831,0.14012,0.145277,0.150303,0.155201,0.159971,0.164616,0.169137,0.173534,0.177808,0.181961,0.185991,0.189901,0.19369,0.197359,0.200909,0.204338,0.207649,0.21084,0.213913,0.216869,0.219707,0.222428,0.225033,0.227523,0.229898,0.232161,0.234311,0.23635,0.238279,0.240099,0.241812,0.243419,0.244922,0.246322,0.24762,0.248817,0.249915,0.250915,0.251817,0.252623,0.253334,0.253948,0.254467,0.25489,0.255217,0.255445,0.255575,0.255603,0.255528,0.255345,0.255052,0.254643,0.254112,0.253454,0.252662,0.251725,0.250636,0.249383,0.247954,0.246335,0.244511,0.242465,0.240177,0.237626,0.234788,0.231638,0.228146,0.224282,0.220008,0.215288,0.21008,0.204335,0.198006,0.191035,0.183363,0.174926,0.165652,0.155465,0.144283,0.132018,0.118577,0.103858,0.0877573,0.0701642,0.0509644,0.0300406,0.00727433,-0.0174514,-0.044249,-0.073222,-0.10446},
{-1.86281,-1.83681,-1.81082,-1.78483,-1.75885,-1.73287,-1.7069,-1.68093,-1.65497,-1.62902,-1.60308,-1.57715,-1.55123,-1.52533,-1.49944,-1.47357,-1.44771,-1.42188,-1.39606,-1.37028,-1.34452,-1.31878,-1.29309,-1.26742,-1.2418,-1.21622,-1.19068,-1.1652,-1.13977,-1.11441,-1.0891,-1.06387,-1.03872,-1.01365,-0.988677,-0.963798,-0.939026,-0.914368,-0.889833,-0.865431,-0.84117,-0.817062,-0.793115,-0.76934,-0.745749,-0.722351,-0.699159,-0.676184,-0.653437,-0.630929,-0.608671,-0.586676,-0.564953,-0.543513,-0.522367,-0.501525,-0.480995,-0.460787,-0.44091,-0.42137,-0.402174,-0.38333,-0.364842,-0.346715,-0.328953,-0.311559,-0.294535,-0.277882,-0.261602,-0.245694,-0.230157,-0.214989,-0.200188,-0.185751,-0.171674,-0.157952,-0.14458,-0.131554,-0.118867,-0.106513,-0.0944851,-0.0827763,-0.0713792,-0.0602865,-0.0494904,-0.0389831,-0.0287567,-0.0188033,-0.00911496,0.000316189,0.00949797,0.0184381,0.0271441,0.0356233,0.0438831,0.0519302,0.0597715,0.0674135,0.0748622,0.0821237,0.0892034,0.0961068,0.102839,0.109404,0.115807,0.122051,0.12814,0.134079,0.139869,0.145513,0.151014,0.156375,0.161597,0.166682,0.171631,0.176446,0.181128,0.185678,0.190097,0.194385,0.198544,0.202573,0.206473,0.210244,0.213888,0.217405,0.220795,0.224058,0.227195,0.230208,0.233096,0.235861,0.238504,0.241025,0.243426,0.245708,0.247872,0.24992,0.251853,0.253673,0.255381,0.256979,0.258468,0.25985,0.261127,0.262299,0.263368,0.264335,0.265201,0.265967,0.266634,0.2672,0.267667,0.268034,0.2683,0.268463,0.268522,0.268473,0.268315,0.268042,0.267651,0.267137,0.266492,0.265709,0.264781,0.263697,0.262447,0.261018,0.259398,0.257569,0.255516,0.253219,0.250656,0.247804,0.244637,0.241127,0.23724,0.232942,0.228195,0.222956,0.217178,0.210812,0.203802,0.196088,0.187605,0.178282,0.168042,0.156804,0.144479,0.130973,0.116187,0.100014,0.0823445,0.0630638,0.0420543,0.0191971,-0.00562537,-0.0325262,-0.06161,-0.0929671},
{-1.90471,-1.87869,-1.85266,-1.82664,-1.80062,-1.7746,-1.74858,-1.72257,-1.69656,-1.67056,-1.64456,-1.61857,-1.59259,-1.56662,-1.54066,-1.51471,-1.48878,-1.46286,-1.43695,-1.41107,-1.38521,-1.35937,-1.33356,-1.30777,-1.28202,-1.2563,-1.23062,-1.20498,-1.17939,-1.15385,-1.12836,-1.10293,-1.07757,-1.05227,-1.02706,-1.00193,-0.97689,-0.95195,-0.927115,-0.902396,-0.877801,-0.853338,-0.829018,-0.804851,-0.780846,-0.757015,-0.733369,-0.709917,-0.686673,-0.663646,-0.640849,-0.618293,-0.595988,-0.573947,-0.55218,-0.530697,-0.509509,-0.488625,-0.468055,-0.447808,-0.427891,-0.408312,-0.389078,-0.370195,-0.351667,-0.333501,-0.315698,-0.298262,-0.281195,-0.264498,-0.248171,-0.232214,-0.216627,-0.201406,-0.186549,-0.172054,-0.157915,-0.14413,-0.130691,-0.117595,-0.104835,-0.0924051,-0.0802978,-0.0685067,-0.0570244,-0.0458436,-0.0349566,-0.0243558,-0.0140335,-0.00398202,0.00580642,0.0153394,0.0246245,0.0336692,0.0424805,0.0510657,0.0594315,0.0675845,0.0755311,0.0832774,0.090829,0.0981915,0.10537,0.11237,0.119195,0.125849,0.132337,0.138663,0.144829,0.150838,0.156694,0.162398,0.167953,0.17336,0.178622,0.18374,0.188715,0.193548,0.198241,0.202794,0.207208,0.211483,0.215621,0.219622,0.223487,0.227216,0.230809,0.234269,0.237595,0.240788,0.243849,0.246779,0.24958,0.252252,0.254797,0.257217,0.259512,0.261685,0.263736,0.265669,0.267484,0.269183,0.270768,0.272241,0.273604,0.274857,0.276004,0.277044,0.277979,0.27881,0.279539,0.280164,0.280687,0.281106,0.281423,0.281634,0.281739,0.281735,0.281619,0.281389,0.281039,0.280564,0.279959,0.279216,0.278328,0.277285,0.276076,0.274691,0.273115,0.271333,0.269329,0.267084,0.264577,0.261785,0.258682,0.255241,0.25143,0.247215,0.242557,0.237416,0.231747,0.225498,0.218618,0.211045,0.202717,0.193565,0.183511,0.172477,0.160376,0.147114,0.132592,0.116708,0.0993501,0.0804058,0.0597573,0.0372857,0.0128723,-0.0135984,-0.0422343,-0.0731315},
{-1.94495,-1.9189,-1.89284,-1.86679,-1.84073,-1.81468,-1.78862,-1.76257,-1.73652,-1.71047,-1.68442,-1.65838,-1.63234,-1.60631,-1.58029,-1.55427,-1.52827,-1.50227,-1.47629,-1.45032,-1.42437,-1.39844,-1.37252,-1.34663,-1.32076,-1.29492,-1.26911,-1.24333,-1.2176,-1.1919,-1.16625,-1.14064,-1.11509,-1.0896,-1.06418,-1.03883,-1.01355,-0.988358,-0.963258,-0.938257,-0.913363,-0.888585,-0.863932,-0.839413,-0.815038,-0.790817,-0.766761,-0.74288,-0.719185,-0.695688,-0.672399,-0.64933,-0.626493,-0.603899,-0.581559,-0.559484,-0.537685,-0.516172,-0.494955,-0.474045,-0.45345,-0.433178,-0.413238,-0.393636,-0.37438,-0.355474,-0.336924,-0.318735,-0.300908,-0.283448,-0.266355,-0.249631,-0.233276,-0.217289,-0.201668,-0.186411,-0.171517,-0.156981,-0.142798,-0.128966,-0.115478,-0.102328,-0.0895121,-0.0770223,-0.0648523,-0.0529953,-0.0414441,-0.0301914,-0.0192299,-0.00855193,0.0018499,0.0119831,0.0218551,0.0314733,0.0408448,0.0499768,0.0588761,0.0675494,0.0760031,0.0842435,0.0922764,0.100107,0.107742,0.115185,0.122441,0.129515,0.136411,0.143132,0.149682,0.156065,0.162282,0.168338,0.174233,0.17997,0.185552,0.190979,0.196253,0.201376,0.206348,0.211171,0.215846,0.220373,0.224753,0.228987,0.233076,0.237021,0.240822,0.244481,0.247997,0.251373,0.254609,0.257707,0.260667,0.263492,0.266182,0.268739,0.271165,0.273462,0.275632,0.277675,0.279595,0.281394,0.283073,0.284634,0.286079,0.28741,0.288628,0.289736,0.290734,0.291624,0.292406,0.293082,0.29365,0.294112,0.294467,0.294714,0.29485,0.294875,0.294785,0.294577,0.294247,0.29379,0.293199,0.292468,0.291589,0.290553,0.289348,0.287965,0.286388,0.284604,0.282594,0.280342,0.277825,0.275021,0.271905,0.268447,0.264617,0.26038,0.255698,0.250531,0.244832,0.238552,0.231637,0.224028,0.21566,0.206465,0.196367,0.185285,0.173132,0.159817,0.145239,0.129295,0.111875,0.0928649,0.0721476,0.0496034,0.0251134,-0.00143856,-0.0301615,-0.0611524},
{-1.98364,-1.95756,-1.93148,-1.9054,-1.87931,-1.85323,-1.82714,-1.80105,-1.77496,-1.74887,-1.72278,-1.69669,-1.6706,-1.64452,-1.61844,-1.59237,-1.5663,-1.54024,-1.51418,-1.48814,-1.46211,-1.43609,-1.41008,-1.38409,-1.35812,-1.33218,-1.30625,-1.28035,-1.25448,-1.22865,-1.20285,-1.17709,-1.15137,-1.12571,-1.1001,-1.07454,-1.04906,-1.02364,-0.998305,-0.973052,-0.947892,-0.922831,-0.89788,-0.873045,-0.848337,-0.823765,-0.799339,-0.775069,-0.750966,-0.72704,-0.703304,-0.679767,-0.656442,-0.633339,-0.610471,-0.587849,-0.565483,-0.543385,-0.521565,-0.500034,-0.478801,-0.457876,-0.437269,-0.416986,-0.397036,-0.377426,-0.358162,-0.339249,-0.320692,-0.302494,-0.28466,-0.267191,-0.250088,-0.233352,-0.216983,-0.20098,-0.185342,-0.170065,-0.155148,-0.140586,-0.126375,-0.11251,-0.0989872,-0.0857996,-0.0729416,-0.0604069,-0.0481889,-0.0362807,-0.0246753,-0.0133656,-0.00234429,0.00839583,0.018862,0.0290616,0.0390015,0.0486889,0.0581306,0.0673333,0.0763035,0.0850475,0.0935712,0.10188,0.10998,0.117877,0.125574,0.133077,0.140389,0.147516,0.154459,0.161224,0.167812,0.174227,0.180472,0.186547,0.192456,0.1982,0.203782,0.209201,0.214461,0.219561,0.224503,0.229289,0.233918,0.238392,0.242712,0.246879,0.250894,0.254757,0.25847,0.262034,0.265451,0.268721,0.271847,0.274829,0.277669,0.28037,0.282932,0.285359,0.287652,0.289813,0.291844,0.293748,0.295526,0.297182,0.298716,0.300131,0.30143,0.302613,0.303682,0.304639,0.305485,0.306221,0.306846,0.307362,0.307769,0.308064,0.308248,0.308317,0.308271,0.308104,0.307815,0.307397,0.306846,0.306154,0.305313,0.304316,0.303152,0.30181,0.300275,0.298535,0.296572,0.294369,0.291905,0.289157,0.2861,0.282707,0.278947,0.274787,0.270189,0.265113,0.259514,0.253344,0.246549,0.239072,0.23085,0.221813,0.211889,0.200998,0.189055,0.175967,0.161639,0.145966,0.12884,0.110147,0.0897721,0.0675942,0.043494,0.0173538,-0.0109383,-0.0414853},
{-2.02089,-1.9948,-1.96869,-1.94259,-1.91647,-1.89036,-1.86424,-1.83812,-1.812,-1.78587,-1.75974,-1.73361,-1.70748,-1.68135,-1.65522,-1.6291,-1.60297,-1.57685,-1.55073,-1.52462,-1.49852,-1.47242,-1.44633,-1.42026,-1.3942,-1.36815,-1.34212,-1.31611,-1.29013,-1.26417,-1.23824,-1.21234,-1.18648,-1.16065,-1.13487,-1.10915,-1.08347,-1.05785,-1.0323,-1.00682,-0.981425,-0.956111,-0.930891,-0.905772,-0.880764,-0.855875,-0.831114,-0.806492,-0.782018,-0.757703,-0.733558,-0.709593,-0.68582,-0.662251,-0.638896,-0.615768,-0.592877,-0.570235,-0.547853,-0.525741,-0.503911,-0.482373,-0.461136,-0.440209,-0.419601,-0.39932,-0.379374,-0.359768,-0.340509,-0.321602,-0.303051,-0.28486,-0.267032,-0.249567,-0.232468,-0.215735,-0.199367,-0.183362,-0.16772,-0.152438,-0.137511,-0.122937,-0.108712,-0.0948292,-0.0812849,-0.068073,-0.0551874,-0.0426219,-0.03037,-0.018425,-0.00677988,0.0045722,0.0156383,0.0264253,0.0369404,0.0471903,0.0571819,0.0669217,0.0764164,0.085672,0.0946948,0.10349,0.112065,0.120422,0.128569,0.136509,0.144246,0.151786,0.159131,0.166285,0.173252,0.180034,0.186635,0.193055,0.199299,0.205366,0.211261,0.216983,0.222535,0.227918,0.233133,0.238181,0.243064,0.247782,0.252337,0.25673,0.260961,0.265032,0.268945,0.2727,0.276299,0.279744,0.283035,0.286176,0.289167,0.292011,0.29471,0.297266,0.299681,0.301958,0.304098,0.306105,0.307981,0.309727,0.311347,0.312842,0.314215,0.315467,0.316601,0.317618,0.31852,0.319306,0.319979,0.320538,0.320983,0.321314,0.321529,0.321626,0.321604,0.32146,0.321188,0.320786,0.320247,0.319564,0.31873,0.317736,0.316573,0.315228,0.313689,0.311941,0.309967,0.30775,0.305269,0.302501,0.299422,0.296003,0.292214,0.288021,0.283387,0.278271,0.272629,0.266411,0.259565,0.252032,0.243749,0.234648,0.224655,0.21369,0.201667,0.188496,0.174078,0.15831,0.141084,0.122287,0.1018,0.0795043,0.0552802,0.0290094,0.000579378,-0.0301137},
{-2.05682,-2.0307,-2.00458,-1.97845,-1.95232,-1.92618,-1.90003,-1.87388,-1.84773,-1.82157,-1.79541,-1.76924,-1.74307,-1.7169,-1.69072,-1.66455,-1.63837,-1.6122,-1.58602,-1.55985,-1.53368,-1.50752,-1.48136,-1.4552,-1.42906,-1.40293,-1.37681,-1.3507,-1.32461,-1.29854,-1.27249,-1.24646,-1.22047,-1.1945,-1.16857,-1.14268,-1.11684,-1.09104,-1.0653,-1.03962,-1.014,-0.988459,-0.962996,-0.937621,-0.912341,-0.887164,-0.8621,-0.837157,-0.812346,-0.787676,-0.763157,-0.738801,-0.714618,-0.690619,-0.666816,-0.643219,-0.619842,-0.596694,-0.573788,-0.551135,-0.528745,-0.506629,-0.484799,-0.463263,-0.442031,-0.421113,-0.400516,-0.380248,-0.360316,-0.340727,-0.321485,-0.302596,-0.284064,-0.265891,-0.24808,-0.230633,-0.21355,-0.196831,-0.180476,-0.164483,-0.148849,-0.133572,-0.118649,-0.104076,-0.0898475,-0.0759595,-0.0624064,-0.0491825,-0.0362819,-0.0236984,-0.0114256,0.000543195,0.0122146,0.0235953,0.0346921,0.0455116,0.0560606,0.0663455,0.0763728,0.0861487,0.0956792,0.10497,0.114027,0.122856,0.131461,0.139847,0.148018,0.15598,0.163736,0.171289,0.178643,0.185801,0.192766,0.19954,0.206126,0.212526,0.218741,0.224774,0.230627,0.2363,0.241795,0.247114,0.252257,0.257226,0.262023,0.266648,0.271103,0.275389,0.279507,0.283459,0.287248,0.290873,0.294338,0.297644,0.300793,0.303787,0.306629,0.309322,0.311866,0.314266,0.316524,0.318642,0.320623,0.322469,0.324184,0.325769,0.327227,0.328561,0.329772,0.330861,0.331832,0.332685,0.333421,0.33404,0.334543,0.33493,0.335199,0.335349,0.335378,0.335284,0.335063,0.334711,0.334221,0.333589,0.332807,0.331867,0.330759,0.329471,0.327992,0.326308,0.324402,0.322258,0.319855,0.317171,0.314182,0.310862,0.30718,0.303104,0.298597,0.293621,0.288131,0.282081,0.275418,0.268086,0.260024,0.251164,0.241435,0.230759,0.219052,0.206225,0.192182,0.176822,0.160038,0.141717,0.121744,0.0999993,0.0763625,0.0507141,0.0229386,-0.00707284},
{-2.0915,-2.06537,-2.03923,-2.01308,-1.98693,-1.96076,-1.9346,-1.90842,-1.88224,-1.85605,-1.82986,-1.80366,-1.77745,-1.75124,-1.72503,-1.69881,-1.67259,-1.64636,-1.62014,-1.59391,-1.56768,-1.54146,-1.51523,-1.48901,-1.46279,-1.43658,-1.41037,-1.38417,-1.35799,-1.33182,-1.30566,-1.27952,-1.25341,-1.22731,-1.20125,-1.17521,-1.14921,-1.12325,-1.09734,-1.07147,-1.04566,-1.01991,-0.99423,-0.968622,-0.943095,-0.917658,-0.892318,-0.867084,-0.841965,-0.81697,-0.79211,-0.767395,-0.742835,-0.718441,-0.694224,-0.670195,-0.646367,-0.62275,-0.599356,-0.576196,-0.553282,-0.530626,-0.508237,-0.486126,-0.464304,-0.442781,-0.421565,-0.400665,-0.380089,-0.359845,-0.339939,-0.320377,-0.301165,-0.282305,-0.263803,-0.24566,-0.227879,-0.210461,-0.193406,-0.176714,-0.160383,-0.144412,-0.128799,-0.113541,-0.0986331,-0.0840723,-0.0698538,-0.0559726,-0.0424234,-0.0292005,-0.0162981,-0.00371001,0.00857,0.0205483,0.0322314,0.0436256,0.0547375,0.0655734,0.0761395,0.0864421,0.0964871,0.10628,0.115827,0.125133,0.134203,0.143043,0.151656,0.160047,0.168219,0.176178,0.183926,0.191466,0.198801,0.205935,0.212869,0.219606,0.226148,0.232496,0.238654,0.244621,0.2504,0.255993,0.2614,0.266623,0.271664,0.276523,0.281203,0.285705,0.29003,0.29418,0.298157,0.301963,0.3056,0.309069,0.312373,0.315516,0.318498,0.321322,0.323992,0.326509,0.328878,0.3311,0.333178,0.335115,0.336914,0.338578,0.340109,0.341509,0.342781,0.343927,0.344949,0.345847,0.346623,0.347278,0.347811,0.348223,0.348513,0.34868,0.348721,0.348634,0.348415,0.348059,0.347562,0.346918,0.346118,0.345155,0.344018,0.342696,0.341177,0.339446,0.337487,0.335281,0.33281,0.33005,0.326977,0.323563,0.319778,0.315588,0.310956,0.305842,0.300202,0.293988,0.287146,0.279619,0.271345,0.262255,0.252277,0.241331,0.229333,0.216191,0.201809,0.186085,0.16891,0.150171,0.129751,0.107532,0.083391,0.0572101,0.0288742,-0.00172406},
{-2.12502,-2.09888,-2.07272,-2.04656,-2.02038,-1.9942,-1.96801,-1.94182,-1.91561,-1.8894,-1.86317,-1.83694,-1.81071,-1.78446,-1.75821,-1.73196,-1.70569,-1.67942,-1.65315,-1.62687,-1.60059,-1.57431,-1.54802,-1.52174,-1.49545,-1.46917,-1.44288,-1.41661,-1.39034,-1.36407,-1.33782,-1.31158,-1.28535,-1.25914,-1.23295,-1.20678,-1.18065,-1.15454,-1.12847,-1.10243,-1.07644,-1.05051,-1.02462,-0.998804,-0.973053,-0.947378,-0.921786,-0.896285,-0.870885,-0.845594,-0.820421,-0.795376,-0.770469,-0.74571,-0.721111,-0.696683,-0.672437,-0.648383,-0.624535,-0.600902,-0.577498,-0.554333,-0.531418,-0.508766,-0.486385,-0.464288,-0.442483,-0.420981,-0.39979,-0.378918,-0.358373,-0.338163,-0.318293,-0.298768,-0.279594,-0.260774,-0.242312,-0.22421,-0.206469,-0.189089,-0.172073,-0.155417,-0.139122,-0.123184,-0.107602,-0.0923723,-0.0774908,-0.0629535,-0.0487558,-0.0348927,-0.0213589,-0.00814879,0.00474335,0.0173235,0.0295977,0.0415722,0.053253,0.0646463,0.0757582,0.0865947,0.0971617,0.107465,0.11751,0.127301,0.136845,0.146146,0.155209,0.164037,0.172636,0.181008,0.189158,0.197089,0.204803,0.212304,0.219594,0.226676,0.233552,0.240224,0.246693,0.252963,0.259033,0.264907,0.270584,0.276068,0.28136,0.286461,0.291372,0.296096,0.300634,0.304989,0.309161,0.313153,0.316968,0.320607,0.324074,0.32737,0.330498,0.333461,0.336263,0.338905,0.341391,0.343725,0.345908,0.347944,0.349837,0.351588,0.353201,0.354679,0.356023,0.357236,0.358321,0.359277,0.360108,0.360814,0.361395,0.361851,0.362182,0.362386,0.362462,0.362407,0.362218,0.36189,0.361419,0.360798,0.36002,0.359077,0.357959,0.356655,0.355152,0.353437,0.351493,0.349303,0.346846,0.3441,0.341042,0.337642,0.333872,0.329698,0.325084,0.319989,0.31437,0.308179,0.301363,0.293864,0.285622,0.276569,0.266631,0.255732,0.243785,0.230701,0.216385,0.200733,0.183638,0.164988,0.144667,0.122554,0.0985287,0.0724714,0.0442649,0.0138032},
{-2.15746,-2.1313,-2.10513,-2.07896,-2.05277,-2.02657,-2.00036,-1.97414,-1.94791,-1.92167,-1.89543,-1.86917,-1.8429,-1.81663,-1.79035,-1.76405,-1.73775,-1.71145,-1.68513,-1.65881,-1.63248,-1.60614,-1.5798,-1.55346,-1.52711,-1.50076,-1.47441,-1.44806,-1.42171,-1.39536,-1.36902,-1.34268,-1.31635,-1.29004,-1.26374,-1.23745,-1.21118,-1.18494,-1.15872,-1.13254,-1.10639,-1.08028,-1.05421,-1.0282,-1.00224,-0.976351,-0.950529,-0.924785,-0.899127,-0.873563,-0.848102,-0.822754,-0.797527,-0.772433,-0.747481,-0.722682,-0.698048,-0.673589,-0.649317,-0.625243,-0.601379,-0.577738,-0.554329,-0.531165,-0.508257,-0.485616,-0.463252,-0.441176,-0.419397,-0.397925,-0.376767,-0.355933,-0.335429,-0.315261,-0.295436,-0.275959,-0.256833,-0.238063,-0.219651,-0.201599,-0.183908,-0.166578,-0.149609,-0.133001,-0.116751,-0.100857,-0.0853166,-0.0701261,-0.0552817,-0.0407791,-0.0266138,-0.0127806,0.000725569,0.0139102,0.0267789,0.0393375,0.0515917,0.0635475,0.0752106,0.0865868,0.0976818,0.108501,0.11905,0.129335,0.139359,0.149129,0.158648,0.167921,0.176952,0.185745,0.194304,0.202631,0.210731,0.218606,0.226259,0.233692,0.240908,0.247909,0.254696,0.261272,0.267639,0.273798,0.279751,0.2855,0.291047,0.296392,0.301539,0.306488,0.311242,0.315803,0.320173,0.324354,0.328348,0.332158,0.335787,0.339238,0.342512,0.345615,0.348547,0.351313,0.353916,0.356358,0.358644,0.360777,0.362759,0.364594,0.366284,0.367834,0.369244,0.370518,0.371657,0.372665,0.373541,0.374287,0.374903,0.37539,0.375748,0.375974,0.376067,0.376026,0.375845,0.375522,0.375051,0.374426,0.373639,0.372683,0.371547,0.37022,0.36869,0.366942,0.36496,0.362726,0.360219,0.357418,0.354296,0.350827,0.34698,0.342721,0.338014,0.332817,0.327086,0.320773,0.313824,0.306182,0.297783,0.288561,0.278441,0.267344,0.255185,0.241873,0.227312,0.211398,0.194023,0.175075,0.154435,0.131985,0.107604,0.0811704,0.0525688,0.0216938},
{-2.18888,-2.16271,-2.13653,-2.11034,-2.08414,-2.05792,-2.0317,-2.00546,-1.97921,-1.95295,-1.92668,-1.9004,-1.87411,-1.84781,-1.82149,-1.79517,-1.76883,-1.74249,-1.71613,-1.68977,-1.6634,-1.63702,-1.61063,-1.58423,-1.55782,-1.53141,-1.505,-1.47858,-1.45216,-1.42573,-1.39931,-1.37289,-1.34647,-1.32005,-1.29365,-1.26725,-1.24087,-1.2145,-1.18815,-1.16183,-1.13553,-1.10926,-1.08303,-1.05684,-1.0307,-1.0046,-0.97857,-0.952602,-0.926706,-0.900892,-0.875166,-0.849538,-0.824017,-0.798612,-0.773333,-0.748191,-0.723196,-0.698359,-0.673692,-0.649206,-0.624913,-0.600823,-0.57695,-0.553304,-0.529898,-0.506742,-0.483847,-0.461225,-0.438885,-0.416838,-0.395093,-0.373659,-0.352544,-0.331755,-0.3113,-0.291184,-0.271413,-0.251992,-0.232924,-0.214213,-0.19586,-0.177867,-0.160235,-0.142964,-0.126053,-0.109501,-0.0933064,-0.0774661,-0.0619773,-0.0468365,-0.0320398,-0.0175829,-0.0034612,0.0103303,0.0237966,0.036943,0.0497751,0.0622981,0.0745178,0.0864395,0.0980688,0.109411,0.120472,0.131255,0.141768,0.152013,0.161996,0.171721,0.181192,0.190414,0.199389,0.208121,0.216614,0.224871,0.232893,0.240685,0.248247,0.255584,0.262696,0.269586,0.276255,0.282706,0.288941,0.294961,0.300768,0.306364,0.311752,0.316932,0.321907,0.32668,0.331252,0.335626,0.339805,0.343791,0.347588,0.351197,0.354623,0.357868,0.360936,0.36383,0.366554,0.369111,0.371504,0.373737,0.375814,0.377737,0.37951,0.381136,0.382618,0.383959,0.38516,0.386224,0.387152,0.387946,0.388606,0.389132,0.389525,0.389783,0.389905,0.389888,0.389729,0.389424,0.388968,0.388354,0.387577,0.386626,0.385493,0.384167,0.382634,0.380881,0.378891,0.376646,0.374125,0.371307,0.368167,0.364675,0.360803,0.356517,0.351778,0.346547,0.340779,0.334426,0.327434,0.319746,0.311298,0.302023,0.291847,0.280691,0.26847,0.255094,0.240464,0.224479,0.20703,0.188005,0.167286,0.144754,0.120287,0.093765,0.065071,0.0340993},
{-2.21935,-2.19317,-2.16697,-2.14077,-2.11455,-2.08833,-2.06209,-2.03583,-2.00957,-1.98329,-1.957,-1.9307,-1.90438,-1.87805,-1.85171,-1.82536,-1.79899,-1.77261,-1.74622,-1.71982,-1.69341,-1.66698,-1.64055,-1.6141,-1.58764,-1.56118,-1.5347,-1.50822,-1.48173,-1.45524,-1.42874,-1.40224,-1.37574,-1.34923,-1.32273,-1.29624,-1.26974,-1.24326,-1.21679,-1.19034,-1.16391,-1.13749,-1.11111,-1.08475,-1.05844,-1.03216,-1.00593,-0.979758,-0.953645,-0.927599,-0.901629,-0.875742,-0.849948,-0.824255,-0.798673,-0.773212,-0.747882,-0.722694,-0.697658,-0.672786,-0.64809,-0.623581,-0.59927,-0.57517,-0.551292,-0.527649,-0.50425,-0.481108,-0.458234,-0.435638,-0.41333,-0.39132,-0.369617,-0.348229,-0.327164,-0.30643,-0.286032,-0.265977,-0.246269,-0.226913,-0.207912,-0.189268,-0.170983,-0.153058,-0.135495,-0.118292,-0.101448,-0.0849623,-0.0688324,-0.0530556,-0.0376288,-0.0225484,-0.00781045,0.00658931,0.0206554,0.0343927,0.0478061,0.0609006,0.0736815,0.0861539,0.098323,0.110194,0.121772,0.133062,0.144068,0.154796,0.16525,0.175435,0.185353,0.19501,0.204409,0.213553,0.222446,0.231091,0.23949,0.247647,0.255563,0.263242,0.270685,0.277895,0.284874,0.291623,0.298145,0.304442,0.310515,0.316367,0.322,0.327416,0.332617,0.337606,0.342386,0.346958,0.351325,0.355491,0.359459,0.363231,0.366812,0.370204,0.373411,0.376436,0.379284,0.381958,0.384462,0.386799,0.388973,0.390988,0.392847,0.394553,0.39611,0.39752,0.398786,0.399909,0.400893,0.401738,0.402445,0.403015,0.403448,0.403742,0.403897,0.403909,0.403777,0.403496,0.40306,0.402466,0.401704,0.400768,0.399646,0.39833,0.396804,0.395057,0.39307,0.390828,0.388308,0.385489,0.382347,0.378852,0.374976,0.370684,0.365939,0.360702,0.354927,0.348566,0.341567,0.333871,0.325416,0.316135,0.305954,0.294794,0.282572,0.269195,0.254568,0.238588,0.221148,0.202134,0.181431,0.158918,0.134475,0.107979,0.0793146,0.0483736},
{-2.24891,-2.22272,-2.19652,-2.1703,-2.14408,-2.11784,-2.09158,-2.06532,-2.03903,-2.01274,-1.98643,-1.96011,-1.93377,-1.90742,-1.88105,-1.85467,-1.82828,-1.80187,-1.77545,-1.74901,-1.72256,-1.69609,-1.66962,-1.64312,-1.61662,-1.5901,-1.56358,-1.53704,-1.51049,-1.48393,-1.45736,-1.43079,-1.40421,-1.37762,-1.35103,-1.32444,-1.29785,-1.27127,-1.24468,-1.21811,-1.19155,-1.16501,-1.13848,-1.11197,-1.0855,-1.05905,-1.03264,-1.00628,-0.979962,-0.953703,-0.927506,-0.901381,-0.875334,-0.849374,-0.82351,-0.797752,-0.77211,-0.746593,-0.721214,-0.695981,-0.670907,-0.646004,-0.621282,-0.596754,-0.572431,-0.548326,-0.524449,-0.500813,-0.47743,-0.454309,-0.431462,-0.4089,-0.386631,-0.364666,-0.343013,-0.32168,-0.300674,-0.280003,-0.259671,-0.239685,-0.220049,-0.200767,-0.181841,-0.163273,-0.145066,-0.127219,-0.109733,-0.0926074,-0.0758406,-0.0594311,-0.0433764,-0.0276738,-0.0123201,0.00268837,0.0173555,0.0316855,0.0456828,0.0593521,0.0726979,0.0857252,0.0984388,0.110844,0.122944,0.134746,0.146253,0.15747,0.168401,0.179051,0.189423,0.199522,0.209351,0.218913,0.228213,0.237252,0.246034,0.254562,0.262838,0.270865,0.278645,0.28618,0.293473,0.300525,0.30734,0.313918,0.320262,0.326374,0.332257,0.337912,0.343343,0.348551,0.35354,0.358313,0.362871,0.367219,0.37136,0.375297,0.379033,0.382573,0.385919,0.389077,0.392049,0.394839,0.397453,0.399892,0.402162,0.404267,0.406209,0.407992,0.40962,0.411096,0.412421,0.4136,0.414633,0.415523,0.41627,0.416875,0.417338,0.417658,0.417835,0.417865,0.417745,0.417473,0.417043,0.416448,0.415683,0.414739,0.413605,0.412271,0.410725,0.408952,0.406935,0.404656,0.402096,0.399231,0.396037,0.392485,0.388544,0.384182,0.37936,0.374038,0.368171,0.361709,0.354601,0.346787,0.338205,0.328786,0.318457,0.307139,0.294745,0.281186,0.266365,0.250177,0.232517,0.21327,0.192319,0.169544,0.144825,0.118039,0.0890716,0.0578138},
{-2.27762,-2.25142,-2.22522,-2.19899,-2.17276,-2.1465,-2.12024,-2.09396,-2.06766,-2.04135,-2.01502,-1.98868,-1.96233,-1.93595,-1.90956,-1.88316,-1.85674,-1.8303,-1.80385,-1.77738,-1.7509,-1.7244,-1.69788,-1.67135,-1.6448,-1.61824,-1.59166,-1.56507,-1.53846,-1.51184,-1.48521,-1.45857,-1.43192,-1.40525,-1.37858,-1.35191,-1.32523,-1.29854,-1.27186,-1.24518,-1.2185,-1.19183,-1.16517,-1.13853,-1.1119,-1.0853,-1.05872,-1.03218,-1.00568,-0.979221,-0.952815,-0.926467,-0.900185,-0.873977,-0.847851,-0.821816,-0.795883,-0.77006,-0.744358,-0.718787,-0.693359,-0.668085,-0.642976,-0.618044,-0.5933,-0.568758,-0.544428,-0.520322,-0.496453,-0.472832,-0.449469,-0.426377,-0.403565,-0.381043,-0.358822,-0.336909,-0.315314,-0.294043,-0.273105,-0.252504,-0.232248,-0.212339,-0.192783,-0.173583,-0.154741,-0.136259,-0.118137,-0.100377,-0.0829785,-0.0659397,-0.0492596,-0.0329364,-0.0169674,-0.00134986,0.0139195,0.0288441,0.043428,0.0576752,0.0715899,0.0851765,0.0984395,0.111383,0.124013,0.136332,0.148346,0.160058,0.171473,0.182595,0.193429,0.203977,0.214243,0.224231,0.233944,0.243386,0.252558,0.261465,0.270108,0.27849,0.286614,0.294482,0.302095,0.309458,0.316571,0.323437,0.330058,0.336437,0.342576,0.348477,0.354144,0.359578,0.364783,0.369762,0.374518,0.379054,0.383374,0.387481,0.391379,0.395073,0.398565,0.401861,0.404964,0.407878,0.410608,0.413158,0.415532,0.417734,0.419768,0.421638,0.423346,0.424898,0.426295,0.42754,0.428635,0.429583,0.430385,0.431041,0.431552,0.431916,0.432135,0.432204,0.432122,0.431884,0.431487,0.430924,0.430189,0.429273,0.428168,0.426862,0.425343,0.423596,0.421607,0.419356,0.416824,0.413989,0.410826,0.407308,0.403403,0.399079,0.394299,0.389022,0.383205,0.376799,0.369751,0.362005,0.353497,0.344161,0.333924,0.322707,0.310426,0.296991,0.282306,0.26627,0.248775,0.229709,0.208955,0.186395,0.161906,0.135367,0.106661,0.0756771},
{-2.30553,-2.27933,-2.25311,-2.22688,-2.20063,-2.17437,-2.1481,-2.1218,-2.09549,-2.06917,-2.04283,-2.01647,-1.9901,-1.9637,-1.93729,-1.91087,-1.88442,-1.85796,-1.83148,-1.80498,-1.77847,-1.75193,-1.72538,-1.69881,-1.67222,-1.64562,-1.61899,-1.59235,-1.56569,-1.53902,-1.51233,-1.48562,-1.4589,-1.43217,-1.40542,-1.37867,-1.3519,-1.32513,-1.29835,-1.27156,-1.24478,-1.21799,-1.19121,-1.16444,-1.13768,-1.11093,-1.0842,-1.05749,-1.03082,-1.00418,-0.977573,-0.951018,-0.924518,-0.898078,-0.871708,-0.845415,-0.81921,-0.7931,-0.767096,-0.741209,-0.715448,-0.689825,-0.664351,-0.639038,-0.613897,-0.588941,-0.564181,-0.539629,-0.515297,-0.491198,-0.467343,-0.443743,-0.420409,-0.397352,-0.374582,-0.35211,-0.329943,-0.308092,-0.286563,-0.265364,-0.244501,-0.223981,-0.203807,-0.183986,-0.164519,-0.14541,-0.126662,-0.108274,-0.090249,-0.0725857,-0.0552841,-0.0383429,-0.0217607,-0.00553515,0.0103361,0.0258559,0.0410276,0.0558546,0.0703406,0.0844896,0.0983055,0.111793,0.124955,0.137796,0.150322,0.162535,0.174439,0.186039,0.197339,0.208342,0.219052,0.229471,0.239604,0.249453,0.259022,0.268312,0.277328,0.286071,0.294544,0.302749,0.310689,0.318366,0.325782,0.33294,0.339843,0.346492,0.35289,0.35904,0.364945,0.370608,0.376031,0.381218,0.386173,0.390898,0.395398,0.399676,0.403737,0.407584,0.411222,0.414654,0.417887,0.420922,0.423767,0.426424,0.428897,0.431193,0.433313,0.435263,0.437047,0.438667,0.440126,0.441429,0.442577,0.443572,0.444415,0.445108,0.445652,0.446045,0.446286,0.446375,0.446307,0.446081,0.44569,0.445129,0.444392,0.44347,0.442354,0.441033,0.439495,0.437725,0.435707,0.433423,0.430854,0.427975,0.424764,0.421191,0.417226,0.412836,0.407983,0.402627,0.396723,0.390224,0.383074,0.375218,0.366591,0.357128,0.346753,0.335389,0.322952,0.309349,0.294486,0.27826,0.260564,0.241285,0.220306,0.197509,0.172771,0.145971,0.116993,0.085725},
{-2.33268,-2.30647,-2.28025,-2.25401,-2.22776,-2.20149,-2.1752,-2.1489,-2.12258,-2.09624,-2.06989,-2.04351,-2.01712,-1.99071,-1.96428,-1.93784,-1.91137,-1.88488,-1.85838,-1.83185,-1.80531,-1.77874,-1.75216,-1.72555,-1.69893,-1.67228,-1.64561,-1.61893,-1.59222,-1.5655,-1.53875,-1.51199,-1.4852,-1.45841,-1.43159,-1.40476,-1.37791,-1.35106,-1.32419,-1.29731,-1.27042,-1.24353,-1.21663,-1.18974,-1.16285,-1.13597,-1.10909,-1.08223,-1.0554,-1.02858,-1.0018,-0.97505,-0.948345,-0.921689,-0.895091,-0.868557,-0.842097,-0.815718,-0.789432,-0.763246,-0.737173,-0.711222,-0.685404,-0.659731,-0.634214,-0.608865,-0.583697,-0.55872,-0.533948,-0.509393,-0.485066,-0.460979,-0.437144,-0.413572,-0.390274,-0.36726,-0.344541,-0.322126,-0.300023,-0.278241,-0.256787,-0.235667,-0.214889,-0.194458,-0.174377,-0.154651,-0.135283,-0.116275,-0.0976291,-0.0793463,-0.061427,-0.0438709,-0.0266772,-0.00984482,0.00662811,0.0227437,0.0385045,0.0539134,0.0689734,0.083688,0.0980606,0.112095,0.125795,0.139164,0.152206,0.164926,0.177326,0.18941,0.201183,0.212648,0.223807,0.234665,0.245224,0.255488,0.265459,0.275141,0.284536,0.293646,0.302475,0.311024,0.319296,0.327294,0.335021,0.342477,0.349667,0.356592,0.363256,0.369661,0.37581,0.381707,0.387354,0.392755,0.397914,0.402834,0.407519,0.411974,0.416202,0.420208,0.423996,0.427571,0.430938,0.434101,0.437065,0.439835,0.442415,0.444809,0.447023,0.449061,0.450925,0.452621,0.454152,0.455521,0.456729,0.457781,0.458677,0.459419,0.460007,0.46044,0.46072,0.460842,0.460806,0.460608,0.460243,0.459706,0.45899,0.458088,0.456989,0.455683,0.454159,0.452401,0.450394,0.448121,0.44556,0.44269,0.439486,0.435921,0.431964,0.427582,0.422737,0.41739,0.411497,0.405008,0.397872,0.390031,0.381423,0.371981,0.361632,0.350297,0.337893,0.324331,0.309513,0.29334,0.275704,0.256493,0.235591,0.212878,0.188234,0.161537,0.132668,0.101517},
{-2.3591,-2.33289,-2.30667,-2.28042,-2.25416,-2.22789,-2.20159,-2.17528,-2.14895,-2.1226,-2.09623,-2.06985,-2.04344,-2.01701,-1.99057,-1.9641,-1.93762,-1.91111,-1.88458,-1.85803,-1.83146,-1.80487,-1.77825,-1.75161,-1.72495,-1.69827,-1.67156,-1.64483,-1.61808,-1.59131,-1.56451,-1.53769,-1.51085,-1.48399,-1.45711,-1.43021,-1.40329,-1.37635,-1.3494,-1.32243,-1.29545,-1.26846,-1.24146,-1.21446,-1.18745,-1.16043,-1.13343,-1.10643,-1.07944,-1.05246,-1.02551,-0.998579,-0.971683,-0.944825,-0.918012,-0.891252,-0.864553,-0.837923,-0.81137,-0.784905,-0.758537,-0.732277,-0.706134,-0.680121,-0.654248,-0.628528,-0.602972,-0.577591,-0.5524,-0.527409,-0.502631,-0.478078,-0.453762,-0.429695,-0.405888,-0.382352,-0.359098,-0.336136,-0.313475,-0.291125,-0.269095,-0.247391,-0.226021,-0.204991,-0.184307,-0.163973,-0.143995,-0.124374,-0.105115,-0.0862181,-0.0676858,-0.0495185,-0.0317163,-0.014279,0.00279452,0.0195056,0.0358559,0.0518478,0.0674836,0.0827661,0.0976984,0.112284,0.126525,0.140426,0.15399,0.167221,0.180122,0.192696,0.204948,0.216879,0.228494,0.239797,0.250788,0.261473,0.271853,0.281932,0.291712,0.301196,0.310386,0.319285,0.327896,0.33622,0.344261,0.352022,0.359503,0.36671,0.373644,0.380308,0.386706,0.392841,0.398715,0.404334,0.4097,0.414818,0.419692,0.424326,0.428724,0.432891,0.436832,0.440552,0.444055,0.447347,0.450432,0.453316,0.456003,0.458498,0.460805,0.46293,0.464877,0.466649,0.46825,0.469684,0.470953,0.47206,0.473007,0.473795,0.474426,0.474898,0.475212,0.475366,0.475358,0.475184,0.474841,0.474322,0.473622,0.472732,0.471644,0.470347,0.468828,0.467073,0.465068,0.462793,0.46023,0.457355,0.454145,0.450572,0.446605,0.442212,0.437356,0.431995,0.426088,0.419584,0.412433,0.404576,0.395952,0.386494,0.37613,0.364781,0.352364,0.33879,0.323963,0.307783,0.290143,0.270931,0.250032,0.227327,0.202693,0.17601,0.14716,0.116029},
{-2.38485,-2.35864,-2.33241,-2.30616,-2.27989,-2.25361,-2.2273,-2.20098,-2.17464,-2.14828,-2.12191,-2.09551,-2.06909,-2.04265,-2.01619,-1.9897,-1.9632,-1.93667,-1.91012,-1.88355,-1.85695,-1.83033,-1.80369,-1.77702,-1.75033,-1.72361,-1.69686,-1.6701,-1.6433,-1.61648,-1.58964,-1.56277,-1.53588,-1.50896,-1.48202,-1.45505,-1.42806,-1.40105,-1.37402,-1.34697,-1.3199,-1.29282,-1.26572,-1.23861,-1.21149,-1.18436,-1.15722,-1.13009,-1.10296,-1.07583,-1.04872,-1.02162,-0.994545,-0.967498,-0.940484,-0.913512,-0.886589,-0.859721,-0.832919,-0.80619,-0.779545,-0.752992,-0.726543,-0.700208,-0.673998,-0.647925,-0.622,-0.596236,-0.570645,-0.545238,-0.520029,-0.495029,-0.470251,-0.445708,-0.42141,-0.39737,-0.373599,-0.350107,-0.326906,-0.304004,-0.281412,-0.259137,-0.237188,-0.215572,-0.194295,-0.173364,-0.152784,-0.132559,-0.112693,-0.0931885,-0.0740483,-0.055274,-0.0368666,-0.0188266,-0.00115403,0.0161517,0.0330917,0.0496674,0.0658805,0.0817332,0.0972278,0.112367,0.127154,0.141591,0.155681,0.169428,0.182835,0.195905,0.20864,0.221045,0.233122,0.244875,0.256305,0.267417,0.278213,0.288695,0.298866,0.30873,0.318288,0.327543,0.336497,0.345154,0.353516,0.361586,0.369365,0.376858,0.384068,0.390996,0.397648,0.404025,0.410133,0.415973,0.421552,0.426872,0.431938,0.436755,0.441327,0.44566,0.449758,0.453626,0.457269,0.460693,0.463903,0.466904,0.469701,0.4723,0.474705,0.476921,0.478953,0.480804,0.482479,0.483982,0.485315,0.486482,0.487484,0.488323,0.489001,0.489517,0.489871,0.490062,0.490087,0.489945,0.48963,0.489137,0.488461,0.487593,0.486525,0.485246,0.483744,0.482005,0.480014,0.477754,0.475204,0.472342,0.469145,0.465585,0.461632,0.457253,0.452411,0.447068,0.441178,0.434696,0.427567,0.419737,0.411144,0.40172,0.391395,0.380092,0.367727,0.354211,0.339451,0.323346,0.30579,0.286672,0.265878,0.243289,0.218782,0.192237,0.163536,0.132564},
{-2.40994,-2.38373,-2.35749,-2.33124,-2.30497,-2.27868,-2.25237,-2.22604,-2.1997,-2.17333,-2.14694,-2.12053,-2.0941,-2.06764,-2.04117,-2.01467,-1.98815,-1.9616,-1.93503,-1.90844,-1.88182,-1.85517,-1.8285,-1.80181,-1.77508,-1.74833,-1.72156,-1.69475,-1.66792,-1.64106,-1.61417,-1.58725,-1.56031,-1.53334,-1.50634,-1.47931,-1.45226,-1.42518,-1.39808,-1.37095,-1.3438,-1.31663,-1.28943,-1.26222,-1.235,-1.20775,-1.1805,-1.15324,-1.12598,-1.09871,-1.07145,-1.04419,-1.01695,-0.989722,-0.96252,-0.935349,-0.908214,-0.881124,-0.854086,-0.827108,-0.800201,-0.773372,-0.746633,-0.719994,-0.693464,-0.667056,-0.640781,-0.614652,-0.588679,-0.562875,-0.537254,-0.511826,-0.486606,-0.461604,-0.436834,-0.412308,-0.388037,-0.364032,-0.340306,-0.316868,-0.293728,-0.270896,-0.248382,-0.226192,-0.204334,-0.182817,-0.161645,-0.140823,-0.120358,-0.100253,-0.0805104,-0.0611338,-0.0421251,-0.0234856,-0.00521617,0.0126829,0.0302119,0.0473714,0.0641626,0.0805868,0.0966458,0.112342,0.127677,0.142653,0.157274,0.171541,0.185459,0.199028,0.212253,0.225137,0.237681,0.249889,0.261764,0.273309,0.284525,0.295417,0.305985,0.316234,0.326165,0.335781,0.345086,0.35408,0.362768,0.371152,0.379234,0.387018,0.394507,0.401705,0.408614,0.415238,0.421581,0.427647,0.433441,0.438966,0.444228,0.44923,0.453979,0.458479,0.462735,0.466752,0.470537,0.474094,0.47743,0.480548,0.483456,0.486158,0.48866,0.490966,0.493082,0.495011,0.496759,0.498328,0.499723,0.500946,0.502,0.502886,0.503606,0.50416,0.504548,0.50477,0.504822,0.504702,0.504407,0.503931,0.503267,0.502409,0.501348,0.500073,0.498573,0.496833,0.494838,0.49257,0.490011,0.487138,0.483927,0.48035,0.476378,0.471978,0.467113,0.461744,0.455827,0.449315,0.442156,0.434293,0.425665,0.416206,0.405845,0.394504,0.382101,0.368547,0.353749,0.337606,0.320013,0.30086,0.280031,0.257409,0.232871,0.206297,0.177568,0.146569},
{-2.43442,-2.4082,-2.38197,-2.35571,-2.32944,-2.30314,-2.27683,-2.25049,-2.22414,-2.19776,-2.17136,-2.14494,-2.1185,-2.09203,-2.06554,-2.03903,-2.01249,-1.98593,-1.95934,-1.93273,-1.90609,-1.87942,-1.85273,-1.826,-1.79925,-1.77247,-1.74566,-1.71882,-1.69195,-1.66505,-1.63812,-1.61116,-1.58417,-1.55715,-1.5301,-1.50301,-1.4759,-1.44876,-1.42159,-1.39439,-1.36716,-1.3399,-1.31262,-1.28532,-1.25799,-1.23065,-1.20328,-1.17591,-1.14852,-1.12112,-1.09371,-1.06631,-1.03891,-1.01151,-0.984133,-0.956773,-0.929439,-0.902138,-0.874878,-0.847666,-0.82051,-0.793421,-0.766407,-0.739479,-0.712646,-0.68592,-0.659312,-0.632834,-0.606498,-0.580315,-0.554299,-0.528462,-0.502816,-0.477374,-0.452149,-0.427153,-0.402399,-0.377899,-0.353663,-0.329704,-0.306031,-0.282657,-0.259589,-0.236838,-0.214411,-0.192317,-0.170563,-0.149154,-0.128098,-0.107398,-0.0870599,-0.0670862,-0.0474804,-0.0282447,-0.00938089,0.00910987,0.0272269,0.0449702,0.0623399,0.0793369,0.0959621,0.112217,0.128103,0.143623,0.158777,0.17357,0.188002,0.202077,0.215796,0.229163,0.24218,0.25485,0.267176,0.279159,0.290802,0.302108,0.31308,0.32372,0.334031,0.344014,0.353674,0.363012,0.372031,0.380735,0.389125,0.397206,0.40498,0.412451,0.419622,0.426498,0.433082,0.439378,0.445391,0.451126,0.456587,0.461779,0.466708,0.471378,0.475796,0.479967,0.483896,0.48759,0.491054,0.494294,0.497315,0.500124,0.502725,0.505125,0.507327,0.509337,0.51116,0.512799,0.514258,0.515541,0.516649,0.517586,0.518352,0.518948,0.519375,0.51963,0.519713,0.519621,0.519351,0.518896,0.518252,0.51741,0.516363,0.515099,0.513608,0.511875,0.509885,0.507621,0.505064,0.502191,0.498979,0.4954,0.491425,0.487022,0.482153,0.476779,0.470858,0.464341,0.457177,0.449311,0.440681,0.431222,0.420862,0.409525,0.397128,0.383585,0.368801,0.352677,0.335109,0.315986,0.295194,0.272614,0.248126,0.22161,0.192944,0.162015},
{-2.45831,-2.43209,-2.40585,-2.37959,-2.35332,-2.32702,-2.3007,-2.27436,-2.24799,-2.22161,-2.1952,-2.16877,-2.14232,-2.11584,-2.08934,-2.06282,-2.03626,-2.00969,-1.98308,-1.95645,-1.92979,-1.9031,-1.87638,-1.84964,-1.82286,-1.79605,-1.76921,-1.74234,-1.71544,-1.6885,-1.66153,-1.63453,-1.6075,-1.58043,-1.55332,-1.52619,-1.49902,-1.47181,-1.44458,-1.41731,-1.39001,-1.36267,-1.33531,-1.30792,-1.2805,-1.25306,-1.22559,-1.1981,-1.17059,-1.14307,-1.11553,-1.08798,-1.06043,-1.03288,-1.00533,-0.977796,-0.950275,-0.922775,-0.895304,-0.86787,-0.840481,-0.813145,-0.78587,-0.758668,-0.731547,-0.704519,-0.677594,-0.650784,-0.624101,-0.597556,-0.571162,-0.544931,-0.518878,-0.493013,-0.46735,-0.441902,-0.416681,-0.3917,-0.36697,-0.342505,-0.318315,-0.294411,-0.270804,-0.247504,-0.224519,-0.20186,-0.179533,-0.157547,-0.135908,-0.114621,-0.0936934,-0.0731283,-0.0529302,-0.0331023,-0.0136473,0.00543282,0.0241364,0.0424626,0.0604107,0.0779809,0.0951734,0.111989,0.128429,0.144494,0.160186,0.175506,0.190458,0.205042,0.21926,0.233116,0.246611,0.259747,0.272528,0.284955,0.297031,0.308758,0.320138,0.331175,0.34187,0.352226,0.362246,0.371933,0.381288,0.390316,0.399019,0.407401,0.415464,0.423213,0.430651,0.437782,0.44461,0.451139,0.457375,0.463322,0.468985,0.474369,0.47948,0.484323,0.488904,0.493229,0.497304,0.501135,0.504728,0.508088,0.511223,0.514138,0.516838,0.519329,0.521616,0.523705,0.525601,0.527306,0.528826,0.530164,0.531323,0.532305,0.533111,0.533742,0.534199,0.534481,0.534587,0.534512,0.534255,0.53381,0.533171,0.532331,0.531282,0.530012,0.528511,0.526764,0.524757,0.522472,0.519889,0.516987,0.513741,0.510124,0.506107,0.501656,0.496737,0.491307,0.485326,0.478744,0.471511,0.46357,0.45486,0.445315,0.434865,0.423433,0.410936,0.397286,0.382391,0.366151,0.348461,0.329212,0.308289,0.285574,0.260946,0.234285,0.205471,0.174388},
{-2.48164,-2.45542,-2.42918,-2.40292,-2.37664,-2.35033,-2.32401,-2.29766,-2.2713,-2.2449,-2.21849,-2.19205,-2.16559,-2.1391,-2.11259,-2.08605,-2.05949,-2.0329,-2.00628,-1.97963,-1.95295,-1.92624,-1.8995,-1.87273,-1.84593,-1.8191,-1.79223,-1.76533,-1.73839,-1.71142,-1.68442,-1.65738,-1.6303,-1.60319,-1.57604,-1.54885,-1.52162,-1.49436,-1.46707,-1.43973,-1.41236,-1.38496,-1.35752,-1.33004,-1.30254,-1.275,-1.24743,-1.21984,-1.19222,-1.16458,-1.13692,-1.10924,-1.08154,-1.05384,-1.02614,-0.998431,-0.970732,-0.943044,-0.915374,-0.88773,-0.860118,-0.832547,-0.805026,-0.777563,-0.750169,-0.722853,-0.695626,-0.668499,-0.641484,-0.614593,-0.587837,-0.56123,-0.534784,-0.508513,-0.482428,-0.456543,-0.430871,-0.405425,-0.380218,-0.355261,-0.330567,-0.306147,-0.282014,-0.258177,-0.234646,-0.211432,-0.188543,-0.165988,-0.143774,-0.121909,-0.100398,-0.0792475,-0.058462,-0.0380459,-0.0180029,0.00166401,0.0209524,0.0398605,0.058387,0.0765308,0.0942918,0.11167,0.128665,0.145279,0.161511,0.177364,0.192838,0.207936,0.222658,0.237007,0.250985,0.264594,0.277836,0.290712,0.303226,0.31538,0.327175,0.338614,0.3497,0.360434,0.370821,0.380862,0.39056,0.399918,0.408939,0.417627,0.425985,0.434017,0.441726,0.449117,0.456195,0.462962,0.469425,0.475589,0.481458,0.487038,0.492336,0.497356,0.502104,0.506588,0.510812,0.514784,0.51851,0.521995,0.525247,0.528271,0.531074,0.533661,0.536037,0.538209,0.540181,0.541958,0.543543,0.544941,0.546155,0.547187,0.548039,0.548712,0.549206,0.549521,0.549655,0.549606,0.549371,0.548945,0.548321,0.547494,0.546454,0.54519,0.543693,0.541947,0.539939,0.537649,0.53506,0.53215,0.528893,0.525264,0.521232,0.516765,0.511827,0.506378,0.500375,0.493771,0.486514,0.478549,0.469814,0.460245,0.44977,0.438313,0.425792,0.41212,0.397204,0.380945,0.363239,0.343976,0.323043,0.300322,0.275692,0.249033,0.220225,0.189152},
{-2.50443,-2.47821,-2.45197,-2.42571,-2.39942,-2.37312,-2.34679,-2.32044,-2.29407,-2.26767,-2.24125,-2.2148,-2.18833,-2.16184,-2.13532,-2.10877,-2.08219,-2.05558,-2.02895,-2.00228,-1.97559,-1.94886,-1.9221,-1.89531,-1.86849,-1.84163,-1.81474,-1.78781,-1.76084,-1.73384,-1.7068,-1.67972,-1.65261,-1.62545,-1.59826,-1.57102,-1.54375,-1.51643,-1.48908,-1.46169,-1.43425,-1.40678,-1.37926,-1.35171,-1.32412,-1.2965,-1.26884,-1.24114,-1.21342,-1.18566,-1.15788,-1.13008,-1.10225,-1.07441,-1.04655,-1.01869,-0.990821,-0.962955,-0.935096,-0.907253,-0.87943,-0.851637,-0.823881,-0.79617,-0.768515,-0.740925,-0.71341,-0.685981,-0.658649,-0.631426,-0.604325,-0.577356,-0.550534,-0.523871,-0.49738,-0.471074,-0.444967,-0.419071,-0.393399,-0.367966,-0.342782,-0.317861,-0.293213,-0.268852,-0.244787,-0.22103,-0.197589,-0.174475,-0.151695,-0.129258,-0.107172,-0.0854419,-0.0640745,-0.043075,-0.022448,-0.00219729,0.0176736,0.0371621,0.0562658,0.0749832,0.093313,0.111254,0.128807,0.145971,0.162747,0.179134,0.195135,0.21075,0.225981,0.240828,0.255293,0.269379,0.283087,0.296418,0.309375,0.32196,0.334175,0.346022,0.357504,0.368622,0.37938,0.389781,0.399826,0.409519,0.418864,0.427863,0.43652,0.444839,0.452824,0.460479,0.467808,0.474817,0.481511,0.487894,0.493973,0.499752,0.505238,0.510436,0.515354,0.519998,0.524373,0.528487,0.532346,0.535956,0.539325,0.542459,0.545363,0.548045,0.550509,0.552762,0.554809,0.556654,0.558302,0.559757,0.561022,0.5621,0.562992,0.563701,0.564226,0.564567,0.564723,0.564691,0.564469,0.564051,0.563431,0.562604,0.561559,0.560288,0.558777,0.557015,0.554985,0.552671,0.550052,0.547107,0.543812,0.54014,0.53606,0.53154,0.526545,0.521033,0.514962,0.508285,0.500949,0.492899,0.484074,0.474408,0.463831,0.452266,0.439631,0.425839,0.410797,0.394405,0.376561,0.357154,0.336071,0.313194,0.288404,0.261579,0.232599,0.20135},
{-2.52671,-2.50049,-2.47425,-2.44798,-2.4217,-2.39539,-2.36906,-2.34271,-2.31633,-2.28993,-2.2635,-2.23705,-2.21057,-2.18407,-2.15754,-2.13098,-2.10439,-2.07777,-2.05112,-2.02444,-1.99773,-1.97099,-1.94421,-1.9174,-1.89056,-1.86368,-1.83676,-1.8098,-1.78281,-1.75578,-1.72871,-1.70159,-1.67444,-1.64725,-1.62001,-1.59273,-1.56541,-1.53804,-1.51064,-1.48318,-1.45569,-1.42815,-1.40057,-1.37294,-1.34527,-1.31756,-1.28982,-1.26203,-1.2342,-1.20634,-1.17845,-1.15052,-1.12257,-1.0946,-1.0666,-1.03858,-1.01055,-0.982517,-0.95448,-0.926446,-0.898424,-0.870418,-0.842439,-0.814493,-0.786589,-0.758737,-0.730947,-0.703229,-0.675595,-0.648055,-0.620621,-0.593306,-0.566122,-0.539082,-0.5122,-0.485487,-0.458959,-0.432628,-0.406507,-0.38061,-0.35495,-0.32954,-0.304392,-0.279518,-0.254931,-0.230641,-0.206658,-0.182994,-0.159658,-0.136658,-0.114002,-0.0916996,-0.0697559,-0.0481777,-0.0269705,-0.00613926,0.0143118,0.0343789,0.0540591,0.0733497,0.0922488,0.110755,0.128866,0.146583,0.163904,0.18083,0.197361,0.213498,0.22924,0.24459,0.259548,0.274116,0.288295,0.302086,0.315492,0.328515,0.341155,0.353416,0.3653,0.376808,0.387943,0.398709,0.409107,0.419141,0.428815,0.43813,0.447092,0.455704,0.463969,0.471894,0.479481,0.486737,0.493666,0.500273,0.506566,0.512548,0.518227,0.523609,0.528701,0.533508,0.538039,0.542299,0.546295,0.550035,0.553526,0.556773,0.559784,0.562565,0.565122,0.567461,0.569587,0.571506,0.573222,0.574739,0.576061,0.577191,0.57813,0.578882,0.579445,0.57982,0.580006,0.580001,0.579801,0.579403,0.578799,0.577984,0.576949,0.575685,0.574178,0.572417,0.570386,0.568068,0.565443,0.562489,0.559183,0.555498,0.551404,0.546868,0.541854,0.536322,0.53023,0.523531,0.516172,0.508098,0.499249,0.489559,0.478958,0.46737,0.454712,0.4409,0.425839,0.409431,0.391573,0.372157,0.351068,0.328189,0.303402,0.276585,0.247618,0.216386},
{-2.5485,-2.52228,-2.49604,-2.46977,-2.44349,-2.41718,-2.39085,-2.36449,-2.33811,-2.3117,-2.28527,-2.25881,-2.23233,-2.20582,-2.17928,-2.15271,-2.12611,-2.09948,-2.07282,-2.04613,-2.0194,-1.99264,-1.96585,-1.93902,-1.91215,-1.88525,-1.85831,-1.83133,-1.80431,-1.77725,-1.75015,-1.72301,-1.69582,-1.66859,-1.64131,-1.61399,-1.58662,-1.55921,-1.53175,-1.50424,-1.47669,-1.44909,-1.42144,-1.39375,-1.36601,-1.33822,-1.31039,-1.28251,-1.25459,-1.22663,-1.19863,-1.17059,-1.14252,-1.11441,-1.08628,-1.05812,-1.02994,-1.00174,-0.973534,-0.945321,-0.917107,-0.8889,-0.860708,-0.832537,-0.804396,-0.776295,-0.748242,-0.720248,-0.692324,-0.66448,-0.636728,-0.60908,-0.581548,-0.554146,-0.526886,-0.499782,-0.472847,-0.446095,-0.419539,-0.393192,-0.36707,-0.341184,-0.315547,-0.290174,-0.265075,-0.240263,-0.21575,-0.191545,-0.167661,-0.144106,-0.12089,-0.098021,-0.0755071,-0.0533556,-0.0315728,-0.0101648,0.0108633,0.0315068,0.0517617,0.0716246,0.0910926,0.110163,0.128835,0.147106,0.164975,0.182441,0.199505,0.216166,0.232424,0.24828,0.263735,0.278789,0.293444,0.307701,0.32156,0.335025,0.348096,0.360776,0.373066,0.384969,0.396487,0.407622,0.418378,0.428758,0.438764,0.448401,0.457672,0.46658,0.47513,0.483328,0.491176,0.498682,0.505849,0.512684,0.519192,0.52538,0.531255,0.536822,0.542088,0.547061,0.551747,0.556154,0.560288,0.564157,0.567768,0.571128,0.574244,0.577122,0.579769,0.582191,0.584394,0.586383,0.588162,0.589737,0.59111,0.592286,0.593266,0.594052,0.594645,0.595045,0.595251,0.595261,0.595071,0.594678,0.594075,0.593256,0.592213,0.590935,0.58941,0.587626,0.585568,0.583217,0.580554,0.577558,0.574204,0.570466,0.566312,0.561711,0.556626,0.551018,0.544843,0.538053,0.530598,0.52242,0.51346,0.503652,0.492925,0.481202,0.468403,0.454441,0.439222,0.422648,0.404616,0.385017,0.363737,0.34066,0.315666,0.288635,0.259446,0.227985},
{-2.56982,-2.5436,-2.51736,-2.4911,-2.46481,-2.4385,-2.41216,-2.3858,-2.35942,-2.33301,-2.30657,-2.28011,-2.25362,-2.2271,-2.20055,-2.17398,-2.14737,-2.12073,-2.09406,-2.06735,-2.04061,-2.01384,-1.98703,-1.96019,-1.9333,-1.90638,-1.87942,-1.85242,-1.82537,-1.79828,-1.77115,-1.74398,-1.71676,-1.68949,-1.66218,-1.63482,-1.60741,-1.57995,-1.55244,-1.52489,-1.49728,-1.46962,-1.44191,-1.41415,-1.38633,-1.35847,-1.33056,-1.3026,-1.27459,-1.24653,-1.21843,-1.19028,-1.1621,-1.13387,-1.10561,-1.07731,-1.04899,-1.02064,-0.992268,-0.963883,-0.935487,-0.907088,-0.878692,-0.850307,-0.82194,-0.7936,-0.765296,-0.737038,-0.708836,-0.6807,-0.652642,-0.624675,-0.596809,-0.569058,-0.541434,-0.513951,-0.486623,-0.459463,-0.432485,-0.405702,-0.37913,-0.352781,-0.326668,-0.300806,-0.275208,-0.249885,-0.22485,-0.200116,-0.175692,-0.151591,-0.127821,-0.104392,-0.0813143,-0.0585946,-0.0362407,-0.0142596,0.00734262,0.0285603,0.0493885,0.0698229,0.0898597,0.109496,0.128728,0.147555,0.165974,0.183983,0.201583,0.218772,0.235551,0.251918,0.267874,0.283419,0.298555,0.313282,0.327601,0.341513,0.355021,0.368125,0.380828,0.393132,0.405038,0.41655,0.42767,0.438401,0.448746,0.45871,0.468295,0.477506,0.486347,0.494823,0.502938,0.510699,0.51811,0.525177,0.531907,0.538306,0.544381,0.550138,0.555585,0.560728,0.565575,0.570134,0.574411,0.578415,0.582152,0.585631,0.588857,0.591839,0.594582,0.597094,0.59938,0.601445,0.603296,0.604936,0.60637,0.6076,0.60863,0.609462,0.610096,0.610533,0.610772,0.61081,0.610646,0.610275,0.609691,0.608887,0.607856,0.606588,0.605071,0.603292,0.601236,0.598885,0.596221,0.593221,0.589861,0.586115,0.581954,0.577343,0.572247,0.566628,0.56044,0.553638,0.546171,0.537981,0.52901,0.519192,0.508456,0.496728,0.483925,0.469962,0.454746,0.438181,0.420161,0.400581,0.379326,0.35628,0.331325,0.304339,0.275204,0.243802},
{-2.59069,-2.56447,-2.53823,-2.51197,-2.48568,-2.45937,-2.43303,-2.40667,-2.38029,-2.35387,-2.32743,-2.30097,-2.27447,-2.24795,-2.22139,-2.19481,-2.16819,-2.14154,-2.11486,-2.08814,-2.06139,-2.0346,-2.00778,-1.98092,-1.95402,-1.92708,-1.90009,-1.87307,-1.846,-1.81889,-1.79173,-1.76453,-1.73728,-1.70998,-1.68263,-1.65523,-1.62779,-1.60028,-1.57273,-1.54512,-1.51746,-1.48975,-1.46198,-1.43416,-1.40628,-1.37834,-1.35036,-1.32231,-1.29422,-1.26607,-1.23787,-1.20962,-1.18133,-1.15299,-1.1246,-1.09618,-1.06771,-1.03922,-1.01069,-0.982142,-0.953573,-0.924991,-0.896401,-0.867811,-0.839227,-0.810659,-0.782115,-0.753604,-0.725135,-0.69672,-0.668369,-0.640094,-0.611906,-0.583819,-0.555845,-0.527997,-0.500289,-0.472734,-0.445347,-0.418142,-0.391132,-0.364332,-0.337756,-0.311418,-0.285331,-0.259508,-0.233963,-0.208708,-0.183754,-0.159115,-0.1348,-0.110819,-0.0871836,-0.0639016,-0.0409819,-0.0184322,0.00374033,0.025529,0.0469281,0.0679322,0.0885367,0.108737,0.128531,0.147914,0.166884,0.185439,0.203577,0.221296,0.238597,0.255478,0.271939,0.287979,0.3036,0.318801,0.333584,0.347949,0.361897,0.375431,0.38855,0.401259,0.413558,0.42545,0.436938,0.448025,0.458714,0.469008,0.478911,0.488428,0.497563,0.50632,0.514705,0.522723,0.53038,0.537682,0.544635,0.551246,0.557521,0.563469,0.569096,0.574409,0.579416,0.584125,0.588544,0.59268,0.596541,0.600134,0.603468,0.606548,0.609382,0.611978,0.61434,0.616475,0.618388,0.620084,0.621567,0.622841,0.623908,0.624771,0.62543,0.625887,0.626139,0.626186,0.626025,0.625651,0.625058,0.624241,0.62319,0.621896,0.620348,0.618531,0.616431,0.61403,0.611309,0.608246,0.604816,0.600992,0.596744,0.592039,0.586841,0.581109,0.574801,0.567869,0.56026,0.551919,0.542786,0.532793,0.521872,0.509945,0.496931,0.482743,0.467289,0.45047,0.432184,0.412322,0.390771,0.367413,0.342132,0.314807,0.285317,0.253546},
{-2.61113,-2.58491,-2.55867,-2.53241,-2.50613,-2.47981,-2.45348,-2.42711,-2.40073,-2.37431,-2.34787,-2.3214,-2.29489,-2.26836,-2.2418,-2.21521,-2.18859,-2.16193,-2.13524,-2.10851,-2.08175,-2.05495,-2.02811,-2.00123,-1.97432,-1.94736,-1.92036,-1.89331,-1.86623,-1.83909,-1.81191,-1.78468,-1.7574,-1.73007,-1.70269,-1.67525,-1.64777,-1.62022,-1.59263,-1.56497,-1.53726,-1.5095,-1.48167,-1.45379,-1.42585,-1.39784,-1.36978,-1.34167,-1.31349,-1.28526,-1.25697,-1.22862,-1.20022,-1.17177,-1.14327,-1.11472,-1.08612,-1.05749,-1.02881,-1.00011,-0.971372,-0.942614,-0.913838,-0.885052,-0.856262,-0.827475,-0.7987,-0.769946,-0.741223,-0.712539,-0.683906,-0.655335,-0.626838,-0.598426,-0.570114,-0.541913,-0.513837,-0.4859,-0.458117,-0.430501,-0.403066,-0.375827,-0.348799,-0.321996,-0.295431,-0.269119,-0.243074,-0.217307,-0.191833,-0.166664,-0.141811,-0.117286,-0.0930986,-0.06926,-0.0457793,-0.0226652,7.41455e-05,0.0224312,0.044399,0.0659715,0.087143,0.107908,0.128263,0.148204,0.167727,0.186829,0.205507,0.223761,0.241588,0.258987,0.275956,0.292497,0.308607,0.324288,0.339539,0.354362,0.368757,0.382725,0.396268,0.409388,0.422085,0.434364,0.446226,0.457674,0.468712,0.479343,0.48957,0.499399,0.508833,0.517877,0.526537,0.534818,0.542727,0.550269,0.55745,0.564279,0.570761,0.576904,0.582716,0.588205,0.593378,0.598243,0.602808,0.607082,0.611072,0.614786,0.618232,0.621417,0.624349,0.627035,0.62948,0.631692,0.633675,0.635435,0.636976,0.638303,0.639417,0.640322,0.641018,0.641507,0.641786,0.641856,0.641713,0.641353,0.64077,0.639959,0.63891,0.637614,0.63606,0.634234,0.63212,0.629703,0.626961,0.623873,0.620415,0.61656,0.612277,0.607534,0.602294,0.596517,0.590161,0.583176,0.575512,0.567113,0.557918,0.547861,0.536872,0.524875,0.511789,0.497527,0.481997,0.465101,0.446737,0.426795,0.405165,0.381728,0.356368,0.328963,0.299395,0.267547},
{-2.63115,-2.60494,-2.5787,-2.55244,-2.52616,-2.49985,-2.47351,-2.44714,-2.42075,-2.39434,-2.36789,-2.34142,-2.31491,-2.28838,-2.26181,-2.23521,-2.20858,-2.18191,-2.15521,-2.12848,-2.1017,-2.07489,-2.04804,-2.02115,-1.99422,-1.96724,-1.94023,-1.91316,-1.88605,-1.8589,-1.83169,-1.80444,-1.77713,-1.74977,-1.72236,-1.69489,-1.66737,-1.63979,-1.61215,-1.58445,-1.55669,-1.52888,-1.501,-1.47306,-1.44506,-1.41699,-1.38886,-1.36067,-1.33242,-1.3041,-1.27572,-1.24728,-1.21878,-1.19023,-1.16161,-1.13294,-1.10422,-1.07546,-1.04664,-1.01779,-0.988892,-0.959966,-0.931013,-0.902039,-0.87305,-0.844054,-0.815058,-0.786071,-0.757102,-0.72816,-0.699256,-0.670401,-0.641605,-0.612881,-0.584242,-0.5557,-0.527269,-0.498963,-0.470795,-0.44278,-0.414932,-0.387267,-0.359798,-0.332541,-0.30551,-0.278719,-0.252183,-0.225916,-0.19993,-0.17424,-0.148857,-0.123794,-0.0990626,-0.0746736,-0.0506373,-0.0269636,-0.00366153,0.0192604,0.0417943,0.063933,0.08567,0.106999,0.127916,0.148414,0.16849,0.188141,0.207362,0.226152,0.244508,0.262427,0.279909,0.296953,0.313557,0.329722,0.345446,0.360731,0.375577,0.389985,0.403956,0.417491,0.430592,0.443262,0.455503,0.467318,0.478709,0.489681,0.500236,0.510381,0.520118,0.529453,0.538392,0.54694,0.555103,0.562888,0.5703,0.577349,0.58404,0.590381,0.59638,0.602045,0.607385,0.612407,0.61712,0.621531,0.62565,0.629485,0.633043,0.636331,0.639359,0.642133,0.644659,0.646944,0.648994,0.650814,0.65241,0.653783,0.654939,0.655879,0.656605,0.657118,0.657416,0.657499,0.657364,0.657006,0.656421,0.655601,0.654539,0.653225,0.651646,0.649791,0.647642,0.645184,0.642396,0.639256,0.63574,0.63182,0.627466,0.622645,0.61732,0.611452,0.604996,0.597904,0.590125,0.581603,0.572277,0.56208,0.550942,0.538786,0.525533,0.511094,0.495377,0.478285,0.459715,0.439558,0.417701,0.39403,0.368425,0.340767,0.310936,0.278816},
{-2.65078,-2.62457,-2.59833,-2.57207,-2.54579,-2.51948,-2.49314,-2.46678,-2.44039,-2.41397,-2.38752,-2.36104,-2.33453,-2.30799,-2.28142,-2.25482,-2.22818,-2.20151,-2.1748,-2.14805,-2.12127,-2.09445,-2.06759,-2.04068,-2.01374,-1.98675,-1.95971,-1.93263,-1.9055,-1.87833,-1.8511,-1.82382,-1.79649,-1.7691,-1.74166,-1.71416,-1.6866,-1.65898,-1.63131,-1.60357,-1.57577,-1.5479,-1.51997,-1.49198,-1.46392,-1.43579,-1.4076,-1.37934,-1.35101,-1.32261,-1.29415,-1.26562,-1.23703,-1.20837,-1.17965,-1.15087,-1.12203,-1.09313,-1.06418,-1.03518,-1.00614,-0.977053,-0.94793,-0.918776,-0.889597,-0.8604,-0.831192,-0.801981,-0.772776,-0.743586,-0.714421,-0.685291,-0.656208,-0.627183,-0.598228,-0.569357,-0.540582,-0.511917,-0.483376,-0.454974,-0.426725,-0.398644,-0.370747,-0.343047,-0.31556,-0.288301,-0.261284,-0.234525,-0.208037,-0.181833,-0.155929,-0.130336,-0.105066,-0.0801329,-0.0555465,-0.0313179,-0.00745717,0.0160262,0.0391235,0.0618265,0.0841276,0.10602,0.127497,0.148554,0.169185,0.189386,0.209152,0.22848,0.247368,0.265811,0.28381,0.30136,0.318463,0.335115,0.351318,0.36707,0.382372,0.397225,0.411629,0.425585,0.439095,0.452162,0.464787,0.476973,0.488723,0.500041,0.510931,0.521396,0.531442,0.541074,0.550296,0.559115,0.567538,0.57557,0.583219,0.590491,0.597395,0.603938,0.610129,0.615975,0.621485,0.626667,0.631531,0.636084,0.640336,0.644294,0.647967,0.651364,0.65449,0.657356,0.659966,0.662329,0.664449,0.666334,0.667986,0.669412,0.670613,0.671593,0.672354,0.672895,0.673218,0.673319,0.673198,0.672849,0.672268,0.671448,0.67038,0.669056,0.667463,0.665589,0.663417,0.66093,0.658109,0.654932,0.651373,0.647406,0.643,0.638122,0.632735,0.626799,0.62027,0.613101,0.60524,0.596629,0.587209,0.576913,0.56567,0.553405,0.540036,0.525477,0.509635,0.492413,0.473707,0.453411,0.431411,0.407592,0.381836,0.354023,0.324034,0.291753},
{-2.67002,-2.64381,-2.61758,-2.59133,-2.56504,-2.53873,-2.5124,-2.48603,-2.45964,-2.43322,-2.40677,-2.38029,-2.35378,-2.32724,-2.30066,-2.27405,-2.24741,-2.22073,-2.19401,-2.16726,-2.14047,-2.11363,-2.08676,-2.05985,-2.03289,-2.00588,-1.97883,-1.95174,-1.92459,-1.89739,-1.87014,-1.84284,-1.81548,-1.78807,-1.7606,-1.73307,-1.70548,-1.67783,-1.65012,-1.62234,-1.5945,-1.56659,-1.53861,-1.51056,-1.48245,-1.45426,-1.42601,-1.39768,-1.36928,-1.34081,-1.31227,-1.28365,-1.25497,-1.22622,-1.19739,-1.1685,-1.13955,-1.11053,-1.08145,-1.05232,-1.02312,-0.993884,-0.964597,-0.935271,-0.905909,-0.876519,-0.847107,-0.817682,-0.78825,-0.758821,-0.729405,-0.700011,-0.670651,-0.641335,-0.612075,-0.582885,-0.553777,-0.524765,-0.495863,-0.467085,-0.438446,-0.409961,-0.381645,-0.353513,-0.325581,-0.297864,-0.270377,-0.243136,-0.216154,-0.189447,-0.163029,-0.136913,-0.111113,-0.0856421,-0.0605114,-0.0357332,-0.0113185,0.0127224,0.0363796,0.0596441,0.0825072,0.104961,0.126999,0.148614,0.169799,0.190551,0.210863,0.230731,0.250152,0.269123,0.28764,0.305701,0.323305,0.340449,0.357133,0.373357,0.389119,0.404421,0.419262,0.433643,0.447567,0.461035,0.474048,0.48661,0.498723,0.510392,0.521619,0.532409,0.542766,0.552697,0.562206,0.571299,0.579984,0.588265,0.596151,0.60365,0.610768,0.617514,0.623896,0.629923,0.635604,0.640946,0.64596,0.650653,0.655035,0.659114,0.6629,0.666399,0.669621,0.672573,0.675263,0.677696,0.67988,0.681821,0.683522,0.684989,0.686225,0.687233,0.688015,0.688571,0.688901,0.689004,0.688877,0.688517,0.687917,0.687071,0.685972,0.684608,0.682968,0.681039,0.678805,0.676249,0.673349,0.670084,0.666429,0.662356,0.657834,0.65283,0.647306,0.641221,0.634531,0.627188,0.619139,0.610327,0.600691,0.590163,0.578673,0.566144,0.552494,0.537635,0.521475,0.503915,0.484852,0.464179,0.441781,0.417544,0.39135,0.363078,0.33261,0.299832},
{-2.68889,-2.66269,-2.63646,-2.61021,-2.58393,-2.55762,-2.53129,-2.50492,-2.47853,-2.45211,-2.42566,-2.39917,-2.37266,-2.34611,-2.31953,-2.29292,-2.26627,-2.23959,-2.21286,-2.1861,-2.1593,-2.13246,-2.10558,-2.07865,-2.05168,-2.02466,-1.9976,-1.97049,-1.94332,-1.91611,-1.88884,-1.86151,-1.83413,-1.8067,-1.7792,-1.75164,-1.72402,-1.69634,-1.66859,-1.64078,-1.61289,-1.58494,-1.55692,-1.52882,-1.50065,-1.47241,-1.4441,-1.41571,-1.38724,-1.3587,-1.33008,-1.30139,-1.27261,-1.24377,-1.21485,-1.18585,-1.15679,-1.12765,-1.09845,-1.06918,-1.03985,-1.01046,-0.981019,-0.951526,-0.921989,-0.892414,-0.862806,-0.833173,-0.803523,-0.773864,-0.744205,-0.714557,-0.684928,-0.655331,-0.625777,-0.596278,-0.566848,-0.537499,-0.508246,-0.479102,-0.450084,-0.421204,-0.39248,-0.363927,-0.335559,-0.307394,-0.279446,-0.251731,-0.224264,-0.197061,-0.170137,-0.143505,-0.117181,-0.0911775,-0.0655077,-0.0401842,-0.0152192,0.00937609,0.0335909,0.0574151,0.0808392,0.103854,0.126452,0.148626,0.170368,0.191672,0.212532,0.232944,0.252903,0.272404,0.291444,0.310021,0.328131,0.345772,0.362944,0.379645,0.395874,0.411631,0.426916,0.44173,0.456074,0.46995,0.483359,0.496304,0.508788,0.520815,0.532387,0.54351,0.554187,0.564425,0.574229,0.583605,0.592559,0.601099,0.609232,0.616965,0.624306,0.631265,0.637849,0.644066,0.649928,0.655441,0.660616,0.665461,0.669986,0.6742,0.678111,0.681729,0.685062,0.688117,0.690903,0.693427,0.695695,0.697713,0.699487,0.701021,0.70232,0.703386,0.704221,0.704827,0.705203,0.705349,0.705261,0.704937,0.704372,0.703558,0.702488,0.701153,0.699541,0.697638,0.69543,0.692899,0.690025,0.686786,0.683158,0.679113,0.674621,0.669648,0.664159,0.658113,0.651465,0.644169,0.636173,0.62742,0.617849,0.607396,0.595988,0.583552,0.570006,0.555263,0.539232,0.521816,0.502913,0.482416,0.460212,0.436188,0.410225,0.382204,0.352006,0.319515},
{-2.70741,-2.68122,-2.65499,-2.62874,-2.60246,-2.57616,-2.54982,-2.52346,-2.49707,-2.47064,-2.44419,-2.41771,-2.39119,-2.36464,-2.33806,-2.31144,-2.28479,-2.2581,-2.23137,-2.2046,-2.17779,-2.15095,-2.12405,-2.09712,-2.07013,-2.0431,-2.01603,-1.9889,-1.96172,-1.93448,-1.9072,-1.87985,-1.85245,-1.82499,-1.79747,-1.76989,-1.74224,-1.71452,-1.68674,-1.65889,-1.63097,-1.60297,-1.57491,-1.54677,-1.51855,-1.49026,-1.46188,-1.43343,-1.4049,-1.37629,-1.3476,-1.31883,-1.28997,-1.26104,-1.23202,-1.20293,-1.17376,-1.14451,-1.11519,-1.08579,-1.05633,-1.0268,-0.997205,-0.967553,-0.937847,-0.908093,-0.878297,-0.848465,-0.818605,-0.788724,-0.758832,-0.728937,-0.69905,-0.669181,-0.639342,-0.609545,-0.579802,-0.550127,-0.520533,-0.491035,-0.461647,-0.432385,-0.403264,-0.374299,-0.345506,-0.316902,-0.288503,-0.260324,-0.232382,-0.204692,-0.17727,-0.150131,-0.12329,-0.0967606,-0.0705581,-0.0446953,-0.0191852,0.00595983,0.0307281,0.0551086,0.0790908,0.102665,0.125822,0.148553,0.17085,0.192707,0.214116,0.235072,0.255569,0.275602,0.295168,0.314262,0.332881,0.351023,0.368685,0.385866,0.402565,0.418781,0.434514,0.449764,0.464532,0.478819,0.492627,0.505959,0.518817,0.531204,0.543124,0.554582,0.565581,0.576129,0.586229,0.595889,0.605114,0.613913,0.622292,0.63026,0.637824,0.644993,0.651777,0.658184,0.664223,0.669903,0.675235,0.680227,0.68489,0.689232,0.693262,0.69699,0.700424,0.703573,0.706444,0.709046,0.711383,0.713464,0.715294,0.716877,0.718218,0.719319,0.720184,0.720812,0.721205,0.721362,0.721279,0.720954,0.720381,0.719555,0.718466,0.717106,0.715462,0.713523,0.711271,0.708689,0.705759,0.702457,0.698758,0.694636,0.690059,0.684994,0.679404,0.673249,0.666484,0.659062,0.65093,0.642032,0.632307,0.621689,0.610107,0.597485,0.583742,0.568792,0.552543,0.534897,0.515753,0.495003,0.472534,0.448234,0.421984,0.393664,0.363157,0.330347},
{-2.72559,-2.6994,-2.67318,-2.64693,-2.62065,-2.59435,-2.56802,-2.54166,-2.51526,-2.48884,-2.46239,-2.4359,-2.40939,-2.38284,-2.35625,-2.32963,-2.30297,-2.27628,-2.24954,-2.22277,-2.19595,-2.1691,-2.14219,-2.11525,-2.08825,-2.06121,-2.03412,-2.00698,-1.97979,-1.95254,-1.92523,-1.89787,-1.87045,-1.84297,-1.81542,-1.78781,-1.76013,-1.73239,-1.70458,-1.67669,-1.64873,-1.6207,-1.59259,-1.56441,-1.53614,-1.5078,-1.47937,-1.45086,-1.42227,-1.39359,-1.36483,-1.33599,-1.30705,-1.27803,-1.24893,-1.21974,-1.19047,-1.16111,-1.13168,-1.10216,-1.07257,-1.0429,-1.01316,-0.983354,-0.953486,-0.92356,-0.893582,-0.863558,-0.833495,-0.8034,-0.773282,-0.74315,-0.713013,-0.682882,-0.652767,-0.622681,-0.592635,-0.562643,-0.532719,-0.502876,-0.473129,-0.443493,-0.413984,-0.384618,-0.35541,-0.326377,-0.297535,-0.268902,-0.240492,-0.212323,-0.184411,-0.156771,-0.12942,-0.102372,-0.0756421,-0.0492451,-0.0231944,0.00249657,0.0278152,0.0527493,0.0772876,0.101419,0.125134,0.148422,0.171276,0.193686,0.215646,0.237148,0.258186,0.278754,0.298848,0.318464,0.337596,0.356242,0.3744,0.392066,0.40924,0.42592,0.442106,0.457798,0.472995,0.4877,0.501913,0.515638,0.528875,0.541629,0.553904,0.565703,0.577031,0.587893,0.598296,0.608246,0.617749,0.626812,0.635444,0.643652,0.651445,0.658832,0.665821,0.672423,0.678646,0.6845,0.689995,0.695141,0.699948,0.704425,0.708581,0.712427,0.71597,0.71922,0.722185,0.724872,0.72729,0.729443,0.731339,0.732982,0.734377,0.735527,0.736435,0.737101,0.737527,0.737711,0.737652,0.737346,0.736789,0.735973,0.734891,0.733534,0.73189,0.729947,0.727687,0.725096,0.722151,0.718832,0.715114,0.710969,0.706367,0.701275,0.695655,0.689468,0.68267,0.675212,0.667044,0.658108,0.648344,0.637687,0.626066,0.613405,0.599624,0.584637,0.568353,0.550675,0.531501,0.510724,0.488235,0.463917,0.437654,0.409328,0.378818,0.346011},
{-2.74344,-2.71725,-2.69103,-2.66479,-2.63852,-2.61222,-2.58588,-2.55952,-2.53313,-2.50671,-2.48026,-2.45377,-2.42726,-2.4007,-2.37411,-2.34749,-2.32083,-2.29413,-2.26739,-2.24061,-2.21379,-2.18693,-2.16002,-2.13306,-2.10606,-2.07901,-2.0519,-2.02475,-1.99754,-1.97028,-1.94296,-1.91558,-1.88813,-1.86063,-1.83306,-1.80543,-1.77773,-1.74996,-1.72211,-1.69419,-1.6662,-1.63813,-1.60999,-1.58176,-1.55345,-1.52505,-1.49658,-1.46801,-1.43936,-1.41062,-1.38179,-1.35287,-1.32387,-1.29477,-1.26558,-1.2363,-1.20693,-1.17747,-1.14792,-1.11829,-1.08857,-1.05877,-1.02889,-0.998938,-0.968913,-0.938822,-0.908668,-0.878459,-0.848201,-0.817899,-0.787564,-0.757202,-0.726824,-0.696438,-0.666057,-0.635691,-0.605351,-0.575052,-0.544807,-0.514629,-0.484532,-0.454533,-0.424646,-0.394888,-0.365275,-0.335822,-0.306548,-0.277468,-0.248601,-0.219961,-0.191567,-0.163435,-0.13558,-0.10802,-0.0807696,-0.0538439,-0.0272579,-0.00102573,0.024839,0.0503234,0.0754148,0.100102,0.124373,0.148217,0.171626,0.19459,0.2171,0.239149,0.260729,0.281834,0.302459,0.322598,0.342246,0.3614,0.380056,0.398211,0.415864,0.433012,0.449655,0.465792,0.481423,0.49655,0.511172,0.525293,0.538914,0.552039,0.564671,0.576815,0.588475,0.599656,0.610364,0.620606,0.630389,0.63972,0.648606,0.657057,0.66508,0.672685,0.67988,0.686677,0.693084,0.699111,0.704769,0.710067,0.715016,0.719625,0.723904,0.727864,0.731512,0.734859,0.737912,0.740679,0.743169,0.745387,0.74734,0.749034,0.750472,0.751659,0.752596,0.753286,0.753729,0.753925,0.75387,0.753563,0.752998,0.752168,0.751067,0.749684,0.748008,0.746026,0.743722,0.741078,0.738076,0.734692,0.730902,0.726678,0.721989,0.716802,0.71108,0.704782,0.697864,0.690279,0.681973,0.67289,0.66297,0.652147,0.64035,0.627503,0.613525,0.59833,0.581827,0.563919,0.544504,0.523476,0.500723,0.476131,0.449583,0.42096,0.390145,0.357021},
{-2.76097,-2.73479,-2.70857,-2.68233,-2.65606,-2.62976,-2.60344,-2.57708,-2.55069,-2.52427,-2.49781,-2.47133,-2.44481,-2.41826,-2.39167,-2.36504,-2.33837,-2.31167,-2.28493,-2.25814,-2.23132,-2.20445,-2.17753,-2.15057,-2.12355,-2.09649,-2.06938,-2.04221,-2.01499,-1.98771,-1.96038,-1.93298,-1.90552,-1.878,-1.85041,-1.82275,-1.79502,-1.76723,-1.73935,-1.71141,-1.68338,-1.65528,-1.62709,-1.59882,-1.57047,-1.54203,-1.5135,-1.48489,-1.45618,-1.42738,-1.39849,-1.3695,-1.34042,-1.31124,-1.28197,-1.2526,-1.22314,-1.19358,-1.16392,-1.13418,-1.10434,-1.07442,-1.0444,-1.01431,-0.984133,-0.953881,-0.923559,-0.893171,-0.862723,-0.832223,-0.801677,-0.771093,-0.740481,-0.70985,-0.679209,-0.648572,-0.617948,-0.58735,-0.556793,-0.526288,-0.495852,-0.465498,-0.435243,-0.405102,-0.375092,-0.345229,-0.315531,-0.286014,-0.256696,-0.227594,-0.198726,-0.170108,-0.141757,-0.113691,-0.0859254,-0.0584765,-0.0313598,-0.00459042,0.021817,0.0478486,0.0734908,0.0987311,0.123557,0.147958,0.171922,0.195439,0.218501,0.241098,0.263223,0.284868,0.306026,0.326692,0.34686,0.366526,0.385685,0.404334,0.42247,0.440092,0.457197,0.473785,0.489856,0.505409,0.520447,0.53497,0.548982,0.562483,0.57548,0.587974,0.599972,0.611478,0.622498,0.633039,0.643107,0.652711,0.661858,0.670557,0.678817,0.686646,0.694055,0.701052,0.70765,0.713856,0.719683,0.72514,0.730238,0.734986,0.739396,0.743476,0.747238,0.750689,0.753838,0.756695,0.759266,0.76156,0.763581,0.765336,0.76683,0.768066,0.769048,0.769776,0.770253,0.770477,0.770446,0.770158,0.769607,0.768788,0.767693,0.766313,0.764636,0.762648,0.760336,0.75768,0.754663,0.75126,0.747449,0.7432,0.738484,0.733268,0.727514,0.721181,0.714228,0.706604,0.698259,0.689136,0.679175,0.668309,0.65647,0.643581,0.629562,0.614328,0.597788,0.579844,0.560397,0.53934,0.516562,0.49195,0.465387,0.436755,0.405934,0.372811},
{-2.77819,-2.75201,-2.72581,-2.69957,-2.6733,-2.64701,-2.62068,-2.59433,-2.56794,-2.54152,-2.51507,-2.48858,-2.46206,-2.43551,-2.40891,-2.38229,-2.35562,-2.32891,-2.30217,-2.27538,-2.24854,-2.22167,-2.19474,-2.16777,-2.14075,-2.11368,-2.08656,-2.05938,-2.03215,-2.00486,-1.9775,-1.95009,-1.92262,-1.89507,-1.86747,-1.83979,-1.81204,-1.78421,-1.75631,-1.72834,-1.70028,-1.67214,-1.64392,-1.61562,-1.58722,-1.55874,-1.53016,-1.5015,-1.47274,-1.44388,-1.41492,-1.38587,-1.35672,-1.32747,-1.29812,-1.26866,-1.23911,-1.20945,-1.1797,-1.14985,-1.11989,-1.08985,-1.0597,-1.02947,-0.99915,-0.968745,-0.93826,-0.907699,-0.877069,-0.846376,-0.815626,-0.784828,-0.753989,-0.723119,-0.692229,-0.661327,-0.630427,-0.59954,-0.568679,-0.537857,-0.50709,-0.476391,-0.445776,-0.415262,-0.384864,-0.3546,-0.324486,-0.29454,-0.264781,-0.235224,-0.205889,-0.176793,-0.147953,-0.119388,-0.0911129,-0.0631463,-0.0355039,-0.00820192,0.0187443,0.0453197,0.07151,0.0973014,0.122681,0.147636,0.172155,0.196226,0.21984,0.242987,0.265658,0.287844,0.309538,0.330734,0.351425,0.371606,0.391271,0.410418,0.429042,0.447142,0.464714,0.481758,0.498273,0.514259,0.529717,0.544648,0.559054,0.572938,0.586303,0.599154,0.611494,0.62333,0.634667,0.645511,0.65587,0.665752,0.675164,0.684116,0.692615,0.700673,0.708298,0.715501,0.722292,0.728682,0.73468,0.740299,0.745549,0.75044,0.754982,0.759187,0.763064,0.766622,0.769871,0.772819,0.775474,0.777844,0.779936,0.781755,0.783307,0.784595,0.785623,0.786392,0.786904,0.787159,0.787154,0.786888,0.786354,0.785549,0.784463,0.783088,0.781412,0.779423,0.777106,0.774443,0.771414,0.767998,0.76417,0.759903,0.755166,0.749927,0.744148,0.73779,0.730808,0.723156,0.714782,0.705629,0.695639,0.684744,0.672877,0.659962,0.645919,0.630664,0.614105,0.596147,0.57669,0.555628,0.532852,0.508248,0.481699,0.453088,0.422296,0.389207},
{-2.79512,-2.76894,-2.74274,-2.71651,-2.69025,-2.66395,-2.63763,-2.61128,-2.58489,-2.55847,-2.53202,-2.50554,-2.47902,-2.45246,-2.42587,-2.39924,-2.37257,-2.34586,-2.31911,-2.29232,-2.26548,-2.2386,-2.21167,-2.18469,-2.15766,-2.13058,-2.10345,-2.07626,-2.04902,-2.02172,-1.99435,-1.96692,-1.93943,-1.91187,-1.88424,-1.85655,-1.82877,-1.80093,-1.773,-1.745,-1.71691,-1.68874,-1.66049,-1.63214,-1.60371,-1.57519,-1.54657,-1.51785,-1.48904,-1.46012,-1.43111,-1.402,-1.37278,-1.34345,-1.31402,-1.28449,-1.25485,-1.2251,-1.19525,-1.16529,-1.13523,-1.10507,-1.0748,-1.04443,-1.01397,-0.983418,-0.952775,-0.922048,-0.891241,-0.860362,-0.829415,-0.798409,-0.767351,-0.73625,-0.705117,-0.67396,-0.642791,-0.611623,-0.580466,-0.549336,-0.518246,-0.487211,-0.456245,-0.425366,-0.394589,-0.363932,-0.333412,-0.303046,-0.272852,-0.24285,-0.213055,-0.183488,-0.154166,-0.125108,-0.0963301,-0.0678512,-0.0396884,-0.0118583,0.0156225,0.0427383,0.0694737,0.0958139,0.121745,0.147253,0.172326,0.196952,0.221118,0.244815,0.268033,0.290763,0.312995,0.334723,0.35594,0.376639,0.396815,0.416463,0.43558,0.454162,0.472206,0.48971,0.506675,0.523098,0.538981,0.554325,0.569131,0.583402,0.597142,0.610353,0.623042,0.635212,0.64687,0.658023,0.668677,0.678841,0.688523,0.697731,0.706476,0.714765,0.722611,0.730023,0.737011,0.743587,0.749761,0.755546,0.76095,0.765986,0.770665,0.774996,0.778991,0.782659,0.78601,0.789052,0.791794,0.794243,0.796408,0.798293,0.799905,0.801247,0.802323,0.803136,0.803687,0.803975,0.803999,0.803757,0.803244,0.802454,0.801381,0.800015,0.798345,0.796359,0.794041,0.791375,0.78834,0.784916,0.781078,0.776799,0.772049,0.766794,0.760999,0.754623,0.747624,0.739955,0.731563,0.722394,0.712388,0.70148,0.689601,0.676677,0.662629,0.647373,0.630818,0.61287,0.593429,0.57239,0.549644,0.525079,0.498578,0.470023,0.439297,0.406283},
{-2.81176,-2.78559,-2.75939,-2.73316,-2.7069,-2.68062,-2.6543,-2.62795,-2.60156,-2.57515,-2.5487,-2.52221,-2.49569,-2.46914,-2.44254,-2.41591,-2.38924,-2.36253,-2.33578,-2.30898,-2.28214,-2.25525,-2.22832,-2.20133,-2.1743,-2.14721,-2.12007,-2.09287,-2.06562,-2.0383,-2.01092,-1.98348,-1.95598,-1.9284,-1.90075,-1.87304,-1.84524,-1.81737,-1.78943,-1.7614,-1.73328,-1.70508,-1.67679,-1.64842,-1.61995,-1.59138,-1.56272,-1.53395,-1.50509,-1.47613,-1.44706,-1.41788,-1.3886,-1.35921,-1.3297,-1.30009,-1.27037,-1.24053,-1.21059,-1.18053,-1.15036,-1.12008,-1.08969,-1.0592,-1.0286,-0.997907,-0.967111,-0.936223,-0.905246,-0.874186,-0.843049,-0.811841,-0.780571,-0.749247,-0.717878,-0.686473,-0.655044,-0.623602,-0.592159,-0.560728,-0.529324,-0.497961,-0.466654,-0.435418,-0.404271,-0.37323,-0.342311,-0.311534,-0.280915,-0.250473,-0.220228,-0.190197,-0.1604,-0.130856,-0.101582,-0.0725966,-0.0439188,-0.0155657,0.0124453,0.0400973,0.0673743,0.0942604,0.12074,0.1468,0.172426,0.197604,0.222323,0.246571,0.270336,0.29361,0.316382,0.338645,0.360389,0.381609,0.402299,0.422451,0.442063,0.461131,0.47965,0.497619,0.515036,0.531901,0.548213,0.563974,0.579184,0.593846,0.607964,0.62154,0.634579,0.647088,0.65907,0.670534,0.681487,0.691936,0.701889,0.711356,0.720347,0.72887,0.736937,0.744558,0.751744,0.758506,0.764856,0.770804,0.776362,0.781542,0.786354,0.790809,0.794919,0.798692,0.802139,0.80527,0.808092,0.810615,0.812844,0.814787,0.816449,0.817835,0.818949,0.819792,0.820367,0.820673,0.820709,0.820473,0.81996,0.819166,0.818081,0.816699,0.815007,0.812992,0.810641,0.807935,0.804856,0.801382,0.797487,0.793146,0.788328,0.782999,0.777124,0.770663,0.763572,0.755804,0.747308,0.738028,0.727905,0.716874,0.704865,0.691806,0.677616,0.662212,0.645503,0.627395,0.607789,0.586579,0.563658,0.538911,0.512225,0.48348,0.452559,0.419346},
{-2.82812,-2.80195,-2.77576,-2.74954,-2.72329,-2.697,-2.67069,-2.64434,-2.61796,-2.59154,-2.5651,-2.53861,-2.51209,-2.48554,-2.45894,-2.43231,-2.40564,-2.37893,-2.35217,-2.32537,-2.29853,-2.27164,-2.2447,-2.21771,-2.19066,-2.16357,-2.13642,-2.10921,-2.08195,-2.05462,-2.02723,-1.99978,-1.97226,-1.94467,-1.917,-1.88927,-1.86146,-1.83357,-1.80559,-1.77754,-1.7494,-1.72117,-1.69285,-1.66444,-1.63593,-1.60733,-1.57863,-1.54982,-1.52091,-1.49189,-1.46277,-1.43354,-1.40419,-1.37473,-1.34516,-1.31547,-1.28567,-1.25575,-1.22571,-1.19556,-1.16529,-1.1349,-1.10439,-1.07378,-1.04305,-1.01221,-0.981272,-0.950227,-0.919085,-0.887851,-0.856529,-0.825126,-0.793651,-0.762109,-0.730511,-0.698865,-0.667183,-0.635475,-0.603753,-0.57203,-0.54032,-0.508636,-0.476995,-0.445412,-0.413903,-0.382485,-0.351176,-0.319995,-0.288958,-0.258086,-0.227396,-0.196909,-0.166644,-0.136619,-0.106855,-0.0773689,-0.048181,-0.0193094,0.00922772,0.0374127,0.0652283,0.0926579,0.119685,0.146295,0.172473,0.198204,0.223475,0.248275,0.272589,0.296409,0.319724,0.342523,0.364799,0.386544,0.40775,0.428412,0.448524,0.468081,0.487081,0.50552,0.523396,0.540708,0.557455,0.573638,0.589258,0.604317,0.618819,0.632766,0.646163,0.659015,0.671329,0.68311,0.694367,0.705106,0.715338,0.72507,0.734312,0.743076,0.75137,0.759207,0.766597,0.773552,0.780083,0.786202,0.791921,0.79725,0.802203,0.806789,0.811021,0.814908,0.81846,0.821688,0.8246,0.827204,0.829509,0.83152,0.833244,0.834686,0.83585,0.836738,0.837352,0.837692,0.837758,0.837547,0.837055,0.836277,0.835206,0.833832,0.832146,0.830134,0.827782,0.825073,0.821988,0.818505,0.8146,0.810246,0.805414,0.80007,0.794178,0.7877,0.780591,0.772805,0.764292,0.754995,0.744857,0.733812,0.721793,0.708725,0.694531,0.679127,0.662424,0.644327,0.624739,0.603554,0.580666,0.555961,0.529325,0.50064,0.469789,0.436654},
{-2.84421,-2.81805,-2.79187,-2.76565,-2.7394,-2.71312,-2.68681,-2.66046,-2.63409,-2.60767,-2.58123,-2.55475,-2.52823,-2.50167,-2.47508,-2.44845,-2.42178,-2.39506,-2.3683,-2.3415,-2.31465,-2.28776,-2.26081,-2.23382,-2.20677,-2.17967,-2.15251,-2.1253,-2.09802,-2.07069,-2.04329,-2.01582,-1.98829,-1.96068,-1.933,-1.90525,-1.87742,-1.84951,-1.82152,-1.79344,-1.76527,-1.73702,-1.70867,-1.68022,-1.65168,-1.62304,-1.5943,-1.56545,-1.5365,-1.50743,-1.47826,-1.44897,-1.41956,-1.39004,-1.3604,-1.33064,-1.30076,-1.27076,-1.24063,-1.21039,-1.18002,-1.14952,-1.11891,-1.08817,-1.05732,-1.02635,-0.995263,-0.964068,-0.932766,-0.901363,-0.869862,-0.838271,-0.806596,-0.774844,-0.743024,-0.711144,-0.679216,-0.647249,-0.615256,-0.583249,-0.55124,-0.519245,-0.487279,-0.455356,-0.423493,-0.391708,-0.360017,-0.328439,-0.296993,-0.265698,-0.234573,-0.203637,-0.17291,-0.142413,-0.112164,-0.0821841,-0.0524921,-0.0231074,0.00595082,0.0346641,0.0630144,0.0909839,0.118556,0.145713,0.172441,0.198723,0.224546,0.249896,0.27476,0.299126,0.322983,0.34632,0.369129,0.3914,0.413125,0.434298,0.454913,0.474963,0.494446,0.513358,0.531695,0.549457,0.566642,0.58325,0.599283,0.614742,0.62963,0.643951,0.657708,0.670906,0.683552,0.695653,0.707215,0.718246,0.728756,0.738753,0.748248,0.75725,0.765771,0.773822,0.781413,0.788558,0.795267,0.801552,0.807426,0.812901,0.817987,0.822698,0.827043,0.831034,0.834681,0.837995,0.840983,0.843656,0.84602,0.848083,0.849851,0.851329,0.852521,0.853429,0.854056,0.854402,0.854467,0.854247,0.853739,0.852937,0.851835,0.850423,0.848691,0.846626,0.844213,0.841435,0.838273,0.834705,0.830705,0.826249,0.821304,0.815838,0.809815,0.803194,0.795933,0.787984,0.779296,0.769813,0.759476,0.748221,0.735978,0.722674,0.70823,0.692561,0.675579,0.65719,0.637294,0.615787,0.592561,0.567504,0.5405,0.511432,0.480182,0.446634},
{-2.86004,-2.83389,-2.80771,-2.7815,-2.75525,-2.72898,-2.70267,-2.67633,-2.64996,-2.62355,-2.5971,-2.57062,-2.54411,-2.51755,-2.49096,-2.46433,-2.43765,-2.41094,-2.38418,-2.35737,-2.33052,-2.30362,-2.27668,-2.24968,-2.22263,-2.19552,-2.16835,-2.14113,-2.11385,-2.0865,-2.05909,-2.03162,-2.00407,-1.97645,-1.94876,-1.92099,-1.89314,-1.86521,-1.8372,-1.8091,-1.78091,-1.75262,-1.72425,-1.69577,-1.6672,-1.63853,-1.60975,-1.58086,-1.55186,-1.52275,-1.49352,-1.46418,-1.43472,-1.40514,-1.37543,-1.3456,-1.31565,-1.28557,-1.25536,-1.22502,-1.19455,-1.16396,-1.13324,-1.10239,-1.07141,-1.04031,-1.00909,-0.977747,-0.94629,-0.914723,-0.883049,-0.851274,-0.819405,-0.787449,-0.755413,-0.723307,-0.691139,-0.658921,-0.626663,-0.594378,-0.562079,-0.52978,-0.497495,-0.46524,-0.433031,-0.400886,-0.368821,-0.336855,-0.305007,-0.273295,-0.241741,-0.210363,-0.179182,-0.148217,-0.11749,-0.0870212,-0.05683,-0.0269367,0.00263873,0.0318769,0.0607588,0.0892658,0.11738,0.145084,0.17236,0.199194,0.225569,0.25147,0.276884,0.301799,0.326201,0.350079,0.373423,0.396224,0.418473,0.440161,0.461283,0.481832,0.501803,0.521192,0.539997,0.558214,0.575843,0.592884,0.609336,0.625202,0.640483,0.655183,0.669307,0.682858,0.695844,0.70827,0.720145,0.731475,0.74227,0.75254,0.762294,0.771543,0.780298,0.78857,0.796371,0.803713,0.810608,0.817068,0.823106,0.828734,0.833964,0.838808,0.843277,0.847383,0.851136,0.854547,0.857625,0.860379,0.862817,0.864947,0.866775,0.868306,0.869544,0.870493,0.871155,0.871531,0.871618,0.871417,0.870922,0.870129,0.869031,0.867618,0.865881,0.863807,0.86138,0.858585,0.855401,0.851808,0.84778,0.843291,0.838312,0.832808,0.826744,0.820079,0.812772,0.804775,0.796037,0.786502,0.776112,0.764803,0.752506,0.739147,0.724649,0.708927,0.691894,0.673454,0.653511,0.631959,0.608692,0.583598,0.556561,0.527465,0.496191,0.462623},
{-2.87562,-2.84948,-2.8233,-2.7971,-2.77086,-2.74459,-2.71828,-2.69195,-2.66558,-2.63917,-2.61273,-2.58625,-2.55974,-2.53318,-2.50659,-2.47996,-2.45329,-2.42657,-2.39981,-2.373,-2.34615,-2.31925,-2.2923,-2.26529,-2.23824,-2.21112,-2.18395,-2.15672,-2.12943,-2.10208,-2.07466,-2.04717,-2.01961,-1.99198,-1.96427,-1.93649,-1.90863,-1.88068,-1.85264,-1.82452,-1.79631,-1.768,-1.7396,-1.7111,-1.6825,-1.65379,-1.62497,-1.59604,-1.567,-1.53785,-1.50858,-1.47918,-1.44967,-1.42003,-1.39026,-1.36037,-1.33034,-1.30018,-1.26989,-1.23947,-1.20891,-1.17822,-1.14739,-1.11643,-1.08533,-1.05411,-1.02275,-0.99127,-0.959664,-0.927938,-0.896096,-0.864144,-0.832087,-0.799933,-0.767687,-0.73536,-0.70296,-0.670497,-0.637982,-0.605427,-0.572845,-0.540249,-0.507653,-0.475074,-0.442527,-0.410029,-0.377598,-0.345252,-0.313009,-0.28089,-0.248914,-0.217101,-0.185472,-0.154048,-0.122849,-0.0918969,-0.0612123,-0.0308159,-0.000728332,0.0290301,0.0584396,0.0874804,0.116134,0.144381,0.172205,0.199587,0.226513,0.252965,0.278929,0.304392,0.32934,0.35376,0.377641,0.400973,0.423747,0.445953,0.467585,0.488634,0.509097,0.528967,0.548242,0.566919,0.584995,0.602471,0.619345,0.63562,0.651298,0.666381,0.680874,0.694782,0.708109,0.720864,0.733052,0.744683,0.755766,0.766309,0.776323,0.785818,0.794807,0.8033,0.811309,0.818847,0.825926,0.832559,0.838758,0.844535,0.849904,0.854876,0.859464,0.863678,0.867529,0.871029,0.874187,0.877013,0.879513,0.881697,0.883571,0.88514,0.886408,0.88738,0.888057,0.888439,0.888527,0.888318,0.887809,0.886994,0.885867,0.884418,0.882636,0.88051,0.878025,0.875162,0.871904,0.868227,0.864108,0.85952,0.854431,0.84881,0.842619,0.835818,0.828364,0.82021,0.811305,0.801593,0.791014,0.779505,0.766996,0.753413,0.738679,0.722709,0.705414,0.686701,0.66647,0.644619,0.621038,0.595617,0.568239,0.538789,0.507148,0.473199},
{-2.89095,-2.86482,-2.83865,-2.81245,-2.78622,-2.75995,-2.73365,-2.70732,-2.68095,-2.65455,-2.62811,-2.60164,-2.57512,-2.54857,-2.52198,-2.49535,-2.46868,-2.44196,-2.4152,-2.38839,-2.36154,-2.33463,-2.30768,-2.28067,-2.25361,-2.22649,-2.19932,-2.17208,-2.14478,-2.11742,-2.08999,-2.06249,-2.03493,-2.00728,-1.97956,-1.95176,-1.92388,-1.89592,-1.86787,-1.83973,-1.81149,-1.78316,-1.75474,-1.72621,-1.69757,-1.66883,-1.63998,-1.61102,-1.58194,-1.55274,-1.52342,-1.49398,-1.46442,-1.43472,-1.40489,-1.37493,-1.34484,-1.31461,-1.28424,-1.25373,-1.22308,-1.1923,-1.16137,-1.1303,-1.09909,-1.06774,-1.03626,-1.00464,-0.972889,-0.941009,-0.909004,-0.87688,-0.844641,-0.812293,-0.779844,-0.747302,-0.714676,-0.681975,-0.649209,-0.61639,-0.583532,-0.550646,-0.517747,-0.484851,-0.451973,-0.419129,-0.386339,-0.353619,-0.320989,-0.288469,-0.256078,-0.223837,-0.191766,-0.159888,-0.128224,-0.0967939,-0.0656208,-0.0347258,-0.00413019,0.0261449,0.0560787,0.0856508,0.114841,0.143631,0.172,0.199931,0.227407,0.254411,0.280926,0.306939,0.332434,0.357398,0.38182,0.405687,0.428989,0.451717,0.473863,0.495418,0.516377,0.536734,0.556485,0.575626,0.594156,0.612072,0.629376,0.646067,0.662147,0.67762,0.692489,0.706759,0.720435,0.733525,0.746035,0.757973,0.76935,0.780173,0.790454,0.800204,0.809433,0.818154,0.82638,0.834121,0.841392,0.848206,0.854574,0.86051,0.866026,0.871136,0.875851,0.880183,0.884144,0.887744,0.890994,0.893903,0.89648,0.898732,0.900667,0.90229,0.903606,0.904619,0.905331,0.905743,0.905854,0.905663,0.905167,0.904359,0.903234,0.901783,0.899995,0.897858,0.895357,0.892476,0.889194,0.88549,0.88134,0.876717,0.871591,0.865929,0.859694,0.852846,0.845343,0.837138,0.828179,0.818412,0.807777,0.79621,0.783643,0.770003,0.755211,0.739184,0.721834,0.703067,0.682784,0.660884,0.637259,0.611796,0.584381,0.554897,0.523227,0.489253},
{-2.90605,-2.87992,-2.85376,-2.82757,-2.80134,-2.77508,-2.74879,-2.72246,-2.6961,-2.6697,-2.64326,-2.61679,-2.59028,-2.56373,-2.53714,-2.51051,-2.48384,-2.45712,-2.43036,-2.40355,-2.37669,-2.34979,-2.32283,-2.29582,-2.26875,-2.24163,-2.21445,-2.18721,-2.15991,-2.13254,-2.1051,-2.07759,-2.05001,-2.02236,-1.99463,-1.96682,-1.93892,-1.91094,-1.88287,-1.85471,-1.82646,-1.79811,-1.76966,-1.7411,-1.71244,-1.68367,-1.65479,-1.62579,-1.59667,-1.56743,-1.53807,-1.50858,-1.47897,-1.44922,-1.41933,-1.38931,-1.35915,-1.32885,-1.2984,-1.26782,-1.23708,-1.2062,-1.17518,-1.14401,-1.11269,-1.08122,-1.04961,-1.01786,-0.985971,-0.953942,-0.92178,-0.889488,-0.857072,-0.824537,-0.791891,-0.75914,-0.726293,-0.69336,-0.66035,-0.627275,-0.594147,-0.560978,-0.527783,-0.494577,-0.461375,-0.428194,-0.395052,-0.361966,-0.328956,-0.296042,-0.263243,-0.23058,-0.198076,-0.16575,-0.133626,-0.101724,-0.0700686,-0.0386803,-0.00758157,0.0232057,0.0536598,0.0837595,0.113484,0.142812,0.171726,0.200204,0.228229,0.255784,0.28285,0.309412,0.335456,0.360965,0.385928,0.410332,0.434165,0.457418,0.48008,0.502144,0.523602,0.544449,0.564679,0.584289,0.603276,0.621637,0.639374,0.656485,0.672972,0.688838,0.704087,0.718723,0.732752,0.746179,0.759014,0.771263,0.782936,0.794042,0.804593,0.814598,0.824071,0.833022,0.841464,0.84941,0.856874,0.863867,0.870404,0.876498,0.882161,0.887407,0.892247,0.896695,0.900762,0.90446,0.907797,0.910785,0.913432,0.915747,0.917736,0.919406,0.920762,0.921807,0.922544,0.922974,0.923097,0.922911,0.922412,0.921597,0.920458,0.918987,0.917173,0.915003,0.912463,0.909537,0.906204,0.902444,0.898231,0.893539,0.888338,0.882594,0.876272,0.869331,0.861728,0.853417,0.844346,0.83446,0.823701,0.812003,0.7993,0.785517,0.770576,0.754395,0.736885,0.717953,0.6975,0.675424,0.651618,0.62597,0.598365,0.568686,0.536816,0.502637},
{-2.92092,-2.8948,-2.86864,-2.84246,-2.81624,-2.78998,-2.76369,-2.73737,-2.71101,-2.68462,-2.65818,-2.63171,-2.60521,-2.57866,-2.55207,-2.52544,-2.49877,-2.47205,-2.44529,-2.41848,-2.39163,-2.36472,-2.33776,-2.31075,-2.28368,-2.25655,-2.22937,-2.20212,-2.17481,-2.14743,-2.11999,-2.09247,-2.06489,-2.03722,-2.00948,-1.98165,-1.95375,-1.92575,-1.89767,-1.86949,-1.84121,-1.81284,-1.78437,-1.75579,-1.7271,-1.6983,-1.66939,-1.64036,-1.6112,-1.58193,-1.55253,-1.52299,-1.49333,-1.46352,-1.43358,-1.4035,-1.37328,-1.34291,-1.3124,-1.28173,-1.25091,-1.21995,-1.18883,-1.15755,-1.12613,-1.09455,-1.06282,-1.03094,-0.998915,-0.966741,-0.934425,-0.901971,-0.869383,-0.836666,-0.803827,-0.770873,-0.737812,-0.704653,-0.671405,-0.63808,-0.604689,-0.571244,-0.53776,-0.50425,-0.470732,-0.43722,-0.403733,-0.370288,-0.336905,-0.303603,-0.270404,-0.237326,-0.204394,-0.171627,-0.139049,-0.106682,-0.0745482,-0.0426715,-0.0110742,0.0202211,0.0511918,0.0818158,0.112071,0.141937,0.171392,0.200416,0.22899,0.257095,0.284712,0.311825,0.338418,0.364475,0.389981,0.414924,0.439291,0.463071,0.486253,0.50883,0.530792,0.552133,0.572847,0.59293,0.612379,0.631191,0.649365,0.666901,0.6838,0.700065,0.715699,0.730707,0.745093,0.758864,0.772028,0.784593,0.796568,0.807963,0.818788,0.829054,0.838774,0.84796,0.856624,0.864779,0.87244,0.879618,0.886328,0.892584,0.898398,0.903785,0.908756,0.913324,0.917502,0.9213,0.92473,0.927802,0.930525,0.932907,0.934957,0.936679,0.93808,0.939163,0.939932,0.940387,0.940529,0.940356,0.939865,0.939052,0.937908,0.936427,0.934598,0.932409,0.929844,0.926888,0.92352,0.91972,0.915464,0.910723,0.905469,0.899667,0.893283,0.886277,0.878605,0.87022,0.861072,0.851107,0.840264,0.82848,0.815688,0.801814,0.786781,0.770506,0.7529,0.733872,0.713322,0.69115,0.667247,0.641503,0.613802,0.584029,0.552065,0.517792},
{-2.93556,-2.90945,-2.8833,-2.85712,-2.83091,-2.80466,-2.77838,-2.75206,-2.7257,-2.69931,-2.67288,-2.64642,-2.61991,-2.59337,-2.56678,-2.54016,-2.51348,-2.48677,-2.46001,-2.4332,-2.40634,-2.37943,-2.35247,-2.32546,-2.29838,-2.27126,-2.24407,-2.21682,-2.1895,-2.16212,-2.13467,-2.10714,-2.07955,-2.05187,-2.02412,-1.99628,-1.96836,-1.94035,-1.91225,-1.88406,-1.85577,-1.82738,-1.79888,-1.77028,-1.74156,-1.71274,-1.6838,-1.65473,-1.62555,-1.59623,-1.56679,-1.53721,-1.5075,-1.47765,-1.44766,-1.41752,-1.38724,-1.3568,-1.32622,-1.29548,-1.26458,-1.23353,-1.20232,-1.17095,-1.13942,-1.10773,-1.07589,-1.04388,-1.01172,-0.979409,-0.946945,-0.914332,-0.881577,-0.848684,-0.815658,-0.782507,-0.749237,-0.715858,-0.682378,-0.648808,-0.61516,-0.581446,-0.547679,-0.513874,-0.480045,-0.446209,-0.412384,-0.378588,-0.344838,-0.311157,-0.277562,-0.244077,-0.210723,-0.177521,-0.144495,-0.111668,-0.0790623,-0.0467023,-0.0146112,0.0171878,0.0486713,0.0798162,0.1106,0.141,0.170995,0.200563,0.229685,0.258339,0.286507,0.314172,0.341314,0.367919,0.393971,0.419455,0.444358,0.468668,0.492374,0.515466,0.537936,0.559775,0.580977,0.601538,0.621453,0.640719,0.659336,0.677302,0.694618,0.711287,0.727311,0.742694,0.757443,0.771563,0.785061,0.797946,0.810227,0.821914,0.833018,0.843549,0.853521,0.862945,0.871834,0.880202,0.888063,0.895429,0.902316,0.908736,0.914704,0.920234,0.925337,0.930028,0.934318,0.93822,0.941744,0.944902,0.947702,0.950153,0.952264,0.95404,0.955487,0.95661,0.957412,0.957893,0.958055,0.957896,0.957413,0.956602,0.955456,0.953966,0.952123,0.949914,0.947326,0.944341,0.94094,0.937101,0.932802,0.928014,0.922708,0.916852,0.910408,0.903338,0.895599,0.887145,0.877923,0.867881,0.856959,0.845094,0.832218,0.818259,0.803138,0.786775,0.769081,0.749964,0.729325,0.707064,0.683074,0.657243,0.629457,0.5996,0.567553,0.533198},
{-2.94999,-2.92389,-2.89775,-2.87157,-2.84536,-2.81912,-2.79284,-2.76653,-2.74018,-2.7138,-2.68737,-2.66091,-2.63441,-2.60786,-2.58128,-2.55466,-2.52799,-2.50127,-2.47451,-2.4477,-2.42084,-2.39393,-2.36697,-2.33996,-2.31288,-2.28575,-2.25856,-2.2313,-2.20398,-2.17659,-2.14914,-2.12161,-2.094,-2.06632,-2.03856,-2.01071,-1.98278,-1.95476,-1.92664,-1.89843,-1.87012,-1.84171,-1.8132,-1.78457,-1.75584,-1.72698,-1.69801,-1.66892,-1.6397,-1.61035,-1.58087,-1.55125,-1.5215,-1.4916,-1.46156,-1.43137,-1.40102,-1.37053,-1.33987,-1.30906,-1.27809,-1.24695,-1.21566,-1.18419,-1.15257,-1.12077,-1.08881,-1.05669,-1.0244,-0.99195,-0.959341,-0.926576,-0.893659,-0.860594,-0.827386,-0.794042,-0.760569,-0.726976,-0.69327,-0.659462,-0.625564,-0.591586,-0.557543,-0.523448,-0.489316,-0.455163,-0.421007,-0.386865,-0.352756,-0.318701,-0.284719,-0.250832,-0.217062,-0.183432,-0.149964,-0.116682,-0.0836099,-0.0507716,-0.0181913,0.014107,0.0460993,0.0777617,0.109071,0.140003,0.170535,0.200646,0.230314,0.259517,0.288236,0.316452,0.344146,0.3713,0.397898,0.423925,0.449367,0.474211,0.498443,0.522055,0.545035,0.567376,0.589071,0.610114,0.6305,0.650226,0.66929,0.68769,0.705429,0.722506,0.738925,0.75469,0.769806,0.784279,0.798117,0.811327,0.823919,0.835903,0.84729,0.858091,0.868318,0.877985,0.887104,0.895689,0.903753,0.911312,0.918379,0.924968,0.931093,0.936769,0.942009,0.946825,0.951232,0.95524,0.958862,0.962109,0.964989,0.967513,0.969689,0.971522,0.97302,0.974186,0.975025,0.975537,0.975723,0.975583,0.975113,0.974309,0.973165,0.971673,0.969823,0.967603,0.964998,0.961992,0.958566,0.954699,0.950368,0.945544,0.940199,0.934301,0.927812,0.920695,0.912906,0.904399,0.895124,0.885026,0.874048,0.862127,0.849194,0.835178,0.820002,0.803584,0.785837,0.766669,0.745983,0.723678,0.699646,0.673778,0.64596,0.616075,0.584003,0.549628},
{-2.96421,-2.93811,-2.91198,-2.88581,-2.85961,-2.83338,-2.8071,-2.7808,-2.75445,-2.72807,-2.70165,-2.67519,-2.64869,-2.62215,-2.59557,-2.56895,-2.54228,-2.51557,-2.48881,-2.462,-2.43514,-2.40823,-2.38127,-2.35425,-2.32718,-2.30004,-2.27285,-2.24559,-2.21826,-2.19087,-2.16341,-2.13587,-2.10826,-2.08057,-2.0528,-2.02494,-1.997,-1.96896,-1.94084,-1.91261,-1.88429,-1.85586,-1.82732,-1.79868,-1.76992,-1.74104,-1.71205,-1.68292,-1.65367,-1.62429,-1.59477,-1.56512,-1.53532,-1.50538,-1.47529,-1.44504,-1.41464,-1.38409,-1.35337,-1.32249,-1.29144,-1.26023,-1.22885,-1.19729,-1.16557,-1.13367,-1.1016,-1.06936,-1.03695,-1.00437,-0.971621,-0.938707,-0.905632,-0.8724,-0.839016,-0.805485,-0.771815,-0.738012,-0.704086,-0.670047,-0.635904,-0.60167,-0.567356,-0.532978,-0.498549,-0.464086,-0.429605,-0.395125,-0.360664,-0.326242,-0.291879,-0.257597,-0.223419,-0.189366,-0.155462,-0.121732,-0.0881992,-0.0548882,-0.0218239,0.010969,0.0434656,0.0756413,0.107472,0.138933,0.17,0.200651,0.230863,0.260615,0.289883,0.31865,0.346894,0.374598,0.401744,0.428316,0.454298,0.479676,0.504437,0.52857,0.552064,0.574911,0.597101,0.618629,0.639489,0.659678,0.679192,0.698031,0.716195,0.733684,0.750502,0.766651,0.782138,0.796967,0.811147,0.824685,0.837591,0.849874,0.861546,0.872618,0.883102,0.893012,0.902361,0.911163,0.919432,0.927182,0.934428,0.941184,0.947465,0.953284,0.958657,0.963596,0.968114,0.972225,0.975939,0.979268,0.982222,0.984811,0.987043,0.988924,0.990461,0.99166,0.992522,0.993051,0.993248,0.99311,0.992635,0.99182,0.990658,0.989141,0.987259,0.985,0.98235,0.979293,0.975809,0.971878,0.967475,0.962574,0.957145,0.951155,0.944569,0.937347,0.929448,0.920823,0.911424,0.901196,0.890081,0.878015,0.864931,0.850758,0.835418,0.81883,0.800907,0.781556,0.760681,0.738181,0.713949,0.687874,0.659842,0.629736,0.597438,0.562829},
{-2.97822,-2.95213,-2.92601,-2.89985,-2.87365,-2.84742,-2.82116,-2.79486,-2.76852,-2.74214,-2.71573,-2.68927,-2.66278,-2.63624,-2.60966,-2.58304,-2.55638,-2.52966,-2.50291,-2.4761,-2.44924,-2.42233,-2.39537,-2.36835,-2.34127,-2.31414,-2.28694,-2.25968,-2.23235,-2.20495,-2.17748,-2.14994,-2.12232,-2.09463,-2.06684,-2.03898,-2.01103,-1.98298,-1.95484,-1.9266,-1.89826,-1.86982,-1.84127,-1.8126,-1.78382,-1.75492,-1.7259,-1.69675,-1.66747,-1.63806,-1.60851,-1.57881,-1.54898,-1.51899,-1.48885,-1.45856,-1.4281,-1.39749,-1.36671,-1.33576,-1.30465,-1.27336,-1.24189,-1.21025,-1.17843,-1.14644,-1.11426,-1.08191,-1.04938,-1.01667,-0.983785,-0.950727,-0.917499,-0.884105,-0.850548,-0.816836,-0.782973,-0.748967,-0.714826,-0.68056,-0.646179,-0.611693,-0.577116,-0.542461,-0.507742,-0.472974,-0.438176,-0.403363,-0.368556,-0.333773,-0.299036,-0.264365,-0.229784,-0.195315,-0.160981,-0.126808,-0.0928195,-0.0590407,-0.0254969,0.00778634,0.0407835,0.0734692,0.105818,0.137805,0.169406,0.200595,0.231351,0.261649,0.291468,0.320785,0.349581,0.377836,0.405531,0.432649,0.459174,0.48509,0.510384,0.535042,0.559054,0.58241,0.6051,0.627118,0.648458,0.669115,0.689085,0.708368,0.726963,0.74487,0.762092,0.778632,0.794495,0.809687,0.824215,0.838087,0.851312,0.8639,0.875863,0.887213,0.89796,0.90812,0.917705,0.92673,0.935209,0.943157,0.950588,0.957517,0.96396,0.969931,0.975443,0.980511,0.985149,0.989369,0.993183,0.996603,0.99964,1.0023,1.0046,1.00654,1.00813,1.00937,1.01027,1.01083,1.01105,1.01093,1.01047,1.00966,1.00849,1.00697,1.00508,1.00281,1.00014,0.997059,0.993548,0.989584,0.985146,0.980205,0.974732,0.968696,0.962061,0.954787,0.946832,0.93815,0.928692,0.918403,0.907225,0.895097,0.88195,0.867713,0.852311,0.83566,0.817676,0.798266,0.777335,0.754781,0.730497,0.704375,0.676298,0.646152,0.613815,0.57917},
{-2.99203,-2.96595,-2.93984,-2.91369,-2.8875,-2.86128,-2.83502,-2.80872,-2.78239,-2.75601,-2.7296,-2.70315,-2.67666,-2.65013,-2.62356,-2.59694,-2.57027,-2.54357,-2.51681,-2.49,-2.46315,-2.43624,-2.40927,-2.38225,-2.35518,-2.32804,-2.30084,-2.27357,-2.24624,-2.21884,-2.19137,-2.16382,-2.1362,-2.10849,-2.08071,-2.05283,-2.02487,-1.99681,-1.96866,-1.94041,-1.91206,-1.8836,-1.85503,-1.82635,-1.79755,-1.76863,-1.73958,-1.7104,-1.6811,-1.65165,-1.62207,-1.59234,-1.56247,-1.53244,-1.50226,-1.47191,-1.44141,-1.41074,-1.3799,-1.34889,-1.3177,-1.28634,-1.2548,-1.22307,-1.19117,-1.15907,-1.1268,-1.09434,-1.06169,-1.02885,-0.995839,-0.962641,-0.929264,-0.895712,-0.861989,-0.828099,-0.794049,-0.759845,-0.725495,-0.691008,-0.656394,-0.621664,-0.586829,-0.551903,-0.516899,-0.481835,-0.446724,-0.411586,-0.376439,-0.341303,-0.306198,-0.271145,-0.236167,-0.201288,-0.16653,-0.13192,-0.0974814,-0.0632401,-0.029222,0.00454674,0.03804,0.0712315,0.104095,0.136605,0.168736,0.200462,0.231759,0.262602,0.292969,0.322838,0.352185,0.380991,0.409236,0.436902,0.463971,0.490427,0.516254,0.541441,0.565973,0.589841,0.613034,0.635546,0.657368,0.678497,0.698928,0.718658,0.737687,0.756016,0.773646,0.79058,0.806824,0.822381,0.837261,0.85147,0.865018,0.877914,0.890171,0.9018,0.912813,0.923224,0.933047,0.942296,0.950987,0.959132,0.966749,0.973852,0.980456,0.986577,0.992228,0.997424,1.00218,1.00651,1.01042,1.01392,1.01704,1.01977,1.02213,1.02412,1.02575,1.02703,1.02796,1.02854,1.02878,1.02866,1.0282,1.02739,1.02621,1.02467,1.02276,1.02045,1.01774,1.01462,1.01106,1.00704,1.00254,0.997536,0.991992,0.985879,0.97916,0.971798,0.963751,0.954971,0.945409,0.935012,0.923722,0.911476,0.898207,0.883845,0.868312,0.851528,0.833406,0.813856,0.79278,0.770079,0.745645,0.719368,0.691135,0.660829,0.628329,0.593515},
{-3.00565,-2.97958,-2.95347,-2.92733,-2.90115,-2.87494,-2.84868,-2.82239,-2.79606,-2.7697,-2.74329,-2.71685,-2.69036,-2.66383,-2.63726,-2.61064,-2.58398,-2.55728,-2.53052,-2.50372,-2.47686,-2.44995,-2.42299,-2.39597,-2.36889,-2.34175,-2.31455,-2.28729,-2.25995,-2.23255,-2.20507,-2.17752,-2.14989,-2.12218,-2.09439,-2.06651,-2.03853,-2.01047,-1.98231,-1.95404,-1.92568,-1.8972,-1.86862,-1.83992,-1.8111,-1.78216,-1.75309,-1.72389,-1.69456,-1.66509,-1.63547,-1.60571,-1.5758,-1.54573,-1.5155,-1.48512,-1.45456,-1.42384,-1.39294,-1.36187,-1.33062,-1.29919,-1.26757,-1.23576,-1.20377,-1.17159,-1.13921,-1.10664,-1.07388,-1.04093,-1.00778,-0.974451,-0.94093,-0.907225,-0.873339,-0.839277,-0.805044,-0.770647,-0.736094,-0.701391,-0.66655,-0.63158,-0.596493,-0.561303,-0.526021,-0.490665,-0.455249,-0.419792,-0.384312,-0.348828,-0.313361,-0.277932,-0.242564,-0.20728,-0.172105,-0.137063,-0.102179,-0.0674807,-0.0329931,0.00125672,0.0352419,0.0689356,0.102311,0.135341,0.167999,0.200259,0.232096,0.263484,0.294399,0.324817,0.354717,0.384075,0.412871,0.441086,0.468701,0.495699,0.522063,0.547781,0.572837,0.597221,0.620922,0.643931,0.666241,0.687846,0.708741,0.728924,0.748393,0.767149,0.785192,0.802526,0.819155,0.835084,0.85032,0.864871,0.878747,0.891957,0.904512,0.916426,0.927709,0.938377,0.948443,0.957921,0.966827,0.975176,0.982983,0.990264,0.997035,1.00331,1.0091,1.01443,1.01931,1.02375,1.02776,1.03136,1.03456,1.03737,1.03979,1.04184,1.04352,1.04484,1.04581,1.04642,1.04667,1.04657,1.04612,1.04531,1.04413,1.04258,1.04065,1.03833,1.0356,1.03245,1.02885,1.02479,1.02025,1.0152,1.0096,1.00343,0.996658,0.989234,0.981121,0.972273,0.962641,0.952171,0.940806,0.928483,0.915136,0.900695,0.885083,0.868219,0.850018,0.830388,0.809235,0.786456,0.761947,0.735597,0.707291,0.676913,0.644343,0.60946},
{-3.01908,-2.99302,-2.96692,-2.94079,-2.91462,-2.88841,-2.86216,-2.83588,-2.80955,-2.78319,-2.75679,-2.73035,-2.70387,-2.67735,-2.65078,-2.62417,-2.59751,-2.5708,-2.54405,-2.51725,-2.4904,-2.46349,-2.43653,-2.40951,-2.38243,-2.35529,-2.32809,-2.30082,-2.27348,-2.24608,-2.2186,-2.19104,-2.16341,-2.13569,-2.10789,-2.08,-2.05202,-2.02395,-1.99578,-1.96751,-1.93913,-1.91064,-1.88204,-1.85332,-1.82449,-1.79553,-1.76644,-1.73722,-1.70786,-1.67836,-1.64871,-1.61892,-1.58897,-1.55887,-1.5286,-1.49817,-1.46757,-1.4368,-1.40585,-1.37472,-1.3434,-1.3119,-1.28021,-1.24833,-1.21625,-1.18397,-1.1515,-1.11883,-1.08596,-1.05289,-1.01963,-0.986162,-0.952501,-0.918647,-0.884603,-0.850374,-0.815963,-0.781379,-0.746626,-0.711714,-0.676651,-0.641447,-0.606114,-0.570665,-0.535111,-0.49947,-0.463755,-0.427985,-0.392177,-0.356352,-0.320529,-0.284731,-0.248978,-0.213297,-0.177709,-0.142241,-0.106919,-0.071768,-0.036816,-0.00208979,0.032383,0.0665747,0.100458,0.134004,0.167187,0.199979,0.232354,0.264284,0.295746,0.326715,0.357165,0.387076,0.416424,0.445189,0.473351,0.500893,0.527797,0.554048,0.579631,0.604534,0.628745,0.652256,0.675057,0.697142,0.718506,0.739146,0.75906,0.778246,0.796707,0.814445,0.831463,0.847768,0.863365,0.878263,0.89247,0.905997,0.918856,0.931057,0.942615,0.953542,0.963853,0.973564,0.982688,0.991243,0.999243,1.0067,1.01364,1.02007,1.02601,1.03147,1.03647,1.04102,1.04514,1.04883,1.05211,1.05499,1.05748,1.05959,1.06132,1.06269,1.06368,1.06432,1.0646,1.06451,1.06406,1.06325,1.06207,1.06051,1.05856,1.05621,1.05346,1.05027,1.04663,1.04253,1.03794,1.03284,1.02718,1.02095,1.01411,1.00662,0.99843,0.989505,0.979793,0.96924,0.957788,0.945377,0.93194,0.917406,0.901701,0.884742,0.866445,0.84672,0.82547,0.802595,0.777989,0.751542,0.72314,0.692666,0.659998,0.625015},
{-3.03233,-3.00628,-2.98019,-2.95406,-2.9279,-2.9017,-2.87546,-2.84918,-2.82286,-2.79651,-2.77011,-2.74368,-2.7172,-2.69068,-2.66412,-2.63751,-2.61085,-2.58415,-2.5574,-2.5306,-2.50375,-2.47684,-2.44988,-2.42286,-2.39579,-2.36865,-2.34144,-2.31418,-2.28684,-2.25943,-2.23195,-2.20439,-2.17675,-2.14903,-2.12122,-2.09333,-2.06534,-2.03726,-2.00908,-1.9808,-1.95241,-1.92391,-1.8953,-1.86657,-1.83771,-1.80873,-1.77963,-1.75038,-1.721,-1.69148,-1.6618,-1.63198,-1.602,-1.57186,-1.54156,-1.51108,-1.48044,-1.44961,-1.41861,-1.38742,-1.35605,-1.32448,-1.29272,-1.26076,-1.2286,-1.19624,-1.16368,-1.13091,-1.09794,-1.06476,-1.03137,-0.997776,-0.96398,-0.929981,-0.895784,-0.861391,-0.826809,-0.792041,-0.757095,-0.721978,-0.686698,-0.651267,-0.615693,-0.57999,-0.544171,-0.50825,-0.472242,-0.436165,-0.400037,-0.363876,-0.327704,-0.291541,-0.255411,-0.219337,-0.183343,-0.147455,-0.111699,-0.0761012,-0.0406896,-0.00549174,0.0294642,0.06415,0.0985371,0.132597,0.166302,0.199623,0.232534,0.265006,0.297014,0.328531,0.359533,0.389996,0.419896,0.449213,0.477925,0.506013,0.533458,0.560245,0.586358,0.611783,0.636509,0.660525,0.683821,0.706391,0.728229,0.74933,0.769692,0.789315,0.808198,0.826345,0.843758,0.860442,0.876405,0.891655,0.906199,0.920048,0.933213,0.945708,0.957543,0.968735,0.979296,0.989243,0.99859,1.00735,1.01555,1.0232,1.0303,1.0369,1.04298,1.04858,1.05371,1.05837,1.06259,1.06638,1.06975,1.07271,1.07527,1.07744,1.07922,1.08063,1.08166,1.08233,1.08263,1.08256,1.08213,1.08132,1.08014,1.07857,1.07661,1.07425,1.07147,1.06825,1.06459,1.06045,1.05582,1.05067,1.04498,1.03869,1.0318,1.02425,1.016,1.00702,0.997243,0.986626,0.975109,0.962631,0.949127,0.934527,0.918754,0.90173,0.883369,0.86358,0.842269,0.819335,0.794673,0.768172,0.739718,0.709194,0.676478,0.641449},
{-3.0454,-3.01936,-2.99328,-2.96716,-2.941,-2.91481,-2.88858,-2.86231,-2.836,-2.80965,-2.78326,-2.75683,-2.73035,-2.70384,-2.67728,-2.65068,-2.62403,-2.59733,-2.57058,-2.54378,-2.51693,-2.49003,-2.46307,-2.43605,-2.40897,-2.38183,-2.35463,-2.32736,-2.30002,-2.27261,-2.24513,-2.21757,-2.18993,-2.1622,-2.13439,-2.10649,-2.0785,-2.05041,-2.02222,-1.99393,-1.96553,-1.93702,-1.90839,-1.87965,-1.85078,-1.82179,-1.79266,-1.76339,-1.73399,-1.70444,-1.67474,-1.64489,-1.61488,-1.58471,-1.55437,-1.52385,-1.49317,-1.4623,-1.43124,-1.4,-1.36857,-1.33694,-1.30511,-1.27308,-1.24084,-1.2084,-1.17575,-1.14289,-1.10981,-1.07652,-1.04302,-1.0093,-0.975371,-0.941232,-0.906886,-0.872335,-0.837584,-0.802639,-0.767504,-0.732187,-0.696697,-0.661043,-0.625235,-0.589284,-0.553205,-0.51701,-0.480716,-0.444338,-0.407895,-0.371406,-0.33489,-0.29837,-0.261868,-0.225408,-0.189014,-0.152711,-0.116527,-0.0804882,-0.0446223,-0.00895787,0.0264766,0.0616519,0.0965391,0.131109,0.165332,0.19918,0.232623,0.265635,0.298187,0.330252,0.361805,0.39282,0.423273,0.453141,0.482403,0.511038,0.539026,0.566351,0.592996,0.618947,0.644189,0.668713,0.692508,0.715565,0.73788,0.759446,0.78026,0.800322,0.819632,0.838191,0.856002,0.87307,0.889403,0.905006,0.91989,0.934064,0.947539,0.960328,0.972445,0.983902,0.994715,1.0049,1.01447,1.02344,1.03184,1.03967,1.04695,1.0537,1.05993,1.06566,1.07091,1.07569,1.08002,1.0839,1.08735,1.09038,1.093,1.09523,1.09706,1.0985,1.09957,1.10026,1.10057,1.10051,1.10008,1.09926,1.09807,1.09648,1.09449,1.0921,1.08928,1.08602,1.08231,1.07811,1.07342,1.0682,1.06243,1.05607,1.04909,1.04145,1.03311,1.02403,1.01415,1.00342,0.991791,0.979196,0.965571,0.950846,0.934945,0.917788,0.899291,0.879364,0.85791,0.834831,0.81002,0.783366,0.754756,0.724071,0.691189,0.655988},
{-3.0583,-3.03226,-3.00619,-2.98008,-2.95393,-2.92775,-2.90152,-2.87526,-2.84896,-2.82261,-2.79623,-2.7698,-2.74334,-2.71683,-2.69027,-2.66367,-2.63703,-2.61033,-2.58359,-2.55679,-2.52994,-2.50304,-2.47608,-2.44907,-2.42199,-2.39485,-2.36765,-2.34038,-2.31304,-2.28563,-2.25814,-2.23058,-2.20294,-2.17521,-2.14739,-2.11949,-2.09149,-2.0634,-2.0352,-2.0069,-1.97849,-1.94997,-1.92133,-1.89258,-1.8637,-1.83468,-1.80554,-1.77626,-1.74683,-1.71726,-1.68754,-1.65766,-1.62762,-1.59741,-1.56704,-1.53649,-1.50576,-1.47485,-1.44375,-1.41245,-1.38096,-1.34927,-1.31738,-1.28528,-1.25297,-1.22045,-1.18771,-1.15475,-1.12158,-1.08818,-1.05457,-1.02073,-0.986676,-0.952402,-0.917911,-0.883206,-0.848292,-0.813173,-0.777854,-0.742343,-0.706647,-0.670775,-0.634738,-0.598546,-0.562212,-0.525749,-0.489173,-0.452501,-0.415749,-0.378937,-0.342084,-0.305212,-0.268344,-0.231503,-0.194714,-0.158003,-0.121396,-0.0849211,-0.0486058,-0.0124792,0.0234294,0.0590905,0.0944742,0.129551,0.16429,0.198661,0.232636,0.266186,0.299281,0.331893,0.363996,0.395564,0.42657,0.456992,0.486805,0.51599,0.544524,0.57239,0.59957,0.626049,0.651813,0.676849,0.701146,0.724697,0.747493,0.769529,0.790802,0.811309,0.83105,0.850027,0.868242,0.8857,0.902407,0.918371,0.933601,0.948106,0.961897,0.974988,0.987391,0.99912,1.01019,1.02062,1.03042,1.03961,1.04821,1.05623,1.06368,1.0706,1.07699,1.08286,1.08824,1.09315,1.09758,1.10156,1.1051,1.10822,1.11091,1.1132,1.11509,1.11659,1.11769,1.11842,1.11876,1.11872,1.1183,1.1175,1.11631,1.11472,1.11273,1.11032,1.10749,1.10421,1.10047,1.09625,1.09153,1.08628,1.08047,1.07407,1.06705,1.05937,1.05099,1.04186,1.03194,1.02117,1.00949,0.996852,0.983184,0.968418,0.952478,0.935286,0.916756,0.8968,0.875321,0.852221,0.827394,0.800729,0.772112,0.741424,0.708543,0.673344},
{-3.07102,-3.045,-3.01893,-2.99283,-2.96669,-2.94052,-2.9143,-2.88804,-2.86175,-2.83541,-2.80903,-2.78261,-2.75615,-2.72965,-2.7031,-2.6765,-2.64986,-2.62317,-2.59643,-2.56964,-2.54279,-2.51589,-2.48894,-2.46192,-2.43485,-2.40771,-2.38051,-2.35324,-2.3259,-2.29849,-2.271,-2.24344,-2.21579,-2.18806,-2.16024,-2.13233,-2.10433,-2.07623,-2.04803,-2.01972,-1.9913,-1.96277,-1.93412,-1.90536,-1.87646,-1.84744,-1.81828,-1.78898,-1.75953,-1.72994,-1.70019,-1.67029,-1.64022,-1.60999,-1.57958,-1.54899,-1.51822,-1.48727,-1.45612,-1.42478,-1.39324,-1.36149,-1.32954,-1.29737,-1.26499,-1.23239,-1.19957,-1.16652,-1.13325,-1.09976,-1.06603,-1.03208,-0.997901,-0.963494,-0.928863,-0.894009,-0.858936,-0.823648,-0.788151,-0.75245,-0.716554,-0.68047,-0.644208,-0.60778,-0.571197,-0.534473,-0.497622,-0.460661,-0.423606,-0.386477,-0.349293,-0.312076,-0.274847,-0.237632,-0.200455,-0.16334,-0.126316,-0.0894104,-0.052651,-0.0160674,0.0203108,0.0564531,0.0923292,0.127908,0.16316,0.198052,0.232556,0.266641,0.300277,0.333436,0.366088,0.398208,0.429768,0.460743,0.491109,0.520843,0.549925,0.578334,0.606052,0.633062,0.659349,0.6849,0.709704,0.733751,0.757032,0.779542,0.801276,0.822232,0.842409,0.861808,0.880431,0.898283,0.915369,0.931697,0.947276,0.962115,0.976226,0.989621,1.00231,1.01432,1.02565,1.03632,1.04636,1.05577,1.06457,1.07278,1.08041,1.0875,1.09404,1.10006,1.10557,1.11059,1.11514,1.11922,1.12285,1.12605,1.12881,1.13116,1.13311,1.13465,1.1358,1.13655,1.13692,1.1369,1.13649,1.13569,1.1345,1.1329,1.1309,1.12848,1.12562,1.12231,1.11854,1.11429,1.10953,1.10423,1.09837,1.09192,1.08485,1.07711,1.06867,1.05948,1.04949,1.03865,1.02691,1.01421,1.00047,0.98564,0.969634,0.952375,0.933781,0.913761,0.892221,0.869061,0.844175,0.817454,0.788782,0.75804,0.725104,0.689851},
{-3.08358,-3.05757,-3.03151,-3.00542,-2.97929,-2.95312,-2.92691,-2.90067,-2.87438,-2.84805,-2.82168,-2.79526,-2.76881,-2.74231,-2.71576,-2.68917,-2.66253,-2.63585,-2.60911,-2.58232,-2.55548,-2.52858,-2.50163,-2.47462,-2.44754,-2.42041,-2.39321,-2.36594,-2.3386,-2.31119,-2.2837,-2.25613,-2.22849,-2.20075,-2.17293,-2.14502,-2.11701,-2.08891,-2.0607,-2.03239,-2.00396,-1.97542,-1.94677,-1.91799,-1.88908,-1.86004,-1.83087,-1.80155,-1.77209,-1.74248,-1.71271,-1.68278,-1.65269,-1.62242,-1.59199,-1.56137,-1.53056,-1.49957,-1.46838,-1.43699,-1.40539,-1.37359,-1.34158,-1.30935,-1.2769,-1.24423,-1.21132,-1.17819,-1.14483,-1.11124,-1.07741,-1.04335,-1.00905,-0.974512,-0.939745,-0.904746,-0.869518,-0.834067,-0.798395,-0.76251,-0.726418,-0.690128,-0.653648,-0.616989,-0.580162,-0.543182,-0.506061,-0.468817,-0.431465,-0.394025,-0.356516,-0.318959,-0.281377,-0.243793,-0.206232,-0.168721,-0.131285,-0.0939537,-0.0567552,-0.0197193,0.0171237,0.053743,0.0901075,0.126186,0.161946,0.197357,0.232387,0.267006,0.301182,0.334885,0.368087,0.400758,0.432871,0.464401,0.49532,0.525607,0.555238,0.584192,0.61245,0.639994,0.666808,0.692879,0.718192,0.742739,0.76651,0.789498,0.811699,0.833109,0.853726,0.873552,0.892588,0.910839,0.928309,0.945007,0.96094,0.976119,0.990554,1.00426,1.01725,1.02953,1.04113,1.05205,1.06232,1.07196,1.08097,1.08937,1.09719,1.10445,1.11115,1.11732,1.12297,1.12811,1.13277,1.13696,1.14069,1.14397,1.14681,1.14923,1.15124,1.15283,1.15402,1.15482,1.15522,1.15522,1.15483,1.15405,1.15286,1.15127,1.14927,1.14684,1.14397,1.14065,1.13686,1.13259,1.1278,1.12248,1.11659,1.11012,1.10301,1.09524,1.08676,1.07754,1.06752,1.05665,1.04488,1.03214,1.01838,1.00353,0.987499,0.970224,0.951618,0.931591,0.910049,0.886893,0.862017,0.835311,0.80666,0.775944,0.74304,0.70782},
{-3.09598,-3.06998,-3.04393,-3.01785,-2.99173,-2.96557,-2.93937,-2.91313,-2.88685,-2.86052,-2.83416,-2.80775,-2.7813,-2.75481,-2.72827,-2.70168,-2.67505,-2.64837,-2.62163,-2.59485,-2.56801,-2.54112,-2.51417,-2.48716,-2.46009,-2.43295,-2.40575,-2.37849,-2.35115,-2.32374,-2.29625,-2.26868,-2.24103,-2.2133,-2.18547,-2.15756,-2.12955,-2.10144,-2.07323,-2.04491,-2.01648,-1.98793,-1.95927,-1.93048,-1.90156,-1.87251,-1.84332,-1.81399,-1.78451,-1.75488,-1.72509,-1.69514,-1.66503,-1.63474,-1.60427,-1.57362,-1.54278,-1.51174,-1.48051,-1.44908,-1.41744,-1.38559,-1.35352,-1.32122,-1.28871,-1.25596,-1.22299,-1.18977,-1.15633,-1.12264,-1.08871,-1.05453,-1.02012,-0.985461,-0.950561,-0.915422,-0.880045,-0.844434,-0.808594,-0.772529,-0.736247,-0.699755,-0.663062,-0.626177,-0.589114,-0.551883,-0.514499,-0.476977,-0.439335,-0.40159,-0.363762,-0.325871,-0.287941,-0.249995,-0.212057,-0.174154,-0.136313,-0.0985615,-0.0609296,-0.0234468,0.013856,0.0509475,0.0877958,0.124369,0.160635,0.19656,0.232114,0.267263,0.301976,0.336223,0.369972,0.403194,0.43586,0.467943,0.499417,0.530255,0.560436,0.589937,0.618736,0.646817,0.67416,0.700752,0.726578,0.751628,0.775892,0.799361,0.822032,0.843898,0.86496,0.885216,0.904668,0.923321,0.941179,0.958249,0.974539,0.99006,1.00482,1.01884,1.03212,1.04469,1.05655,1.06773,1.07824,1.0881,1.09732,1.10592,1.11393,1.12135,1.12821,1.13452,1.14031,1.14558,1.15035,1.15464,1.15845,1.16182,1.16473,1.16722,1.16928,1.17092,1.17215,1.17297,1.17339,1.17342,1.17304,1.17225,1.17107,1.16947,1.16744,1.16499,1.1621,1.15875,1.15492,1.15061,1.14577,1.1404,1.13446,1.12793,1.12076,1.11293,1.10438,1.09509,1.085,1.07406,1.06221,1.0494,1.03556,1.02063,1.00452,0.987168,0.968483,0.948378,0.926758,0.903525,0.878571,0.851788,0.823059,0.792264,0.759277,0.723972},
{-3.10822,-3.08223,-3.0562,-3.03012,-3.00401,-2.97786,-2.95167,-2.92543,-2.89916,-2.87284,-2.84649,-2.82009,-2.79364,-2.76715,-2.74062,-2.71404,-2.68741,-2.66073,-2.634,-2.60722,-2.58039,-2.5535,-2.52655,-2.49955,-2.47248,-2.44535,-2.41815,-2.39088,-2.36354,-2.33613,-2.30865,-2.28108,-2.25343,-2.2257,-2.19787,-2.16995,-2.14194,-2.11383,-2.08561,-2.05729,-2.02885,-2.0003,-1.97163,-1.94283,-1.9139,-1.88484,-1.85564,-1.8263,-1.7968,-1.76716,-1.73735,-1.70738,-1.67724,-1.64692,-1.61643,-1.58575,-1.55487,-1.52381,-1.49254,-1.46106,-1.42937,-1.39747,-1.36535,-1.333,-1.30042,-1.26761,-1.23456,-1.20127,-1.16773,-1.13395,-1.09992,-1.06565,-1.03112,-0.996343,-0.961316,-0.92604,-0.890518,-0.854752,-0.818747,-0.782508,-0.746041,-0.709353,-0.672452,-0.635348,-0.598052,-0.560576,-0.522935,-0.485142,-0.447215,-0.409171,-0.37103,-0.332812,-0.29454,-0.256237,-0.217928,-0.17964,-0.141398,-0.103233,-0.0651728,-0.0272483,0.0105093,0.0480683,0.0853962,0.12246,0.159227,0.195664,0.231738,0.267415,0.302664,0.337452,0.371747,0.405518,0.438737,0.471374,0.503402,0.534794,0.565526,0.595575,0.624918,0.653537,0.681412,0.708528,0.73487,0.760427,0.785186,0.809141,0.832285,0.854613,0.876122,0.896813,0.916686,0.935745,0.953994,0.971441,0.988093,1.00396,1.01905,1.03339,1.04697,1.05982,1.07196,1.08339,1.09414,1.10422,1.11366,1.12246,1.13065,1.13825,1.14527,1.15173,1.15765,1.16305,1.16793,1.17232,1.17624,1.17968,1.18267,1.18522,1.18734,1.18902,1.19029,1.19115,1.1916,1.19163,1.19126,1.19049,1.18929,1.18768,1.18565,1.18318,1.18026,1.17688,1.17302,1.16866,1.16379,1.15837,1.15238,1.14578,1.13856,1.13066,1.12206,1.1127,1.10254,1.09153,1.07961,1.06673,1.05282,1.03781,1.02163,1.0042,0.985445,0.965268,0.943577,0.920272,0.895248,0.868394,0.839593,0.808725,0.775663,0.740277},
{-3.12031,-3.09433,-3.06831,-3.04224,-3.01614,-2.99,-2.96381,-2.93759,-2.91132,-2.88501,-2.85866,-2.83227,-2.80583,-2.77935,-2.75282,-2.72624,-2.69962,-2.67295,-2.64622,-2.61945,-2.59262,-2.56573,-2.53879,-2.51179,-2.48472,-2.45759,-2.4304,-2.40313,-2.3758,-2.34839,-2.3209,-2.29333,-2.26569,-2.23795,-2.21012,-2.18221,-2.15419,-2.12608,-2.09786,-2.06953,-2.04109,-2.01253,-1.98385,-1.95505,-1.92611,-1.89704,-1.86783,-1.83847,-1.80896,-1.7793,-1.74948,-1.71949,-1.68933,-1.65899,-1.62847,-1.59776,-1.56686,-1.53575,-1.50445,-1.47293,-1.4412,-1.40925,-1.37708,-1.34467,-1.31203,-1.27916,-1.24604,-1.21267,-1.17906,-1.14519,-1.11107,-1.07669,-1.04205,-1.00716,-0.97201,-0.936602,-0.900939,-0.865024,-0.82886,-0.792451,-0.755803,-0.718924,-0.68182,-0.644502,-0.606979,-0.569265,-0.531371,-0.493313,-0.455106,-0.416769,-0.378321,-0.339782,-0.301174,-0.262521,-0.223846,-0.185178,-0.146542,-0.107968,-0.069485,-0.0311239,0.00708372,0.0451056,0.0829087,0.12046,0.157725,0.19467,0.231261,0.267464,0.303246,0.338573,0.373413,0.407734,0.441505,0.474696,0.507279,0.539225,0.57051,0.601109,0.630998,0.660157,0.688567,0.716211,0.743073,0.769139,0.794399,0.818844,0.842465,0.865259,0.887221,0.908351,0.92865,0.94812,0.966766,0.984595,1.00161,1.01783,1.03326,1.04792,1.06181,1.07495,1.08736,1.09906,1.11005,1.12037,1.13002,1.13903,1.14741,1.15518,1.16237,1.16898,1.17505,1.18057,1.18558,1.19008,1.19409,1.19762,1.20069,1.20331,1.20549,1.20723,1.20855,1.20944,1.20992,1.20999,1.20964,1.20887,1.20769,1.20608,1.20404,1.20156,1.19863,1.19523,1.19136,1.18698,1.18208,1.17663,1.17061,1.16398,1.15672,1.14879,1.14015,1.13076,1.12056,1.10952,1.09757,1.08465,1.07071,1.05568,1.03947,1.02203,1.00325,0.983063,0.961363,0.938054,0.913031,0.886181,0.857389,0.826532,0.793482,0.75811},
{-3.13225,-3.10628,-3.08027,-3.05421,-3.02812,-3.00199,-2.97581,-2.94959,-2.92333,-2.89703,-2.87069,-2.8443,-2.81787,-2.7914,-2.76487,-2.73831,-2.71169,-2.68502,-2.6583,-2.63153,-2.6047,-2.57782,-2.55088,-2.52388,-2.49682,-2.46969,-2.4425,-2.41524,-2.38791,-2.3605,-2.33301,-2.30545,-2.2778,-2.25007,-2.22224,-2.19432,-2.16631,-2.13819,-2.10997,-2.08163,-2.05319,-2.02463,-1.99594,-1.96713,-1.93819,-1.90911,-1.87989,-1.85052,-1.821,-1.79132,-1.76149,-1.73148,-1.7013,-1.67094,-1.64039,-1.60966,-1.57873,-1.54759,-1.51625,-1.4847,-1.45293,-1.42093,-1.38871,-1.35625,-1.32356,-1.29062,-1.25743,-1.22399,-1.1903,-1.15635,-1.12214,-1.08766,-1.05292,-1.01792,-0.982648,-0.947113,-0.911313,-0.875253,-0.838933,-0.802359,-0.765537,-0.728471,-0.69117,-0.653643,-0.615899,-0.577951,-0.539811,-0.501493,-0.463013,-0.424389,-0.38564,-0.346785,-0.307847,-0.268849,-0.229815,-0.190772,-0.151748,-0.11277,-0.07387,-0.0350774,0.00357541,0.0420555,0.0803296,0.118363,0.156123,0.193572,0.230678,0.267404,0.303717,0.339582,0.374966,0.409835,0.444158,0.477903,0.511041,0.543543,0.575382,0.606532,0.636969,0.666672,0.69562,0.723794,0.751179,0.777759,0.803524,0.828462,0.852566,0.87583,0.89825,0.919824,0.940554,0.960441,0.979489,0.997704,1.0151,1.03167,1.04744,1.06242,1.07663,1.09006,1.10276,1.11472,1.12596,1.13652,1.14639,1.15561,1.16419,1.17215,1.1795,1.18628,1.19249,1.19815,1.20328,1.20789,1.21201,1.21564,1.2188,1.22149,1.22374,1.22554,1.22691,1.22786,1.22838,1.22847,1.22815,1.22741,1.22625,1.22465,1.22262,1.22015,1.21722,1.21383,1.20995,1.20556,1.20066,1.1952,1.18917,1.18254,1.17527,1.16734,1.15869,1.14929,1.13909,1.12805,1.1161,1.1032,1.08927,1.07426,1.05808,1.04067,1.02194,1.00179,0.980152,0.956909,0.93196,0.905193,0.876492,0.845733,0.812788,0.777525},
{-3.14404,-3.11808,-3.09208,-3.06604,-3.03995,-3.01383,-2.98766,-2.96145,-2.9352,-2.90891,-2.88258,-2.8562,-2.82977,-2.8033,-2.77679,-2.75022,-2.72361,-2.69695,-2.67024,-2.64347,-2.61665,-2.58977,-2.56283,-2.53584,-2.50878,-2.48166,-2.45447,-2.42721,-2.39988,-2.37247,-2.34499,-2.31743,-2.28978,-2.26205,-2.23422,-2.2063,-2.17829,-2.15017,-2.12194,-2.09361,-2.06516,-2.0366,-2.00791,-1.97909,-1.95014,-1.92105,-1.89182,-1.86245,-1.83292,-1.80323,-1.77337,-1.74335,-1.71315,-1.68277,-1.65221,-1.62145,-1.59049,-1.55933,-1.52795,-1.49637,-1.46456,-1.43252,-1.40025,-1.36774,-1.33499,-1.30199,-1.26874,-1.23524,-1.20147,-1.16744,-1.13314,-1.09857,-1.06373,-1.02862,-0.993233,-0.957574,-0.921643,-0.885441,-0.848971,-0.812238,-0.775244,-0.737998,-0.700505,-0.662774,-0.624814,-0.586638,-0.548257,-0.509685,-0.470938,-0.432033,-0.392988,-0.353823,-0.314561,-0.275224,-0.235836,-0.196425,-0.157018,-0.117642,-0.0783295,-0.0391104,-1.7408e-05,0.0389164,0.0776569,0.11617,0.154419,0.192371,0.229988,0.267235,0.304077,0.340478,0.376404,0.411821,0.446695,0.480994,0.514688,0.547746,0.58014,0.611844,0.642832,0.67308,0.702569,0.731277,0.759189,0.786287,0.812561,0.837997,0.862588,0.886328,0.909211,0.931235,0.952401,0.972709,0.992165,1.01077,1.02854,1.04548,1.0616,1.07691,1.09143,1.10518,1.11815,1.13039,1.14189,1.15269,1.1628,1.17223,1.18101,1.18916,1.19669,1.20363,1.21,1.2158,1.22107,1.2258,1.23003,1.23377,1.23702,1.2398,1.24213,1.24401,1.24544,1.24645,1.24702,1.24717,1.24689,1.24619,1.24506,1.2435,1.2415,1.23905,1.23615,1.23278,1.22892,1.22456,1.21968,1.21425,1.20824,1.20164,1.19441,1.1865,1.17789,1.16854,1.15839,1.14741,1.13553,1.12269,1.10885,1.09393,1.07786,1.06056,1.04196,1.02196,1.00047,0.9774,0.952637,0.926073,0.89759,0.867064,0.834366,0.799363},
{-3.1557,-3.12975,-3.10375,-3.07772,-3.05165,-3.02553,-2.99937,-2.97317,-2.94693,-2.92065,-2.89432,-2.86795,-2.84153,-2.81507,-2.78856,-2.762,-2.73539,-2.70874,-2.68203,-2.65527,-2.62845,-2.60158,-2.57465,-2.54766,-2.5206,-2.49349,-2.4663,-2.43904,-2.41172,-2.38431,-2.35683,-2.32927,-2.30163,-2.27389,-2.24607,-2.21815,-2.19014,-2.16202,-2.13379,-2.10546,-2.07701,-2.04844,-2.01975,-1.99092,-1.96197,-1.93288,-1.90364,-1.87425,-1.84471,-1.81501,-1.78515,-1.75511,-1.72489,-1.6945,-1.66391,-1.63313,-1.60215,-1.57096,-1.53955,-1.50793,-1.47609,-1.44401,-1.4117,-1.37914,-1.34634,-1.31329,-1.27998,-1.2464,-1.21256,-1.17846,-1.14407,-1.10942,-1.07448,-1.03927,-1.00377,-0.967992,-0.931933,-0.895595,-0.85898,-0.822091,-0.784933,-0.74751,-0.70983,-0.671901,-0.633732,-0.595333,-0.556717,-0.517897,-0.478889,-0.439708,-0.400374,-0.360906,-0.321326,-0.281656,-0.241921,-0.202148,-0.162363,-0.122596,-0.0828765,-0.0432367,-0.00370901,0.0356731,0.0748752,0.113862,0.152598,0.191046,0.229171,0.266935,0.304303,0.341238,0.377704,0.413666,0.44909,0.483943,0.518192,0.551806,0.584756,0.617013,0.648553,0.679349,0.70938,0.738624,0.767064,0.794684,0.821468,0.847406,0.872488,0.896706,0.920055,0.942533,0.964138,0.984873,1.00474,1.02375,1.0419,1.0592,1.07567,1.09132,1.10616,1.12021,1.13348,1.14598,1.15775,1.16879,1.17913,1.18878,1.19777,1.20611,1.21382,1.22093,1.22745,1.2334,1.23879,1.24366,1.248,1.25184,1.25518,1.25805,1.26046,1.2624,1.2639,1.26496,1.26559,1.26578,1.26555,1.26488,1.26378,1.26225,1.26027,1.25785,1.25497,1.25161,1.24777,1.24343,1.23856,1.23314,1.22716,1.22057,1.21336,1.20548,1.1969,1.18757,1.17746,1.16652,1.15468,1.14191,1.12813,1.11327,1.09728,1.08008,1.06158,1.04169,1.02033,0.997402,0.972791,0.946392,0.918086,0.887749,0.855251,0.820456},
{-3.16721,-3.14127,-3.11529,-3.08927,-3.0632,-3.0371,-3.01095,-2.98476,-2.95852,-2.93225,-2.90593,-2.87956,-2.85315,-2.8267,-2.80019,-2.77364,-2.74704,-2.72039,-2.69369,-2.66693,-2.64012,-2.61326,-2.58633,-2.55934,-2.53229,-2.50518,-2.478,-2.45075,-2.42342,-2.39602,-2.36855,-2.34099,-2.31334,-2.28561,-2.25779,-2.22987,-2.20186,-2.17374,-2.14551,-2.11718,-2.08873,-2.06016,-2.03146,-2.00264,-1.97368,-1.94458,-1.91534,-1.88594,-1.85639,-1.82668,-1.79681,-1.76676,-1.73653,-1.70611,-1.67551,-1.64471,-1.6137,-1.58249,-1.55106,-1.51941,-1.48753,-1.45541,-1.42306,-1.39046,-1.35761,-1.32451,-1.29114,-1.2575,-1.2236,-1.18941,-1.15495,-1.12021,-1.08518,-1.04987,-1.01427,-0.978374,-0.942194,-0.905725,-0.86897,-0.831931,-0.794614,-0.757021,-0.719161,-0.68104,-0.642667,-0.604053,-0.565209,-0.526148,-0.486885,-0.447437,-0.407821,-0.368057,-0.328167,-0.288172,-0.248097,-0.20797,-0.167816,-0.127665,-0.0875469,-0.0474942,-0.00753944,0.0322834,0.0719395,0.111393,0.150608,0.189546,0.228172,0.266447,0.304335,0.341797,0.378798,0.415301,0.45127,0.486671,0.521471,0.555637,0.589139,0.621947,0.654034,0.685374,0.715944,0.745722,0.774688,0.802826,0.830119,0.856555,0.882124,0.906818,0.93063,0.953557,0.975598,0.996754,1.01703,1.03642,1.05495,1.07262,1.08943,1.10541,1.12056,1.1349,1.14845,1.16122,1.17324,1.18451,1.19507,1.20492,1.21409,1.22261,1.23048,1.23773,1.24438,1.25044,1.25595,1.2609,1.26532,1.26922,1.27263,1.27554,1.27798,1.27995,1.28146,1.28252,1.28314,1.28331,1.28304,1.28234,1.28119,1.2796,1.27756,1.27506,1.27209,1.26864,1.26469,1.26023,1.25524,1.24969,1.24356,1.23682,1.22944,1.22139,1.21262,1.2031,1.19279,1.18162,1.16956,1.15654,1.14251,1.12739,1.11111,1.09361,1.0748,1.05458,1.03287,1.00957,0.984562,0.957745,0.928994,0.898183,0.865177,0.829839},
{-3.17858,-3.15266,-3.12669,-3.10067,-3.07462,-3.04852,-3.02239,-2.9962,-2.96998,-2.94371,-2.9174,-2.89104,-2.86464,-2.83819,-2.8117,-2.78515,-2.75856,-2.73191,-2.70522,-2.67847,-2.65166,-2.6248,-2.59788,-2.5709,-2.54385,-2.51674,-2.48957,-2.46232,-2.435,-2.4076,-2.38013,-2.35257,-2.32493,-2.29721,-2.26939,-2.24147,-2.21346,-2.18534,-2.15711,-2.12878,-2.10033,-2.07176,-2.04306,-2.01423,-1.98527,-1.95617,-1.92692,-1.89752,-1.86796,-1.83825,-1.80836,-1.7783,-1.74806,-1.71763,-1.68701,-1.65619,-1.62516,-1.59392,-1.56247,-1.53079,-1.49888,-1.46673,-1.43434,-1.4017,-1.3688,-1.33565,-1.30222,-1.26853,-1.23456,-1.20031,-1.16577,-1.13095,-1.09583,-1.06042,-1.02472,-0.988714,-0.952415,-0.915819,-0.878928,-0.841745,-0.804272,-0.766515,-0.728478,-0.69017,-0.651598,-0.612773,-0.573706,-0.534409,-0.494897,-0.455186,-0.415293,-0.375238,-0.335042,-0.294727,-0.254318,-0.21384,-0.173321,-0.13279,-0.092278,-0.0518161,-0.0114378,0.0288227,0.06893,0.108848,0.148539,0.187967,0.227092,0.265878,0.304285,0.342275,0.379811,0.416856,0.453372,0.489324,0.524678,0.5594,0.593458,0.626822,0.659462,0.691353,0.722469,0.752787,0.782287,0.81095,0.838761,0.865705,0.891771,0.916951,0.941237,0.964626,0.987115,1.0087,1.0294,1.0492,1.06812,1.08616,1.10333,1.11965,1.13513,1.14979,1.16364,1.17669,1.18897,1.2005,1.2113,1.22138,1.23076,1.23947,1.24753,1.25496,1.26177,1.26798,1.27362,1.27871,1.28325,1.28726,1.29077,1.29377,1.29629,1.29834,1.29993,1.30105,1.30172,1.30195,1.30174,1.30107,1.29997,1.29842,1.29641,1.29394,1.291,1.28758,1.28367,1.27924,1.27428,1.26876,1.26266,1.25596,1.24862,1.24062,1.2319,1.22244,1.21218,1.20109,1.18911,1.17618,1.16224,1.14723,1.13108,1.1137,1.09504,1.07498,1.05344,1.03033,1.00553,0.978935,0.950418,0.919854,0.887109,0.852042},
{-3.18982,-3.16391,-3.13795,-3.11195,-3.08591,-3.05982,-3.03369,-3.00752,-2.9813,-2.95505,-2.92874,-2.90239,-2.876,-2.84956,-2.82307,-2.79653,-2.76995,-2.74331,-2.71662,-2.68987,-2.66308,-2.63622,-2.6093,-2.58233,-2.55529,-2.52818,-2.50101,-2.47377,-2.44645,-2.41906,-2.39159,-2.36404,-2.3364,-2.30868,-2.28086,-2.25295,-2.22493,-2.19682,-2.1686,-2.14026,-2.11181,-2.08324,-2.05454,-2.02571,-1.99675,-1.96764,-1.93839,-1.90899,-1.87942,-1.8497,-1.8198,-1.78973,-1.75948,-1.72904,-1.69841,-1.66757,-1.63652,-1.60527,-1.57379,-1.54208,-1.51014,-1.47796,-1.44554,-1.41286,-1.37992,-1.34672,-1.31324,-1.27949,-1.24546,-1.21114,-1.17653,-1.14163,-1.10643,-1.07093,-1.03513,-0.999021,-0.962608,-0.925891,-0.888869,-0.851546,-0.813923,-0.776006,-0.737799,-0.69931,-0.660545,-0.621515,-0.582231,-0.542704,-0.502949,-0.462981,-0.422818,-0.382479,-0.341984,-0.301355,-0.260618,-0.219797,-0.17892,-0.138016,-0.0971153,-0.0562505,-0.0154548,0.0252373,0.06579,0.106167,0.14633,0.186241,0.225862,0.265153,0.304075,0.34259,0.380658,0.418242,0.455303,0.491804,0.52771,0.562986,0.5976,0.631518,0.664712,0.697153,0.728816,0.759675,0.78971,0.818901,0.847231,0.874685,0.901251,0.926919,0.951681,0.975534,0.998473,1.0205,1.04162,1.06183,1.08113,1.09955,1.11709,1.13376,1.14957,1.16454,1.17869,1.19203,1.20458,1.21636,1.2274,1.2377,1.2473,1.25621,1.26445,1.27205,1.27902,1.28539,1.29116,1.29637,1.30103,1.30515,1.30875,1.31185,1.31445,1.31657,1.31822,1.3194,1.32013,1.3204,1.32023,1.3196,1.31853,1.317,1.31502,1.31257,1.30965,1.30625,1.30235,1.29793,1.29299,1.28749,1.28141,1.27472,1.2674,1.25941,1.25072,1.24129,1.23107,1.22001,1.20807,1.19519,1.18131,1.16637,1.15029,1.13301,1.11443,1.09448,1.07306,1.05006,1.0254,0.998944,0.970579,0.940174,0.907593,0.872693},
{-3.20094,-3.17503,-3.14909,-3.1231,-3.09707,-3.07099,-3.04487,-3.01871,-2.9925,-2.96625,-2.93996,-2.91361,-2.88723,-2.8608,-2.83431,-2.80778,-2.78121,-2.75457,-2.72789,-2.70115,-2.67436,-2.64751,-2.6206,-2.59363,-2.5666,-2.5395,-2.51233,-2.48509,-2.45778,-2.43039,-2.40293,-2.37538,-2.34775,-2.32003,-2.29221,-2.2643,-2.23629,-2.20818,-2.17996,-2.15163,-2.12318,-2.09461,-2.06591,-2.03708,-2.00812,-1.97901,-1.94975,-1.92035,-1.89078,-1.86105,-1.83115,-1.80107,-1.77081,-1.74036,-1.70971,-1.67886,-1.6478,-1.61652,-1.58502,-1.55329,-1.52132,-1.48912,-1.45666,-1.42394,-1.39096,-1.35772,-1.32419,-1.29039,-1.2563,-1.22192,-1.18725,-1.15227,-1.11699,-1.0814,-1.04551,-1.0093,-0.972776,-0.935941,-0.898793,-0.861335,-0.823568,-0.785496,-0.747124,-0.708459,-0.669507,-0.630278,-0.590782,-0.551032,-0.51104,-0.470822,-0.430395,-0.389777,-0.348989,-0.308053,-0.266994,-0.225835,-0.184606,-0.143335,-0.102052,-0.0607905,-0.0195829,0.0215354,0.0625285,0.103359,0.143989,0.18438,0.224492,0.264285,0.30372,0.342757,0.381355,0.419475,0.457079,0.494129,0.530587,0.566417,0.601586,0.636061,0.669809,0.702803,0.735014,0.766418,0.796991,0.826713,0.855566,0.883534,0.910603,0.936764,0.962008,0.986329,1.00972,1.03219,1.05374,1.07436,1.09407,1.11287,1.13078,1.1478,1.16395,1.17924,1.19369,1.20732,1.22015,1.2322,1.24348,1.25402,1.26384,1.27295,1.28139,1.28917,1.29631,1.30284,1.30876,1.31411,1.31889,1.32313,1.32684,1.33004,1.33273,1.33494,1.33667,1.33792,1.33872,1.33905,1.33894,1.33837,1.33735,1.33587,1.33394,1.33154,1.32866,1.3253,1.32145,1.31708,1.31218,1.30673,1.30071,1.29408,1.28683,1.27891,1.2703,1.26095,1.25082,1.23987,1.22804,1.21529,1.20154,1.18675,1.17084,1.15373,1.13535,1.1156,1.09441,1.07167,1.04726,1.02109,0.993022,0.962932,0.930681,0.896124},
{-3.21192,-3.18603,-3.1601,-3.13412,-3.1081,-3.08203,-3.05592,-3.02977,-3.00357,-2.97733,-2.95104,-2.92471,-2.89833,-2.87191,-2.84544,-2.81891,-2.79234,-2.76572,-2.73904,-2.71231,-2.68552,-2.65868,-2.63178,-2.60481,-2.57778,-2.55069,-2.52353,-2.4963,-2.46899,-2.44161,-2.41415,-2.3866,-2.35898,-2.33126,-2.30345,-2.27554,-2.24754,-2.21943,-2.19121,-2.16288,-2.13443,-2.10586,-2.07717,-2.04834,-2.01938,-1.99027,-1.96101,-1.9316,-1.90203,-1.8723,-1.84239,-1.81231,-1.78204,-1.75158,-1.72092,-1.69005,-1.65898,-1.62769,-1.59617,-1.56442,-1.53243,-1.50019,-1.4677,-1.43495,-1.40194,-1.36865,-1.33509,-1.30123,-1.26709,-1.23265,-1.19791,-1.16287,-1.12751,-1.09184,-1.05585,-1.01955,-0.982924,-0.945977,-0.908709,-0.871121,-0.833215,-0.794994,-0.756463,-0.717628,-0.678495,-0.639073,-0.599373,-0.559405,-0.519183,-0.478722,-0.438037,-0.397149,-0.356075,-0.31484,-0.273465,-0.231977,-0.190403,-0.148772,-0.107114,-0.0654621,-0.0238497,0.0176881,0.0591147,0.100393,0.141484,0.182348,0.222945,0.263235,0.303178,0.342731,0.381854,0.420508,0.458651,0.496246,0.533253,0.569635,0.605358,0.640386,0.674688,0.708233,0.740992,0.772939,0.80405,0.834304,0.86368,0.892162,0.919737,0.946391,0.972117,0.996908,1.02076,1.04367,1.06565,1.08668,1.10679,1.12598,1.14425,1.16162,1.17811,1.19373,1.20849,1.22241,1.23551,1.24782,1.25935,1.27012,1.28015,1.28947,1.2981,1.30605,1.31336,1.32003,1.3261,1.33157,1.33648,1.34082,1.34463,1.34792,1.3507,1.35298,1.35477,1.35608,1.35693,1.35731,1.35724,1.3567,1.35571,1.35426,1.35235,1.34997,1.34711,1.34377,1.33993,1.33557,1.33068,1.32525,1.31923,1.31262,1.30538,1.29748,1.28889,1.27956,1.26946,1.25854,1.24675,1.23404,1.22034,1.2056,1.18975,1.17271,1.15441,1.13475,1.11365,1.09101,1.06672,1.04066,1.01271,0.982738,0.950609,0.916172},
{-3.22278,-3.1969,-3.17098,-3.14502,-3.119,-3.09295,-3.06685,-3.04071,-3.01452,-2.98829,-2.96201,-2.93569,-2.90932,-2.8829,-2.85644,-2.82992,-2.80336,-2.77674,-2.75007,-2.72335,-2.69657,-2.66973,-2.64283,-2.61588,-2.58885,-2.56177,-2.53461,-2.50738,-2.48008,-2.45271,-2.42525,-2.39771,-2.37009,-2.34238,-2.31457,-2.28667,-2.25867,-2.23057,-2.20235,-2.17403,-2.14558,-2.11702,-2.08832,-2.05949,-2.03053,-2.00142,-1.97217,-1.94276,-1.91319,-1.88345,-1.85354,-1.82345,-1.79317,-1.7627,-1.73204,-1.70116,-1.67008,-1.63877,-1.60723,-1.57546,-1.54345,-1.51119,-1.47868,-1.4459,-1.41285,-1.37952,-1.34592,-1.31202,-1.27783,-1.24333,-1.20853,-1.17342,-1.13799,-1.10225,-1.06617,-1.02978,-0.993052,-0.955997,-0.918613,-0.8809,-0.84286,-0.804496,-0.765811,-0.726811,-0.687503,-0.647894,-0.607995,-0.567815,-0.527369,-0.48667,-0.445734,-0.40458,-0.363227,-0.321698,-0.280014,-0.238202,-0.196289,-0.154303,-0.112276,-0.0702393,-0.0282271,0.0137252,0.0555808,0.0973019,0.138849,0.180183,0.221263,0.262047,0.302494,0.342562,0.38221,0.421395,0.460078,0.498217,0.535773,0.572709,0.608987,0.644571,0.679429,0.713528,0.746839,0.779334,0.810988,0.841777,0.871682,0.900685,0.928771,0.955926,0.982142,1.00741,1.03173,1.05509,1.0775,1.09896,1.11948,1.13906,1.15772,1.17545,1.19229,1.20824,1.22332,1.23754,1.25093,1.26351,1.2753,1.28632,1.29658,1.30612,1.31496,1.32311,1.3306,1.33744,1.34367,1.3493,1.35434,1.35882,1.36276,1.36616,1.36905,1.37144,1.37333,1.37474,1.37568,1.37615,1.37616,1.3757,1.37479,1.37342,1.37159,1.36929,1.36652,1.36326,1.35951,1.35524,1.35045,1.34512,1.33921,1.33272,1.32561,1.31784,1.3094,1.30023,1.2903,1.27957,1.26798,1.25549,1.24203,1.22755,1.21198,1.19525,1.17727,1.15796,1.13724,1.115,1.09114,1.06554,1.03808,1.00862,0.977036,0.943166},
{-3.23352,-3.20766,-3.18175,-3.15579,-3.12979,-3.10375,-3.07766,-3.05153,-3.02535,-2.99913,-2.97286,-2.94654,-2.92018,-2.89377,-2.86732,-2.84081,-2.81425,-2.78764,-2.76098,-2.73427,-2.70749,-2.68066,-2.65377,-2.62682,-2.59981,-2.57273,-2.54558,-2.51836,-2.49106,-2.46369,-2.43624,-2.40871,-2.38109,-2.35339,-2.32559,-2.29769,-2.2697,-2.2416,-2.21339,-2.18506,-2.15662,-2.12806,-2.09937,-2.07055,-2.04158,-2.01248,-1.98322,-1.95381,-1.92424,-1.8945,-1.86459,-1.8345,-1.80422,-1.77374,-1.74307,-1.71219,-1.68109,-1.64977,-1.61822,-1.58643,-1.5544,-1.52212,-1.48958,-1.45678,-1.4237,-1.39034,-1.35669,-1.32276,-1.28852,-1.25397,-1.21912,-1.18394,-1.14845,-1.11263,-1.07647,-1.03999,-1.00317,-0.966013,-0.928519,-0.890687,-0.852519,-0.814018,-0.775186,-0.736028,-0.696551,-0.656762,-0.616671,-0.576287,-0.535624,-0.494695,-0.453516,-0.412105,-0.37048,-0.328664,-0.28668,-0.244552,-0.202308,-0.159977,-0.117588,-0.0751753,-0.0327717,0.00958686,0.0518634,0.0940197,0.136016,0.177812,0.219367,0.260638,0.301583,0.342159,0.382324,0.422036,0.461251,0.49993,0.538031,0.575515,0.612343,0.64848,0.68389,0.71854,0.7524,0.78544,0.817633,0.848957,0.879389,0.90891,0.937504,0.965159,0.991862,1.01761,1.04239,1.0662,1.08905,1.11093,1.13185,1.15182,1.17085,1.18895,1.20613,1.22241,1.2378,1.25232,1.266,1.27884,1.29088,1.30214,1.31262,1.32237,1.3314,1.33973,1.34739,1.35439,1.36077,1.36653,1.37169,1.37629,1.38033,1.38383,1.3868,1.38926,1.39122,1.3927,1.39369,1.39421,1.39426,1.39385,1.39297,1.39163,1.38982,1.38755,1.3848,1.38156,1.37782,1.37358,1.3688,1.36348,1.3576,1.35112,1.34403,1.33629,1.32787,1.31873,1.30884,1.29814,1.2866,1.27416,1.26076,1.24634,1.23084,1.21418,1.19629,1.17707,1.15645,1.13431,1.11056,1.08507,1.05772,1.02839,0.99691,0.963144},
{-3.24414,-3.21829,-3.19239,-3.16645,-3.14046,-3.11443,-3.08835,-3.06223,-3.03606,-3.00985,-2.98359,-2.95728,-2.93093,-2.90453,-2.87808,-2.85158,-2.82504,-2.79843,-2.77178,-2.74507,-2.71831,-2.69148,-2.6646,-2.63766,-2.61065,-2.58357,-2.55643,-2.52922,-2.50193,-2.47457,-2.44712,-2.4196,-2.39199,-2.36429,-2.33649,-2.3086,-2.28061,-2.25252,-2.22431,-2.196,-2.16756,-2.139,-2.11032,-2.0815,-2.05254,-2.02344,-1.99418,-1.96477,-1.9352,-1.90547,-1.87555,-1.84546,-1.81517,-1.7847,-1.75402,-1.72313,-1.69202,-1.66069,-1.62913,-1.59733,-1.56529,-1.53299,-1.50043,-1.4676,-1.43449,-1.4011,-1.36742,-1.33344,-1.29916,-1.26457,-1.22966,-1.19443,-1.15887,-1.12298,-1.08675,-1.05018,-1.01327,-0.976021,-0.938421,-0.900476,-0.862185,-0.823551,-0.784577,-0.745267,-0.705627,-0.665664,-0.625386,-0.584804,-0.54393,-0.502777,-0.46136,-0.419697,-0.377808,-0.335712,-0.293432,-0.250995,-0.208426,-0.165754,-0.12301,-0.0802256,-0.0374356,0.00532438,0.0480172,0.0906043,0.133046,0.1753,0.217326,0.259081,0.300522,0.341604,0.382286,0.422522,0.46227,0.501489,0.540135,0.578168,0.615549,0.652241,0.688206,0.723411,0.757823,0.791413,0.824151,0.856015,0.88698,0.917026,0.946137,0.974298,1.0015,1.02773,1.05298,1.07725,1.10055,1.12286,1.1442,1.16458,1.18399,1.20247,1.22,1.23662,1.25234,1.26718,1.28115,1.29428,1.30659,1.3181,1.32883,1.33881,1.34805,1.35659,1.36444,1.37163,1.37817,1.38409,1.38941,1.39415,1.39833,1.40196,1.40506,1.40764,1.40971,1.41129,1.41239,1.41301,1.41316,1.41285,1.41207,1.41083,1.40913,1.40695,1.40431,1.40118,1.39755,1.39343,1.38878,1.38359,1.37785,1.37152,1.36459,1.35703,1.3488,1.33986,1.33018,1.31973,1.30844,1.29627,1.28317,1.26907,1.25391,1.23763,1.22013,1.20134,1.18117,1.15953,1.13629,1.11136,1.0846,1.05588,1.02506,0.991977},
{-3.25464,-3.2288,-3.20292,-3.17699,-3.15101,-3.12499,-3.09892,-3.07281,-3.04666,-3.02045,-2.9942,-2.96791,-2.94156,-2.91517,-2.88873,-2.86224,-2.8357,-2.80911,-2.78247,-2.75576,-2.72901,-2.70219,-2.67532,-2.64838,-2.62138,-2.59431,-2.56718,-2.53997,-2.51269,-2.48533,-2.4579,-2.43038,-2.40277,-2.37508,-2.34729,-2.31941,-2.29143,-2.26334,-2.23514,-2.20683,-2.1784,-2.14985,-2.12116,-2.09235,-2.06339,-2.0343,-2.00505,-1.97564,-1.94607,-1.91634,-1.88642,-1.85633,-1.82605,-1.79557,-1.76488,-1.73399,-1.70288,-1.67154,-1.63997,-1.60816,-1.5761,-1.54379,-1.51121,-1.47836,-1.44522,-1.41181,-1.3781,-1.34408,-1.30976,-1.27513,-1.24017,-1.20489,-1.16927,-1.13331,-1.09702,-1.06037,-1.02338,-0.986033,-0.948334,-0.91028,-0.871873,-0.833114,-0.794004,-0.754549,-0.714752,-0.674622,-0.634166,-0.593393,-0.552316,-0.510947,-0.469301,-0.427395,-0.385248,-0.34288,-0.300315,-0.257576,-0.214691,-0.171688,-0.128597,-0.0854504,-0.0422829,0.000869746,0.0439702,0.0869795,0.129857,0.172562,0.215052,0.257283,0.299211,0.340793,0.381984,0.422738,0.463013,0.502765,0.541951,0.580528,0.618457,0.655699,0.692215,0.727971,0.762932,0.797067,0.830349,0.862749,0.894244,0.924813,0.954438,0.983104,1.0108,1.03751,1.06323,1.08796,1.1117,1.13444,1.1562,1.17698,1.19678,1.21562,1.23351,1.25047,1.26651,1.28166,1.29592,1.30933,1.3219,1.33365,1.34462,1.35481,1.36426,1.37299,1.38102,1.38838,1.39508,1.40115,1.40661,1.41147,1.41577,1.4195,1.4227,1.42537,1.42753,1.4292,1.43037,1.43106,1.43127,1.43102,1.4303,1.42912,1.42746,1.42534,1.42274,1.41966,1.41609,1.41202,1.40742,1.40229,1.39661,1.39035,1.38349,1.37599,1.36784,1.35899,1.34941,1.33906,1.32788,1.31584,1.30287,1.28892,1.27392,1.25779,1.24048,1.22189,1.20192,1.18049,1.15749,1.13279,1.10628,1.07781,1.04724,1.01442},
{-3.26503,-3.23921,-3.21334,-3.18742,-3.16145,-3.13544,-3.10939,-3.08329,-3.05714,-3.03095,-3.00471,-2.97842,-2.95209,-2.92571,-2.89927,-2.87279,-2.84626,-2.81968,-2.79304,-2.76635,-2.7396,-2.71279,-2.68592,-2.659,-2.632,-2.60494,-2.57782,-2.55062,-2.52334,-2.49599,-2.46857,-2.44106,-2.41346,-2.38577,-2.35799,-2.33012,-2.30214,-2.27406,-2.24587,-2.21756,-2.18914,-2.16059,-2.13192,-2.10311,-2.07416,-2.04506,-2.01582,-1.98642,-1.95686,-1.92712,-1.89721,-1.86712,-1.83684,-1.80636,-1.77567,-1.74478,-1.71366,-1.68232,-1.65074,-1.61892,-1.58685,-1.55452,-1.52193,-1.48906,-1.45591,-1.42247,-1.38873,-1.35468,-1.32033,-1.28565,-1.25065,-1.21532,-1.17965,-1.14363,-1.10727,-1.07055,-1.03348,-0.996045,-0.958252,-0.920096,-0.881577,-0.842698,-0.803458,-0.763863,-0.723917,-0.683625,-0.642996,-0.602039,-0.560765,-0.519186,-0.477317,-0.435174,-0.392776,-0.350144,-0.307299,-0.264265,-0.22107,-0.177741,-0.134309,-0.0908063,-0.047267,-0.00372708,0.0397758,0.0832025,0.126512,0.169663,0.212613,0.255316,0.29773,0.339808,0.381505,0.422777,0.463577,0.503862,0.543587,0.58271,0.621188,0.658981,0.696051,0.73236,0.767874,0.80256,0.836388,0.869331,0.901362,0.932461,0.962608,0.991786,1.01998,1.04718,1.07339,1.09859,1.12278,1.14596,1.16815,1.18933,1.20953,1.22876,1.24702,1.26433,1.28071,1.29618,1.31075,1.32445,1.3373,1.34932,1.36054,1.37098,1.38066,1.3896,1.39784,1.40539,1.41227,1.41852,1.42414,1.42917,1.43361,1.43749,1.44083,1.44364,1.44593,1.44772,1.44901,1.44983,1.45017,1.45003,1.44944,1.44837,1.44685,1.44485,1.44239,1.43945,1.43602,1.4321,1.42767,1.42271,1.41721,1.41114,1.40449,1.39722,1.38931,1.38072,1.37141,1.36136,1.3505,1.3388,1.3262,1.31265,1.29807,1.28241,1.26559,1.24752,1.22811,1.20728,1.18492,1.1609,1.1351,1.1074,1.07763,1.04564},
{-3.27531,-3.2495,-3.22364,-3.19773,-3.17178,-3.14578,-3.11974,-3.09365,-3.06751,-3.04133,-3.0151,-2.98882,-2.9625,-2.93613,-2.90971,-2.88323,-2.85671,-2.83014,-2.80351,-2.77682,-2.75008,-2.72328,-2.69642,-2.6695,-2.64252,-2.61547,-2.58835,-2.56116,-2.53389,-2.50655,-2.47913,-2.45163,-2.42404,-2.39636,-2.36859,-2.34072,-2.31275,-2.28468,-2.25649,-2.2282,-2.19978,-2.17124,-2.14257,-2.11377,-2.08483,-2.05574,-2.0265,-1.99711,-1.96755,-1.93782,-1.90792,-1.87783,-1.84755,-1.81707,-1.78639,-1.75549,-1.72437,-1.69303,-1.66144,-1.62962,-1.59754,-1.5652,-1.53259,-1.49971,-1.46654,-1.43308,-1.39932,-1.36524,-1.33086,-1.29615,-1.26111,-1.22573,-1.19001,-1.15394,-1.11751,-1.08073,-1.04358,-1.00607,-0.968187,-0.929934,-0.891311,-0.852318,-0.812956,-0.773228,-0.733138,-0.692693,-0.651899,-0.610765,-0.569301,-0.527521,-0.485437,-0.443066,-0.400426,-0.357537,-0.314421,-0.271101,-0.227604,-0.183959,-0.140195,-0.0963448,-0.0524424,-0.00852391,0.0353729,0.0792084,0.122942,0.166531,0.209932,0.253101,0.295992,0.338559,0.380757,0.422539,0.463859,0.504671,0.544931,0.584594,0.623616,0.661957,0.699577,0.736437,0.7725,0.807735,0.842108,0.875591,0.908157,0.939785,0.970452,1.00014,1.02884,1.05653,1.08322,1.10888,1.13353,1.15715,1.17976,1.20136,1.22196,1.24157,1.26019,1.27786,1.29458,1.31037,1.32525,1.33924,1.35237,1.36466,1.37613,1.3868,1.39671,1.40586,1.4143,1.42204,1.42911,1.43552,1.4413,1.44648,1.45107,1.45509,1.45856,1.46149,1.4639,1.4658,1.46721,1.46813,1.46857,1.46855,1.46805,1.4671,1.46567,1.46379,1.46144,1.45861,1.4553,1.45151,1.4472,1.44239,1.43703,1.43112,1.42464,1.41755,1.40983,1.40144,1.39236,1.38254,1.37195,1.36052,1.34822,1.33498,1.32075,1.30545,1.28902,1.27137,1.25241,1.23205,1.21019,1.1867,1.16146,1.13433,1.10517,1.07381},
{-3.28548,-3.25968,-3.23383,-3.20794,-3.182,-3.15602,-3.12998,-3.1039,-3.07778,-3.05161,-3.02539,-2.99912,-2.97281,-2.94644,-2.92003,-2.89357,-2.86706,-2.84049,-2.81387,-2.78719,-2.76046,-2.73367,-2.70682,-2.67991,-2.65293,-2.62589,-2.59878,-2.5716,-2.54434,-2.51701,-2.4896,-2.4621,-2.43452,-2.40685,-2.37909,-2.35123,-2.32327,-2.2952,-2.26703,-2.23874,-2.21033,-2.1818,-2.15314,-2.12435,-2.09541,-2.06633,-2.0371,-2.00771,-1.97816,-1.94844,-1.91854,-1.88846,-1.85818,-1.82771,-1.79703,-1.76613,-1.73501,-1.70367,-1.67208,-1.64025,-1.60817,-1.57582,-1.54321,-1.51031,-1.47713,-1.44365,-1.40987,-1.37577,-1.34136,-1.30661,-1.27154,-1.23612,-1.20035,-1.16423,-1.12775,-1.09091,-1.05369,-1.0161,-0.978139,-0.939796,-0.901074,-0.861973,-0.822495,-0.78264,-0.742414,-0.701822,-0.66087,-0.619566,-0.57792,-0.535945,-0.493654,-0.451062,-0.408187,-0.365049,-0.321669,-0.278071,-0.23428,-0.190326,-0.146237,-0.102047,-0.0577883,-0.0134982,0.0307857,0.0750236,0.119174,0.163195,0.207043,0.250671,0.294035,0.337087,0.379781,0.42207,0.463906,0.505243,0.546035,0.586236,0.625802,0.664691,0.70286,0.740271,0.776886,0.81267,0.84759,0.881617,0.914722,0.946881,0.978073,1.00828,1.03748,1.06568,1.09284,1.11898,1.14409,1.16817,1.19121,1.21323,1.23424,1.25423,1.27324,1.29127,1.30833,1.32446,1.33966,1.35396,1.36738,1.37994,1.39167,1.4026,1.41274,1.42213,1.43079,1.43873,1.446,1.4526,1.45856,1.46391,1.46867,1.47285,1.47647,1.47955,1.48211,1.48416,1.48571,1.48677,1.48736,1.48747,1.48712,1.48631,1.48504,1.48332,1.48112,1.47847,1.47534,1.47173,1.46762,1.46301,1.45788,1.45221,1.44597,1.43915,1.43172,1.42365,1.4149,1.40543,1.39522,1.3842,1.37234,1.35957,1.34584,1.33108,1.31522,1.29819,1.27989,1.26023,1.23911,1.21641,1.19201,1.16577,1.13755,1.10717},
{-3.29554,-3.26976,-3.24392,-3.21804,-3.19212,-3.16614,-3.14012,-3.11405,-3.08794,-3.06178,-3.03557,-3.00931,-2.98301,-2.95666,-2.93025,-2.9038,-2.8773,-2.85074,-2.82413,-2.79746,-2.77074,-2.74396,-2.71712,-2.69021,-2.66325,-2.63621,-2.60911,-2.58194,-2.55469,-2.52737,-2.49996,-2.47248,-2.44491,-2.41725,-2.38949,-2.36164,-2.33369,-2.30563,-2.27747,-2.24919,-2.22079,-2.19227,-2.16362,-2.13483,-2.10591,-2.07684,-2.04762,-2.01824,-1.98869,-1.95898,-1.92909,-1.89901,-1.86874,-1.83827,-1.80759,-1.7767,-1.74559,-1.71425,-1.68266,-1.65083,-1.61875,-1.58639,-1.55377,-1.52087,-1.48767,-1.45418,-1.42038,-1.38627,-1.35183,-1.31706,-1.28195,-1.2465,-1.21069,-1.17453,-1.138,-1.10109,-1.06382,-1.02616,-0.988117,-0.94969,-0.910876,-0.871675,-0.832087,-0.792113,-0.751758,-0.711026,-0.669924,-0.628458,-0.586639,-0.544478,-0.501988,-0.459184,-0.416083,-0.372705,-0.32907,-0.285202,-0.241128,-0.196873,-0.152469,-0.107948,-0.0633424,-0.0186899,0.0259719,0.0706033,0.115163,0.159607,0.203892,0.247972,0.2918,0.33533,0.378513,0.421302,0.463648,0.505504,0.546823,0.587557,0.627662,0.667094,0.705809,0.743768,0.780931,0.817263,0.852728,0.887296,0.920939,0.95363,0.985346,1.01607,1.04578,1.07447,1.10212,1.12874,1.15431,1.17883,1.20231,1.22476,1.24617,1.26656,1.28595,1.30434,1.32175,1.33821,1.35373,1.36834,1.38205,1.39489,1.40689,1.41807,1.42846,1.43807,1.44695,1.4551,1.46256,1.46935,1.4755,1.48102,1.48594,1.49027,1.49405,1.49728,1.49998,1.50217,1.50386,1.50506,1.50579,1.50604,1.50583,1.50516,1.50404,1.50246,1.50042,1.49793,1.49496,1.49153,1.48761,1.4832,1.47827,1.47282,1.46683,1.46026,1.4531,1.44531,1.43687,1.42774,1.41788,1.40725,1.39579,1.38346,1.3702,1.35594,1.34062,1.32415,1.30646,1.28744,1.267,1.24502,1.22139,1.19595,1.16857,1.13906},
{-3.3055,-3.27973,-3.25391,-3.22804,-3.20213,-3.17616,-3.15015,-3.1241,-3.098,-3.07185,-3.04565,-3.0194,-2.99311,-2.96677,-2.94037,-2.91393,-2.88744,-2.86089,-2.83429,-2.80763,-2.78092,-2.75414,-2.72731,-2.70042,-2.67346,-2.64644,-2.61934,-2.59218,-2.56494,-2.53763,-2.51023,-2.48276,-2.4552,-2.42755,-2.3998,-2.37196,-2.34402,-2.31597,-2.28782,-2.25955,-2.23116,-2.20265,-2.17401,-2.14523,-2.11632,-2.08726,-2.05805,-2.02868,-1.99914,-1.96944,-1.93956,-1.90949,-1.87923,-1.84876,-1.8181,-1.78721,-1.7561,-1.72476,-1.69318,-1.66135,-1.62927,-1.59692,-1.56429,-1.53138,-1.49818,-1.46467,-1.43086,-1.39673,-1.36228,-1.32748,-1.29235,-1.25687,-1.22103,-1.18482,-1.14824,-1.11129,-1.07396,-1.03623,-0.998123,-0.959618,-0.920719,-0.881423,-0.841732,-0.801647,-0.76117,-0.720306,-0.679061,-0.637441,-0.595456,-0.553117,-0.510436,-0.467427,-0.424109,-0.380499,-0.336618,-0.292489,-0.248138,-0.203592,-0.158881,-0.114036,-0.0690927,-0.0240857,0.0209463,0.0659635,0.110924,0.155785,0.200501,0.245026,0.289313,0.333314,0.376982,0.420265,0.463117,0.505488,0.54733,0.588595,0.629237,0.66921,0.70847,0.746976,0.784688,0.821567,0.857579,0.892691,0.926873,0.960098,0.992343,1.02359,1.05381,1.083,1.11115,1.13824,1.16428,1.18926,1.21319,1.23606,1.25789,1.27869,1.29846,1.31722,1.335,1.3518,1.36766,1.38258,1.3966,1.40973,1.42201,1.43345,1.44409,1.45395,1.46306,1.47144,1.47911,1.48611,1.49245,1.49817,1.50327,1.50779,1.51174,1.51515,1.51802,1.52038,1.52224,1.52361,1.5245,1.52493,1.5249,1.52441,1.52347,1.52209,1.52025,1.51797,1.51522,1.51202,1.50835,1.5042,1.49955,1.4944,1.48871,1.48248,1.47568,1.46828,1.46025,1.45155,1.44216,1.43202,1.4211,1.40935,1.3967,1.3831,1.36847,1.35275,1.33585,1.31769,1.29815,1.27714,1.25452,1.23016,1.20391,1.17561},
{-3.31535,-3.28959,-3.26379,-3.23793,-3.21203,-3.18608,-3.16009,-3.13404,-3.10795,-3.08181,-3.05563,-3.02939,-3.00311,-2.97678,-2.95039,-2.92396,-2.89748,-2.87094,-2.84435,-2.8177,-2.791,-2.76423,-2.73741,-2.71053,-2.68358,-2.65656,-2.62948,-2.60233,-2.5751,-2.54779,-2.52041,-2.49294,-2.46539,-2.43775,-2.41002,-2.38219,-2.35426,-2.32622,-2.29808,-2.26982,-2.24144,-2.21294,-2.18432,-2.15555,-2.12665,-2.0976,-2.0684,-2.03904,-2.00952,-1.97982,-1.94995,-1.91989,-1.88964,-1.85919,-1.82853,-1.79765,-1.76655,-1.73522,-1.70365,-1.67182,-1.63974,-1.60739,-1.57476,-1.54185,-1.50865,-1.47514,-1.44132,-1.40717,-1.3727,-1.33789,-1.30274,-1.26723,-1.23136,-1.19512,-1.1585,-1.1215,-1.08412,-1.04634,-1.00816,-0.969589,-0.930611,-0.891228,-0.851442,-0.811253,-0.770662,-0.729674,-0.688294,-0.646529,-0.604387,-0.561878,-0.519016,-0.475813,-0.432286,-0.388454,-0.344336,-0.299956,-0.255339,-0.210512,-0.165503,-0.120346,-0.0750738,-0.0297223,0.01567,0.0610633,0.106415,0.151683,0.196821,0.241782,0.286519,0.330984,0.375127,0.418899,0.462249,0.505128,0.547487,0.589276,0.630449,0.670959,0.71076,0.74981,0.788066,0.825491,0.862047,0.897701,0.932421,0.966179,0.998951,1.03071,1.06145,1.09115,1.11979,1.14736,1.17387,1.19931,1.22368,1.24699,1.26924,1.29044,1.3106,1.32974,1.34788,1.36503,1.38122,1.39646,1.41079,1.42422,1.43678,1.44849,1.45939,1.46949,1.47884,1.48744,1.49533,1.50254,1.50909,1.51499,1.52029,1.52499,1.52912,1.5327,1.53575,1.53828,1.54031,1.54186,1.54293,1.54353,1.54367,1.54337,1.54262,1.54143,1.5398,1.53773,1.53521,1.53225,1.52882,1.52493,1.52056,1.51571,1.51034,1.50444,1.498,1.49098,1.48335,1.4751,1.46617,1.45653,1.44615,1.43496,1.42292,1.40996,1.39603,1.38105,1.36493,1.3476,1.32895,1.30887,1.28725,1.26394,1.2388,1.21166},
{-3.3251,-3.29936,-3.27357,-3.24773,-3.22184,-3.1959,-3.16992,-3.14389,-3.11781,-3.09168,-3.06551,-3.03928,-3.01301,-2.98669,-2.96032,-2.93389,-2.90742,-2.88089,-2.85431,-2.82767,-2.80098,-2.77423,-2.74741,-2.72054,-2.6936,-2.6666,-2.63952,-2.61238,-2.58516,-2.55787,-2.5305,-2.50304,-2.4755,-2.44787,-2.42015,-2.39233,-2.36441,-2.33639,-2.30826,-2.28001,-2.25164,-2.22316,-2.19454,-2.16579,-2.1369,-2.10786,-2.07868,-2.04933,-2.01982,-1.99014,-1.96028,-1.93023,-1.89999,-1.86955,-1.8389,-1.80804,-1.77695,-1.74562,-1.71406,-1.68224,-1.65016,-1.61782,-1.5852,-1.55229,-1.51908,-1.48557,-1.45174,-1.41759,-1.38311,-1.34829,-1.31312,-1.27759,-1.24169,-1.20542,-1.16877,-1.13174,-1.09431,-1.05648,-1.01824,-0.979604,-0.940554,-0.901092,-0.861218,-0.820931,-0.780235,-0.739131,-0.697624,-0.655722,-0.613431,-0.570762,-0.527726,-0.484337,-0.44061,-0.396565,-0.35222,-0.307598,-0.262723,-0.217623,-0.172326,-0.126865,-0.081273,-0.0355856,0.0101587,0.0559198,0.101656,0.147322,0.192874,0.238265,0.283445,0.328367,0.37298,0.417234,0.461078,0.504461,0.547333,0.589644,0.631345,0.672389,0.71273,0.752322,0.791123,0.829094,0.866195,0.902393,0.937654,0.971949,1.00525,1.03754,1.06879,1.099,1.12814,1.1562,1.18319,1.2091,1.23392,1.25767,1.28035,1.30196,1.32253,1.34206,1.36057,1.37808,1.39462,1.4102,1.42484,1.43858,1.45144,1.46344,1.47461,1.48499,1.49458,1.50344,1.51157,1.51901,1.52578,1.53191,1.53742,1.54233,1.54667,1.55046,1.55372,1.55646,1.5587,1.56045,1.56173,1.56256,1.56293,1.56286,1.56235,1.56141,1.56005,1.55825,1.55602,1.55336,1.55026,1.54671,1.54271,1.53823,1.53327,1.52782,1.52184,1.51531,1.50822,1.50053,1.49221,1.48322,1.47352,1.46307,1.45182,1.43971,1.42667,1.41265,1.39756,1.38132,1.36384,1.34501,1.32471,1.3028,1.27916,1.2536},
{-3.33476,-3.30903,-3.28325,-3.25743,-3.23155,-3.20563,-3.17966,-3.15364,-3.12757,-3.10145,-3.07529,-3.04908,-3.02281,-2.9965,-2.97014,-2.94373,-2.91727,-2.89075,-2.86418,-2.83755,-2.81087,-2.78413,-2.75732,-2.73046,-2.70353,-2.67654,-2.64947,-2.62234,-2.59514,-2.56785,-2.54049,-2.51305,-2.48552,-2.4579,-2.43019,-2.40238,-2.37448,-2.34647,-2.31835,-2.29011,-2.26176,-2.23329,-2.20469,-2.17595,-2.14707,-2.11805,-2.08888,-2.05955,-2.03005,-2.00038,-1.97054,-1.9405,-1.91028,-1.87985,-1.84922,-1.81836,-1.78729,-1.75597,-1.72442,-1.69261,-1.66055,-1.62821,-1.59559,-1.56269,-1.52949,-1.49598,-1.46215,-1.428,-1.39351,-1.35868,-1.3235,-1.28795,-1.25204,-1.21574,-1.17907,-1.14199,-1.10453,-1.06665,-1.02837,-0.989671,-0.950557,-0.911023,-0.871068,-0.830693,-0.789898,-0.748687,-0.707063,-0.665032,-0.622601,-0.57978,-0.536581,-0.493015,-0.449099,-0.40485,-0.360287,-0.315433,-0.270311,-0.224948,-0.179374,-0.133619,-0.0877167,-0.0417034,0.00438296,0.0505022,0.0966121,0.142669,0.188626,0.234437,0.280052,0.325423,0.370498,0.415227,0.459558,0.503438,0.546818,0.589645,0.631871,0.673445,0.714322,0.754454,0.793798,0.832313,0.869959,0.906699,0.942501,0.977334,1.01117,1.04398,1.07576,1.10647,1.13612,1.16468,1.19215,1.21852,1.24381,1.268,1.29112,1.31315,1.33413,1.35406,1.37295,1.39084,1.40773,1.42365,1.43863,1.45269,1.46586,1.47816,1.48962,1.50027,1.51013,1.51925,1.52763,1.53532,1.54233,1.5487,1.55444,1.55959,1.56416,1.56818,1.57166,1.57463,1.5771,1.57909,1.58062,1.58169,1.58231,1.58251,1.58228,1.58162,1.58055,1.57907,1.57717,1.57486,1.57213,1.56897,1.56538,1.56134,1.55685,1.55189,1.54643,1.54047,1.53398,1.52693,1.5193,1.51104,1.50212,1.49251,1.48215,1.47099,1.45897,1.44604,1.43211,1.41711,1.40095,1.38353,1.36473,1.34443,1.32249,1.29875},
{-3.34431,-3.3186,-3.29284,-3.26703,-3.24116,-3.21525,-3.18929,-3.16329,-3.13723,-3.11113,-3.08498,-3.05877,-3.03252,-3.00622,-2.97987,-2.95347,-2.92702,-2.90051,-2.87395,-2.84734,-2.82066,-2.79393,-2.76714,-2.74029,-2.71337,-2.68639,-2.65934,-2.63221,-2.60502,-2.57775,-2.5504,-2.52297,-2.49545,-2.46784,-2.44015,-2.41235,-2.38446,-2.35646,-2.32836,-2.30014,-2.2718,-2.24334,-2.21475,-2.18603,-2.15717,-2.12816,-2.099,-2.06969,-2.04021,-2.01056,-1.98073,-1.95071,-1.9205,-1.89009,-1.85947,-1.82863,-1.79757,-1.76627,-1.73473,-1.70294,-1.67089,-1.63856,-1.60595,-1.57306,-1.53986,-1.50636,-1.47254,-1.43839,-1.4039,-1.36906,-1.33387,-1.29832,-1.26239,-1.22608,-1.18938,-1.15228,-1.11478,-1.07687,-1.03854,-0.999797,-0.960626,-0.921028,-0.881001,-0.840546,-0.799662,-0.758352,-0.716619,-0.674469,-0.631908,-0.588946,-0.545592,-0.50186,-0.457765,-0.413323,-0.368553,-0.323478,-0.278119,-0.232505,-0.186664,-0.140626,-0.0944249,-0.0480966,-0.00167904,0.0447876,0.0912611,0.137697,0.18405,0.230271,0.276312,0.322123,0.367652,0.412847,0.457657,0.502028,0.545908,0.589245,0.631989,0.674089,0.715497,0.756165,0.796049,0.835105,0.873294,0.910576,0.946919,0.982289,1.01666,1.05,1.0823,1.11353,1.14367,1.17273,1.20069,1.22754,1.25329,1.27794,1.30149,1.32396,1.34535,1.36568,1.38497,1.40323,1.42049,1.43677,1.45209,1.46648,1.47996,1.49257,1.50433,1.51527,1.52542,1.53481,1.54347,1.55141,1.55868,1.5653,1.57129,1.57669,1.5815,1.58577,1.5895,1.59272,1.59544,1.59769,1.59948,1.60082,1.60173,1.60222,1.60229,1.60195,1.60121,1.60007,1.59854,1.59661,1.59428,1.59155,1.58842,1.58486,1.58089,1.57647,1.5716,1.56626,1.56043,1.55408,1.5472,1.53974,1.53168,1.52298,1.51359,1.50347,1.49257,1.48082,1.46816,1.45452,1.43981,1.42393,1.40678,1.38824,1.36818,1.34644},
{-3.35378,-3.32808,-3.30233,-3.27653,-3.25068,-3.22479,-3.19884,-3.17285,-3.1468,-3.12071,-3.09457,-3.06838,-3.04214,-3.01585,-2.98952,-2.96312,-2.93668,-2.91019,-2.88364,-2.85703,-2.83037,-2.80365,-2.77687,-2.75003,-2.72312,-2.69615,-2.66911,-2.642,-2.61482,-2.58756,-2.56022,-2.5328,-2.5053,-2.47771,-2.45002,-2.42224,-2.39436,-2.36638,-2.33829,-2.31008,-2.28176,-2.25332,-2.22474,-2.19604,-2.16719,-2.1382,-2.10906,-2.07976,-2.0503,-2.02067,-1.99086,-1.96086,-1.93067,-1.90027,-1.86967,-1.83885,-1.80781,-1.77653,-1.745,-1.71323,-1.68119,-1.64888,-1.61628,-1.5834,-1.55022,-1.51672,-1.48291,-1.44877,-1.41428,-1.37945,-1.34426,-1.3087,-1.27276,-1.23644,-1.19972,-1.16261,-1.12508,-1.08714,-1.04878,-1.00999,-0.970766,-0.931112,-0.891022,-0.850494,-0.80953,-0.76813,-0.726297,-0.684037,-0.641356,-0.598262,-0.554765,-0.510877,-0.466612,-0.421987,-0.377021,-0.331734,-0.28615,-0.240295,-0.194196,-0.147886,-0.101396,-0.0547633,-0.00802452,0.0387797,0.0856071,0.132413,0.179152,0.225775,0.272233,0.318476,0.364451,0.410106,0.455388,0.500244,0.54462,0.588463,0.631721,0.674344,0.71628,0.757483,0.797905,0.837502,0.876234,0.91406,0.950944,0.986854,1.02176,1.05564,1.08846,1.12021,1.15087,1.18043,1.20888,1.23622,1.26245,1.28756,1.31156,1.33447,1.35629,1.37704,1.39673,1.41539,1.43303,1.44967,1.46535,1.48009,1.49392,1.50685,1.51894,1.53019,1.54064,1.55033,1.55928,1.56751,1.57507,1.58197,1.58824,1.59392,1.59901,1.60356,1.60758,1.61109,1.61411,1.61666,1.61876,1.62043,1.62167,1.6225,1.62293,1.62297,1.62263,1.62191,1.62081,1.61935,1.61751,1.6153,1.61271,1.60974,1.60637,1.60261,1.59844,1.59385,1.58881,1.58331,1.57732,1.57083,1.56379,1.55619,1.54797,1.53911,1.52955,1.51923,1.50811,1.4961,1.48315,1.46915,1.45402,1.43765,1.4199,1.40064},
{-3.36314,-3.33746,-3.31173,-3.28594,-3.26011,-3.23423,-3.20829,-3.18231,-3.15628,-3.1302,-3.10407,-3.0779,-3.05167,-3.02539,-2.99907,-2.97269,-2.94626,-2.91977,-2.89323,-2.86664,-2.83999,-2.81328,-2.78651,-2.75968,-2.73279,-2.70583,-2.6788,-2.6517,-2.62453,-2.59728,-2.56996,-2.54255,-2.51506,-2.48748,-2.45981,-2.43205,-2.40418,-2.37621,-2.34814,-2.31995,-2.29164,-2.26322,-2.23466,-2.20597,-2.17715,-2.14817,-2.11905,-2.08977,-2.06033,-2.03071,-2.00092,-1.97094,-1.94077,-1.9104,-1.87982,-1.84902,-1.818,-1.78674,-1.75523,-1.72347,-1.69145,-1.65916,-1.62659,-1.59372,-1.56055,-1.52707,-1.49327,-1.45914,-1.42466,-1.38984,-1.35465,-1.31909,-1.28315,-1.24683,-1.2101,-1.17297,-1.13543,-1.09746,-1.05907,-1.02025,-0.980986,-0.941285,-0.901139,-0.860549,-0.819514,-0.778034,-0.736112,-0.693752,-0.650961,-0.607745,-0.564115,-0.520082,-0.47566,-0.430864,-0.385712,-0.340226,-0.294428,-0.248344,-0.202001,-0.15543,-0.108664,-0.0617385,-0.0146904,0.0324396,0.0796093,0.126774,0.173888,0.220902,0.267767,0.314431,0.360843,0.406949,0.452695,0.498026,0.54289,0.587232,0.630998,0.674137,0.716598,0.75833,0.799287,0.839423,0.878695,0.917063,0.95449,0.99094,1.02638,1.06079,1.09414,1.12642,1.1576,1.18767,1.21662,1.24445,1.27116,1.29674,1.3212,1.34456,1.36682,1.38799,1.4081,1.42716,1.44519,1.46222,1.47828,1.49338,1.50755,1.52084,1.53325,1.54484,1.55561,1.56562,1.57487,1.58342,1.59128,1.59848,1.60506,1.61104,1.61644,1.6213,1.62563,1.62946,1.6328,1.63569,1.63814,1.64016,1.64177,1.64298,1.64382,1.64427,1.64437,1.64411,1.6435,1.64255,1.64125,1.63961,1.63763,1.6353,1.63262,1.62959,1.62619,1.62241,1.61824,1.61367,1.60868,1.60324,1.59734,1.59093,1.58401,1.57652,1.56842,1.55968,1.55024,1.54004,1.52901,1.51709,1.50418,1.49018,1.475,1.45849},
{-3.37242,-3.34675,-3.32104,-3.29527,-3.26945,-3.24358,-3.21766,-3.19169,-3.16567,-3.1396,-3.11349,-3.08732,-3.06111,-3.03484,-3.00853,-2.98216,-2.95574,-2.92927,-2.90274,-2.87616,-2.84952,-2.82282,-2.79607,-2.76925,-2.74237,-2.71542,-2.6884,-2.66132,-2.63416,-2.60693,-2.57961,-2.55222,-2.52475,-2.49718,-2.46953,-2.44178,-2.41393,-2.38597,-2.35791,-2.32974,-2.30145,-2.27304,-2.24451,-2.21584,-2.18703,-2.15808,-2.12897,-2.09971,-2.07029,-2.0407,-2.01093,-1.98097,-1.95082,-1.92047,-1.88992,-1.85914,-1.82814,-1.7969,-1.76542,-1.73368,-1.70169,-1.66942,-1.63686,-1.60402,-1.57087,-1.53741,-1.50362,-1.46951,-1.43505,-1.40023,-1.36506,-1.3295,-1.29357,-1.25724,-1.22052,-1.18338,-1.14583,-1.10785,-1.06943,-1.03059,-0.991292,-0.951552,-0.911362,-0.870719,-0.829622,-0.788072,-0.746071,-0.703623,-0.660733,-0.617407,-0.573656,-0.52949,-0.484921,-0.439966,-0.394643,-0.34897,-0.302971,-0.25667,-0.210096,-0.163277,-0.116248,-0.0690418,-0.0216972,0.0257461,0.0732457,0.120757,0.168234,0.215628,0.262888,0.309963,0.356801,0.403348,0.449548,0.495347,0.540691,0.585524,0.629792,0.673441,0.71642,0.758678,0.800167,0.840839,0.88065,0.919558,0.957526,0.994518,1.0305,1.06545,1.09933,1.13213,1.16383,1.19441,1.22387,1.2522,1.2794,1.30546,1.3304,1.35421,1.37692,1.39853,1.41907,1.43855,1.45699,1.47441,1.49085,1.50633,1.52088,1.53452,1.5473,1.55923,1.57035,1.58069,1.59028,1.59916,1.60735,1.61488,1.62179,1.6281,1.63384,1.63903,1.64371,1.64789,1.6516,1.65486,1.65769,1.66011,1.66213,1.66378,1.66506,1.66598,1.66657,1.66683,1.66676,1.66638,1.66569,1.66468,1.66338,1.66177,1.65985,1.65762,1.65507,1.6522,1.64901,1.64546,1.64157,1.6373,1.63264,1.62757,1.62206,1.61608,1.60961,1.6026,1.59501,1.5868,1.5779,1.56826,1.5578,1.54644,1.53409,1.52063},
{-3.38161,-3.35596,-3.33025,-3.3045,-3.27869,-3.25284,-3.22693,-3.20098,-3.17497,-3.14892,-3.12281,-3.09666,-3.07046,-3.04421,-3.0179,-2.99155,-2.96514,-2.93868,-2.91216,-2.88559,-2.85897,-2.83228,-2.80554,-2.77873,-2.75186,-2.72493,-2.69792,-2.67085,-2.64371,-2.61649,-2.58919,-2.56181,-2.53435,-2.5068,-2.47916,-2.45143,-2.42359,-2.39566,-2.36762,-2.33946,-2.31119,-2.2828,-2.25428,-2.22563,-2.19685,-2.16791,-2.13883,-2.1096,-2.0802,-2.05063,-2.02088,-1.99095,-1.96082,-1.9305,-1.89997,-1.86922,-1.83824,-1.80703,-1.77557,-1.74386,-1.71189,-1.67965,-1.64712,-1.6143,-1.58118,-1.54774,-1.51398,-1.47988,-1.44544,-1.41064,-1.37548,-1.33994,-1.30402,-1.2677,-1.23098,-1.19385,-1.15629,-1.1183,-1.07988,-1.04101,-1.00169,-0.961925,-0.921698,-0.881011,-0.839863,-0.798253,-0.756184,-0.713658,-0.67068,-0.627255,-0.583394,-0.539106,-0.494403,-0.449301,-0.403817,-0.357969,-0.311781,-0.265276,-0.218482,-0.171428,-0.124146,-0.0766717,-0.0290421,0.018703,0.0665215,0.114369,0.162198,0.209961,0.257607,0.305085,0.35234,0.399319,0.445967,0.492227,0.538045,0.583363,0.628128,0.672285,0.71578,0.758562,0.800581,0.841788,0.882139,0.921591,0.960103,0.99764,1.03417,1.06966,1.10408,1.13741,1.16964,1.20075,1.23073,1.25957,1.28727,1.31382,1.33925,1.36354,1.38671,1.40878,1.42976,1.44968,1.46855,1.4864,1.50325,1.51913,1.53408,1.54811,1.56127,1.57358,1.58507,1.59579,1.60575,1.615,1.62356,1.63146,1.63874,1.64543,1.65155,1.65714,1.66221,1.6668,1.67093,1.67462,1.6779,1.68078,1.68329,1.68543,1.68724,1.68872,1.68988,1.69074,1.69132,1.69161,1.69162,1.69137,1.69085,1.69008,1.68905,1.68776,1.68622,1.68441,1.68234,1.68,1.67738,1.67447,1.67126,1.66774,1.66388,1.65967,1.65508,1.65009,1.64466,1.63876,1.63235,1.62539,1.6178,1.60954,1.60054,1.5907},
{-3.39071,-3.36507,-3.33938,-3.31364,-3.28785,-3.26201,-3.23612,-3.21018,-3.18419,-3.15815,-3.13205,-3.10591,-3.07972,-3.05348,-3.02719,-3.00085,-2.97445,-2.94801,-2.9215,-2.89494,-2.86833,-2.84166,-2.81492,-2.78813,-2.76127,-2.73435,-2.70736,-2.68031,-2.65317,-2.62597,-2.59869,-2.57132,-2.54388,-2.51634,-2.48872,-2.461,-2.43319,-2.40527,-2.37724,-2.34911,-2.32086,-2.29249,-2.26399,-2.23536,-2.2066,-2.17769,-2.14863,-2.11942,-2.09004,-2.06049,-2.03077,-2.00087,-1.97077,-1.94047,-1.90997,-1.87925,-1.8483,-1.81712,-1.78569,-1.75401,-1.72207,-1.68985,-1.65736,-1.62456,-1.59147,-1.55806,-1.52433,-1.49026,-1.45584,-1.42107,-1.38593,-1.35041,-1.31451,-1.2782,-1.24149,-1.20437,-1.16681,-1.12883,-1.0904,-1.05153,-1.0122,-0.972409,-0.932156,-0.891437,-0.850249,-0.808591,-0.766465,-0.723873,-0.680819,-0.637309,-0.593351,-0.548955,-0.504132,-0.458896,-0.413265,-0.367258,-0.320894,-0.2742,-0.227201,-0.179926,-0.132407,-0.0846794,-0.0367794,0.0112532,0.0593762,0.107545,0.155714,0.203833,0.251852,0.299719,0.34738,0.39478,0.441864,0.488576,0.534858,0.580654,0.625908,0.670565,0.714571,0.757872,0.800417,0.842158,0.883047,0.923041,0.962099,1.00018,1.03726,1.07329,1.10826,1.14213,1.1749,1.20654,1.23705,1.26641,1.29462,1.32168,1.3476,1.37238,1.39604,1.41858,1.44003,1.4604,1.47972,1.49801,1.51529,1.53161,1.54697,1.56142,1.57499,1.5877,1.5996,1.61072,1.62108,1.63073,1.63969,1.64801,1.6557,1.6628,1.66935,1.67536,1.68088,1.68592,1.69051,1.69469,1.69846,1.70186,1.7049,1.70761,1.71,1.71209,1.71389,1.71543,1.7167,1.71774,1.71854,1.71911,1.71947,1.71962,1.71956,1.7193,1.71885,1.71821,1.71737,1.71633,1.7151,1.71366,1.71202,1.71016,1.70808,1.70577,1.7032,1.70037,1.69725,1.69383,1.69007,1.68594,1.68141,1.67644,1.67097,1.66496}
};
//LS coefficient for A=atomic weight * 1.05
double ls_coefficients_ahi[][200]=
{
{-0.028652,-0.0271877,-0.0257939,-0.0244672,-0.0232045,-0.0220027,-0.020859,-0.0197704,-0.0187344,-0.0177484,-0.01681,-0.0159169,-0.0150667,-0.0142575,-0.0134872,-0.0127539,-0.0120557,-0.0113909,-0.0107578,-0.0101549,-0.00958055,-0.00903336,-0.00851195,-0.00801502,-0.0075413,-0.00708961,-0.00665881,-0.00624782,-0.00585562,-0.00548121,-0.00512366,-0.0047821,-0.00445566,-0.00414355,-0.00384499,-0.00355925,-0.00328565,-0.0030235,-0.00277219,-0.00253111,-0.00229968,-0.00207737,-0.00186365,-0.00165802,-0.00146002,-0.00126919,-0.00108512,-0.000907375,-0.000735584,-0.000569373,-0.000408386,-0.000252289,-0.00010076,4.65082e-05,0.000189806,0.000329412,0.000465591,0.000598596,0.000728667,0.000856035,0.000980918,0.00110352,0.00122405,0.00134269,0.00145962,0.00157501,0.00168902,0.00180181,0.00191352,0.00202429,0.00213426,0.00224354,0.00235224,0.00246049,0.00256838,0.002676,0.00278345,0.0028908,0.00299813,0.0031055,0.00321298,0.00332061,0.00342846,0.00353655,0.00364491,0.00375358,0.00386256,0.00397187,0.00408152,0.00419149,0.00430177,0.00441233,0.00452316,0.0046342,0.00474541,0.00485673,0.0049681,0.00507943,0.00519064,0.00530163,0.0054123,0.00552252,0.00563217,0.00574112,0.0058492,0.00595626,0.00606212,0.0061666,0.0062695,0.00637061,0.00646972,0.00656659,0.00666097,0.0067526,0.00684122,0.00692653,0.00700825,0.00708604,0.00715959,0.00722855,0.00729256,0.00735124,0.00740419,0.00745098,0.00749118,0.00752432,0.00754989,0.00756739,0.00757625,0.00757586,0.0075656,0.00754478,0.00751266,0.00746844,0.00741128,0.00734022,0.00725427,0.0071523,0.00703312,0.00689539,0.00673767,0.00655837,0.00635573,0.00612782,0.00587253,0.00558751,0.00527017,0.00491767,0.00452686,0.00409426,0.00361602,0.00308789,0.00250519,0.00186272,0.00115475,0.000374946,-0.000483707,-0.00142894,-0.00246931,-0.00361426,-0.00487421,-0.00626069,-0.00778639,-0.00946535,-0.011313,-0.0133465,-0.0155845,-0.0180477,-0.020759,-0.0237434,-0.0270284,-0.0306443,-0.0346242,-0.0390045,-0.043825,-0.0491292,-0.0549645,-0.0613826,-0.0684396,-0.0761965,-0.0847189,-0.0940776,-0.104351,-0.115617,-0.127962,-0.141477,-0.156258,-0.172402,-0.190009,-0.20918,-0.230012,-0.252597,-0.277018,-0.303341,-0.331611,-0.361839,-0.393993,-0.427979,-0.463627,-0.500662},
{-0.108742,-0.103547,-0.0985764,-0.0938216,-0.0892748,-0.0849281,-0.0807738,-0.0768045,-0.0730127,-0.0693914,-0.0659336,-0.0626326,-0.0594818,-0.0564749,-0.0536057,-0.0508684,-0.0482571,-0.0457663,-0.0433906,-0.041125,-0.0389644,-0.0369041,-0.0349394,-0.033066,-0.0312796,-0.0295762,-0.0279517,-0.0264026,-0.0249251,-0.0235158,-0.0221715,-0.0208889,-0.0196651,-0.0184971,-0.0173822,-0.0163177,-0.0153012,-0.0143301,-0.0134022,-0.0125153,-0.0116672,-0.010856,-0.0100798,-0.00933658,-0.00862474,-0.00794257,-0.00728848,-0.00666094,-0.0060585,-0.00547979,-0.00492348,-0.00438831,-0.00387307,-0.00337663,-0.0028979,-0.00243582,-0.00198941,-0.00155772,-0.00113986,-0.000734952,-0.000342188,3.92142e-05,0.000409998,0.00077087,0.0011225,0.00146554,0.00180059,0.00212824,0.00244903,0.00276348,0.00307209,0.00337534,0.00367367,0.00396749,0.00425721,0.00454319,0.0048258,0.00510537,0.00538219,0.00565656,0.00592874,0.00619899,0.00646753,0.00673456,0.00700028,0.00726485,0.00752842,0.00779112,0.00805305,0.00831432,0.00857497,0.00883507,0.00909465,0.0093537,0.00961224,0.00987021,0.0101276,0.0103843,0.0106402,0.0108952,0.0111492,0.011402,0.0116535,0.0119034,0.0121516,0.0123977,0.0126416,0.0128829,0.0131214,0.0133566,0.0135884,0.0138163,0.0140399,0.0142589,0.0144727,0.0146811,0.0148834,0.0150794,0.0152683,0.0154498,0.0156232,0.0157881,0.0159439,0.0160898,0.0162255,0.0163501,0.0164629,0.0165634,0.0166507,0.016724,0.0167824,0.0168252,0.0168514,0.0168598,0.0168496,0.0168194,0.016768,0.016694,0.016596,0.0164722,0.016321,0.0161403,0.0159279,0.0156816,0.0153987,0.0150764,0.0147113,0.0143001,0.0138388,0.0133232,0.0127484,0.0121093,0.0114,0.0106141,0.00974453,0.00878334,0.00772188,0.00655053,0.00525867,0.00383458,0.0022653,0.000536535,-0.00136749,-0.00346418,-0.0057727,-0.00831416,-0.0111118,-0.0141913,-0.0175806,-0.0213106,-0.0254152,-0.0299315,-0.0349001,-0.040366,-0.0463763,-0.0529843,-0.0602472,-0.0682268,-0.0769901,-0.0866092,-0.0971611,-0.108728,-0.121398,-0.135262,-0.150415,-0.166958,-0.18499,-0.204612,-0.225921,-0.249008,-0.273956,-0.300825,-0.329657,-0.360457,-0.393183,-0.42773,-0.463911,-0.501428,-0.539844,-0.578537},
{-0.223932,-0.214128,-0.204676,-0.195571,-0.186804,-0.178367,-0.170252,-0.162452,-0.154956,-0.147758,-0.140847,-0.134216,-0.127856,-0.121758,-0.115914,-0.110315,-0.104952,-0.0998167,-0.0949016,-0.0901983,-0.0856986,-0.0813949,-0.0772795,-0.073345,-0.069584,-0.0659896,-0.0625547,-0.0592728,-0.0561373,-0.053142,-0.0502807,-0.0475476,-0.044937,-0.0424434,-0.0400615,-0.0377862,-0.0356125,-0.0335359,-0.0315516,-0.0296554,-0.0278429,-0.0261103,-0.0244536,-0.022869,-0.0213531,-0.0199024,-0.0185136,-0.0171836,-0.0159094,-0.0146881,-0.013517,-0.0123934,-0.0113149,-0.0102789,-0.00928334,-0.00832586,-0.00740442,-0.00651699,-0.00566168,-0.00483665,-0.00404016,-0.00327054,-0.00252622,-0.00180567,-0.00110745,-0.000430186,0.000227427,0.000866641,0.00148864,0.00209456,0.00268547,0.00326239,0.00382628,0.00437808,0.00491864,0.00544879,0.00596931,0.00648093,0.00698435,0.00748021,0.00796912,0.00845166,0.00892834,0.00939967,0.0098661,0.010328,0.0107859,0.01124,0.0116906,0.0121381,0.0125826,0.0130244,0.0134637,0.0139005,0.014335,0.0147672,0.0151972,0.015625,0.0160506,0.0164738,0.0168946,0.0173128,0.0177283,0.0181409,0.0185503,0.0189563,0.0193586,0.0197569,0.0201507,0.0205399,0.0209238,0.0213022,0.0216744,0.0220402,0.0223989,0.02275,0.0230931,0.0234274,0.0237524,0.0240676,0.0243722,0.0246658,0.0249474,0.0252167,0.0254727,0.0257148,0.0259423,0.0261543,0.0263502,0.0265291,0.0266901,0.0268324,0.0269549,0.0270567,0.0271368,0.027194,0.0272271,0.0272349,0.0272158,0.0271683,0.0270908,0.0269815,0.0268382,0.0266589,0.026441,0.0261819,0.0258786,0.0255277,0.0251257,0.0246684,0.0241514,0.0235696,0.0229177,0.0221894,0.0213781,0.0204761,0.0194752,0.0183661,0.0171388,0.0157819,0.014283,0.0126284,0.0108028,0.00878956,0.00657008,0.00412401,0.00142888,-0.00154002,-0.00480989,-0.00841096,-0.0123755,-0.0167397,-0.0215429,-0.0268283,-0.0326429,-0.0390379,-0.0460692,-0.0537971,-0.062287,-0.0716095,-0.0818403,-0.0930603,-0.105356,-0.118817,-0.13354,-0.149623,-0.167168,-0.186277,-0.207049,-0.22958,-0.253958,-0.280256,-0.308526,-0.338791,-0.371031,-0.405172,-0.441063,-0.478458,-0.516969,-0.556072},
{-0.356361,-0.342264,-0.328568,-0.315273,-0.302375,-0.289874,-0.277765,-0.266043,-0.254706,-0.243747,-0.233161,-0.222942,-0.213082,-0.203575,-0.194414,-0.185591,-0.177098,-0.168926,-0.161068,-0.153515,-0.146259,-0.13929,-0.1326,-0.12618,-0.120022,-0.114117,-0.108457,-0.103032,-0.0978346,-0.0928563,-0.088089,-0.0835247,-0.0791555,-0.0749737,-0.0709719,-0.0671427,-0.063479,-0.0599739,-0.0566207,-0.0534127,-0.0503438,-0.0474077,-0.0445985,-0.0419106,-0.0393383,-0.0368762,-0.0345194,-0.0322628,-0.0301015,-0.0280311,-0.0260472,-0.0241453,-0.0223216,-0.020572,-0.0188928,-0.0172804,-0.0157313,-0.0142423,-0.0128101,-0.0114317,-0.0101043,-0.00882497,-0.00759112,-0.0064002,-0.00524978,-0.00413754,-0.00306127,-0.00201884,-0.00100825,-2.75802e-05,0.00092501,0.00185126,0.00275283,0.00363129,0.00448814,0.00532481,0.00614264,0.0069429,0.00772679,0.00849547,0.00924999,0.00999137,0.0107205,0.0114384,0.0121458,0.0128434,0.013532,0.0142123,0.0148848,0.01555,0.0162085,0.0168607,0.017507,0.0181477,0.018783,0.0194133,0.0200387,0.0206592,0.0212751,0.0218862,0.0224927,0.0230944,0.0236913,0.0242831,0.0248697,0.0254509,0.0260263,0.0265956,0.0271585,0.0277146,0.0282634,0.0288045,0.0293374,0.0298615,0.0303763,0.0308813,0.0313757,0.031859,0.0323305,0.0327897,0.0332357,0.0336679,0.0340857,0.0344883,0.0348749,0.0352449,0.0355974,0.0359318,0.0362473,0.036543,0.0368182,0.037072,0.0373035,0.0375119,0.0376962,0.0378554,0.0379884,0.0380941,0.0381713,0.0382187,0.0382348,0.0382181,0.0381668,0.0380791,0.0379528,0.0377857,0.0375751,0.0373183,0.0370121,0.036653,0.036237,0.0357599,0.0352168,0.0346023,0.0339105,0.0331348,0.0322678,0.0313013,0.0302265,0.0290331,0.0277101,0.0262453,0.0246251,0.0228344,0.0208567,0.0186736,0.0162649,0.0136082,0.0106792,0.00745078,0.00389327,-2.59715e-05,-0.00434272,-0.00909618,-0.0143293,-0.0200888,-0.0264259,-0.0333961,-0.0410598,-0.0494822,-0.0587339,-0.0688905,-0.0800332,-0.0922481,-0.105627,-0.120265,-0.136262,-0.15372,-0.172743,-0.193433,-0.215888,-0.240199,-0.266444,-0.29468,-0.324936,-0.357203,-0.391409,-0.42743,-0.465029,-0.503851},
{-0.492364,-0.474857,-0.457728,-0.440984,-0.424628,-0.408666,-0.3931,-0.377933,-0.363166,-0.348801,-0.334836,-0.321272,-0.308107,-0.295338,-0.282963,-0.270978,-0.259378,-0.248159,-0.237315,-0.226841,-0.216729,-0.206974,-0.197567,-0.188502,-0.179771,-0.171364,-0.163276,-0.155496,-0.148016,-0.140827,-0.133922,-0.127291,-0.120925,-0.114816,-0.108954,-0.103333,-0.0979416,-0.0927731,-0.0878188,-0.0830706,-0.0785206,-0.0741608,-0.0699837,-0.0659818,-0.0621478,-0.0584747,-0.0549556,-0.0515838,-0.0483528,-0.0452563,-0.0422883,-0.0394428,-0.0367143,-0.0340971,-0.031586,-0.0291759,-0.0268619,-0.0246393,-0.0225035,-0.0204501,-0.0184749,-0.0165739,-0.0147433,-0.0129792,-0.0112782,-0.00963687,-0.00805189,-0.00652017,-0.00503873,-0.0036047,-0.00221537,-0.000868131,0.000439496,0.00170987,0.00294525,0.00414777,0.00531946,0.00646226,0.00757799,0.0086684,0.00973511,0.0107797,0.0118036,0.0128081,0.0137946,0.0147643,0.0157183,0.0166576,0.0175831,0.0184959,0.0193965,0.0202859,0.0211646,0.0220333,0.0228924,0.0237424,0.0245837,0.0254166,0.0262412,0.0270579,0.0278667,0.0286676,0.0294607,0.0302458,0.0310229,0.0317918,0.0325521,0.0333037,0.0340461,0.0347791,0.0355021,0.0362146,0.0369163,0.0376064,0.0382844,0.0389498,0.0396018,0.0402399,0.0408632,0.0414712,0.042063,0.0426381,0.0431956,0.0437348,0.0442549,0.0447553,0.0452351,0.0456935,0.04613,0.0465436,0.0469336,0.0472992,0.0476396,0.047954,0.0482416,0.0485014,0.0487326,0.0489341,0.0491049,0.0492439,0.0493499,0.0494215,0.0494572,0.0494555,0.0494146,0.0493324,0.0492069,0.0490355,0.0488154,0.0485438,0.0482171,0.0478315,0.0473828,0.0468663,0.0462767,0.0456081,0.0448539,0.044007,0.0430591,0.0420013,0.0408236,0.039515,0.0380632,0.0364545,0.0346741,0.0327051,0.0305293,0.0281265,0.0254743,0.0225479,0.0193204,0.0157619,0.0118396,0.00751756,0.00275633,-0.00248722,-0.0082602,-0.014614,-0.0216047,-0.0292928,-0.0377443,-0.04703,-0.0572264,-0.0684151,-0.0806832,-0.0941227,-0.10883,-0.124907,-0.142456,-0.161582,-0.182389,-0.204978,-0.22944,-0.255855,-0.284284,-0.314754,-0.347265,-0.381754,-0.418088,-0.45604},
{-0.623829,-0.60385,-0.584191,-0.564861,-0.545871,-0.527229,-0.508944,-0.491023,-0.473474,-0.456302,-0.439514,-0.423115,-0.407107,-0.391495,-0.376281,-0.361467,-0.347053,-0.333039,-0.319425,-0.306208,-0.293388,-0.28096,-0.268921,-0.257266,-0.245991,-0.235091,-0.224559,-0.214388,-0.204573,-0.195106,-0.185979,-0.177184,-0.168714,-0.16056,-0.152713,-0.145165,-0.137908,-0.130932,-0.124229,-0.11779,-0.111606,-0.105669,-0.0999693,-0.0944993,-0.0892501,-0.0842136,-0.0793815,-0.0747458,-0.0702987,-0.0660326,-0.0619398,-0.0580131,-0.0542454,-0.0506298,-0.0471596,-0.0438282,-0.0406293,-0.0375568,-0.0346049,-0.0317677,-0.0290397,-0.0264157,-0.0238906,-0.0214593,-0.0191172,-0.0168596,-0.0146823,-0.0125809,-0.0105514,-0.00859005,-0.00669304,-0.00485684,-0.00307806,-0.00135346,0.000320066,0.00194546,0.00352554,0.00506298,0.00656032,0.00802,0.00944428,0.0108354,0.0121953,0.0135259,0.0148292,0.0161068,0.0173602,0.0185911,0.0198007,0.0209904,0.0221614,0.0233147,0.0244514,0.0255723,0.0266782,0.0277699,0.028848,0.029913,0.0309653,0.0320054,0.0330335,0.0340498,0.0350545,0.0360475,0.037029,0.0379986,0.0389564,0.0399021,0.0408353,0.0417557,0.042663,0.0435566,0.044436,0.0453007,0.0461502,0.0469837,0.0478006,0.0486002,0.0493819,0.0501448,0.0508883,0.0516117,0.052314,0.0529948,0.053653,0.0542881,0.0548992,0.0554857,0.0560467,0.0565816,0.0570896,0.0575701,0.0580222,0.0584453,0.0588386,0.0592014,0.0595329,0.0598323,0.0600986,0.060331,0.0605284,0.0606899,0.0608141,0.0608997,0.0609453,0.0609493,0.0609097,0.0608246,0.0606917,0.0605083,0.0602716,0.0599782,0.0596246,0.0592066,0.0587196,0.0581586,0.0575177,0.0567905,0.05597,0.0550481,0.0540159,0.0528637,0.0515805,0.0501542,0.0485713,0.0468168,0.0448743,0.0427257,0.0403507,0.0377272,0.0348306,0.031634,0.0281077,0.0242189,0.019932,0.0152077,0.0100028,0.00427049,-0.00204061,-0.00898631,-0.0166273,-0.0250292,-0.0342632,-0.0444054,-0.0555378,-0.0677475,-0.0811271,-0.0957737,-0.111789,-0.129277,-0.148343,-0.169095,-0.191633,-0.216053,-0.242436,-0.270851,-0.301334,-0.333886,-0.368455,-0.404921},
{-0.746999,-0.72531,-0.703874,-0.682705,-0.661812,-0.641207,-0.620901,-0.600905,-0.581228,-0.561881,-0.542874,-0.524214,-0.505911,-0.487972,-0.470404,-0.453213,-0.436406,-0.419986,-0.403958,-0.388324,-0.373088,-0.35825,-0.343812,-0.329773,-0.316133,-0.302889,-0.290039,-0.277581,-0.265511,-0.253823,-0.242514,-0.231578,-0.221008,-0.210798,-0.200942,-0.191432,-0.182259,-0.173418,-0.164899,-0.156694,-0.148794,-0.141191,-0.133876,-0.126841,-0.120076,-0.113573,-0.107322,-0.101316,-0.0955458,-0.0900021,-0.0846769,-0.0795619,-0.0746488,-0.0699296,-0.0653964,-0.0610416,-0.0568576,-0.0528372,-0.0489731,-0.0452585,-0.0416866,-0.038251,-0.0349452,-0.0317631,-0.0286989,-0.0257469,-0.0229015,-0.0201573,-0.0175094,-0.0149528,-0.0124828,-0.0100948,-0.00778441,-0.00554754,-0.00338018,-0.00127849,0.000761173,0.0027423,0.00466821,0.00654206,0.00836687,0.0101455,0.0118806,0.0135749,0.0152306,0.0168501,0.0184355,0.0199889,0.0215121,0.0230068,0.0244748,0.0259174,0.0273361,0.0287321,0.0301065,0.0314605,0.0327949,0.0341106,0.0354081,0.0366882,0.0379513,0.0391978,0.0404279,0.041642,0.0428401,0.0440222,0.0451882,0.0463381,0.0474716,0.0485883,0.0496881,0.0507703,0.0518345,0.0528802,0.0539069,0.0549138,0.0559003,0.0568657,0.0578094,0.0587305,0.0596283,0.060502,0.0613509,0.0621742,0.0629711,0.0637409,0.0644828,0.0651961,0.0658801,0.066534,0.0671571,0.0677489,0.0683085,0.0688353,0.0693287,0.0697879,0.0702124,0.0706012,0.0709538,0.0712692,0.0715467,0.0717852,0.0719838,0.0721413,0.0722564,0.0723276,0.0723534,0.072332,0.0722612,0.0721387,0.0719619,0.0717278,0.0714331,0.0710739,0.0706461,0.0701449,0.0695649,0.0689,0.0681437,0.0672885,0.0663259,0.0652467,0.0640405,0.0626958,0.0611998,0.0595385,0.0576961,0.0556553,0.0533968,0.0508995,0.04814,0.0450925,0.0417285,0.038017,0.0339234,0.0294102,0.0244361,0.0189559,0.0129203,0.00627548,-0.001037,-0.00908067,-0.0179242,-0.0276415,-0.0383124,-0.0500217,-0.06286,-0.0769228,-0.0923103,-0.109126,-0.127477,-0.147471,-0.169213,-0.1928,-0.218331,-0.245878,-0.275499,-0.307216,-0.341008,-0.376798},
{-0.86075,-0.837895,-0.815236,-0.792785,-0.770551,-0.748547,-0.726783,-0.70527,-0.684021,-0.663047,-0.642358,-0.621965,-0.60188,-0.582112,-0.562672,-0.543568,-0.524811,-0.506408,-0.488367,-0.470695,-0.453399,-0.436484,-0.419955,-0.403817,-0.388071,-0.372722,-0.35777,-0.343216,-0.329061,-0.315303,-0.30194,-0.288972,-0.276393,-0.264202,-0.252393,-0.240962,-0.229903,-0.21921,-0.208877,-0.198896,-0.189261,-0.179965,-0.170998,-0.162353,-0.154021,-0.145995,-0.138265,-0.130822,-0.123659,-0.116765,-0.110132,-0.103752,-0.097615,-0.0917129,-0.0860369,-0.0805786,-0.0753295,-0.0702814,-0.0654263,-0.0607562,-0.0562633,-0.0519402,-0.0477794,-0.0437737,-0.0399163,-0.0362003,-0.0326191,-0.0291664,-0.0258362,-0.0226223,-0.0195191,-0.0165211,-0.013623,-0.0108196,-0.00810606,-0.00547762,-0.00292978,-0.000458224,0.0019412,0.00427243,0.00653924,0.00874521,0.0108938,0.0129881,0.0150313,0.0170263,0.0189758,0.0208824,0.0227485,0.0245763,0.026368,0.0281255,0.0298506,0.031545,0.0332103,0.0348477,0.0364587,0.0380442,0.0396052,0.0411427,0.0426573,0.0441497,0.0456204,0.0470698,0.0484981,0.0499054,0.051292,0.0526577,0.0540024,0.0553259,0.0566279,0.057908,0.0591659,0.060401,0.0616127,0.0628005,0.0639636,0.0651015,0.0662133,0.0672984,0.068356,0.0693852,0.0703854,0.0713558,0.0722956,0.073204,0.0740803,0.0749237,0.0757336,0.0765093,0.0772502,0.0779554,0.0786246,0.0792569,0.0798519,0.0804089,0.0809273,0.0814065,0.0818458,0.0822446,0.0826022,0.0829176,0.0831902,0.0834188,0.0836023,0.0837396,0.0838291,0.0838694,0.0838584,0.0837942,0.0836743,0.083496,0.0832562,0.0829515,0.0825779,0.082131,0.0816057,0.0809964,0.0802967,0.0794997,0.0785974,0.0775809,0.0764404,0.075165,0.0737424,0.0721591,0.0704001,0.0684488,0.0662868,0.0638937,0.061247,0.058322,0.0550913,0.0515248,0.0475895,0.043249,0.0384635,0.0331894,0.0273789,0.0209801,0.0139362,0.00618571,-0.00233812,-0.0117074,-0.0219996,-0.0332979,-0.0456911,-0.0592729,-0.0741425,-0.090403,-0.108161,-0.127524,-0.148599,-0.171492,-0.196302,-0.223114,-0.251995,-0.282987,-0.316094,-0.351267},
{-0.96529,-0.941636,-0.918132,-0.894787,-0.871612,-0.848616,-0.82581,-0.803204,-0.78081,-0.758637,-0.736698,-0.715004,-0.693566,-0.672395,-0.651503,-0.630901,-0.610599,-0.590608,-0.570939,-0.5516,-0.532602,-0.513952,-0.495659,-0.477731,-0.460174,-0.442994,-0.426197,-0.409786,-0.393767,-0.37814,-0.362909,-0.348075,-0.333638,-0.319598,-0.305953,-0.292702,-0.279841,-0.267368,-0.255279,-0.243568,-0.232232,-0.221263,-0.210656,-0.200403,-0.190499,-0.180935,-0.171704,-0.162797,-0.154206,-0.145924,-0.13794,-0.130247,-0.122836,-0.115698,-0.108823,-0.102203,-0.0958299,-0.0896938,-0.0837864,-0.0780992,-0.0726235,-0.0673511,-0.0622738,-0.0573836,-0.0526726,-0.0481331,-0.0437577,-0.0395391,-0.0354701,-0.031544,-0.0277541,-0.0240939,-0.0205571,-0.0171379,-0.0138303,-0.0106287,-0.00752786,-0.00452252,-0.00160775,0.0012212,0.00396887,0.00663959,0.00923751,0.0117666,0.0142305,0.0166328,0.0189769,0.0212659,0.0235029,0.0256906,0.0278317,0.0299285,0.0319835,0.0339987,0.035976,0.0379172,0.0398239,0.0416977,0.0435397,0.0453513,0.0471333,0.0488866,0.0506121,0.0523102,0.0539814,0.0556261,0.0572446,0.0588368,0.0604029,0.0619427,0.063456,0.0649425,0.0664019,0.0678336,0.0692373,0.0706122,0.0719579,0.0732736,0.0745586,0.0758121,0.0770335,0.0782219,0.0793766,0.0804968,0.0815818,0.0826307,0.0836429,0.0846176,0.0855541,0.0864518,0.08731,0.0881281,0.0889055,0.0896417,0.090336,0.090988,0.0915971,0.0921628,0.0926844,0.0931613,0.0935931,0.0939788,0.0943178,0.0946091,0.0948518,0.0950447,0.0951864,0.0952756,0.0953105,0.095289,0.0952089,0.0950676,0.0948622,0.0945892,0.0942448,0.0938246,0.0933238,0.0927368,0.0920574,0.0912786,0.0903925,0.0893904,0.0882625,0.0869979,0.0855844,0.0840087,0.0822557,0.0803088,0.0781496,0.0757579,0.0731111,0.0701844,0.0669506,0.0633796,0.0594382,0.0550901,0.0502954,0.0450105,0.0391876,0.0327746,0.0257148,0.0179463,0.00940253,1.11106e-05,-0.0103057,-0.0216312,-0.0340544,-0.0476696,-0.0625761,-0.0788777,-0.0966814,-0.116094,-0.137228,-0.160188,-0.185073,-0.211972,-0.240954,-0.272065,-0.305311,-0.34065},
{-1.06138,-1.03717,-1.01307,-0.989095,-0.965251,-0.941547,-0.917992,-0.894596,-0.871366,-0.848315,-0.825451,-0.802786,-0.780331,-0.758096,-0.736092,-0.714332,-0.692826,-0.671586,-0.650622,-0.629947,-0.60957,-0.589503,-0.569755,-0.550336,-0.531256,-0.512523,-0.494145,-0.47613,-0.458485,-0.441215,-0.424326,-0.407823,-0.391709,-0.375987,-0.360659,-0.345726,-0.33119,-0.317048,-0.303301,-0.289945,-0.27698,-0.264401,-0.252203,-0.240384,-0.228937,-0.217857,-0.207137,-0.19677,-0.186751,-0.17707,-0.167721,-0.158695,-0.149984,-0.141579,-0.133472,-0.125654,-0.118117,-0.11085,-0.103846,-0.0970958,-0.09059,-0.0843199,-0.0782769,-0.0724524,-0.0668378,-0.0614249,-0.0562053,-0.0511711,-0.0463144,-0.0416275,-0.037103,-0.0327335,-0.0285121,-0.0244318,-0.020486,-0.0166682,-0.0129724,-0.00939248,-0.00592272,-0.00255758,0.00070824,0.00387982,0.00696203,0.00995951,0.0128767,0.0157178,0.0184868,0.0211875,0.0238235,0.0263981,0.0289146,0.0313759,0.0337847,0.0361437,0.0384552,0.0407215,0.0429445,0.0451262,0.0472681,0.0493717,0.0514384,0.0534693,0.0554655,0.0574277,0.0593566,0.0612528,0.0631167,0.0649486,0.0667486,0.0685167,0.0702529,0.071957,0.0736287,0.0752676,0.0768732,0.0784452,0.0799828,0.0814856,0.0829527,0.0843835,0.0857773,0.0871333,0.0884509,0.0897291,0.0909674,0.0921649,0.0933211,0.0944351,0.0955064,0.0965344,0.0975184,0.0984579,0.0993525,0.100202,0.101005,0.101761,0.102471,0.103134,0.103749,0.104316,0.104835,0.105304,0.105724,0.106093,0.106411,0.106678,0.106891,0.107049,0.107152,0.107197,0.107183,0.107107,0.106967,0.106759,0.106481,0.106128,0.105695,0.105178,0.104572,0.103868,0.103061,0.102143,0.101103,0.099932,0.0986187,0.0971504,0.095513,0.0936909,0.0916669,0.0894218,0.0869345,0.0841815,0.0811372,0.077773,0.0740578,0.0699569,0.0654328,0.0604439,0.0549449,0.0488863,0.0422139,0.0348691,0.0267878,0.0179009,0.0081338,-0.00259377,-0.0143677,-0.0272796,-0.0414262,-0.0569093,-0.0738348,-0.0923099,-0.112447,-0.134355,-0.158139,-0.183897,-0.211713,-0.241651,-0.273745,-0.307989},
{-1.14994,-1.12533,-1.1008,-1.07637,-1.05204,-1.02783,-1.00373,-0.97975,-0.955907,-0.932205,-0.908654,-0.885263,-0.862042,-0.839001,-0.81615,-0.793499,-0.771061,-0.748846,-0.726864,-0.705129,-0.68365,-0.662439,-0.641507,-0.620866,-0.600526,-0.580497,-0.560789,-0.541413,-0.522377,-0.503689,-0.485358,-0.467391,-0.449794,-0.432574,-0.415734,-0.39928,-0.383215,-0.367541,-0.35226,-0.337373,-0.322881,-0.308782,-0.295075,-0.281758,-0.268828,-0.256281,-0.244114,-0.232321,-0.220897,-0.209835,-0.199131,-0.188775,-0.178763,-0.169085,-0.159733,-0.150701,-0.141978,-0.133558,-0.12543,-0.117587,-0.110018,-0.102716,-0.0956717,-0.0888756,-0.0823192,-0.0759935,-0.06989,-0.0640001,-0.0583152,-0.0528272,-0.0475278,-0.0424091,-0.0374633,-0.0326828,-0.0280603,-0.0235886,-0.0192608,-0.01507,-0.0110099,-0.00707407,-0.00325657,0.000448436,0.00404653,0.00754304,0.0109431,0.0142515,0.017473,0.020612,0.0236726,0.0266588,0.0295743,0.0324227,0.0352072,0.0379309,0.0405966,0.0432071,0.0457647,0.0482716,0.05073,0.0531416,0.0555081,0.0578309,0.0601114,0.0623505,0.0645494,0.0667087,0.068829,0.0709108,0.0729544,0.07496,0.0769277,0.0788573,0.0807488,0.0826018,0.0844159,0.0861908,0.0879258,0.0896206,0.0912743,0.0928864,0.0944561,0.0959828,0.0974657,0.0989042,0.100297,0.101645,0.102946,0.104199,0.105405,0.106563,0.107671,0.10873,0.10974,0.110699,0.111607,0.112464,0.11327,0.114024,0.114726,0.115376,0.115973,0.116517,0.117007,0.117443,0.117824,0.11815,0.118419,0.11863,0.118782,0.118874,0.118903,0.118868,0.118766,0.118594,0.118348,0.118026,0.117622,0.117132,0.11655,0.11587,0.115085,0.114186,0.113165,0.112012,0.110715,0.109262,0.107639,0.10583,0.103819,0.101587,0.0991112,0.0963699,0.093337,0.0899843,0.0862804,0.0821913,0.0776791,0.0727027,0.0672168,0.061172,0.0545144,0.0471854,0.0391212,0.0302528,0.0205057,0.00979973,-0.00195099,-0.0148379,-0.028958,-0.0444132,-0.0613083,-0.0797548,-0.0998626,-0.121742,-0.145501,-0.171238,-0.199041,-0.228977,-0.261086,-0.295369},
{-1.23188,-1.20696,-1.18212,-1.15735,-1.13267,-1.10807,-1.08356,-1.05915,-1.03485,-1.01066,-0.986593,-0.962653,-0.938851,-0.915195,-0.891694,-0.868358,-0.845197,-0.822221,-0.799441,-0.776867,-0.754511,-0.732385,-0.710498,-0.688863,-0.66749,-0.646392,-0.625578,-0.605061,-0.584849,-0.564955,-0.545387,-0.526154,-0.507266,-0.48873,-0.470554,-0.452744,-0.435308,-0.418249,-0.401573,-0.385283,-0.369382,-0.353873,-0.338755,-0.32403,-0.309698,-0.295756,-0.282204,-0.269038,-0.256255,-0.243852,-0.231822,-0.220162,-0.208865,-0.197925,-0.187335,-0.177089,-0.167177,-0.157594,-0.14833,-0.139378,-0.130728,-0.122372,-0.114302,-0.106508,-0.0989812,-0.091713,-0.0846944,-0.0779165,-0.0713704,-0.0650475,-0.0589391,-0.0530367,-0.0473321,-0.041817,-0.0364835,-0.0313237,-0.02633,-0.0214951,-0.0168119,-0.0122732,-0.00787244,-0.00360312,0.000541018,0.00456598,0.00847754,0.0122812,0.0159823,0.0195857,0.0230964,0.0265187,0.0298571,0.0331156,0.036298,0.0394078,0.0424484,0.0454229,0.0483342,0.0511849,0.0539774,0.056714,0.0593967,0.0620272,0.0646071,0.0671378,0.0696206,0.0720563,0.0744459,0.07679,0.0790892,0.0813437,0.0835538,0.0857195,0.0878409,0.0899177,0.0919497,0.0939365,0.0958778,0.097773,0.0996215,0.101423,0.103176,0.104881,0.106537,0.108142,0.109698,0.111202,0.112654,0.114054,0.115401,0.116695,0.117934,0.11912,0.12025,0.121326,0.122347,0.123312,0.124221,0.125074,0.125871,0.126612,0.127296,0.127924,0.128494,0.129007,0.129462,0.129859,0.130196,0.130474,0.13069,0.130843,0.130933,0.130957,0.130912,0.130797,0.130609,0.130343,0.129996,0.129563,0.12904,0.128419,0.127696,0.126861,0.125907,0.124824,0.123601,0.122227,0.120688,0.11897,0.117056,0.114928,0.112566,0.109947,0.107048,0.103841,0.100296,0.0963806,0.0920582,0.0872892,0.0820303,0.0762338,0.0698479,0.0628159,0.0550764,0.0465624,0.037202,0.0269172,0.0156246,0.00323492,-0.0103468,-0.0252197,-0.04149,-0.0592659,-0.0786585,-0.0997799,-0.12274,-0.147645,-0.174588,-0.203651,-0.23489,-0.268328},
{-1.30799,-1.28285,-1.25776,-1.23274,-1.20778,-1.18289,-1.15807,-1.13334,-1.10869,-1.08412,-1.05966,-1.0353,-1.01105,-0.986921,-0.962918,-0.93905,-0.915325,-0.891754,-0.868345,-0.845109,-0.822055,-0.799195,-0.77654,-0.7541,-0.731886,-0.709909,-0.688182,-0.666716,-0.64552,-0.624608,-0.603989,-0.583673,-0.563672,-0.543996,-0.524652,-0.50565,-0.486999,-0.468706,-0.450777,-0.433219,-0.416037,-0.399235,-0.382818,-0.366788,-0.351147,-0.335897,-0.321038,-0.306569,-0.29249,-0.278799,-0.265493,-0.252568,-0.240021,-0.227847,-0.21604,-0.204596,-0.193507,-0.182767,-0.172369,-0.162306,-0.152568,-0.14315,-0.134041,-0.125233,-0.116719,-0.108488,-0.100533,-0.0928434,-0.0854113,-0.0782276,-0.0712834,-0.0645698,-0.0580782,-0.0517999,-0.0457265,-0.0398497,-0.0341613,-0.0286535,-0.0233185,-0.0181486,-0.0131367,-0.00827557,-0.00355839,0.00102147,0.00547039,0.00979449,0.0139997,0.0180915,0.0220754,0.0259564,0.0297395,0.0334291,0.0370297,0.0405452,0.0439796,0.0473363,0.0506188,0.05383,0.0569729,0.0600499,0.0630635,0.0660157,0.0689086,0.0717437,0.0745226,0.0772465,0.0799164,0.0825334,0.085098,0.0876109,0.0900724,0.0924826,0.0948419,0.09715,0.0994069,0.101612,0.103766,0.105867,0.107916,0.109911,0.111852,0.113739,0.115571,0.117347,0.119067,0.120731,0.122336,0.123884,0.125373,0.126804,0.128175,0.129487,0.130739,0.13193,0.133061,0.134132,0.135142,0.136091,0.13698,0.137808,0.138574,0.13928,0.139925,0.140507,0.141029,0.141487,0.141883,0.142216,0.142484,0.142686,0.142822,0.142888,0.142884,0.142807,0.142653,0.14242,0.142104,0.1417,0.141203,0.140608,0.139908,0.139095,0.138162,0.137098,0.135894,0.134538,0.133016,0.131314,0.129416,0.127304,0.124957,0.122354,0.119471,0.116279,0.112751,0.108852,0.104548,0.0997977,0.0945591,0.0887844,0.0824221,0.0754157,0.067704,0.0592205,0.0498932,0.0396447,0.0283915,0.0160447,0.00250942,-0.0123133,-0.0285301,-0.0462492,-0.0655824,-0.0866423,-0.10954,-0.134384,-0.16127,-0.190281,-0.221481,-0.254896},
{-1.37898,-1.35366,-1.32839,-1.30317,-1.27799,-1.25288,-1.22782,-1.20283,-1.1779,-1.15305,-1.12828,-1.10359,-1.079,-1.0545,-1.0301,-1.00581,-0.981644,-0.957602,-0.933694,-0.909931,-0.88632,-0.862872,-0.839596,-0.816503,-0.793604,-0.770908,-0.748428,-0.726175,-0.704159,-0.682392,-0.660886,-0.639651,-0.618699,-0.59804,-0.577685,-0.557644,-0.537927,-0.518543,-0.4995,-0.480807,-0.462471,-0.4445,-0.426898,-0.409671,-0.392823,-0.376359,-0.36028,-0.34459,-0.329288,-0.314376,-0.299852,-0.285716,-0.271966,-0.258598,-0.245609,-0.232996,-0.220753,-0.208875,-0.197356,-0.18619,-0.17537,-0.164889,-0.154739,-0.144913,-0.135402,-0.126197,-0.117291,-0.108675,-0.100339,-0.0922749,-0.084474,-0.0769272,-0.0696256,-0.0625603,-0.0557225,-0.0491038,-0.0426954,-0.0364891,-0.0304766,-0.02465,-0.0190013,-0.0135229,-0.00820756,-0.00304794,0.00196283,0.00683145,0.0115643,0.0161677,0.0206475,0.0250092,0.0292584,0.0334001,0.0374392,0.0413802,0.0452274,0.048985,0.0526565,0.0562456,0.0597555,0.0631892,0.0665493,0.0698384,0.0730587,0.0762122,0.0793006,0.0823256,0.0852884,0.0881902,0.0910319,0.0938143,0.0965378,0.0992029,0.10181,0.104359,0.10685,0.109283,0.111657,0.113972,0.116229,0.118426,0.120563,0.122639,0.124655,0.126608,0.1285,0.130329,0.132094,0.133796,0.135434,0.137008,0.138517,0.139961,0.14134,0.142654,0.143902,0.145085,0.146203,0.147255,0.148242,0.149164,0.150021,0.150813,0.15154,0.152202,0.152799,0.15333,0.153796,0.154195,0.154528,0.154792,0.154988,0.155113,0.155166,0.155145,0.155047,0.154869,0.154607,0.154258,0.153817,0.153278,0.152636,0.151883,0.151011,0.150012,0.148876,0.147592,0.146146,0.144526,0.142715,0.140697,0.138452,0.135959,0.133195,0.130134,0.126748,0.123004,0.118869,0.114304,0.109268,0.103714,0.0975946,0.0908535,0.0834319,0.0752655,0.0662846,0.0564137,0.045572,0.0336724,0.0206232,0.00632504,-0.00932496,-0.0264346,-0.0451153,-0.0654804,-0.0876431,-0.111714,-0.137797,-0.165983,-0.196348,-0.228938},
{-1.44545,-1.41999,-1.39457,-1.36919,-1.34385,-1.31855,-1.2933,-1.26811,-1.24297,-1.21789,-1.19287,-1.16792,-1.14305,-1.11825,-1.09354,-1.06892,-1.0444,-1.01998,-0.995678,-0.971491,-0.947432,-0.923508,-0.89973,-0.876106,-0.852647,-0.829361,-0.806261,-0.783355,-0.760656,-0.738174,-0.715921,-0.693908,-0.672146,-0.650646,-0.62942,-0.608479,-0.587833,-0.567492,-0.547467,-0.527768,-0.508402,-0.48938,-0.470708,-0.452393,-0.434443,-0.416863,-0.399658,-0.382832,-0.366388,-0.350329,-0.334657,-0.319372,-0.304474,-0.289963,-0.275838,-0.262094,-0.248731,-0.235744,-0.223128,-0.21088,-0.198992,-0.18746,-0.176276,-0.165434,-0.154927,-0.144746,-0.134883,-0.125332,-0.116082,-0.107126,-0.0984542,-0.0900587,-0.0819301,-0.0740597,-0.0664386,-0.059058,-0.0519091,-0.0449833,-0.0382719,-0.0317667,-0.0254594,-0.0193419,-0.0134064,-0.00764529,-0.00205107,0.00338341,0.00866509,0.0138007,0.0187965,0.0236589,0.0283936,0.0330063,0.0375023,0.0418866,0.0461641,0.0503391,0.054416,0.0583987,0.0622907,0.0660955,0.0698161,0.0734554,0.077016,0.0805002,0.0839101,0.0872474,0.0905138,0.0937106,0.0968391,0.0999001,0.102894,0.105823,0.108685,0.111482,0.114214,0.116881,0.119482,0.122017,0.124487,0.126891,0.129227,0.131497,0.133699,0.135833,0.137899,0.139896,0.141824,0.143681,0.145469,0.147187,0.148834,0.15041,0.151916,0.15335,0.154714,0.156007,0.15723,0.158382,0.159464,0.160476,0.161418,0.16229,0.163093,0.163827,0.164491,0.165085,0.16561,0.166065,0.166449,0.166762,0.167003,0.167169,0.167261,0.167275,0.167209,0.167061,0.166826,0.166502,0.166083,0.165564,0.164939,0.164202,0.163344,0.162356,0.161229,0.159952,0.158513,0.156896,0.155087,0.15307,0.150823,0.148327,0.145559,0.142491,0.139096,0.135342,0.131195,0.126617,0.121565,0.115995,0.109856,0.103094,0.0956489,0.0874572,0.0784488,0.0685483,0.0576745,0.0457404,0.0326539,0.0183156,0.00262228,-0.0145343,-0.0332658,-0.0536862,-0.0759096,-0.100048,-0.126205,-0.154475,-0.184936,-0.217637},
{-1.50792,-1.48235,-1.4568,-1.43129,-1.40581,-1.38037,-1.35497,-1.32961,-1.30429,-1.27903,-1.25381,-1.22866,-1.20356,-1.17853,-1.15356,-1.12867,-1.10387,-1.07914,-1.05451,-1.02998,-1.00556,-0.981249,-0.95706,-0.933001,-0.909082,-0.88531,-0.861696,-0.838249,-0.81498,-0.7919,-0.769018,-0.746347,-0.723897,-0.701679,-0.679705,-0.657986,-0.636534,-0.615359,-0.594472,-0.573884,-0.553605,-0.533645,-0.514013,-0.494718,-0.475768,-0.45717,-0.438931,-0.421059,-0.403556,-0.386429,-0.369681,-0.353315,-0.337333,-0.321736,-0.306525,-0.291699,-0.277257,-0.263197,-0.249517,-0.236213,-0.22328,-0.210716,-0.198513,-0.186666,-0.17517,-0.164017,-0.153199,-0.142711,-0.132543,-0.122688,-0.113137,-0.103883,-0.0949149,-0.0862258,-0.0778064,-0.0696478,-0.0617413,-0.054078,-0.0466493,-0.0394464,-0.0324609,-0.0256845,-0.0191089,-0.0127261,-0.0065282,-0.000507725,0.00534276,0.0110304,0.016562,0.0219443,0.0271836,0.032286,0.0372572,0.0421028,0.046828,0.0514377,0.0559366,0.0603289,0.0646188,0.06881,0.072906,0.0769099,0.0808247,0.084653,0.0883972,0.0920595,0.0956416,0.0991452,0.102572,0.105922,0.109198,0.112399,0.115527,0.118582,0.121564,0.124473,0.12731,0.130074,0.132764,0.135382,0.137926,0.140396,0.142793,0.145114,0.147361,0.149532,0.151628,0.153648,0.155592,0.15746,0.159251,0.160966,0.162605,0.164167,0.165653,0.167063,0.168397,0.169656,0.17084,0.171949,0.172984,0.173945,0.174832,0.175646,0.176387,0.177055,0.17765,0.178172,0.178621,0.178995,0.179295,0.179519,0.179666,0.179734,0.179721,0.179625,0.179441,0.179167,0.178799,0.178331,0.177758,0.177073,0.176269,0.175338,0.174269,0.173053,0.171678,0.17013,0.168395,0.166455,0.164293,0.161888,0.159217,0.156257,0.152978,0.149351,0.145342,0.140915,0.136028,0.130639,0.124698,0.118152,0.110944,0.103012,0.0942869,0.0846957,0.0741594,0.0625932,0.0499055,0.0360002,0.0207751,0.00412325,-0.0140665,-0.033908,-0.0555163,-0.0790053,-0.104484,-0.132052,-0.161797,-0.193781},
{-1.56681,-1.54115,-1.5155,-1.48989,-1.4643,-1.43873,-1.41321,-1.38771,-1.36225,-1.33683,-1.31146,-1.28613,-1.26085,-1.23562,-1.21045,-1.18534,-1.1603,-1.13532,-1.11043,-1.08562,-1.06089,-1.03626,-1.01174,-0.98732,-0.963019,-0.938844,-0.914803,-0.890905,-0.86716,-0.843576,-0.820165,-0.796937,-0.773902,-0.751071,-0.728456,-0.706068,-0.683918,-0.662017,-0.640377,-0.619008,-0.597923,-0.57713,-0.556641,-0.536466,-0.516614,-0.497094,-0.477914,-0.459083,-0.440606,-0.422491,-0.404744,-0.387368,-0.370368,-0.353747,-0.337508,-0.321652,-0.306179,-0.29109,-0.276384,-0.262058,-0.248111,-0.23454,-0.22134,-0.208507,-0.196036,-0.183922,-0.172158,-0.160738,-0.149654,-0.1389,-0.128468,-0.118349,-0.108536,-0.0990197,-0.089792,-0.0808443,-0.0721676,-0.0637534,-0.0555928,-0.0476771,-0.0399977,-0.0325459,-0.0253135,-0.018292,-0.0114733,-0.00484949,0.00158714,0.00784412,0.0139287,0.019848,0.0256087,0.0312174,0.0366801,0.0420029,0.0471915,0.052251,0.0571867,0.0620032,0.0667049,0.071296,0.0757804,0.0801615,0.0844426,0.0886268,0.0927166,0.0967145,0.100623,0.104443,0.108177,0.111826,0.115391,0.118874,0.122275,0.125594,0.128833,0.131991,0.135069,0.138066,0.140983,0.14382,0.146576,0.149251,0.151844,0.154356,0.156787,0.159135,0.161401,0.163585,0.165686,0.167704,0.16964,0.171493,0.173263,0.174952,0.176558,0.178082,0.179525,0.180887,0.182169,0.18337,0.184493,0.185536,0.186501,0.187387,0.188196,0.188928,0.189582,0.190159,0.190658,0.19108,0.191422,0.191686,0.191868,0.191968,0.191984,0.191912,0.19175,0.191495,0.191142,0.190686,0.190122,0.189443,0.188642,0.18771,0.186638,0.185415,0.184029,0.182467,0.180714,0.178754,0.176566,0.174132,0.171429,0.16843,0.165108,0.161433,0.157371,0.152884,0.147933,0.142471,0.136451,0.129818,0.122516,0.11448,0.105642,0.0959278,0.0852581,0.0735474,0.0607034,0.046629,0.0312215,0.0143733,-0.00402739,-0.0240952,-0.0459458,-0.0696932,-0.0954472,-0.123308,-0.153362,-0.185673},
{-1.62251,-1.59677,-1.57104,-1.54533,-1.51965,-1.49399,-1.46835,-1.44274,-1.41717,-1.39162,-1.36611,-1.34064,-1.3152,-1.28981,-1.26447,-1.23918,-1.21394,-1.18876,-1.16365,-1.1386,-1.11363,-1.08873,-1.06393,-1.03921,-1.01459,-0.990079,-0.96568,-0.941403,-0.917256,-0.893249,-0.86939,-0.845689,-0.822156,-0.798801,-0.775636,-0.752671,-0.729918,-0.707386,-0.685089,-0.663036,-0.641239,-0.61971,-0.59846,-0.577498,-0.556836,-0.536484,-0.516451,-0.496746,-0.477378,-0.458354,-0.439682,-0.421369,-0.403419,-0.385839,-0.368632,-0.351801,-0.33535,-0.319279,-0.30359,-0.288283,-0.273357,-0.25881,-0.24464,-0.230845,-0.21742,-0.204361,-0.191664,-0.179323,-0.167331,-0.155683,-0.144371,-0.133388,-0.122727,-0.11238,-0.102338,-0.0925936,-0.083138,-0.0739626,-0.0650589,-0.056418,-0.0480315,-0.0398907,-0.0319869,-0.0243118,-0.0168569,-0.00961425,-0.00257568,0.00426658,0.0109201,0.0173923,0.0236903,0.029821,0.0357908,0.0416062,0.0472732,0.0527974,0.0581844,0.0634391,0.0685665,0.073571,0.0784568,0.0832279,0.0878877,0.0924395,0.0968864,0.101231,0.105476,0.109623,0.113674,0.117631,0.121495,0.125268,0.12895,0.132543,0.136046,0.13946,0.142786,0.146023,0.149172,0.152234,0.155206,0.158091,0.160887,0.163594,0.166212,0.168741,0.171181,0.173531,0.175792,0.177964,0.180046,0.18204,0.183944,0.18576,0.187487,0.189127,0.190679,0.192145,0.193524,0.194818,0.196027,0.197151,0.198192,0.19915,0.200024,0.200817,0.201527,0.202155,0.202701,0.203165,0.203545,0.203842,0.204053,0.204178,0.204214,0.204158,0.204008,0.203761,0.203411,0.202953,0.202383,0.201694,0.200877,0.199925,0.198827,0.197574,0.196151,0.194547,0.192744,0.190728,0.188477,0.185972,0.183188,0.1801,0.17668,0.172896,0.168713,0.164094,0.158996,0.153374,0.147177,0.140352,0.132839,0.124573,0.115484,0.105497,0.0945311,0.0824978,0.0693045,0.0548525,0.0390375,0.0217504,0.0028784,-0.017694,-0.0400828,-0.0644019,-0.0907606,-0.119257,-0.149975,-0.182972},
{-1.67533,-1.64952,-1.62372,-1.59794,-1.57218,-1.54643,-1.52071,-1.495,-1.46932,-1.44367,-1.41805,-1.39245,-1.36689,-1.34136,-1.31588,-1.29043,-1.26503,-1.23968,-1.21438,-1.18913,-1.16395,-1.13883,-1.11379,-1.08882,-1.06393,-1.03914,-1.01444,-0.989841,-0.965355,-0.940987,-0.916747,-0.892643,-0.868684,-0.844881,-0.821243,-0.79778,-0.774503,-0.751424,-0.728552,-0.7059,-0.683478,-0.661298,-0.639371,-0.617709,-0.596322,-0.575221,-0.554416,-0.533918,-0.513737,-0.49388,-0.474358,-0.455178,-0.436346,-0.417871,-0.399757,-0.382009,-0.364633,-0.347631,-0.331006,-0.314759,-0.298892,-0.283405,-0.268297,-0.253567,-0.239212,-0.22523,-0.211617,-0.198369,-0.185481,-0.172947,-0.160762,-0.148919,-0.137411,-0.126232,-0.115374,-0.104828,-0.094587,-0.0846429,-0.074987,-0.0656109,-0.056506,-0.0476639,-0.0390759,-0.0307335,-0.0226284,-0.0147522,-0.00709662,0.000346239,0.00758426,0.0146251,0.0214761,0.0281445,0.0346373,0.0409609,0.0471219,0.0531262,0.0589797,0.0646878,0.0702557,0.0756881,0.0809897,0.0861646,0.0912168,0.0961498,0.100967,0.105671,0.110265,0.114751,0.119132,0.123409,0.127583,0.131657,0.135631,0.139507,0.143285,0.146966,0.15055,0.154037,0.157429,0.160724,0.163924,0.167027,0.170035,0.172946,0.175762,0.178481,0.181104,0.183631,0.186062,0.188398,0.190637,0.192781,0.194831,0.196785,0.198646,0.200413,0.202088,0.203671,0.205163,0.206564,0.207876,0.209099,0.210234,0.211282,0.212244,0.21312,0.213911,0.214618,0.21524,0.215777,0.216229,0.216596,0.216877,0.21707,0.217175,0.217188,0.217107,0.216929,0.216651,0.216267,0.215773,0.215163,0.21443,0.213565,0.212561,0.211406,0.21009,0.208599,0.20692,0.205035,0.202929,0.200579,0.197966,0.195064,0.191846,0.188284,0.184343,0.179988,0.175181,0.169876,0.164028,0.157584,0.150487,0.142677,0.134087,0.124644,0.114271,0.102884,0.0903936,0.0767037,0.0617134,0.0453163,0.0274014,0.00785421,-0.013442,-0.0366034,-0.0617441,-0.0889708,-0.118379,-0.150046},
{-1.72555,-1.69968,-1.67382,-1.64797,-1.62214,-1.59633,-1.57052,-1.54474,-1.51898,-1.49323,-1.46751,-1.44181,-1.41614,-1.3905,-1.36489,-1.33931,-1.31377,-1.28827,-1.26281,-1.2374,-1.21204,-1.18673,-1.16149,-1.13631,-1.11119,-1.08616,-1.0612,-1.03633,-1.01155,-0.986878,-0.962312,-0.937863,-0.913539,-0.889349,-0.865303,-0.84141,-0.81768,-0.794123,-0.77075,-0.747573,-0.724601,-0.701846,-0.67932,-0.657034,-0.634999,-0.613226,-0.591727,-0.570512,-0.549591,-0.528975,-0.508673,-0.488694,-0.469047,-0.449741,-0.430781,-0.412175,-0.393929,-0.376048,-0.358535,-0.341395,-0.324629,-0.308241,-0.29223,-0.276597,-0.261341,-0.246461,-0.231955,-0.217819,-0.204051,-0.190645,-0.177598,-0.164903,-0.152555,-0.140548,-0.128874,-0.117527,-0.106499,-0.0957828,-0.0853698,-0.0752522,-0.0654216,-0.0558698,-0.0465882,-0.0375684,-0.0288021,-0.0202808,-0.0119963,-0.00394054,0.00389461,0.0115169,0.0189341,0.0261534,0.0331821,0.0400272,0.0466952,0.0531926,0.0595254,0.0656994,0.0717201,0.0775926,0.0833218,0.0889122,0.094368,0.099693,0.104891,0.109965,0.114918,0.119753,0.124472,0.129077,0.133571,0.137954,0.142228,0.146394,0.150454,0.154408,0.158256,0.162,0.165639,0.169174,0.172605,0.175932,0.179155,0.182275,0.185291,0.188203,0.191012,0.193718,0.196321,0.198821,0.201219,0.203515,0.205709,0.207803,0.209797,0.211691,0.213487,0.215185,0.216786,0.218292,0.219703,0.221021,0.222246,0.22338,0.224423,0.225376,0.226241,0.227016,0.227705,0.228305,0.228817,0.229242,0.229578,0.229824,0.229979,0.230041,0.230009,0.229878,0.229645,0.229307,0.228859,0.228294,0.227607,0.226789,0.225832,0.224727,0.223462,0.222025,0.220403,0.218579,0.216537,0.214256,0.211717,0.208895,0.205765,0.202296,0.198459,0.194216,0.189531,0.184361,0.17866,0.172376,0.165456,0.157839,0.14946,0.140249,0.130128,0.119017,0.106827,0.0934642,0.0788288,0.0628159,0.0453153,0.0262131,0.00539268,-0.0172632,-0.0418705,-0.0685397,-0.0973717,-0.128452},
{-1.7734,-1.74748,-1.72157,-1.69567,-1.66978,-1.6439,-1.61804,-1.59218,-1.56634,-1.54052,-1.51471,-1.48893,-1.46316,-1.43742,-1.4117,-1.38601,-1.36035,-1.33473,-1.30913,-1.28358,-1.25807,-1.2326,-1.20718,-1.18181,-1.15651,-1.13126,-1.10608,-1.08098,-1.05595,-1.03102,-1.00617,-0.981423,-0.956784,-0.93226,-0.90786,-0.883593,-0.859468,-0.835495,-0.811684,-0.788045,-0.76459,-0.741328,-0.718271,-0.69543,-0.672816,-0.650442,-0.628317,-0.606454,-0.584863,-0.563555,-0.542541,-0.52183,-0.501432,-0.481356,-0.461611,-0.442205,-0.423144,-0.404436,-0.386086,-0.368099,-0.350479,-0.33323,-0.316354,-0.299853,-0.283728,-0.267979,-0.252605,-0.237605,-0.222976,-0.208716,-0.194821,-0.181286,-0.168108,-0.15528,-0.142796,-0.130651,-0.118838,-0.107349,-0.0961772,-0.0853148,-0.0747539,-0.0644865,-0.0545045,-0.0447996,-0.0353635,-0.0261879,-0.0172647,-0.00858552,-0.000142429,0.00807254,0.0160672,0.023849,0.0314255,0.0388037,0.0459906,0.0529928,0.0598165,0.066468,0.0729528,0.0792766,0.0854443,0.0914608,0.0973306,0.103058,0.108646,0.1141,0.119421,0.124613,0.129679,0.134621,0.139441,0.14414,0.148721,0.153185,0.157532,0.161765,0.165883,0.169887,0.173779,0.177557,0.181223,0.184777,0.188219,0.191549,0.194768,0.197876,0.200872,0.203757,0.206532,0.209197,0.211753,0.214199,0.216537,0.218767,0.22089,0.222907,0.22482,0.226628,0.228334,0.229937,0.231441,0.232845,0.23415,0.235359,0.236471,0.237489,0.238412,0.239242,0.239979,0.240623,0.241174,0.241633,0.241998,0.242269,0.242445,0.242522,0.2425,0.242375,0.242144,0.241803,0.241345,0.240767,0.24006,0.239217,0.23823,0.237088,0.23578,0.234293,0.232613,0.230724,0.228609,0.226246,0.223615,0.220691,0.217447,0.213854,0.209878,0.205484,0.200631,0.195277,0.189375,0.182871,0.17571,0.16783,0.159164,0.149641,0.139181,0.127701,0.115111,0.101316,0.0862134,0.069697,0.0516553,0.031973,0.010533,-0.0127826,-0.038089,-0.0654951,-0.0950991,-0.126982},
{-1.81909,-1.79313,-1.76718,-1.74123,-1.71529,-1.68936,-1.66343,-1.63752,-1.61162,-1.58573,-1.55985,-1.53399,-1.50814,-1.48231,-1.4565,-1.43071,-1.40495,-1.37921,-1.3535,-1.32782,-1.30218,-1.27657,-1.251,-1.22548,-1.2,-1.17458,-1.14921,-1.1239,-1.09866,-1.07349,-1.0484,-1.0234,-0.998486,-0.973672,-0.948964,-0.924372,-0.899902,-0.875564,-0.851369,-0.827324,-0.803442,-0.779731,-0.756203,-0.732868,-0.709738,-0.686824,-0.664138,-0.64169,-0.619492,-0.597555,-0.57589,-0.554509,-0.53342,-0.512634,-0.492161,-0.47201,-0.452189,-0.432706,-0.413567,-0.394781,-0.376351,-0.358283,-0.340581,-0.323249,-0.306288,-0.2897,-0.273486,-0.257646,-0.24218,-0.227084,-0.212359,-0.197999,-0.184002,-0.170363,-0.157077,-0.14414,-0.131545,-0.119285,-0.107354,-0.0957454,-0.0844513,-0.0734642,-0.0627763,-0.0523798,-0.0422664,-0.0324282,-0.0228571,-0.0135449,-0.00448359,0.00433479,0.0129181,0.0212739,0.0294098,0.0373331,0.0450509,0.0525699,0.0598968,0.0670378,0.0739989,0.0807858,0.0874039,0.0938582,0.100154,0.106294,0.112284,0.118128,0.123828,0.129388,0.134811,0.140099,0.145255,0.150281,0.155178,0.159948,0.164592,0.169111,0.173507,0.177781,0.181932,0.185961,0.18987,0.193658,0.197325,0.200873,0.204301,0.20761,0.2108,0.213871,0.216824,0.21966,0.222379,0.224981,0.227469,0.229841,0.2321,0.234247,0.236282,0.238207,0.240023,0.241732,0.243334,0.244831,0.246225,0.247516,0.248707,0.249797,0.250789,0.251682,0.252479,0.253178,0.253781,0.254287,0.254696,0.255008,0.25522,0.255332,0.25534,0.255243,0.255037,0.254717,0.25428,0.253718,0.253026,0.252195,0.251218,0.250084,0.248781,0.247298,0.245619,0.243729,0.241611,0.239244,0.236606,0.233674,0.230419,0.226813,0.222822,0.218411,0.21354,0.208166,0.202241,0.195712,0.188525,0.180616,0.171919,0.162363,0.151868,0.14035,0.127721,0.113884,0.0987382,0.0821758,0.0640855,0.0443522,0.0228578,-0.000515635,-0.0258841,-0.0533575,-0.0830356,-0.115001},
{-1.86281,-1.83681,-1.81082,-1.78483,-1.75885,-1.73287,-1.7069,-1.68093,-1.65497,-1.62902,-1.60308,-1.57715,-1.55123,-1.52533,-1.49944,-1.47357,-1.44771,-1.42188,-1.39606,-1.37028,-1.34452,-1.31878,-1.29309,-1.26742,-1.2418,-1.21622,-1.19068,-1.1652,-1.13977,-1.11441,-1.0891,-1.06387,-1.03872,-1.01365,-0.988677,-0.963798,-0.939026,-0.914368,-0.889834,-0.865432,-0.841171,-0.817062,-0.793116,-0.769341,-0.74575,-0.722353,-0.699161,-0.676185,-0.653438,-0.63093,-0.608673,-0.586678,-0.564955,-0.543515,-0.522369,-0.501527,-0.480997,-0.46079,-0.440912,-0.421372,-0.402177,-0.383333,-0.364845,-0.346718,-0.328956,-0.311562,-0.294539,-0.277887,-0.261607,-0.245699,-0.230162,-0.214994,-0.200193,-0.185756,-0.171679,-0.157958,-0.144587,-0.131561,-0.118874,-0.10652,-0.0944924,-0.0827838,-0.0713871,-0.0602947,-0.0494989,-0.0389919,-0.0287658,-0.0188128,-0.00912481,0.000305972,0.00948737,0.0184271,0.0271327,0.0356115,0.0438708,0.0519176,0.0597584,0.0673999,0.0748482,0.0821091,0.0891884,0.0960912,0.102823,0.109387,0.115789,0.122033,0.128122,0.134059,0.139849,0.145492,0.150993,0.156353,0.161574,0.166658,0.171606,0.17642,0.181102,0.18565,0.190068,0.194355,0.198512,0.20254,0.206438,0.210209,0.213851,0.217366,0.220754,0.224015,0.22715,0.230161,0.233047,0.235809,0.238449,0.240967,0.243365,0.245644,0.247804,0.249848,0.251777,0.253592,0.255295,0.256887,0.258371,0.259746,0.261015,0.26218,0.263241,0.264199,0.265055,0.26581,0.266465,0.267019,0.267472,0.267823,0.268072,0.268217,0.268256,0.268186,0.268003,0.267704,0.267285,0.266739,0.266059,0.265239,0.264269,0.26314,0.26184,0.260356,0.258675,0.256781,0.254655,0.252278,0.249629,0.246681,0.243409,0.239783,0.23577,0.231334,0.226435,0.22103,0.21507,0.208505,0.201277,0.193325,0.184582,0.174974,0.164426,0.152851,0.140161,0.126259,0.111043,0.0944076,0.0762396,0.0564239,0.0348423,0.0113762,-0.0140909,-0.0416698,-0.0714612,-0.103549},
{-1.90471,-1.87869,-1.85266,-1.82664,-1.80062,-1.7746,-1.74858,-1.72257,-1.69656,-1.67056,-1.64456,-1.61857,-1.59259,-1.56662,-1.54066,-1.51471,-1.48878,-1.46286,-1.43695,-1.41107,-1.38521,-1.35937,-1.33356,-1.30777,-1.28202,-1.2563,-1.23062,-1.20498,-1.17939,-1.15385,-1.12836,-1.10293,-1.07757,-1.05227,-1.02706,-1.00193,-0.976891,-0.95195,-0.927116,-0.902397,-0.877801,-0.853339,-0.829019,-0.804852,-0.780847,-0.757016,-0.73337,-0.709919,-0.686674,-0.663648,-0.640851,-0.618294,-0.59599,-0.573949,-0.552182,-0.530699,-0.509511,-0.488628,-0.468058,-0.447811,-0.427894,-0.408315,-0.389081,-0.370198,-0.351671,-0.333504,-0.315701,-0.298266,-0.281199,-0.264502,-0.248176,-0.232219,-0.216632,-0.201411,-0.186555,-0.17206,-0.157921,-0.144136,-0.130698,-0.117602,-0.104842,-0.0924124,-0.0803055,-0.0685146,-0.0570327,-0.0458521,-0.0349655,-0.0243651,-0.0140431,-0.00399199,0.00579608,0.0153287,0.0246134,0.0336577,0.0424686,0.0510533,0.0594187,0.0675713,0.0755174,0.0832631,0.0908142,0.0981762,0.105354,0.112353,0.119178,0.125832,0.132319,0.138644,0.144809,0.150818,0.156673,0.162376,0.16793,0.173337,0.178598,0.183715,0.188689,0.193521,0.198212,0.202764,0.207177,0.211451,0.215588,0.219587,0.22345,0.227177,0.230769,0.234226,0.23755,0.240741,0.2438,0.246728,0.249526,0.252195,0.254737,0.257153,0.259445,0.261613,0.263661,0.265589,0.267399,0.269092,0.270672,0.272138,0.273494,0.27474,0.275878,0.276909,0.277835,0.278656,0.279372,0.279985,0.280494,0.280899,0.281198,0.281392,0.281477,0.281451,0.281312,0.281056,0.280678,0.280172,0.279533,0.278753,0.277824,0.276736,0.275479,0.274039,0.272404,0.270558,0.268482,0.266159,0.263567,0.260681,0.257475,0.253921,0.249986,0.245635,0.240828,0.235524,0.229676,0.223232,0.216137,0.208331,0.199748,0.190316,0.17996,0.168595,0.156135,0.142483,0.12754,0.1112,0.0933517,0.0738802,0.0526675,0.0295945,0.00454336,-0.0225994,-0.0519386,-0.0835646},
{-1.94495,-1.9189,-1.89284,-1.86679,-1.84073,-1.81468,-1.78862,-1.76257,-1.73652,-1.71047,-1.68442,-1.65838,-1.63234,-1.60631,-1.58029,-1.55427,-1.52827,-1.50227,-1.47629,-1.45032,-1.42437,-1.39844,-1.37252,-1.34663,-1.32076,-1.29492,-1.26911,-1.24334,-1.2176,-1.1919,-1.16625,-1.14064,-1.11509,-1.0896,-1.06418,-1.03883,-1.01355,-0.988359,-0.963259,-0.938258,-0.913364,-0.888586,-0.863933,-0.839414,-0.815039,-0.790818,-0.766762,-0.742881,-0.719186,-0.695689,-0.6724,-0.649332,-0.626495,-0.603901,-0.581561,-0.559486,-0.537687,-0.516174,-0.494958,-0.474048,-0.453452,-0.433181,-0.413241,-0.393639,-0.374383,-0.355478,-0.336928,-0.318739,-0.300913,-0.283452,-0.26636,-0.249636,-0.233281,-0.217294,-0.201673,-0.186417,-0.171523,-0.156987,-0.142805,-0.128973,-0.115485,-0.102336,-0.0895197,-0.0770302,-0.0648606,-0.0530039,-0.041453,-0.0302007,-0.0192395,-0.00856189,0.00183956,0.0119724,0.021844,0.0314617,0.0408329,0.0499644,0.0588632,0.0675361,0.0759893,0.0842292,0.0922615,0.100092,0.107726,0.115168,0.122424,0.129497,0.136393,0.143113,0.149663,0.156044,0.162261,0.168315,0.17421,0.179946,0.185527,0.190953,0.196226,0.201348,0.206319,0.211141,0.215814,0.22034,0.224719,0.228952,0.233039,0.236982,0.240782,0.244438,0.247953,0.251326,0.25456,0.257655,0.260612,0.263434,0.266121,0.268675,0.271097,0.27339,0.275555,0.277594,0.279509,0.281303,0.282975,0.28453,0.285968,0.287291,0.288502,0.2896,0.290589,0.291468,0.292238,0.292901,0.293456,0.293903,0.294241,0.294469,0.294586,0.294589,0.294476,0.294242,0.293883,0.293394,0.292769,0.292001,0.291081,0.289999,0.288746,0.287308,0.285672,0.283822,0.281742,0.279411,0.276808,0.27391,0.270689,0.267118,0.263163,0.25879,0.253959,0.248627,0.242749,0.236273,0.229143,0.221299,0.212676,0.203201,0.192799,0.181386,0.168873,0.155167,0.140167,0.123767,0.105855,0.086317,0.0650343,0.0418876,0.0167585,-0.0104672,-0.0398952,-0.0716191},
{-1.98364,-1.95756,-1.93148,-1.9054,-1.87931,-1.85323,-1.82714,-1.80105,-1.77496,-1.74887,-1.72278,-1.69669,-1.6706,-1.64452,-1.61844,-1.59237,-1.5663,-1.54024,-1.51418,-1.48814,-1.46211,-1.43609,-1.41008,-1.38409,-1.35812,-1.33218,-1.30625,-1.28035,-1.25448,-1.22865,-1.20285,-1.17709,-1.15137,-1.12571,-1.1001,-1.07455,-1.04906,-1.02364,-0.998305,-0.973053,-0.947892,-0.922832,-0.897881,-0.873046,-0.848338,-0.823766,-0.79934,-0.77507,-0.750967,-0.727042,-0.703305,-0.679768,-0.656443,-0.633341,-0.610473,-0.58785,-0.565485,-0.543387,-0.521567,-0.500036,-0.478804,-0.457879,-0.437272,-0.416989,-0.397039,-0.377429,-0.358165,-0.339253,-0.320696,-0.302499,-0.284664,-0.267195,-0.250093,-0.233357,-0.216988,-0.200986,-0.185348,-0.170071,-0.155154,-0.140592,-0.126382,-0.112517,-0.0989945,-0.0858073,-0.0729496,-0.0604153,-0.0481976,-0.0362897,-0.0246847,-0.0133753,-0.0023544,0.00838534,0.0188511,0.0290503,0.0389898,0.0486767,0.058118,0.0673203,0.07629,0.0850334,0.0935566,0.101865,0.109965,0.117861,0.125557,0.133059,0.140371,0.147497,0.15444,0.161204,0.167792,0.174206,0.180449,0.186524,0.192432,0.198175,0.203755,0.209174,0.214432,0.219531,0.224472,0.229256,0.233884,0.238357,0.242675,0.246841,0.250853,0.254715,0.258426,0.261988,0.265402,0.26867,0.271793,0.274772,0.277609,0.280306,0.282865,0.285288,0.287576,0.289733,0.291759,0.293657,0.29543,0.297079,0.298606,0.300014,0.301304,0.302479,0.303538,0.304485,0.305319,0.306042,0.306654,0.307156,0.307545,0.307823,0.307987,0.308035,0.307965,0.307773,0.307456,0.307007,0.306422,0.305693,0.304813,0.303771,0.302559,0.301163,0.29957,0.297766,0.295733,0.293452,0.290903,0.288062,0.284904,0.281399,0.277517,0.273223,0.268478,0.263241,0.257466,0.251103,0.244097,0.236389,0.227915,0.218604,0.208382,0.197165,0.184868,0.171397,0.156653,0.14053,0.12292,0.103708,0.0827746,0.0600018,0.0352696,0.008462,-0.0205302,-0.0518057},
{-2.02089,-1.9948,-1.96869,-1.94259,-1.91647,-1.89036,-1.86424,-1.83812,-1.812,-1.78587,-1.75974,-1.73361,-1.70748,-1.68135,-1.65522,-1.6291,-1.60297,-1.57685,-1.55073,-1.52462,-1.49852,-1.47242,-1.44633,-1.42026,-1.3942,-1.36815,-1.34212,-1.31611,-1.29013,-1.26417,-1.23824,-1.21234,-1.18648,-1.16065,-1.13488,-1.10915,-1.08347,-1.05785,-1.0323,-1.00683,-0.981426,-0.956112,-0.930892,-0.905773,-0.880765,-0.855876,-0.831115,-0.806493,-0.782019,-0.757704,-0.733559,-0.709594,-0.685822,-0.662253,-0.638898,-0.61577,-0.592879,-0.570237,-0.547855,-0.525744,-0.503914,-0.482376,-0.461138,-0.440212,-0.419604,-0.399323,-0.379377,-0.359772,-0.340513,-0.321606,-0.303056,-0.284865,-0.267036,-0.249572,-0.232473,-0.21574,-0.199372,-0.183368,-0.167726,-0.152444,-0.137518,-0.122944,-0.108719,-0.0948369,-0.0812929,-0.0680813,-0.0551961,-0.042631,-0.0303794,-0.0184347,-0.00679002,0.00456167,0.0156273,0.026414,0.0369286,0.0471781,0.0571692,0.0669086,0.0764027,0.0856579,0.0946801,0.103475,0.112049,0.120406,0.128552,0.136491,0.144228,0.151767,0.159111,0.166265,0.173231,0.180012,0.186612,0.193032,0.199274,0.205341,0.211234,0.216956,0.222506,0.227888,0.233102,0.238149,0.24303,0.247747,0.2523,0.256691,0.26092,0.26499,0.2689,0.272653,0.27625,0.279692,0.282981,0.286118,0.289106,0.291947,0.294642,0.297194,0.299605,0.301877,0.304012,0.306014,0.307883,0.309623,0.311236,0.312723,0.314088,0.315332,0.316456,0.317462,0.318352,0.319126,0.319784,0.320328,0.320757,0.321069,0.321265,0.321341,0.321295,0.321125,0.320825,0.320392,0.319818,0.319098,0.318224,0.317185,0.315973,0.314574,0.312976,0.311163,0.309119,0.306824,0.304258,0.301396,0.298214,0.294683,0.290771,0.286443,0.281661,0.276383,0.270563,0.264151,0.257093,0.249328,0.240793,0.231416,0.221122,0.20983,0.197453,0.183896,0.169061,0.152843,0.135131,0.115811,0.0947645,0.0718722,0.0470141,0.0200737,-0.00905876,-0.040483},
{-2.05682,-2.0307,-2.00458,-1.97845,-1.95232,-1.92618,-1.90003,-1.87388,-1.84773,-1.82157,-1.79541,-1.76924,-1.74307,-1.7169,-1.69072,-1.66455,-1.63837,-1.6122,-1.58602,-1.55985,-1.53368,-1.50752,-1.48136,-1.4552,-1.42906,-1.40293,-1.37681,-1.3507,-1.32461,-1.29854,-1.27249,-1.24646,-1.22047,-1.1945,-1.16857,-1.14268,-1.11684,-1.09104,-1.0653,-1.03962,-1.014,-0.98846,-0.962997,-0.937622,-0.912341,-0.887165,-0.862101,-0.837158,-0.812347,-0.787677,-0.763158,-0.738802,-0.714619,-0.69062,-0.666817,-0.643221,-0.619844,-0.596696,-0.57379,-0.551137,-0.528747,-0.506632,-0.484801,-0.463266,-0.442034,-0.421116,-0.400519,-0.380251,-0.36032,-0.34073,-0.321489,-0.3026,-0.284068,-0.265896,-0.248085,-0.230638,-0.213556,-0.196837,-0.180482,-0.164489,-0.148855,-0.133579,-0.118656,-0.104083,-0.0898552,-0.0759675,-0.0624147,-0.0491912,-0.036291,-0.0237079,-0.0114354,0.000532993,0.012204,0.0235843,0.0346806,0.0454997,0.0560482,0.0663327,0.0763595,0.0861349,0.0956649,0.104955,0.114012,0.12284,0.131444,0.139829,0.148001,0.155962,0.163717,0.171269,0.178622,0.18578,0.192744,0.199517,0.206102,0.212501,0.218715,0.224747,0.230599,0.23627,0.241764,0.247082,0.252224,0.257192,0.261987,0.26661,0.271063,0.275347,0.279463,0.283413,0.287199,0.290822,0.294284,0.297587,0.300733,0.303724,0.306563,0.309251,0.311792,0.314187,0.31644,0.318552,0.320527,0.322368,0.324075,0.325653,0.327103,0.328428,0.329629,0.330709,0.331668,0.332508,0.333231,0.333835,0.334322,0.334691,0.334941,0.33507,0.335077,0.334957,0.334708,0.334326,0.333803,0.333135,0.332313,0.331329,0.330173,0.328833,0.327297,0.32555,0.323575,0.321355,0.318868,0.316093,0.313005,0.309575,0.305773,0.301566,0.296915,0.291781,0.286119,0.27988,0.27301,0.265453,0.257144,0.248016,0.237994,0.227,0.214947,0.201744,0.187294,0.171494,0.154235,0.135404,0.114883,0.092553,0.0682936,0.0419861,0.0135171,-0.0172186},
{-2.0915,-2.06537,-2.03923,-2.01308,-1.98693,-1.96076,-1.9346,-1.90842,-1.88224,-1.85605,-1.82986,-1.80366,-1.77745,-1.75124,-1.72503,-1.69881,-1.67259,-1.64636,-1.62014,-1.59391,-1.56768,-1.54146,-1.51523,-1.48901,-1.46279,-1.43658,-1.41037,-1.38417,-1.35799,-1.33182,-1.30566,-1.27952,-1.25341,-1.22731,-1.20125,-1.17521,-1.14921,-1.12325,-1.09734,-1.07147,-1.04566,-1.01991,-0.994231,-0.968622,-0.943096,-0.917658,-0.892318,-0.867084,-0.841966,-0.816971,-0.792111,-0.767396,-0.742836,-0.718442,-0.694225,-0.670197,-0.646369,-0.622752,-0.599358,-0.576198,-0.553285,-0.530628,-0.508239,-0.486129,-0.464307,-0.442784,-0.421568,-0.400668,-0.380093,-0.359849,-0.339943,-0.320382,-0.301169,-0.28231,-0.263808,-0.245665,-0.227885,-0.210467,-0.193412,-0.17672,-0.16039,-0.144419,-0.128806,-0.113548,-0.0986409,-0.0840805,-0.0698623,-0.0559815,-0.0424326,-0.0292102,-0.0163081,-0.00372046,0.00855914,0.020537,0.0322196,0.0436134,0.0547249,0.0655603,0.0761259,0.086428,0.0964724,0.106265,0.115811,0.125117,0.134186,0.143025,0.151637,0.160028,0.1682,0.176158,0.183905,0.191444,0.198778,0.205911,0.212844,0.21958,0.226121,0.232468,0.238625,0.244591,0.250369,0.25596,0.261366,0.266587,0.271626,0.276484,0.281162,0.285662,0.289985,0.294133,0.298107,0.30191,0.305544,0.309011,0.312312,0.31545,0.318429,0.321249,0.323915,0.326427,0.328791,0.331007,0.333079,0.33501,0.336802,0.338458,0.339981,0.341372,0.342634,0.343769,0.344779,0.345664,0.346426,0.347066,0.347583,0.347977,0.348247,0.348392,0.348409,0.348296,0.348048,0.347662,0.347131,0.346449,0.345608,0.3446,0.343414,0.342038,0.34046,0.338664,0.336634,0.334351,0.331795,0.328941,0.325766,0.322239,0.318331,0.314006,0.309226,0.303951,0.298135,0.291727,0.284674,0.276916,0.26839,0.259026,0.248749,0.237478,0.225126,0.211601,0.196805,0.180632,0.162974,0.143715,0.122739,0.0999252,0.0751528,0.048304,0.0192651,-0.0120638},
{-2.12502,-2.09888,-2.07272,-2.04656,-2.02039,-1.9942,-1.96801,-1.94182,-1.91561,-1.8894,-1.86317,-1.83694,-1.81071,-1.78446,-1.75821,-1.73196,-1.70569,-1.67942,-1.65315,-1.62687,-1.60059,-1.57431,-1.54802,-1.52174,-1.49545,-1.46917,-1.44288,-1.41661,-1.39034,-1.36407,-1.33782,-1.31158,-1.28535,-1.25914,-1.23295,-1.20679,-1.18065,-1.15454,-1.12847,-1.10243,-1.07644,-1.05051,-1.02462,-0.998805,-0.973054,-0.947378,-0.921787,-0.896286,-0.870886,-0.845595,-0.820422,-0.795377,-0.77047,-0.745712,-0.721113,-0.696685,-0.672438,-0.648385,-0.624537,-0.600904,-0.5775,-0.554335,-0.531421,-0.508768,-0.486388,-0.464291,-0.442486,-0.420984,-0.399793,-0.378922,-0.358377,-0.338167,-0.318297,-0.298773,-0.279599,-0.260779,-0.242317,-0.224215,-0.206474,-0.189096,-0.172079,-0.155424,-0.139129,-0.123192,-0.10761,-0.0923804,-0.0774992,-0.0629623,-0.048765,-0.0349022,-0.0213688,-0.00815916,0.00473256,0.0173123,0.0295861,0.0415601,0.0532404,0.0646332,0.0757446,0.0865806,0.097147,0.10745,0.117494,0.127285,0.136828,0.146129,0.15519,0.164018,0.172616,0.180988,0.189137,0.197066,0.20478,0.21228,0.219569,0.22665,0.233525,0.240196,0.246664,0.252932,0.259001,0.264873,0.27055,0.276032,0.281322,0.286421,0.291331,0.296053,0.300589,0.304941,0.309111,0.313101,0.316912,0.320549,0.324012,0.327304,0.330429,0.333388,0.336185,0.338823,0.341304,0.343632,0.345809,0.347839,0.349724,0.351468,0.353073,0.354541,0.355876,0.357078,0.358151,0.359095,0.359912,0.360602,0.361166,0.361604,0.361915,0.362098,0.36215,0.362069,0.361852,0.361493,0.360987,0.360329,0.35951,0.358523,0.357355,0.355998,0.354436,0.352656,0.350642,0.348374,0.345832,0.342993,0.339832,0.336321,0.332428,0.32812,0.323359,0.318103,0.312308,0.305924,0.298898,0.29117,0.282678,0.273352,0.263117,0.251894,0.239596,0.226131,0.211402,0.195305,0.177729,0.158563,0.137688,0.114984,0.0903294,0.0636065,0.0346999,0.00350747},
{-2.15746,-2.1313,-2.10513,-2.07896,-2.05277,-2.02657,-2.00036,-1.97414,-1.94791,-1.92167,-1.89543,-1.86917,-1.8429,-1.81663,-1.79035,-1.76405,-1.73775,-1.71145,-1.68513,-1.65881,-1.63248,-1.60614,-1.5798,-1.55346,-1.52711,-1.50076,-1.47441,-1.44806,-1.42171,-1.39536,-1.36902,-1.34268,-1.31635,-1.29004,-1.26374,-1.23745,-1.21118,-1.18494,-1.15872,-1.13254,-1.10639,-1.08028,-1.05421,-1.0282,-1.00224,-0.976352,-0.95053,-0.924786,-0.899128,-0.873564,-0.848103,-0.822755,-0.797529,-0.772434,-0.747482,-0.722684,-0.698049,-0.673591,-0.649319,-0.625245,-0.601382,-0.57774,-0.554332,-0.531168,-0.50826,-0.485619,-0.463255,-0.44118,-0.419401,-0.397929,-0.376771,-0.355937,-0.335433,-0.315266,-0.295441,-0.275964,-0.256839,-0.238069,-0.219657,-0.201605,-0.183914,-0.166585,-0.149616,-0.133008,-0.116759,-0.100865,-0.0853252,-0.070135,-0.055291,-0.0407888,-0.0266239,-0.0127911,0.000714594,0.0138988,0.0267671,0.0393252,0.0515789,0.0635341,0.0751967,0.0865724,0.0976668,0.108486,0.119034,0.129318,0.139342,0.149111,0.158629,0.167901,0.176932,0.185724,0.194282,0.202609,0.210708,0.218582,0.226234,0.233666,0.24088,0.24788,0.254666,0.261241,0.267606,0.273764,0.279716,0.285463,0.291008,0.296352,0.301496,0.306444,0.311196,0.315754,0.320121,0.324299,0.328291,0.332098,0.335724,0.339171,0.342442,0.34554,0.348467,0.351229,0.353826,0.356263,0.358543,0.360669,0.362644,0.36447,0.366153,0.367692,0.369093,0.370355,0.371483,0.372477,0.373339,0.374069,0.374669,0.375137,0.375474,0.375678,0.375748,0.375679,0.37547,0.375115,0.374609,0.373946,0.373117,0.372115,0.370929,0.369548,0.367957,0.366143,0.364089,0.361776,0.359182,0.356286,0.35306,0.349477,0.345505,0.34111,0.336253,0.330892,0.324982,0.318473,0.311311,0.303436,0.294783,0.285284,0.274862,0.263437,0.250922,0.237224,0.222245,0.20588,0.188019,0.168548,0.147349,0.124302,0.0992847,0.07218,0.0428725,0.0112614},
{-2.18888,-2.16271,-2.13653,-2.11034,-2.08414,-2.05792,-2.0317,-2.00546,-1.97921,-1.95295,-1.92668,-1.9004,-1.87411,-1.84781,-1.82149,-1.79517,-1.76883,-1.74249,-1.71613,-1.68977,-1.6634,-1.63702,-1.61063,-1.58423,-1.55782,-1.53141,-1.505,-1.47858,-1.45216,-1.42573,-1.39931,-1.37289,-1.34647,-1.32005,-1.29365,-1.26725,-1.24087,-1.2145,-1.18815,-1.16183,-1.13553,-1.10926,-1.08303,-1.05684,-1.0307,-1.0046,-0.97857,-0.952602,-0.926707,-0.900893,-0.875167,-0.849539,-0.824018,-0.798613,-0.773334,-0.748192,-0.723198,-0.698361,-0.673694,-0.649208,-0.624915,-0.600826,-0.576953,-0.553307,-0.5299,-0.506745,-0.48385,-0.461228,-0.438889,-0.416842,-0.395097,-0.373663,-0.352548,-0.331759,-0.311305,-0.291189,-0.271419,-0.251998,-0.23293,-0.214219,-0.195866,-0.177874,-0.160242,-0.142971,-0.126061,-0.109509,-0.093315,-0.0774751,-0.0619867,-0.0468463,-0.03205,-0.0175935,-0.00347222,0.0103188,0.0237846,0.0369306,0.0497621,0.0622847,0.0745038,0.086425,0.0980537,0.109395,0.120455,0.131239,0.14175,0.151995,0.161977,0.171701,0.181172,0.190393,0.199367,0.208098,0.21659,0.224846,0.232867,0.240658,0.248219,0.255555,0.262665,0.269554,0.276222,0.282672,0.288905,0.294924,0.300729,0.306323,0.311709,0.316887,0.32186,0.32663,0.3312,0.335571,0.339747,0.34373,0.347523,0.351129,0.354551,0.357792,0.360855,0.363745,0.366463,0.369014,0.371401,0.373627,0.375697,0.377612,0.379377,0.380993,0.382465,0.383794,0.384983,0.386034,0.386948,0.387726,0.388368,0.388876,0.389249,0.389484,0.389581,0.389537,0.389349,0.389012,0.388521,0.387869,0.387049,0.386053,0.384869,0.383488,0.381894,0.380075,0.378012,0.375687,0.373079,0.370166,0.36692,0.363314,0.359317,0.354893,0.350004,0.344608,0.338661,0.332111,0.324905,0.316982,0.308279,0.298726,0.288248,0.276763,0.264186,0.250422,0.235374,0.218937,0.201001,0.181453,0.160173,0.137043,0.111939,0.0847439,0.0553438,0.0236344},
{-2.21935,-2.19317,-2.16697,-2.14077,-2.11455,-2.08833,-2.06209,-2.03583,-2.00957,-1.98329,-1.957,-1.9307,-1.90438,-1.87805,-1.85171,-1.82536,-1.79899,-1.77261,-1.74622,-1.71982,-1.69341,-1.66698,-1.64055,-1.6141,-1.58764,-1.56118,-1.5347,-1.50822,-1.48173,-1.45524,-1.42874,-1.40224,-1.37574,-1.34923,-1.32273,-1.29624,-1.26975,-1.24326,-1.2168,-1.19034,-1.16391,-1.13749,-1.11111,-1.08475,-1.05844,-1.03216,-1.00593,-0.979759,-0.953646,-0.9276,-0.90163,-0.875743,-0.849949,-0.824257,-0.798675,-0.773214,-0.747884,-0.722695,-0.69766,-0.672788,-0.648092,-0.623583,-0.599273,-0.575173,-0.551295,-0.527652,-0.504253,-0.481112,-0.458238,-0.435642,-0.413334,-0.391324,-0.369621,-0.348233,-0.327169,-0.306435,-0.286038,-0.265983,-0.246275,-0.226919,-0.207918,-0.189274,-0.17099,-0.153066,-0.135503,-0.1183,-0.101457,-0.0849712,-0.0688417,-0.0530653,-0.0376389,-0.0225589,-0.00782145,0.00657785,0.0206435,0.0343803,0.0477931,0.0608872,0.0736675,0.0861393,0.0983079,0.110178,0.121756,0.133045,0.144051,0.154778,0.165231,0.175415,0.185333,0.194989,0.204387,0.21353,0.222422,0.231066,0.239464,0.24762,0.255535,0.263213,0.270655,0.277863,0.28484,0.291588,0.298109,0.304404,0.310475,0.316326,0.321957,0.327371,0.33257,0.337556,0.342333,0.346902,0.351267,0.35543,0.359394,0.363163,0.366739,0.370127,0.373329,0.37635,0.379193,0.381861,0.384358,0.386689,0.388855,0.390862,0.392712,0.394409,0.395956,0.397354,0.398608,0.399718,0.400687,0.401517,0.402207,0.402758,0.403169,0.403441,0.403571,0.403557,0.403395,0.403081,0.402611,0.401978,0.401174,0.400191,0.399019,0.397647,0.396061,0.394247,0.392188,0.389865,0.387258,0.384344,0.381096,0.377487,0.373485,0.369056,0.364161,0.358759,0.352804,0.346247,0.339034,0.331104,0.322395,0.312836,0.302353,0.290865,0.278286,0.264523,0.249478,0.233047,0.215121,0.195586,0.174324,0.151214,0.126135,0.0989672,0.0695971,0.0379184},
{-2.24891,-2.22272,-2.19652,-2.1703,-2.14408,-2.11784,-2.09158,-2.06532,-2.03903,-2.01274,-1.98643,-1.96011,-1.93377,-1.90742,-1.88105,-1.85467,-1.82828,-1.80187,-1.77545,-1.74901,-1.72256,-1.69609,-1.66962,-1.64313,-1.61662,-1.59011,-1.56358,-1.53704,-1.51049,-1.48393,-1.45736,-1.43079,-1.40421,-1.37762,-1.35103,-1.32444,-1.29785,-1.27127,-1.24468,-1.21811,-1.19155,-1.16501,-1.13848,-1.11197,-1.0855,-1.05905,-1.03264,-1.00628,-0.979963,-0.953704,-0.927507,-0.901382,-0.875335,-0.849375,-0.823512,-0.797754,-0.772112,-0.746595,-0.721215,-0.695983,-0.670909,-0.646006,-0.621284,-0.596756,-0.572434,-0.548328,-0.524452,-0.500817,-0.477433,-0.454313,-0.431466,-0.408904,-0.386636,-0.364671,-0.343018,-0.321685,-0.300679,-0.280008,-0.259677,-0.239692,-0.220056,-0.200774,-0.181848,-0.163281,-0.145074,-0.127227,-0.109742,-0.0926164,-0.07585,-0.0594409,-0.0433867,-0.0276845,-0.0123313,0.00267674,0.0173434,0.0316729,0.0456697,0.0593384,0.0726837,0.0857104,0.0984234,0.110828,0.122928,0.134729,0.146235,0.157451,0.168381,0.17903,0.189402,0.1995,0.209328,0.21889,0.228188,0.237227,0.246008,0.254535,0.26281,0.270835,0.278614,0.286148,0.293439,0.30049,0.307303,0.313879,0.320221,0.326331,0.332212,0.337866,0.343294,0.3485,0.353487,0.358256,0.362812,0.367157,0.371294,0.375227,0.378959,0.382494,0.385836,0.388988,0.391955,0.39474,0.397346,0.399779,0.402042,0.404138,0.406071,0.407845,0.409462,0.410926,0.41224,0.413405,0.414423,0.415297,0.416026,0.416612,0.417054,0.417351,0.417502,0.417505,0.417355,0.41705,0.416584,0.41595,0.415142,0.414151,0.412965,0.411575,0.409967,0.408126,0.406035,0.403676,0.401027,0.398065,0.394764,0.391095,0.387027,0.382526,0.377551,0.372062,0.366013,0.359353,0.352028,0.343977,0.335137,0.325438,0.314804,0.303154,0.2904,0.276452,0.261208,0.244566,0.226415,0.206642,0.185127,0.161751,0.136393,0.108931,0.0792533,0.0472538},
{-2.27762,-2.25142,-2.22522,-2.19899,-2.17276,-2.1465,-2.12024,-2.09396,-2.06766,-2.04135,-2.01502,-1.98868,-1.96233,-1.93595,-1.90956,-1.88316,-1.85674,-1.8303,-1.80385,-1.77738,-1.7509,-1.7244,-1.69788,-1.67135,-1.6448,-1.61824,-1.59166,-1.56507,-1.53846,-1.51184,-1.48521,-1.45857,-1.43192,-1.40525,-1.37858,-1.35191,-1.32523,-1.29854,-1.27186,-1.24518,-1.2185,-1.19183,-1.16517,-1.13853,-1.1119,-1.0853,-1.05872,-1.03218,-1.00568,-0.979222,-0.952816,-0.926468,-0.900186,-0.873978,-0.847852,-0.821818,-0.795884,-0.770062,-0.74436,-0.718789,-0.693361,-0.668087,-0.642978,-0.618046,-0.593303,-0.56876,-0.544431,-0.520325,-0.496457,-0.472835,-0.449473,-0.426381,-0.403569,-0.381048,-0.358826,-0.336914,-0.315319,-0.294049,-0.273111,-0.25251,-0.232254,-0.212346,-0.192791,-0.173591,-0.154749,-0.136267,-0.118146,-0.100386,-0.0829878,-0.0659494,-0.0492698,-0.0329469,-0.0169784,-0.00136137,0.0139075,0.0288316,0.043415,0.0576616,0.0715758,0.0851618,0.0984242,0.111368,0.123996,0.136315,0.148328,0.160039,0.171454,0.182575,0.193408,0.203955,0.21422,0.224208,0.23392,0.24336,0.252532,0.261437,0.270079,0.27846,0.286583,0.294449,0.302062,0.309422,0.316534,0.323398,0.330018,0.336395,0.342532,0.348431,0.354095,0.359527,0.364729,0.369705,0.374458,0.378991,0.383308,0.387411,0.391305,0.394995,0.398482,0.401773,0.40487,0.407779,0.410502,0.413045,0.415412,0.417606,0.419631,0.42149,0.423189,0.424729,0.426113,0.427345,0.428426,0.429357,0.430141,0.430778,0.431268,0.43161,0.431803,0.431845,0.431733,0.431463,0.43103,0.430428,0.42965,0.428688,0.427531,0.426169,0.424589,0.422775,0.420712,0.418381,0.415761,0.41283,0.409561,0.405927,0.401896,0.397434,0.392503,0.387061,0.381064,0.374461,0.367199,0.359218,0.350455,0.340841,0.330302,0.318757,0.30612,0.292299,0.277197,0.260711,0.24273,0.223143,0.201831,0.178675,0.153552,0.126341,0.0969292,0.0652072},
{-2.30553,-2.27933,-2.25311,-2.22688,-2.20063,-2.17437,-2.1481,-2.1218,-2.09549,-2.06917,-2.04283,-2.01647,-1.9901,-1.9637,-1.93729,-1.91087,-1.88442,-1.85796,-1.83148,-1.80498,-1.77847,-1.75193,-1.72538,-1.69881,-1.67222,-1.64562,-1.61899,-1.59235,-1.56569,-1.53902,-1.51233,-1.48562,-1.4589,-1.43217,-1.40542,-1.37867,-1.3519,-1.32513,-1.29835,-1.27156,-1.24478,-1.21799,-1.19121,-1.16444,-1.13768,-1.11093,-1.0842,-1.05749,-1.03082,-1.00418,-0.977574,-0.95102,-0.924519,-0.898079,-0.871709,-0.845417,-0.819211,-0.793102,-0.767098,-0.741211,-0.71545,-0.689827,-0.664354,-0.639041,-0.6139,-0.588944,-0.564184,-0.539632,-0.515301,-0.491202,-0.467346,-0.443746,-0.420413,-0.397356,-0.374587,-0.352115,-0.329948,-0.308097,-0.286569,-0.26537,-0.244507,-0.223987,-0.203815,-0.183993,-0.164527,-0.145419,-0.12667,-0.108283,-0.0902583,-0.0725955,-0.0552943,-0.0383536,-0.0217718,-0.00554682,0.0103239,0.0258432,0.0410144,0.0558408,0.0703263,0.0844747,0.09829,0.111776,0.124938,0.137779,0.150303,0.162516,0.17442,0.186019,0.197318,0.20832,0.219029,0.229447,0.239579,0.249427,0.258995,0.268284,0.277299,0.28604,0.294512,0.302716,0.310654,0.31833,0.325744,0.332901,0.339801,0.346448,0.352845,0.358993,0.364895,0.370556,0.375976,0.381161,0.386112,0.390834,0.39533,0.399605,0.403661,0.407504,0.411137,0.414564,0.417791,0.420821,0.423658,0.426308,0.428774,0.431061,0.433173,0.435113,0.436886,0.438494,0.439941,0.44123,0.442362,0.443341,0.444167,0.44484,0.445362,0.445732,0.445948,0.446009,0.445911,0.445651,0.445224,0.444623,0.443843,0.442874,0.441706,0.440328,0.438727,0.436889,0.434796,0.432431,0.429772,0.426796,0.423477,0.419787,0.415694,0.411164,0.406159,0.400636,0.39455,0.387851,0.380484,0.372391,0.363507,0.353762,0.343083,0.331388,0.318591,0.304599,0.289315,0.272635,0.254451,0.234647,0.213106,0.189709,0.164333,0.136859,0.107171,0.0751611},
{-2.33268,-2.30647,-2.28025,-2.25401,-2.22776,-2.20149,-2.1752,-2.1489,-2.12258,-2.09624,-2.06989,-2.04351,-2.01712,-1.99071,-1.96428,-1.93784,-1.91137,-1.88488,-1.85838,-1.83185,-1.80531,-1.77874,-1.75216,-1.72555,-1.69893,-1.67228,-1.64561,-1.61893,-1.59222,-1.5655,-1.53875,-1.51199,-1.4852,-1.45841,-1.43159,-1.40476,-1.37791,-1.35106,-1.32419,-1.29731,-1.27042,-1.24353,-1.21664,-1.18974,-1.16285,-1.13597,-1.10909,-1.08224,-1.0554,-1.02858,-1.0018,-0.975051,-0.948346,-0.921691,-0.895092,-0.868558,-0.842098,-0.81572,-0.789433,-0.763248,-0.737175,-0.711224,-0.685406,-0.659733,-0.634216,-0.608868,-0.5837,-0.558723,-0.533952,-0.509396,-0.485069,-0.460983,-0.437148,-0.413576,-0.390279,-0.367265,-0.344546,-0.322131,-0.300029,-0.278247,-0.256793,-0.235674,-0.214896,-0.194465,-0.174385,-0.154659,-0.135291,-0.116284,-0.0976385,-0.0793561,-0.0614372,-0.0438815,-0.0266884,-0.00985645,0.00661597,0.022731,0.0384913,0.0538996,0.0689591,0.083673,0.0980451,0.112079,0.125778,0.139147,0.152188,0.164907,0.177306,0.18939,0.201162,0.212625,0.223784,0.234641,0.245199,0.255462,0.265432,0.275113,0.284506,0.293616,0.302443,0.310991,0.319262,0.327258,0.334983,0.342437,0.349625,0.356549,0.36321,0.369613,0.37576,0.381654,0.387299,0.392697,0.397853,0.402769,0.407451,0.411902,0.416126,0.420127,0.42391,0.42748,0.430842,0.433999,0.436956,0.439719,0.442291,0.444677,0.446882,0.448909,0.450763,0.452448,0.453966,0.45532,0.456514,0.457549,0.458427,0.459149,0.459716,0.460126,0.46038,0.460475,0.460409,0.460177,0.459776,0.459199,0.45844,0.457489,0.456339,0.454976,0.453389,0.451564,0.449482,0.447127,0.444477,0.44151,0.438199,0.434517,0.430432,0.42591,0.420913,0.4154,0.409324,0.402638,0.395285,0.387208,0.378344,0.368622,0.357969,0.346305,0.333544,0.319594,0.304359,0.287734,0.269611,0.249878,0.228417,0.205108,0.179828,0.152459,0.122883,0.0909917},
{-2.3591,-2.33289,-2.30667,-2.28042,-2.25416,-2.22789,-2.20159,-2.17528,-2.14895,-2.1226,-2.09623,-2.06985,-2.04344,-2.01701,-1.99057,-1.9641,-1.93762,-1.91111,-1.88458,-1.85803,-1.83146,-1.80487,-1.77825,-1.75161,-1.72495,-1.69827,-1.67156,-1.64483,-1.61808,-1.59131,-1.56451,-1.53769,-1.51085,-1.48399,-1.45711,-1.43021,-1.40329,-1.37635,-1.3494,-1.32243,-1.29545,-1.26846,-1.24146,-1.21446,-1.18745,-1.16044,-1.13343,-1.10643,-1.07944,-1.05246,-1.02551,-0.99858,-0.971684,-0.944826,-0.918014,-0.891254,-0.864555,-0.837924,-0.811372,-0.784907,-0.758539,-0.732279,-0.706136,-0.680123,-0.654251,-0.62853,-0.602974,-0.577594,-0.552403,-0.527412,-0.502635,-0.478082,-0.453766,-0.429699,-0.405892,-0.382356,-0.359103,-0.336141,-0.313481,-0.291131,-0.269101,-0.247398,-0.226028,-0.204998,-0.184315,-0.163982,-0.144003,-0.124383,-0.105124,-0.0862279,-0.067696,-0.0495291,-0.0317275,-0.0142906,0.00278236,0.0194929,0.0358427,0.0518339,0.0674692,0.0827512,0.0976828,0.112267,0.126508,0.140408,0.153972,0.167202,0.180102,0.192676,0.204926,0.216857,0.228471,0.239772,0.250763,0.261447,0.271826,0.281904,0.291682,0.301165,0.310354,0.319252,0.327861,0.336184,0.344223,0.351981,0.359462,0.366666,0.373598,0.38026,0.386655,0.392787,0.39866,0.404275,0.409638,0.414753,0.419623,0.424253,0.428647,0.43281,0.436746,0.44046,0.443958,0.447244,0.450322,0.453199,0.455878,0.458364,0.460663,0.462778,0.464713,0.466474,0.468062,0.469482,0.470736,0.471826,0.472755,0.473524,0.474132,0.474581,0.47487,0.474996,0.474957,0.47475,0.47437,0.473811,0.473068,0.47213,0.47099,0.469635,0.468054,0.466231,0.46415,0.461794,0.459141,0.456169,0.452852,0.449162,0.445067,0.440534,0.435525,0.429998,0.423909,0.417207,0.409839,0.401747,0.392866,0.383129,0.372461,0.360784,0.34801,0.33405,0.318805,0.302175,0.284049,0.264317,0.24286,0.219559,0.194291,0.166938,0.137381,0.105511},
{-2.38485,-2.35864,-2.33241,-2.30616,-2.27989,-2.25361,-2.2273,-2.20098,-2.17464,-2.14828,-2.12191,-2.09551,-2.06909,-2.04265,-2.01619,-1.9897,-1.9632,-1.93667,-1.91012,-1.88355,-1.85695,-1.83033,-1.80369,-1.77702,-1.75033,-1.72361,-1.69686,-1.6701,-1.6433,-1.61648,-1.58964,-1.56277,-1.53588,-1.50896,-1.48202,-1.45505,-1.42806,-1.40105,-1.37402,-1.34697,-1.3199,-1.29282,-1.26572,-1.23861,-1.21149,-1.18436,-1.15722,-1.13009,-1.10296,-1.07583,-1.04872,-1.02162,-0.994546,-0.967499,-0.940486,-0.913514,-0.88659,-0.859723,-0.832921,-0.806192,-0.779547,-0.752994,-0.726545,-0.70021,-0.674001,-0.647928,-0.622003,-0.596239,-0.570648,-0.545241,-0.520032,-0.495033,-0.470255,-0.445712,-0.421415,-0.397375,-0.373604,-0.350113,-0.326911,-0.30401,-0.281418,-0.259143,-0.237195,-0.215579,-0.194303,-0.173373,-0.152793,-0.132568,-0.112702,-0.0931982,-0.0740585,-0.0552846,-0.0368777,-0.0188382,-0.00116615,0.0161391,0.0330785,0.0496536,0.0658661,0.0817182,0.0972122,0.112351,0.127137,0.141573,0.155663,0.169409,0.182815,0.195884,0.208619,0.221023,0.233099,0.24485,0.25628,0.267391,0.278185,0.288666,0.298836,0.308699,0.318255,0.327509,0.336462,0.345117,0.353478,0.361545,0.369323,0.376814,0.384021,0.390948,0.397597,0.403972,0.410076,0.415914,0.421489,0.426806,0.431869,0.436682,0.44125,0.445578,0.449671,0.453533,0.457171,0.460589,0.463792,0.466786,0.469576,0.472166,0.474562,0.476768,0.478788,0.480628,0.48229,0.483779,0.485097,0.486247,0.487231,0.488051,0.488707,0.489199,0.489528,0.489691,0.489686,0.48951,0.489158,0.488626,0.487906,0.48699,0.48587,0.484533,0.482969,0.481162,0.479097,0.476755,0.474115,0.471157,0.467853,0.464176,0.460095,0.455577,0.450584,0.445074,0.439004,0.432324,0.424981,0.416916,0.408067,0.398367,0.387741,0.37611,0.36339,0.349491,0.334316,0.317763,0.299725,0.28009,0.258742,0.23556,0.210423,0.183212,0.153807,0.122097},
{-2.40994,-2.38373,-2.35749,-2.33124,-2.30497,-2.27868,-2.25237,-2.22604,-2.1997,-2.17333,-2.14694,-2.12053,-2.0941,-2.06764,-2.04117,-2.01467,-1.98815,-1.9616,-1.93503,-1.90844,-1.88182,-1.85517,-1.8285,-1.80181,-1.77508,-1.74833,-1.72156,-1.69475,-1.66792,-1.64106,-1.61417,-1.58725,-1.56031,-1.53334,-1.50634,-1.47931,-1.45226,-1.42518,-1.39808,-1.37095,-1.3438,-1.31663,-1.28943,-1.26222,-1.235,-1.20775,-1.1805,-1.15324,-1.12598,-1.09871,-1.07145,-1.04419,-1.01695,-0.989723,-0.962522,-0.93535,-0.908215,-0.881125,-0.854087,-0.82711,-0.800203,-0.773374,-0.746635,-0.719996,-0.693466,-0.667059,-0.640784,-0.614654,-0.588682,-0.562879,-0.537257,-0.51183,-0.486609,-0.461608,-0.436839,-0.412312,-0.388042,-0.364038,-0.340311,-0.316874,-0.293734,-0.270903,-0.248388,-0.226199,-0.204342,-0.182825,-0.161653,-0.140832,-0.120367,-0.100262,-0.0805205,-0.0611445,-0.0421363,-0.0234973,-0.00522835,0.0126702,0.0301986,0.0473576,0.0641481,0.0805717,0.0966301,0.112325,0.12766,0.142635,0.157255,0.171522,0.185439,0.199007,0.212232,0.225114,0.237658,0.249865,0.261739,0.273282,0.284497,0.295388,0.305955,0.316202,0.326132,0.335747,0.34505,0.354043,0.362729,0.371111,0.379191,0.386973,0.39446,0.401655,0.408562,0.415184,0.421524,0.427587,0.433378,0.4389,0.444158,0.449156,0.453901,0.458396,0.462647,0.466659,0.470438,0.473989,0.477318,0.480429,0.483329,0.486023,0.488515,0.490811,0.492916,0.494833,0.496568,0.498123,0.499502,0.500708,0.501744,0.50261,0.503308,0.503839,0.504201,0.504394,0.504416,0.504263,0.50393,0.503414,0.502707,0.501801,0.500687,0.499355,0.497791,0.495983,0.493913,0.491564,0.488915,0.485944,0.482625,0.478931,0.474832,0.470292,0.465275,0.45974,0.453642,0.446932,0.439557,0.431459,0.422576,0.41284,0.402177,0.390509,0.377751,0.363814,0.348601,0.332011,0.313936,0.294266,0.272883,0.24967,0.224502,0.197262,0.16783,0.136094},
{-2.43442,-2.4082,-2.38197,-2.35571,-2.32944,-2.30314,-2.27683,-2.25049,-2.22414,-2.19776,-2.17136,-2.14494,-2.1185,-2.09203,-2.06554,-2.03903,-2.01249,-1.98593,-1.95934,-1.93273,-1.90609,-1.87942,-1.85273,-1.826,-1.79925,-1.77247,-1.74566,-1.71882,-1.69195,-1.66505,-1.63812,-1.61116,-1.58417,-1.55715,-1.5301,-1.50301,-1.4759,-1.44876,-1.42159,-1.39439,-1.36716,-1.3399,-1.31262,-1.28532,-1.25799,-1.23065,-1.20329,-1.17591,-1.14852,-1.12112,-1.09371,-1.06631,-1.03891,-1.01151,-0.984134,-0.956774,-0.92944,-0.902139,-0.874879,-0.847667,-0.820512,-0.793423,-0.766409,-0.739481,-0.712649,-0.685923,-0.659315,-0.632837,-0.606501,-0.580318,-0.554302,-0.528465,-0.50282,-0.477378,-0.452153,-0.427158,-0.402404,-0.377904,-0.353668,-0.329709,-0.306038,-0.282663,-0.259596,-0.236845,-0.214419,-0.192325,-0.170571,-0.149163,-0.128107,-0.107408,-0.0870701,-0.0670969,-0.0474916,-0.0282564,-0.00939309,0.00909712,0.0272136,0.0449563,0.0623254,0.0793217,0.0959463,0.1122,0.128086,0.143605,0.158759,0.17355,0.187982,0.202055,0.215774,0.22914,0.242157,0.254826,0.26715,0.279132,0.290774,0.302079,0.31305,0.323688,0.333998,0.34398,0.353638,0.362974,0.371992,0.380693,0.389082,0.397161,0.404932,0.412401,0.41957,0.426443,0.433024,0.439317,0.445327,0.451059,0.456516,0.461704,0.466629,0.471294,0.475707,0.479873,0.483796,0.487484,0.490941,0.494173,0.497187,0.499987,0.502579,0.504968,0.507159,0.509158,0.510967,0.512592,0.514036,0.515302,0.516392,0.517308,0.518052,0.518625,0.519025,0.519252,0.519305,0.519179,0.518871,0.518376,0.517688,0.516798,0.515698,0.514377,0.512823,0.511021,0.508956,0.506611,0.503964,0.500993,0.497673,0.493978,0.489875,0.485332,0.48031,0.474771,0.468668,0.461954,0.454575,0.446475,0.43759,0.427854,0.417193,0.40553,0.392781,0.378855,0.363658,0.347089,0.329041,0.309403,0.288059,0.26489,0.239775,0.212594,0.183227,0.151563},
{-2.45831,-2.43209,-2.40585,-2.37959,-2.35332,-2.32702,-2.3007,-2.27436,-2.24799,-2.22161,-2.1952,-2.16877,-2.14232,-2.11584,-2.08934,-2.06282,-2.03626,-2.00969,-1.98308,-1.95645,-1.92979,-1.9031,-1.87638,-1.84964,-1.82286,-1.79605,-1.76921,-1.74234,-1.71544,-1.6885,-1.66153,-1.63453,-1.6075,-1.58043,-1.55332,-1.52619,-1.49902,-1.47181,-1.44458,-1.41731,-1.39001,-1.36267,-1.33531,-1.30792,-1.2805,-1.25306,-1.22559,-1.1981,-1.17059,-1.14307,-1.11553,-1.08799,-1.06043,-1.03288,-1.00534,-0.977798,-0.950276,-0.922776,-0.895306,-0.867872,-0.840483,-0.813146,-0.785872,-0.75867,-0.73155,-0.704521,-0.677597,-0.650787,-0.624104,-0.597559,-0.571165,-0.544935,-0.518881,-0.493017,-0.467354,-0.441906,-0.416686,-0.391705,-0.366976,-0.342511,-0.318321,-0.294418,-0.270811,-0.247511,-0.224527,-0.201868,-0.179542,-0.157556,-0.135917,-0.114631,-0.0937036,-0.0731391,-0.0529415,-0.0331141,-0.0136596,0.00541993,0.0241229,0.0424485,0.060396,0.0779656,0.0951574,0.111972,0.128411,0.144476,0.160167,0.175487,0.190437,0.20502,0.219238,0.233093,0.246587,0.259722,0.272502,0.284928,0.297002,0.308728,0.320107,0.331142,0.341836,0.352191,0.362209,0.371894,0.381248,0.390274,0.398975,0.407355,0.415416,0.423162,0.430598,0.437726,0.444551,0.451077,0.45731,0.463253,0.468912,0.474292,0.479399,0.484237,0.488813,0.493133,0.497202,0.501027,0.504612,0.507966,0.511092,0.513998,0.516688,0.519169,0.521445,0.523522,0.525404,0.527096,0.5286,0.529921,0.531061,0.532022,0.532806,0.533413,0.533844,0.534097,0.534171,0.534063,0.533768,0.533282,0.532599,0.53171,0.530607,0.52928,0.527715,0.525899,0.523816,0.521447,0.518774,0.515773,0.512419,0.508684,0.504538,0.499947,0.494874,0.489277,0.483113,0.476332,0.468883,0.460706,0.45174,0.441917,0.431165,0.419405,0.406553,0.39252,0.37721,0.360523,0.342352,0.322586,0.30111,0.277804,0.252548,0.225222,0.195705,0.163886},
{-2.48164,-2.45542,-2.42918,-2.40292,-2.37664,-2.35033,-2.32401,-2.29766,-2.2713,-2.2449,-2.21849,-2.19205,-2.16559,-2.1391,-2.11259,-2.08605,-2.05949,-2.0329,-2.00628,-1.97963,-1.95295,-1.92624,-1.8995,-1.87273,-1.84593,-1.8191,-1.79223,-1.76533,-1.73839,-1.71142,-1.68442,-1.65738,-1.6303,-1.60319,-1.57604,-1.54885,-1.52163,-1.49436,-1.46707,-1.43973,-1.41236,-1.38496,-1.35752,-1.33004,-1.30254,-1.275,-1.24744,-1.21984,-1.19222,-1.16458,-1.13692,-1.10924,-1.08154,-1.05384,-1.02614,-0.998432,-0.970733,-0.943045,-0.915376,-0.887731,-0.86012,-0.832549,-0.805028,-0.777565,-0.750171,-0.722855,-0.695628,-0.668502,-0.641487,-0.614596,-0.587841,-0.561234,-0.534788,-0.508517,-0.482432,-0.456548,-0.430876,-0.40543,-0.380223,-0.355266,-0.330573,-0.306154,-0.282021,-0.258184,-0.234654,-0.21144,-0.188552,-0.165997,-0.143784,-0.121919,-0.100408,-0.0792582,-0.0584733,-0.0380577,-0.0180153,0.00165105,0.0209389,0.0398464,0.0583722,0.0765154,0.0942756,0.111653,0.128648,0.14526,0.161492,0.177344,0.192817,0.207914,0.222636,0.236984,0.250961,0.264569,0.277809,0.290685,0.303197,0.315349,0.327143,0.338581,0.349665,0.360399,0.370784,0.380823,0.390519,0.399875,0.408895,0.417581,0.425937,0.433966,0.441673,0.449061,0.456135,0.4629,0.469359,0.475519,0.481385,0.486961,0.492254,0.497269,0.502013,0.506491,0.510709,0.514675,0.518393,0.521871,0.525115,0.52813,0.530923,0.533499,0.535864,0.538024,0.539983,0.541745,0.543314,0.544695,0.54589,0.546901,0.547731,0.548379,0.548847,0.549133,0.549236,0.549153,0.54888,0.548412,0.547744,0.546867,0.545774,0.544452,0.542891,0.541075,0.53899,0.536618,0.533938,0.530928,0.527563,0.523815,0.519654,0.515047,0.509955,0.504338,0.498153,0.49135,0.483877,0.475676,0.466685,0.456837,0.44606,0.434276,0.4214,0.407345,0.392015,0.37531,0.357124,0.337346,0.315861,0.29255,0.267294,0.239971,0.210461,0.178653},
{-2.50443,-2.47821,-2.45197,-2.42571,-2.39942,-2.37312,-2.34679,-2.32044,-2.29407,-2.26767,-2.24125,-2.2148,-2.18833,-2.16184,-2.13532,-2.10877,-2.08219,-2.05558,-2.02895,-2.00228,-1.97559,-1.94886,-1.9221,-1.89531,-1.86849,-1.84163,-1.81474,-1.78781,-1.76084,-1.73384,-1.7068,-1.67972,-1.65261,-1.62545,-1.59826,-1.57102,-1.54375,-1.51644,-1.48908,-1.46169,-1.43425,-1.40678,-1.37926,-1.35171,-1.32412,-1.2965,-1.26884,-1.24114,-1.21342,-1.18567,-1.15788,-1.13008,-1.10225,-1.07441,-1.04655,-1.01869,-0.990822,-0.962956,-0.935098,-0.907254,-0.879432,-0.851639,-0.823882,-0.796172,-0.768517,-0.740927,-0.713412,-0.685984,-0.658652,-0.63143,-0.604328,-0.57736,-0.550538,-0.523875,-0.497384,-0.471079,-0.444971,-0.419076,-0.393405,-0.367972,-0.342788,-0.317867,-0.29322,-0.268859,-0.244795,-0.221038,-0.197598,-0.174484,-0.151705,-0.129268,-0.107182,-0.0854528,-0.0640859,-0.043087,-0.0224605,-0.00221042,0.0176599,0.0371477,0.0562508,0.0749675,0.0932966,0.111237,0.128789,0.145952,0.162727,0.179114,0.195114,0.210728,0.225958,0.240804,0.255269,0.269353,0.28306,0.29639,0.309346,0.321929,0.334143,0.345989,0.357469,0.368586,0.379342,0.389741,0.399784,0.409476,0.418818,0.427815,0.43647,0.444786,0.452769,0.460421,0.467748,0.474754,0.481444,0.487823,0.493898,0.499673,0.505154,0.510348,0.515261,0.519898,0.524267,0.528375,0.532226,0.535829,0.53919,0.542314,0.545209,0.54788,0.550333,0.552574,0.554607,0.556437,0.558069,0.559506,0.560752,0.561809,0.562679,0.563363,0.563861,0.564172,0.564296,0.56423,0.563969,0.563509,0.562844,0.561967,0.560868,0.559537,0.557963,0.55613,0.554023,0.551624,0.548914,0.545868,0.542464,0.538672,0.534462,0.5298,0.524649,0.518968,0.512713,0.505836,0.498282,0.489995,0.480912,0.470966,0.460085,0.448191,0.4352,0.421023,0.405565,0.388726,0.3704,0.350476,0.328839,0.305371,0.279953,0.252461,0.222779,0.190793},
{-2.52671,-2.50049,-2.47425,-2.44798,-2.4217,-2.39539,-2.36906,-2.34271,-2.31633,-2.28993,-2.2635,-2.23705,-2.21057,-2.18407,-2.15754,-2.13098,-2.10439,-2.07777,-2.05112,-2.02444,-1.99773,-1.97099,-1.94421,-1.9174,-1.89056,-1.86368,-1.83676,-1.8098,-1.78281,-1.75578,-1.72871,-1.70159,-1.67444,-1.64725,-1.62001,-1.59273,-1.56541,-1.53804,-1.51064,-1.48318,-1.45569,-1.42815,-1.40057,-1.37294,-1.34527,-1.31757,-1.28982,-1.26203,-1.2342,-1.20634,-1.17845,-1.15053,-1.12257,-1.0946,-1.0666,-1.03858,-1.01055,-0.982519,-0.954481,-0.926448,-0.898425,-0.87042,-0.842441,-0.814495,-0.786591,-0.75874,-0.73095,-0.703232,-0.675598,-0.648058,-0.620624,-0.59331,-0.566126,-0.539086,-0.512204,-0.485492,-0.458964,-0.432633,-0.406513,-0.380616,-0.354957,-0.329547,-0.304399,-0.279526,-0.254939,-0.230649,-0.206667,-0.183003,-0.159667,-0.136668,-0.114013,-0.0917105,-0.0697674,-0.0481897,-0.0269831,-0.00615246,0.014298,0.0343645,0.054044,0.0733339,0.0922323,0.110737,0.128848,0.146564,0.163885,0.18081,0.19734,0.213475,0.229217,0.244566,0.259523,0.27409,0.288267,0.302058,0.315463,0.328484,0.341123,0.353382,0.365264,0.376771,0.387905,0.398669,0.409065,0.419097,0.428768,0.438082,0.447041,0.45565,0.463914,0.471835,0.47942,0.486672,0.493598,0.500202,0.50649,0.512468,0.518143,0.52352,0.528606,0.533408,0.537932,0.542185,0.546175,0.549907,0.553389,0.556627,0.559628,0.562398,0.564943,0.56727,0.569382,0.571286,0.572986,0.574485,0.575788,0.576897,0.577814,0.57854,0.579076,0.579422,0.579576,0.579535,0.579297,0.578856,0.578207,0.577342,0.576253,0.574929,0.573357,0.571525,0.569417,0.567014,0.564297,0.561243,0.557827,0.554022,0.549797,0.545118,0.539949,0.534248,0.527972,0.521072,0.513495,0.505184,0.496078,0.486108,0.475203,0.463286,0.450273,0.436076,0.4206,0.403746,0.385408,0.365475,0.343835,0.320367,0.294953,0.267471,0.237803,0.205835},
{-2.5485,-2.52228,-2.49604,-2.46977,-2.44349,-2.41718,-2.39085,-2.36449,-2.33811,-2.3117,-2.28527,-2.25881,-2.23233,-2.20582,-2.17928,-2.15271,-2.12611,-2.09948,-2.07282,-2.04613,-2.0194,-1.99264,-1.96585,-1.93902,-1.91215,-1.88525,-1.85831,-1.83133,-1.80431,-1.77725,-1.75015,-1.72301,-1.69582,-1.66859,-1.64131,-1.61399,-1.58662,-1.55921,-1.53175,-1.50424,-1.47669,-1.44909,-1.42144,-1.39375,-1.36601,-1.33822,-1.31039,-1.28251,-1.25459,-1.22663,-1.19863,-1.17059,-1.14252,-1.11441,-1.08628,-1.05812,-1.02994,-1.00174,-0.973536,-0.945322,-0.917109,-0.888902,-0.860709,-0.832539,-0.804398,-0.776297,-0.748245,-0.720251,-0.692327,-0.664483,-0.636731,-0.609083,-0.581552,-0.55415,-0.526891,-0.499787,-0.472852,-0.4461,-0.419544,-0.393198,-0.367076,-0.34119,-0.315554,-0.290181,-0.265083,-0.240271,-0.215758,-0.191555,-0.167671,-0.144116,-0.120901,-0.0980321,-0.0755188,-0.0533678,-0.0315856,-0.0101782,0.0108492,0.0314921,0.0517464,0.0716086,0.0910758,0.110146,0.128816,0.147086,0.164955,0.18242,0.199483,0.216143,0.232401,0.248256,0.263709,0.278763,0.293416,0.307672,0.32153,0.334993,0.348063,0.360741,0.37303,0.384931,0.396447,0.407581,0.418335,0.428713,0.438717,0.448352,0.45762,0.466526,0.475073,0.483268,0.491113,0.498615,0.505779,0.51261,0.519115,0.525298,0.531168,0.53673,0.541991,0.546958,0.551638,0.556038,0.560165,0.564026,0.567628,0.570979,0.574085,0.576952,0.579587,0.581996,0.584185,0.586158,0.587921,0.589477,0.590831,0.591986,0.592942,0.593703,0.594269,0.594639,0.594812,0.594786,0.594557,0.594121,0.593472,0.592602,0.591503,0.590165,0.588574,0.586719,0.584581,0.582145,0.579389,0.576291,0.572826,0.568966,0.56468,0.559935,0.554694,0.548914,0.542553,0.535561,0.527885,0.519469,0.510249,0.500158,0.489125,0.477072,0.463915,0.449566,0.433929,0.416906,0.398391,0.378274,0.35644,0.332771,0.307148,0.27945,0.249558,0.217358},
{-2.56982,-2.5436,-2.51736,-2.4911,-2.46481,-2.4385,-2.41216,-2.3858,-2.35942,-2.33301,-2.30657,-2.28011,-2.25362,-2.2271,-2.20055,-2.17398,-2.14737,-2.12073,-2.09406,-2.06735,-2.04061,-2.01384,-1.98703,-1.96019,-1.9333,-1.90638,-1.87942,-1.85242,-1.82537,-1.79828,-1.77115,-1.74398,-1.71676,-1.68949,-1.66218,-1.63482,-1.60741,-1.57995,-1.55244,-1.52489,-1.49728,-1.46962,-1.44191,-1.41415,-1.38633,-1.35847,-1.33056,-1.3026,-1.27459,-1.24653,-1.21843,-1.19029,-1.1621,-1.13387,-1.10561,-1.07731,-1.04899,-1.02064,-0.99227,-0.963884,-0.935489,-0.90709,-0.878694,-0.850309,-0.821942,-0.793602,-0.765299,-0.737041,-0.708839,-0.680703,-0.652646,-0.624678,-0.596813,-0.569062,-0.541438,-0.513956,-0.486628,-0.459468,-0.43249,-0.405708,-0.379136,-0.352787,-0.326675,-0.300814,-0.275215,-0.249893,-0.224859,-0.200125,-0.175702,-0.151601,-0.127831,-0.104404,-0.081326,-0.0586068,-0.0362536,-0.0142731,0.0073285,0.0285455,0.049373,0.0698067,0.0898428,0.109478,0.12871,0.147535,0.165953,0.183962,0.201561,0.21875,0.235527,0.251893,0.267848,0.283392,0.298527,0.313252,0.32757,0.341481,0.354988,0.36809,0.380792,0.393093,0.404998,0.416508,0.427626,0.438355,0.448699,0.45866,0.468243,0.477451,0.486289,0.494762,0.502874,0.510632,0.518039,0.525103,0.531829,0.538223,0.544293,0.550045,0.555486,0.560624,0.565465,0.570016,0.574286,0.578282,0.582011,0.58548,0.588696,0.591666,0.594398,0.596896,0.599168,0.601218,0.603052,0.604674,0.606088,0.607297,0.608304,0.60911,0.609716,0.610123,0.610328,0.610331,0.610128,0.609713,0.609083,0.608228,0.607142,0.605813,0.60423,0.602379,0.600244,0.597807,0.595049,0.591947,0.588476,0.584609,0.580315,0.57556,0.570308,0.564517,0.558144,0.55114,0.543452,0.535024,0.525793,0.515694,0.504653,0.492595,0.479435,0.465087,0.449455,0.432442,0.413941,0.393845,0.372038,0.348402,0.32282,0.29517,0.265334,0.233196},
{-2.59069,-2.56447,-2.53823,-2.51197,-2.48568,-2.45937,-2.43303,-2.40667,-2.38029,-2.35387,-2.32743,-2.30097,-2.27447,-2.24795,-2.22139,-2.19481,-2.16819,-2.14154,-2.11486,-2.08814,-2.06139,-2.0346,-2.00778,-1.98092,-1.95402,-1.92708,-1.90009,-1.87307,-1.846,-1.81889,-1.79173,-1.76453,-1.73728,-1.70998,-1.68263,-1.65524,-1.62779,-1.60028,-1.57273,-1.54512,-1.51746,-1.48975,-1.46198,-1.43416,-1.40628,-1.37834,-1.35036,-1.32231,-1.29422,-1.26607,-1.23787,-1.20962,-1.18133,-1.15299,-1.1246,-1.09618,-1.06771,-1.03922,-1.01069,-0.982144,-0.953575,-0.924993,-0.896403,-0.867813,-0.83923,-0.810662,-0.782118,-0.753606,-0.725138,-0.696723,-0.668372,-0.640097,-0.61191,-0.583823,-0.555849,-0.528001,-0.500294,-0.472739,-0.445353,-0.418148,-0.391138,-0.364339,-0.337763,-0.311425,-0.285339,-0.259516,-0.233972,-0.208717,-0.183764,-0.159125,-0.13481,-0.110831,-0.0871955,-0.0639141,-0.040995,-0.0184459,0.00372587,0.0255139,0.0469123,0.0679156,0.0885194,0.108719,0.128512,0.147894,0.166863,0.185417,0.203554,0.221273,0.238573,0.255452,0.271912,0.287951,0.303571,0.318771,0.333552,0.347916,0.361863,0.375394,0.388513,0.40122,0.413517,0.425407,0.436894,0.447978,0.458665,0.468956,0.478857,0.488371,0.497503,0.506257,0.514639,0.522654,0.530307,0.537605,0.544554,0.55116,0.557431,0.563373,0.568994,0.574301,0.579302,0.584004,0.588415,0.592543,0.596395,0.599979,0.603302,0.606371,0.609193,0.611774,0.614122,0.616241,0.618137,0.619814,0.621277,0.622529,0.623572,0.624409,0.62504,0.625466,0.625684,0.625695,0.625493,0.625075,0.624435,0.623565,0.622458,0.621102,0.619487,0.617596,0.615416,0.612928,0.610111,0.606944,0.6034,0.599453,0.59507,0.590219,0.584861,0.578957,0.57246,0.565322,0.55749,0.548907,0.539511,0.529234,0.518003,0.505742,0.492367,0.47779,0.461916,0.444645,0.425873,0.40549,0.383382,0.359431,0.333519,0.305524,0.275329,0.242819},
{-2.61113,-2.58491,-2.55867,-2.53241,-2.50613,-2.47981,-2.45348,-2.42711,-2.40073,-2.37431,-2.34787,-2.3214,-2.29489,-2.26836,-2.2418,-2.21521,-2.18859,-2.16193,-2.13524,-2.10851,-2.08175,-2.05495,-2.02811,-2.00123,-1.97432,-1.94736,-1.92036,-1.89331,-1.86623,-1.83909,-1.81191,-1.78468,-1.7574,-1.73007,-1.70269,-1.67525,-1.64777,-1.62022,-1.59263,-1.56497,-1.53726,-1.5095,-1.48167,-1.45379,-1.42585,-1.39785,-1.36979,-1.34167,-1.31349,-1.28526,-1.25697,-1.22862,-1.20022,-1.17177,-1.14327,-1.11472,-1.08612,-1.05749,-1.02881,-1.00011,-0.971374,-0.942616,-0.91384,-0.885054,-0.856264,-0.827478,-0.798703,-0.769949,-0.741225,-0.712542,-0.683909,-0.655338,-0.626841,-0.59843,-0.570118,-0.541917,-0.513842,-0.485906,-0.458122,-0.430506,-0.403072,-0.375834,-0.348806,-0.322003,-0.295439,-0.269128,-0.243082,-0.217317,-0.191843,-0.166674,-0.141822,-0.117297,-0.0931107,-0.0692727,-0.0457926,-0.0226791,5.95186e-05,0.0224158,0.044383,0.0659547,0.0871254,0.10789,0.128244,0.148184,0.167706,0.186807,0.205485,0.223737,0.241563,0.258961,0.275929,0.292468,0.308577,0.324257,0.339507,0.354328,0.368722,0.382688,0.39623,0.409347,0.422044,0.43432,0.44618,0.457627,0.468662,0.47929,0.489515,0.499341,0.508772,0.517813,0.52647,0.534748,0.542653,0.55019,0.557368,0.564191,0.570669,0.576807,0.582613,0.588096,0.593262,0.59812,0.602677,0.606943,0.610924,0.614628,0.618063,0.621237,0.624156,0.626828,0.629259,0.631454,0.63342,0.635161,0.636682,0.637986,0.639076,0.639955,0.640622,0.641079,0.641325,0.641357,0.641173,0.640769,0.640138,0.639274,0.638168,0.63681,0.635188,0.633287,0.631093,0.628587,0.62575,0.622557,0.618985,0.615006,0.610588,0.605697,0.600297,0.594346,0.587799,0.580609,0.572721,0.564079,0.55462,0.544278,0.53298,0.520648,0.507201,0.492549,0.476598,0.45925,0.4404,0.419938,0.39775,0.37372,0.347729,0.319656,0.289382,0.256794},
{-2.63115,-2.60494,-2.5787,-2.55244,-2.52616,-2.49985,-2.47351,-2.44714,-2.42075,-2.39434,-2.36789,-2.34142,-2.31491,-2.28838,-2.26181,-2.23521,-2.20858,-2.18191,-2.15521,-2.12848,-2.1017,-2.07489,-2.04804,-2.02115,-1.99422,-1.96725,-1.94023,-1.91316,-1.88605,-1.8589,-1.83169,-1.80444,-1.77713,-1.74977,-1.72236,-1.69489,-1.66737,-1.63979,-1.61215,-1.58445,-1.55669,-1.52888,-1.501,-1.47306,-1.44506,-1.41699,-1.38886,-1.36067,-1.33242,-1.3041,-1.27572,-1.24728,-1.21878,-1.19023,-1.16161,-1.13295,-1.10423,-1.07546,-1.04664,-1.01779,-0.988893,-0.959968,-0.931015,-0.902041,-0.873052,-0.844056,-0.815061,-0.786074,-0.757105,-0.728163,-0.69926,-0.670404,-0.641609,-0.612885,-0.584247,-0.555705,-0.527274,-0.498968,-0.4708,-0.442786,-0.414939,-0.387274,-0.359805,-0.332549,-0.305518,-0.278728,-0.252192,-0.225925,-0.19994,-0.17425,-0.148868,-0.123806,-0.0990749,-0.0746865,-0.0506508,-0.0269778,-0.00367645,0.0192447,0.0417779,0.0639159,0.085652,0.106981,0.127896,0.148393,0.168469,0.188118,0.207339,0.226128,0.244482,0.262401,0.279882,0.296924,0.313527,0.32969,0.345413,0.360697,0.375541,0.389947,0.403916,0.41745,0.430549,0.443217,0.455456,0.467268,0.478657,0.489627,0.50018,0.510321,0.520056,0.529388,0.538323,0.546868,0.555027,0.562807,0.570216,0.577259,0.583945,0.590281,0.596274,0.601933,0.607266,0.61228,0.616985,0.621388,0.625498,0.629322,0.632869,0.636146,0.639161,0.641921,0.644432,0.646701,0.648733,0.650534,0.652108,0.653459,0.65459,0.655503,0.6562,0.656681,0.656944,0.656989,0.656812,0.65641,0.655775,0.654902,0.653782,0.652404,0.650757,0.648826,0.646595,0.644047,0.641162,0.637916,0.634284,0.630238,0.625747,0.620777,0.61529,0.609245,0.602597,0.595297,0.587292,0.578525,0.568932,0.558447,0.546997,0.534504,0.520886,0.506055,0.489915,0.472367,0.453308,0.432627,0.410211,0.385943,0.359704,0.331375,0.300836,0.267974},
{-2.65078,-2.62457,-2.59833,-2.57207,-2.54579,-2.51948,-2.49314,-2.46678,-2.44039,-2.41397,-2.38752,-2.36104,-2.33453,-2.30799,-2.28142,-2.25482,-2.22818,-2.20151,-2.1748,-2.14805,-2.12127,-2.09445,-2.06759,-2.04068,-2.01374,-1.98675,-1.95971,-1.93263,-1.9055,-1.87833,-1.8511,-1.82382,-1.79649,-1.7691,-1.74166,-1.71416,-1.6866,-1.65898,-1.63131,-1.60357,-1.57577,-1.5479,-1.51997,-1.49198,-1.46392,-1.43579,-1.4076,-1.37934,-1.35101,-1.32261,-1.29415,-1.26562,-1.23703,-1.20837,-1.17965,-1.15087,-1.12203,-1.09314,-1.06419,-1.03519,-1.00614,-0.977055,-0.947932,-0.918778,-0.889599,-0.860402,-0.831194,-0.801984,-0.772779,-0.743589,-0.714425,-0.685295,-0.656212,-0.627187,-0.598233,-0.569362,-0.540587,-0.511922,-0.483382,-0.45498,-0.426732,-0.398651,-0.370754,-0.343054,-0.315568,-0.288309,-0.261293,-0.234534,-0.208047,-0.181844,-0.15594,-0.130348,-0.105079,-0.080146,-0.0555603,-0.0313323,-0.00747232,0.0160103,0.0391068,0.061809,0.0841093,0.106001,0.127477,0.148533,0.169163,0.189363,0.209128,0.228455,0.247341,0.265784,0.283781,0.301331,0.318432,0.335083,0.351284,0.367035,0.382335,0.397186,0.411588,0.425543,0.439051,0.452116,0.464739,0.476923,0.488671,0.499986,0.510873,0.521336,0.531379,0.541007,0.550226,0.559041,0.56746,0.575488,0.583132,0.590399,0.597298,0.603836,0.61002,0.61586,0.621363,0.626538,0.631394,0.635938,0.64018,0.644128,0.64779,0.651174,0.654288,0.657139,0.659735,0.662081,0.664183,0.666048,0.667679,0.669081,0.670257,0.67121,0.671941,0.67245,0.672737,0.6728,0.672636,0.672242,0.671611,0.670737,0.669611,0.668222,0.666559,0.664608,0.662353,0.659776,0.656857,0.653572,0.649897,0.645802,0.641258,0.63623,0.630679,0.624566,0.617844,0.610465,0.602376,0.593518,0.58383,0.573244,0.561688,0.549084,0.53535,0.520396,0.50413,0.486451,0.467255,0.446434,0.423873,0.399456,0.373065,0.34458,0.313882,0.280857},
{-2.67002,-2.64381,-2.61758,-2.59133,-2.56504,-2.53873,-2.5124,-2.48603,-2.45964,-2.43322,-2.40677,-2.38029,-2.35378,-2.32724,-2.30066,-2.27405,-2.24741,-2.22073,-2.19401,-2.16726,-2.14047,-2.11363,-2.08676,-2.05985,-2.03289,-2.00588,-1.97883,-1.95174,-1.92459,-1.89739,-1.87014,-1.84284,-1.81548,-1.78807,-1.7606,-1.73307,-1.70548,-1.67783,-1.65012,-1.62234,-1.5945,-1.56659,-1.53861,-1.51056,-1.48245,-1.45426,-1.42601,-1.39768,-1.36928,-1.34081,-1.31227,-1.28366,-1.25497,-1.22622,-1.1974,-1.16851,-1.13955,-1.11053,-1.08145,-1.05232,-1.02313,-0.993885,-0.964599,-0.935273,-0.905911,-0.876521,-0.84711,-0.817685,-0.788253,-0.758825,-0.729408,-0.700015,-0.670655,-0.641339,-0.61208,-0.58289,-0.553783,-0.524771,-0.495869,-0.467091,-0.438453,-0.409968,-0.381652,-0.353521,-0.32559,-0.297873,-0.270387,-0.243146,-0.216165,-0.189458,-0.163041,-0.136926,-0.111126,-0.0856555,-0.0605256,-0.0357481,-0.0113341,0.012706,0.0363624,0.059626,0.0824883,0.104941,0.126978,0.148592,0.169777,0.190527,0.210838,0.230705,0.250125,0.269095,0.28761,0.30567,0.323273,0.340416,0.357098,0.37332,0.389081,0.404381,0.41922,0.4336,0.447522,0.460987,0.473998,0.486558,0.498669,0.510334,0.521559,0.532346,0.5427,0.552628,0.562133,0.571223,0.579903,0.58818,0.596061,0.603555,0.610668,0.617408,0.623784,0.629804,0.635477,0.640812,0.645817,0.650501,0.654874,0.658943,0.662716,0.666204,0.669412,0.67235,0.675023,0.677439,0.679605,0.681525,0.683204,0.684647,0.685858,0.686838,0.687588,0.688111,0.688405,0.688468,0.688298,0.687891,0.68724,0.686339,0.685179,0.683749,0.682038,0.680031,0.677712,0.675062,0.672062,0.668688,0.664913,0.66071,0.656047,0.650889,0.645198,0.638932,0.632045,0.624488,0.616207,0.607144,0.597235,0.586413,0.574605,0.561731,0.54771,0.532451,0.51586,0.497838,0.478279,0.457074,0.434109,0.409268,0.382433,0.353482,0.3223,0.288772},
{-2.68889,-2.66269,-2.63646,-2.61021,-2.58393,-2.55762,-2.53129,-2.50492,-2.47853,-2.45211,-2.42566,-2.39917,-2.37266,-2.34611,-2.31953,-2.29292,-2.26627,-2.23959,-2.21286,-2.1861,-2.1593,-2.13246,-2.10558,-2.07865,-2.05168,-2.02466,-1.9976,-1.97049,-1.94332,-1.91611,-1.88884,-1.86151,-1.83413,-1.8067,-1.7792,-1.75164,-1.72402,-1.69634,-1.66859,-1.64078,-1.61289,-1.58494,-1.55692,-1.52882,-1.50065,-1.47241,-1.4441,-1.41571,-1.38724,-1.3587,-1.33008,-1.30139,-1.27262,-1.24377,-1.21485,-1.18586,-1.15679,-1.12765,-1.09845,-1.06918,-1.03985,-1.01046,-0.981021,-0.951528,-0.921992,-0.892416,-0.862808,-0.833176,-0.803526,-0.773867,-0.744209,-0.71456,-0.684932,-0.655335,-0.625781,-0.596283,-0.566853,-0.537504,-0.508251,-0.479108,-0.45009,-0.421211,-0.392488,-0.363935,-0.335568,-0.307403,-0.279455,-0.25174,-0.224274,-0.197072,-0.170148,-0.143518,-0.117194,-0.0911909,-0.0655218,-0.0401991,-0.0152348,0.00935972,0.0335737,0.0573971,0.0808203,0.103835,0.126432,0.148604,0.170345,0.191648,0.212508,0.232918,0.252876,0.272375,0.291415,0.30999,0.328098,0.345739,0.362909,0.379608,0.395836,0.411591,0.426874,0.441686,0.456029,0.469902,0.483309,0.496252,0.508733,0.520757,0.532327,0.543446,0.554121,0.564355,0.574156,0.583528,0.592478,0.601013,0.609141,0.616869,0.624205,0.631158,0.637736,0.643947,0.649801,0.655306,0.660472,0.665309,0.669824,0.674027,0.677927,0.681533,0.684852,0.687893,0.690663,0.693169,0.695419,0.697417,0.699169,0.700679,0.701952,0.702989,0.703794,0.704366,0.704706,0.704812,0.704682,0.704311,0.703695,0.702826,0.701696,0.700295,0.698612,0.696631,0.694339,0.691715,0.688741,0.685393,0.681646,0.677472,0.67284,0.667715,0.662061,0.655834,0.648992,0.641484,0.633258,0.624256,0.614416,0.603671,0.591948,0.579171,0.565257,0.550119,0.533662,0.515789,0.496395,0.475371,0.452607,0.427984,0.401386,0.372693,0.341786,0.308552},
{-2.70741,-2.68122,-2.65499,-2.62874,-2.60246,-2.57616,-2.54982,-2.52346,-2.49707,-2.47064,-2.44419,-2.41771,-2.39119,-2.36464,-2.33806,-2.31144,-2.28479,-2.2581,-2.23137,-2.2046,-2.17779,-2.15095,-2.12405,-2.09712,-2.07013,-2.0431,-2.01603,-1.9889,-1.96172,-1.93449,-1.9072,-1.87985,-1.85245,-1.82499,-1.79747,-1.76989,-1.74224,-1.71452,-1.68674,-1.65889,-1.63097,-1.60297,-1.57491,-1.54677,-1.51855,-1.49026,-1.46188,-1.43343,-1.4049,-1.37629,-1.3476,-1.31883,-1.28997,-1.26104,-1.23203,-1.20293,-1.17376,-1.14451,-1.11519,-1.0858,-1.05633,-1.0268,-0.997207,-0.967555,-0.93785,-0.908096,-0.878299,-0.848468,-0.818607,-0.788727,-0.758835,-0.728941,-0.699054,-0.669185,-0.639347,-0.60955,-0.579808,-0.550133,-0.520539,-0.491041,-0.461654,-0.432392,-0.403271,-0.374307,-0.345515,-0.316911,-0.288513,-0.260334,-0.232393,-0.204703,-0.177282,-0.150143,-0.123303,-0.0967744,-0.0705725,-0.0447105,-0.0192012,0.00594307,0.0307105,0.0550901,0.0790714,0.102645,0.1258,0.148531,0.170827,0.192683,0.214091,0.235045,0.255541,0.275573,0.295138,0.31423,0.332848,0.350988,0.368649,0.385829,0.402526,0.41874,0.434471,0.449719,0.464485,0.47877,0.492576,0.505905,0.51876,0.531144,0.543062,0.554516,0.565513,0.576057,0.586153,0.595809,0.60503,0.613824,0.622199,0.630161,0.63772,0.644884,0.651661,0.65806,0.664092,0.669765,0.675088,0.680071,0.684723,0.689054,0.693073,0.696788,0.700208,0.703342,0.706197,0.708781,0.7111,0.71316,0.714967,0.716526,0.71784,0.718913,0.719746,0.72034,0.720696,0.720812,0.720686,0.720313,0.719688,0.718805,0.717655,0.716228,0.714512,0.712493,0.710155,0.70748,0.704448,0.701035,0.697216,0.692963,0.688244,0.683024,0.677266,0.670929,0.663966,0.65633,0.647966,0.638816,0.628818,0.617906,0.606005,0.59304,0.578926,0.563577,0.546898,0.528791,0.509152,0.487873,0.46484,0.439938,0.413049,0.384054,0.352835,0.319278},
{-2.72559,-2.6994,-2.67318,-2.64693,-2.62065,-2.59435,-2.56802,-2.54166,-2.51526,-2.48884,-2.46239,-2.4359,-2.40939,-2.38284,-2.35625,-2.32963,-2.30297,-2.27628,-2.24954,-2.22277,-2.19595,-2.1691,-2.14219,-2.11525,-2.08825,-2.06121,-2.03412,-2.00698,-1.97979,-1.95254,-1.92523,-1.89787,-1.87045,-1.84297,-1.81542,-1.78781,-1.76013,-1.73239,-1.70458,-1.67669,-1.64873,-1.6207,-1.59259,-1.56441,-1.53614,-1.5078,-1.47937,-1.45086,-1.42227,-1.3936,-1.36483,-1.33599,-1.30705,-1.27804,-1.24893,-1.21974,-1.19047,-1.16111,-1.13168,-1.10216,-1.07257,-1.0429,-1.01316,-0.983357,-0.953488,-0.923562,-0.893585,-0.863561,-0.833498,-0.803403,-0.773286,-0.743154,-0.713017,-0.682886,-0.652772,-0.622686,-0.59264,-0.562649,-0.532725,-0.502882,-0.473135,-0.4435,-0.413991,-0.384625,-0.355418,-0.326386,-0.297545,-0.268912,-0.240503,-0.212334,-0.184423,-0.156784,-0.129433,-0.102386,-0.0756567,-0.0492604,-0.0232105,0.00247963,0.0277974,0.0527306,0.077268,0.101399,0.125112,0.1484,0.171252,0.193662,0.21562,0.237121,0.258157,0.278725,0.298817,0.318431,0.337562,0.356207,0.374363,0.392028,0.4092,0.425878,0.442062,0.457752,0.472947,0.48765,0.501861,0.515583,0.528818,0.541569,0.55384,0.565636,0.576961,0.58782,0.598219,0.608165,0.617663,0.626722,0.635349,0.643552,0.65134,0.65872,0.665703,0.672298,0.678513,0.684359,0.689846,0.694982,0.699779,0.704244,0.708389,0.712221,0.715751,0.718986,0.721934,0.724604,0.727002,0.729134,0.731007,0.732626,0.733994,0.735115,0.735991,0.736623,0.737011,0.737155,0.737052,0.736698,0.736088,0.735215,0.734072,0.732648,0.730931,0.728907,0.726562,0.723876,0.720829,0.717399,0.71356,0.709284,0.704539,0.699292,0.693504,0.687134,0.680138,0.672466,0.664065,0.654877,0.644841,0.633889,0.621949,0.608946,0.594795,0.579409,0.562697,0.544558,0.524891,0.503587,0.480534,0.455616,0.428717,0.399716,0.368497,0.334944},
{-2.74344,-2.71725,-2.69103,-2.66479,-2.63852,-2.61222,-2.58588,-2.55952,-2.53313,-2.50671,-2.48026,-2.45377,-2.42726,-2.4007,-2.37411,-2.34749,-2.32083,-2.29413,-2.26739,-2.24061,-2.21379,-2.18693,-2.16002,-2.13306,-2.10606,-2.07901,-2.0519,-2.02475,-1.99754,-1.97028,-1.94296,-1.91558,-1.88813,-1.86063,-1.83306,-1.80543,-1.77773,-1.74996,-1.72211,-1.6942,-1.6662,-1.63813,-1.60999,-1.58176,-1.55345,-1.52506,-1.49658,-1.46801,-1.43936,-1.41062,-1.38179,-1.35288,-1.32387,-1.29477,-1.26558,-1.2363,-1.20693,-1.17747,-1.14792,-1.11829,-1.08857,-1.05877,-1.02889,-0.99894,-0.968916,-0.938824,-0.908671,-0.878462,-0.848203,-0.817903,-0.787567,-0.757206,-0.726828,-0.696443,-0.666061,-0.635695,-0.605357,-0.575058,-0.544813,-0.514635,-0.484539,-0.45454,-0.424654,-0.394896,-0.365283,-0.335831,-0.306558,-0.277479,-0.248611,-0.219973,-0.191579,-0.163447,-0.135594,-0.108034,-0.0807845,-0.0538596,-0.0272744,-0.00104309,0.0248208,0.0503042,0.0753947,0.10008,0.12435,0.148194,0.171602,0.194564,0.217073,0.239121,0.2607,0.281804,0.302427,0.322565,0.342211,0.361364,0.380018,0.398172,0.415823,0.432969,0.44961,0.465745,0.481374,0.496498,0.511118,0.525236,0.538855,0.551977,0.564606,0.576746,0.588403,0.59958,0.610285,0.620523,0.630301,0.639627,0.648508,0.656953,0.664971,0.672569,0.679759,0.686548,0.692947,0.698966,0.704615,0.709903,0.714841,0.719439,0.723706,0.727652,0.731286,0.734617,0.737654,0.740403,0.742873,0.74507,0.747,0.748668,0.750079,0.751235,0.752141,0.752796,0.7532,0.753354,0.753255,0.752899,0.75228,0.751393,0.750228,0.748777,0.747027,0.744963,0.742571,0.739832,0.736726,0.733229,0.729316,0.724959,0.720125,0.714781,0.708888,0.702406,0.695287,0.687485,0.678944,0.669607,0.659411,0.64829,0.636172,0.622978,0.608627,0.59303,0.576096,0.557724,0.537813,0.516253,0.492933,0.467738,0.44055,0.41125,0.379722,0.345849},
{-2.76097,-2.73479,-2.70857,-2.68233,-2.65606,-2.62976,-2.60344,-2.57708,-2.55069,-2.52427,-2.49781,-2.47133,-2.44481,-2.41826,-2.39167,-2.36504,-2.33837,-2.31167,-2.28493,-2.25814,-2.23132,-2.20445,-2.17753,-2.15057,-2.12355,-2.09649,-2.06938,-2.04221,-2.01499,-1.98771,-1.96038,-1.93298,-1.90552,-1.878,-1.85041,-1.82275,-1.79502,-1.76723,-1.73935,-1.71141,-1.68338,-1.65528,-1.62709,-1.59882,-1.57047,-1.54203,-1.5135,-1.48489,-1.45618,-1.42738,-1.39849,-1.3695,-1.34042,-1.31124,-1.28197,-1.2526,-1.22314,-1.19358,-1.16393,-1.13418,-1.10434,-1.07442,-1.04441,-1.01431,-0.984135,-0.953884,-0.923562,-0.893174,-0.862726,-0.832226,-0.80168,-0.771097,-0.740485,-0.709854,-0.679214,-0.648576,-0.617953,-0.587356,-0.556799,-0.526295,-0.495859,-0.465505,-0.435251,-0.40511,-0.375101,-0.345238,-0.315541,-0.286024,-0.256707,-0.227606,-0.198738,-0.170121,-0.141771,-0.113705,-0.0859405,-0.0584924,-0.0313765,-0.00460799,0.0217986,0.0478292,0.0734705,0.0987097,0.123535,0.147934,0.171897,0.195413,0.218474,0.24107,0.263194,0.284837,0.305994,0.326658,0.346825,0.366489,0.385646,0.404293,0.422428,0.440048,0.457151,0.473737,0.489805,0.505357,0.520392,0.534913,0.548921,0.56242,0.575413,0.587904,0.599898,0.611401,0.622417,0.632954,0.643018,0.652617,0.661759,0.670452,0.678706,0.686529,0.69393,0.700921,0.70751,0.713709,0.719526,0.724973,0.73006,0.734797,0.739194,0.743262,0.747008,0.750444,0.753576,0.756415,0.758966,0.761237,0.763235,0.764965,0.766431,0.767637,0.768586,0.769279,0.769717,0.769899,0.769823,0.769486,0.768881,0.768004,0.766846,0.765396,0.763644,0.761575,0.759174,0.756423,0.7533,0.749785,0.74585,0.741468,0.736607,0.731232,0.725307,0.71879,0.711635,0.703794,0.695214,0.685836,0.6756,0.664437,0.652277,0.639042,0.62465,0.609015,0.592043,0.573637,0.553695,0.532108,0.508765,0.483552,0.45635,0.427043,0.395511,0.36164},
{-2.77819,-2.75201,-2.72581,-2.69957,-2.6733,-2.64701,-2.62068,-2.59433,-2.56794,-2.54152,-2.51507,-2.48858,-2.46206,-2.43551,-2.40891,-2.38229,-2.35562,-2.32891,-2.30217,-2.27538,-2.24854,-2.22167,-2.19474,-2.16777,-2.14075,-2.11368,-2.08656,-2.05938,-2.03215,-2.00486,-1.9775,-1.95009,-1.92262,-1.89507,-1.86747,-1.83979,-1.81204,-1.78421,-1.75632,-1.72834,-1.70028,-1.67215,-1.64392,-1.61562,-1.58722,-1.55874,-1.53016,-1.5015,-1.47274,-1.44388,-1.41492,-1.38587,-1.35672,-1.32747,-1.29812,-1.26866,-1.23911,-1.20946,-1.1797,-1.14985,-1.1199,-1.08985,-1.05971,-1.02947,-0.999153,-0.968747,-0.938262,-0.907702,-0.877072,-0.846379,-0.815629,-0.784831,-0.753993,-0.723124,-0.692233,-0.661332,-0.630432,-0.599546,-0.568685,-0.537864,-0.507097,-0.476398,-0.445784,-0.41527,-0.384873,-0.354609,-0.324496,-0.294551,-0.264792,-0.235236,-0.205901,-0.176806,-0.147967,-0.119402,-0.0911282,-0.0631623,-0.0355208,-0.00821968,0.0187256,0.0453001,0.0714894,0.0972798,0.122658,0.147612,0.17213,0.1962,0.219813,0.242959,0.265628,0.287813,0.309506,0.3307,0.351389,0.371568,0.391232,0.410377,0.428999,0.447097,0.464667,0.481709,0.498222,0.514206,0.529661,0.544589,0.558993,0.572874,0.586236,0.599083,0.61142,0.623252,0.634584,0.645425,0.655779,0.665656,0.675063,0.684009,0.692503,0.700554,0.708172,0.715367,0.72215,0.728531,0.734521,0.74013,0.745369,0.750248,0.754778,0.758969,0.762831,0.766373,0.769605,0.772534,0.775169,0.777518,0.779586,0.781379,0.782903,0.78416,0.785155,0.785889,0.786362,0.786575,0.786524,0.786208,0.785621,0.784756,0.783607,0.782162,0.780411,0.778341,0.775934,0.773175,0.770041,0.766512,0.76256,0.758159,0.753277,0.74788,0.74193,0.735386,0.728204,0.720334,0.711725,0.702318,0.692052,0.680861,0.668674,0.655413,0.640999,0.625343,0.608354,0.589936,0.569985,0.548396,0.525056,0.499853,0.472668,0.443384,0.411882,0.378049},
{-2.79512,-2.76894,-2.74274,-2.71651,-2.69025,-2.66395,-2.63763,-2.61128,-2.58489,-2.55847,-2.53202,-2.50554,-2.47902,-2.45246,-2.42587,-2.39924,-2.37257,-2.34586,-2.31911,-2.29232,-2.26548,-2.2386,-2.21167,-2.18469,-2.15766,-2.13058,-2.10345,-2.07626,-2.04902,-2.02172,-1.99435,-1.96692,-1.93943,-1.91187,-1.88424,-1.85655,-1.82877,-1.80093,-1.773,-1.745,-1.71691,-1.68874,-1.66049,-1.63214,-1.60371,-1.57519,-1.54657,-1.51785,-1.48904,-1.46012,-1.43111,-1.402,-1.37278,-1.34345,-1.31403,-1.28449,-1.25485,-1.2251,-1.19525,-1.16529,-1.13523,-1.10507,-1.0748,-1.04444,-1.01397,-0.98342,-0.952778,-0.922051,-0.891244,-0.860365,-0.829418,-0.798412,-0.767355,-0.736255,-0.705121,-0.673965,-0.642796,-0.611628,-0.580472,-0.549343,-0.518253,-0.487218,-0.456253,-0.425374,-0.394598,-0.363941,-0.333422,-0.303056,-0.272863,-0.242861,-0.213068,-0.183501,-0.15418,-0.125122,-0.0963454,-0.0678674,-0.0397054,-0.0118763,0.0156037,0.0427185,0.0694528,0.095792,0.121722,0.147229,0.172301,0.196925,0.22109,0.244786,0.268003,0.290731,0.312962,0.334689,0.355904,0.376601,0.396775,0.416422,0.435537,0.454116,0.472158,0.489661,0.506623,0.523044,0.538924,0.554265,0.569069,0.583337,0.597073,0.610281,0.622966,0.635132,0.646786,0.657935,0.668585,0.678744,0.68842,0.697623,0.706361,0.714644,0.722483,0.729887,0.736867,0.743434,0.7496,0.755374,0.760767,0.765792,0.770458,0.774775,0.778755,0.782407,0.78574,0.788763,0.791485,0.793912,0.796053,0.797912,0.799496,0.800808,0.801851,0.802628,0.803139,0.803385,0.803363,0.80307,0.802503,0.801655,0.800517,0.799082,0.797337,0.795268,0.792861,0.790098,0.786959,0.783421,0.779459,0.775046,0.77015,0.764738,0.758771,0.752211,0.745011,0.737124,0.728498,0.719075,0.708795,0.697591,0.685393,0.672125,0.657707,0.642052,0.625069,0.606662,0.58673,0.565165,0.541859,0.516698,0.489563,0.460339,0.428906,0.39515},
{-2.81176,-2.78559,-2.75939,-2.73316,-2.7069,-2.68062,-2.6543,-2.62795,-2.60156,-2.57515,-2.5487,-2.52221,-2.49569,-2.46914,-2.44254,-2.41591,-2.38924,-2.36253,-2.33578,-2.30898,-2.28214,-2.25525,-2.22832,-2.20133,-2.1743,-2.14721,-2.12007,-2.09287,-2.06562,-2.0383,-2.01092,-1.98348,-1.95598,-1.9284,-1.90075,-1.87304,-1.84524,-1.81738,-1.78943,-1.7614,-1.73328,-1.70508,-1.6768,-1.64842,-1.61995,-1.59138,-1.56272,-1.53396,-1.50509,-1.47613,-1.44706,-1.41788,-1.3886,-1.35921,-1.32971,-1.30009,-1.27037,-1.24053,-1.21059,-1.18053,-1.15036,-1.12008,-1.0897,-1.0592,-1.02861,-0.997909,-0.967114,-0.936226,-0.905249,-0.874189,-0.843052,-0.811845,-0.780575,-0.749251,-0.717882,-0.686478,-0.655049,-0.623607,-0.592165,-0.560735,-0.529331,-0.497968,-0.466661,-0.435427,-0.40428,-0.373239,-0.342321,-0.311544,-0.280926,-0.250485,-0.220241,-0.190211,-0.160415,-0.130871,-0.101597,-0.0726132,-0.0439362,-0.015584,0.012426,0.0400771,0.067353,0.094238,0.120717,0.146776,0.1724,0.197577,0.222295,0.246541,0.270305,0.293577,0.316348,0.338609,0.360352,0.38157,0.402258,0.422409,0.442019,0.461084,0.479601,0.497568,0.514983,0.531845,0.548155,0.563913,0.57912,0.593779,0.607893,0.621466,0.634502,0.647006,0.658985,0.670444,0.681392,0.691835,0.701783,0.711245,0.720229,0.728746,0.736805,0.744419,0.751597,0.75835,0.76469,0.770628,0.776175,0.781342,0.786141,0.790583,0.794677,0.798434,0.801863,0.804975,0.807776,0.810276,0.812481,0.814398,0.816031,0.817386,0.818466,0.819273,0.819807,0.82007,0.82006,0.819773,0.819205,0.81835,0.817201,0.815748,0.813979,0.811882,0.80944,0.806637,0.803451,0.799862,0.795842,0.791365,0.7864,0.780912,0.774865,0.768217,0.760924,0.752937,0.744204,0.734669,0.72427,0.712941,0.700611,0.687206,0.672644,0.656839,0.639701,0.621133,0.601034,0.579297,0.555814,0.53047,0.503149,0.473733,0.442104,0.408147},
{-2.82812,-2.80195,-2.77576,-2.74954,-2.72329,-2.697,-2.67069,-2.64434,-2.61796,-2.59154,-2.5651,-2.53861,-2.51209,-2.48554,-2.45894,-2.43231,-2.40564,-2.37893,-2.35217,-2.32537,-2.29853,-2.27164,-2.2447,-2.21771,-2.19066,-2.16357,-2.13642,-2.10921,-2.08195,-2.05462,-2.02723,-1.99978,-1.97226,-1.94467,-1.917,-1.88927,-1.86146,-1.83357,-1.80559,-1.77754,-1.7494,-1.72117,-1.69285,-1.66444,-1.63593,-1.60733,-1.57863,-1.54982,-1.52091,-1.49189,-1.46277,-1.43354,-1.40419,-1.37473,-1.34516,-1.31547,-1.28567,-1.25575,-1.22571,-1.19556,-1.16529,-1.1349,-1.1044,-1.07378,-1.04305,-1.01222,-0.981274,-0.95023,-0.919088,-0.887854,-0.856532,-0.82513,-0.793654,-0.762113,-0.730515,-0.69887,-0.667188,-0.63548,-0.603759,-0.572036,-0.540326,-0.508644,-0.477003,-0.44542,-0.413912,-0.382495,-0.351186,-0.320005,-0.288969,-0.258098,-0.227409,-0.196923,-0.166658,-0.136634,-0.10687,-0.0773856,-0.0481986,-0.0193279,0.00920823,0.0373922,0.0652068,0.0926353,0.119662,0.14627,0.172447,0.198177,0.223447,0.248244,0.272558,0.296376,0.319689,0.342487,0.364761,0.386504,0.407708,0.428368,0.448478,0.468034,0.487032,0.505468,0.523342,0.540651,0.557395,0.573575,0.589193,0.604249,0.618747,0.63269,0.646084,0.658932,0.671241,0.683018,0.69427,0.705004,0.71523,0.724956,0.734193,0.742949,0.751237,0.759066,0.766447,0.773393,0.779914,0.786023,0.79173,0.797048,0.801987,0.80656,0.810776,0.814646,0.81818,0.821389,0.824279,0.826861,0.829141,0.831126,0.832821,0.834232,0.835361,0.836212,0.836786,0.837083,0.837102,0.83684,0.836293,0.835454,0.834318,0.832873,0.83111,0.829015,0.826573,0.823765,0.820574,0.816976,0.812946,0.808456,0.803477,0.797974,0.79191,0.785244,0.777934,0.769929,0.76118,0.751629,0.741215,0.729874,0.717534,0.704122,0.689558,0.673755,0.656624,0.638069,0.61799,0.596281,0.572834,0.547535,0.520267,0.490914,0.459358,0.425482},
{-2.84421,-2.81805,-2.79187,-2.76565,-2.7394,-2.71312,-2.68681,-2.66046,-2.63409,-2.60767,-2.58123,-2.55475,-2.52823,-2.50167,-2.47508,-2.44845,-2.42178,-2.39506,-2.3683,-2.3415,-2.31465,-2.28776,-2.26081,-2.23382,-2.20677,-2.17967,-2.15251,-2.1253,-2.09802,-2.07069,-2.04329,-2.01582,-1.98829,-1.96068,-1.933,-1.90525,-1.87742,-1.84951,-1.82152,-1.79344,-1.76527,-1.73702,-1.70867,-1.68022,-1.65168,-1.62304,-1.5943,-1.56545,-1.5365,-1.50743,-1.47826,-1.44897,-1.41956,-1.39004,-1.3604,-1.33064,-1.30076,-1.27076,-1.24064,-1.21039,-1.18002,-1.14952,-1.11891,-1.08817,-1.05732,-1.02635,-0.995266,-0.964071,-0.932769,-0.901366,-0.869866,-0.838275,-0.8066,-0.774848,-0.743028,-0.711149,-0.679221,-0.647255,-0.615262,-0.583255,-0.551247,-0.519253,-0.487287,-0.455364,-0.423502,-0.391717,-0.360027,-0.32845,-0.297005,-0.26571,-0.234586,-0.203651,-0.172925,-0.142428,-0.11218,-0.0822013,-0.0525102,-0.0231265,0.00593072,0.034643,0.0629921,0.0909605,0.118531,0.145687,0.172414,0.198695,0.224516,0.249865,0.274727,0.299092,0.322947,0.346283,0.36909,0.391359,0.413082,0.434253,0.454866,0.474914,0.494395,0.513304,0.531639,0.549398,0.56658,0.583186,0.599215,0.614671,0.629556,0.643873,0.657626,0.67082,0.683462,0.695557,0.707114,0.71814,0.728644,0.738636,0.748124,0.757119,0.765633,0.773675,0.781258,0.788393,0.795092,0.801367,0.807229,0.812691,0.817764,0.82246,0.826789,0.830763,0.834392,0.837685,0.840652,0.843302,0.845641,0.847676,0.849414,0.85086,0.852017,0.852888,0.853474,0.853775,0.853791,0.853519,0.852954,0.852091,0.850922,0.849438,0.847628,0.845478,0.842972,0.840094,0.836823,0.833137,0.829011,0.824416,0.819321,0.813694,0.807495,0.800685,0.793219,0.785048,0.776121,0.766379,0.755764,0.744208,0.731641,0.717989,0.70317,0.687098,0.669685,0.650833,0.630441,0.608406,0.584616,0.558959,0.531319,0.501578,0.469619,0.435326},
{-2.86004,-2.83389,-2.80771,-2.7815,-2.75525,-2.72898,-2.70267,-2.67633,-2.64996,-2.62355,-2.5971,-2.57062,-2.54411,-2.51755,-2.49096,-2.46433,-2.43765,-2.41094,-2.38418,-2.35737,-2.33052,-2.30363,-2.27668,-2.24968,-2.22263,-2.19552,-2.16835,-2.14113,-2.11385,-2.0865,-2.05909,-2.03162,-2.00407,-1.97645,-1.94876,-1.92099,-1.89314,-1.86521,-1.8372,-1.8091,-1.78091,-1.75262,-1.72425,-1.69577,-1.6672,-1.63853,-1.60975,-1.58086,-1.55186,-1.52275,-1.49352,-1.46418,-1.43472,-1.40514,-1.37543,-1.34561,-1.31565,-1.28557,-1.25536,-1.22502,-1.19456,-1.16396,-1.13324,-1.10239,-1.07141,-1.04031,-1.00909,-0.977749,-0.946293,-0.914726,-0.883052,-0.851278,-0.819409,-0.787453,-0.755418,-0.723312,-0.691145,-0.658927,-0.626669,-0.594385,-0.562086,-0.529788,-0.497503,-0.465249,-0.43304,-0.400895,-0.368831,-0.336866,-0.305018,-0.273308,-0.241754,-0.210377,-0.179196,-0.148233,-0.117507,-0.0870386,-0.0568483,-0.0269561,0.00261831,0.0318554,0.0607362,0.0892421,0.117355,0.145058,0.172333,0.199165,0.225538,0.251438,0.276851,0.301764,0.326164,0.350041,0.373383,0.396182,0.418429,0.440115,0.461235,0.481782,0.50175,0.521137,0.539939,0.558154,0.57578,0.592818,0.609267,0.625129,0.640407,0.655103,0.669223,0.68277,0.695752,0.708173,0.720042,0.731367,0.742157,0.75242,0.762167,0.771409,0.780156,0.78842,0.796212,0.803545,0.81043,0.816879,0.822905,0.82852,0.833737,0.838565,0.843019,0.847107,0.850842,0.854232,0.857288,0.860019,0.862431,0.864533,0.866331,0.867829,0.869033,0.869944,0.870564,0.870894,0.870933,0.870679,0.870127,0.869272,0.868106,0.866621,0.864805,0.862645,0.860125,0.857229,0.853936,0.850225,0.846069,0.841442,0.836312,0.830646,0.824406,0.817552,0.810039,0.80182,0.792842,0.783049,0.77238,0.76077,0.74815,0.734443,0.71957,0.703446,0.685981,0.66708,0.646642,0.624564,0.600734,0.575042,0.54737,0.517602,0.485621,0.451309},
{-2.87562,-2.84948,-2.8233,-2.7971,-2.77086,-2.74459,-2.71828,-2.69195,-2.66558,-2.63917,-2.61273,-2.58625,-2.55974,-2.53318,-2.50659,-2.47996,-2.45329,-2.42657,-2.39981,-2.373,-2.34615,-2.31925,-2.2923,-2.26529,-2.23824,-2.21112,-2.18395,-2.15672,-2.12943,-2.10208,-2.07466,-2.04717,-2.01961,-1.99198,-1.96427,-1.93649,-1.90863,-1.88068,-1.85264,-1.82452,-1.79631,-1.768,-1.7396,-1.7111,-1.6825,-1.65379,-1.62497,-1.59604,-1.56701,-1.53785,-1.50858,-1.47919,-1.44967,-1.42003,-1.39026,-1.36037,-1.33034,-1.30018,-1.26989,-1.23947,-1.20891,-1.17822,-1.14739,-1.11643,-1.08534,-1.05411,-1.02275,-0.991273,-0.959667,-0.927941,-0.8961,-0.864148,-0.832091,-0.799937,-0.767692,-0.735365,-0.702966,-0.670503,-0.637988,-0.605434,-0.572852,-0.540257,-0.507662,-0.475083,-0.442537,-0.410039,-0.377609,-0.345263,-0.313021,-0.280903,-0.248927,-0.217115,-0.185487,-0.154064,-0.122866,-0.0919149,-0.0612312,-0.0308359,-0.000749366,0.029008,0.0584162,0.0874559,0.116108,0.144354,0.172176,0.199558,0.226481,0.252932,0.278895,0.304356,0.329302,0.35372,0.3776,0.40093,0.423702,0.445906,0.467535,0.488582,0.509043,0.528911,0.548183,0.566857,0.58493,0.602402,0.619274,0.635545,0.651219,0.666299,0.680788,0.694691,0.708014,0.720763,0.732946,0.744572,0.755648,0.766185,0.776192,0.78568,0.79466,0.803145,0.811145,0.818673,0.825742,0.832363,0.83855,0.844315,0.849669,0.854626,0.859197,0.863393,0.867225,0.870705,0.87384,0.876641,0.879115,0.881271,0.883114,0.884649,0.885882,0.886814,0.887448,0.887785,0.887823,0.88756,0.886993,0.886114,0.884918,0.883394,0.881532,0.879319,0.876739,0.873774,0.870404,0.866607,0.862358,0.857629,0.852388,0.846601,0.840232,0.833238,0.825576,0.817198,0.80805,0.798076,0.787215,0.775401,0.762565,0.748631,0.733518,0.717142,0.699413,0.680234,0.659505,0.637122,0.612975,0.586951,0.558935,0.528809,0.496456,0.46176},
{-2.89095,-2.86482,-2.83865,-2.81245,-2.78622,-2.75995,-2.73365,-2.70732,-2.68095,-2.65455,-2.62811,-2.60164,-2.57512,-2.54857,-2.52198,-2.49535,-2.46868,-2.44196,-2.4152,-2.38839,-2.36154,-2.33463,-2.30768,-2.28067,-2.25361,-2.22649,-2.19932,-2.17208,-2.14478,-2.11742,-2.08999,-2.06249,-2.03493,-2.00728,-1.97956,-1.95176,-1.92388,-1.89592,-1.86787,-1.83973,-1.81149,-1.78316,-1.75474,-1.72621,-1.69757,-1.66883,-1.63998,-1.61102,-1.58194,-1.55274,-1.52343,-1.49398,-1.46442,-1.43472,-1.40489,-1.37493,-1.34484,-1.31461,-1.28424,-1.25373,-1.22308,-1.1923,-1.16137,-1.1303,-1.09909,-1.06775,-1.03626,-1.00464,-0.972892,-0.941012,-0.909008,-0.876884,-0.844645,-0.812298,-0.779849,-0.747308,-0.714681,-0.68198,-0.649215,-0.616397,-0.583539,-0.550654,-0.517756,-0.48486,-0.451982,-0.41914,-0.38635,-0.353631,-0.321002,-0.288482,-0.256091,-0.223851,-0.191782,-0.159904,-0.128241,-0.0968121,-0.0656401,-0.0347461,-0.00415157,0.0261224,0.056055,0.0856258,0.114815,0.143603,0.171971,0.199901,0.227375,0.254377,0.280891,0.306902,0.332395,0.357358,0.381778,0.405643,0.428943,0.451669,0.473812,0.495365,0.516321,0.536676,0.556424,0.575562,0.594089,0.612002,0.629302,0.64599,0.662067,0.677536,0.692401,0.706666,0.720338,0.733422,0.745926,0.757859,0.769229,0.780046,0.79032,0.800062,0.809284,0.817996,0.826212,0.833944,0.841205,0.848006,0.854362,0.860284,0.865787,0.870881,0.875579,0.879893,0.883835,0.887414,0.890641,0.893525,0.896075,0.898299,0.900202,0.901791,0.903071,0.904044,0.904713,0.905078,0.90514,0.904894,0.904339,0.903467,0.902273,0.900747,0.898878,0.896653,0.894057,0.891072,0.887678,0.883854,0.879573,0.874808,0.869529,0.863701,0.857287,0.850247,0.842535,0.834105,0.824903,0.814874,0.803957,0.792086,0.779192,0.7652,0.75003,0.733598,0.715813,0.696581,0.675802,0.653371,0.629181,0.603117,0.575065,0.544907,0.512526,0.477805},
{-2.90605,-2.87992,-2.85376,-2.82757,-2.80134,-2.77508,-2.74879,-2.72246,-2.6961,-2.6697,-2.64326,-2.61679,-2.59028,-2.56373,-2.53714,-2.51051,-2.48384,-2.45712,-2.43036,-2.40355,-2.37669,-2.34979,-2.32283,-2.29582,-2.26875,-2.24163,-2.21445,-2.18721,-2.15991,-2.13254,-2.1051,-2.07759,-2.05001,-2.02236,-1.99463,-1.96682,-1.93892,-1.91094,-1.88287,-1.85471,-1.82646,-1.79811,-1.76966,-1.7411,-1.71244,-1.68367,-1.65479,-1.62579,-1.59667,-1.56743,-1.53807,-1.50858,-1.47897,-1.44922,-1.41933,-1.38931,-1.35915,-1.32885,-1.29841,-1.26782,-1.23708,-1.20621,-1.17518,-1.14401,-1.11269,-1.08123,-1.04962,-1.01787,-0.985975,-0.953946,-0.921784,-0.889492,-0.857076,-0.824542,-0.791895,-0.759145,-0.726299,-0.693366,-0.660357,-0.627282,-0.594154,-0.560986,-0.527792,-0.494586,-0.461385,-0.428204,-0.395063,-0.361978,-0.328969,-0.296055,-0.263257,-0.230595,-0.198091,-0.165767,-0.133643,-0.101743,-0.0700883,-0.0387011,-0.00760347,0.0231826,0.0536355,0.0837339,0.113457,0.142784,0.171696,0.200173,0.228196,0.255749,0.282814,0.309375,0.335416,0.360924,0.385885,0.410287,0.434118,0.457368,0.480028,0.502089,0.523545,0.544389,0.564617,0.584224,0.603207,0.621566,0.639298,0.656406,0.672889,0.688751,0.703996,0.718627,0.732651,0.746073,0.758902,0.771145,0.782812,0.793912,0.804455,0.814453,0.823917,0.832859,0.841292,0.849228,0.85668,0.863662,0.870186,0.876266,0.881915,0.887145,0.891968,0.896398,0.900445,0.90412,0.907435,0.910398,0.913018,0.915303,0.91726,0.918896,0.920214,0.921219,0.921912,0.922295,0.922367,0.922125,0.921567,0.920687,0.919478,0.91793,0.916034,0.913775,0.911139,0.908108,0.904662,0.90078,0.896435,0.8916,0.886244,0.880333,0.873831,0.866695,0.858882,0.850344,0.841028,0.830879,0.819835,0.807832,0.7948,0.780664,0.765344,0.748756,0.73081,0.711411,0.69046,0.667853,0.64348,0.617229,0.588986,0.558632,0.526049,0.491122},
{-2.92092,-2.8948,-2.86864,-2.84246,-2.81624,-2.78998,-2.76369,-2.73737,-2.71101,-2.68462,-2.65818,-2.63171,-2.60521,-2.57866,-2.55207,-2.52544,-2.49877,-2.47205,-2.44529,-2.41848,-2.39163,-2.36472,-2.33776,-2.31075,-2.28368,-2.25655,-2.22937,-2.20212,-2.17481,-2.14743,-2.11999,-2.09247,-2.06489,-2.03722,-2.00948,-1.98165,-1.95375,-1.92575,-1.89767,-1.86949,-1.84122,-1.81284,-1.78437,-1.75579,-1.7271,-1.6983,-1.66939,-1.64036,-1.6112,-1.58193,-1.55253,-1.52299,-1.49333,-1.46353,-1.43359,-1.40351,-1.37328,-1.34291,-1.3124,-1.28173,-1.25092,-1.21995,-1.18883,-1.15756,-1.12613,-1.09455,-1.06282,-1.03095,-0.998918,-0.966744,-0.934429,-0.901975,-0.869387,-0.836671,-0.803832,-0.770879,-0.737818,-0.704659,-0.671412,-0.638087,-0.604696,-0.571252,-0.537768,-0.504259,-0.470741,-0.43723,-0.403744,-0.3703,-0.336918,-0.303617,-0.270418,-0.237342,-0.20441,-0.171644,-0.139067,-0.106701,-0.0745683,-0.0426927,-0.0110966,0.0201975,0.051167,0.0817897,0.112044,0.141908,0.171362,0.200384,0.228957,0.25706,0.284675,0.311787,0.338377,0.364432,0.389937,0.414877,0.439242,0.46302,0.4862,0.508774,0.530733,0.552072,0.572783,0.592863,0.612308,0.631117,0.649287,0.66682,0.683715,0.699976,0.715606,0.730608,0.744989,0.758756,0.771914,0.784473,0.796441,0.807829,0.818647,0.828905,0.838617,0.847793,0.856448,0.864593,0.872242,0.879408,0.886106,0.892347,0.898147,0.903517,0.90847,0.91302,0.917177,0.920954,0.92436,0.927407,0.930102,0.932454,0.934471,0.936159,0.937522,0.938564,0.939289,0.939696,0.939786,0.939558,0.939006,0.938127,0.936912,0.935355,0.933442,0.931163,0.928501,0.925439,0.921958,0.918035,0.913645,0.90876,0.903351,0.897382,0.890816,0.883614,0.875731,0.867119,0.857725,0.847495,0.836368,0.824278,0.811157,0.796929,0.781517,0.764834,0.746793,0.727298,0.70625,0.683546,0.659077,0.632731,0.604392,0.573944,0.541268,0.506247},
{-2.93556,-2.90945,-2.8833,-2.85712,-2.83091,-2.80466,-2.77838,-2.75206,-2.7257,-2.69931,-2.67288,-2.64642,-2.61991,-2.59337,-2.56678,-2.54016,-2.51348,-2.48677,-2.46001,-2.4332,-2.40634,-2.37943,-2.35247,-2.32546,-2.29838,-2.27126,-2.24407,-2.21682,-2.1895,-2.16212,-2.13467,-2.10714,-2.07955,-2.05187,-2.02412,-1.99628,-1.96836,-1.94035,-1.91225,-1.88406,-1.85577,-1.82738,-1.79888,-1.77028,-1.74156,-1.71274,-1.6838,-1.65473,-1.62555,-1.59623,-1.56679,-1.53721,-1.5075,-1.47765,-1.44766,-1.41752,-1.38724,-1.3568,-1.32622,-1.29548,-1.26458,-1.23353,-1.20232,-1.17095,-1.13942,-1.10774,-1.07589,-1.04389,-1.01173,-0.979412,-0.946948,-0.914336,-0.881582,-0.848688,-0.815663,-0.782512,-0.749243,-0.715864,-0.682385,-0.648816,-0.615168,-0.581454,-0.547688,-0.513883,-0.480055,-0.44622,-0.412396,-0.3786,-0.344851,-0.31117,-0.277577,-0.244092,-0.210739,-0.177538,-0.144513,-0.111687,-0.0790828,-0.0467239,-0.0146339,0.0171638,0.0486459,0.0797895,0.110572,0.140971,0.170964,0.200531,0.22965,0.258303,0.28647,0.314132,0.341273,0.367876,0.393925,0.419407,0.444308,0.468616,0.492319,0.515409,0.537876,0.559712,0.580912,0.601469,0.621381,0.640644,0.659257,0.677219,0.694531,0.711195,0.727215,0.742594,0.757337,0.771451,0.784944,0.797823,0.810097,0.821777,0.832873,0.843397,0.853359,0.862774,0.871654,0.880011,0.88786,0.895215,0.902088,0.908494,0.914447,0.91996,0.925046,0.929717,0.933987,0.937866,0.941367,0.944498,0.94727,0.949691,0.951769,0.95351,0.954919,0.956,0.956757,0.95719,0.9573,0.957084,0.95654,0.955662,0.954444,0.952877,0.95095,0.948651,0.945964,0.942873,0.939357,0.935395,0.930961,0.926029,0.920567,0.914542,0.907916,0.90065,0.892699,0.884016,0.874548,0.864241,0.853034,0.840862,0.827657,0.813344,0.797844,0.781073,0.762943,0.743359,0.722223,0.699431,0.674875,0.648443,0.620019,0.589488,0.556729,0.521626},
{-2.94999,-2.92389,-2.89775,-2.87157,-2.84536,-2.81912,-2.79284,-2.76653,-2.74018,-2.7138,-2.68737,-2.66091,-2.63441,-2.60786,-2.58128,-2.55466,-2.52799,-2.50127,-2.47451,-2.4477,-2.42084,-2.39393,-2.36697,-2.33996,-2.31288,-2.28575,-2.25856,-2.2313,-2.20398,-2.17659,-2.14914,-2.12161,-2.094,-2.06632,-2.03856,-2.01071,-1.98278,-1.95476,-1.92664,-1.89843,-1.87012,-1.84171,-1.8132,-1.78457,-1.75584,-1.72698,-1.69801,-1.66892,-1.6397,-1.61035,-1.58087,-1.55126,-1.5215,-1.4916,-1.46156,-1.43137,-1.40102,-1.37053,-1.33987,-1.30906,-1.27809,-1.24696,-1.21566,-1.1842,-1.15257,-1.12077,-1.08881,-1.05669,-1.0244,-0.991954,-0.959345,-0.92658,-0.893663,-0.860598,-0.827391,-0.794048,-0.760575,-0.726982,-0.693277,-0.65947,-0.625572,-0.591595,-0.557552,-0.523457,-0.489326,-0.455174,-0.421018,-0.386877,-0.352769,-0.318714,-0.284733,-0.250847,-0.217078,-0.183449,-0.149982,-0.116702,-0.0836307,-0.0507936,-0.0182145,0.0140826,0.0460735,0.0777345,0.109042,0.139973,0.170504,0.200613,0.230279,0.259481,0.288198,0.316412,0.344103,0.371255,0.397852,0.423877,0.449316,0.474157,0.498387,0.521996,0.544974,0.567312,0.589004,0.610044,0.630426,0.650149,0.669209,0.687605,0.705339,0.722412,0.738827,0.754587,0.769697,0.784165,0.797997,0.811201,0.823786,0.835763,0.847142,0.857935,0.868153,0.877811,0.886919,0.895493,0.903547,0.911093,0.918146,0.924721,0.930831,0.93649,0.941711,0.946508,0.950894,0.95488,0.958478,0.961698,0.96455,0.967043,0.969185,0.970983,0.972442,0.973566,0.974359,0.974823,0.974956,0.974759,0.974227,0.973356,0.97214,0.97057,0.968635,0.966324,0.96362,0.960507,0.956967,0.952975,0.948509,0.94354,0.938039,0.931971,0.9253,0.917986,0.909984,0.901249,0.891728,0.881366,0.870102,0.857874,0.844612,0.830243,0.814687,0.797863,0.779681,0.760048,0.738865,0.71603,0.691434,0.664966,0.636512,0.605953,0.573172,0.538049},
{-2.96421,-2.93811,-2.91198,-2.88581,-2.85961,-2.83338,-2.8071,-2.7808,-2.75445,-2.72807,-2.70165,-2.67519,-2.64869,-2.62215,-2.59557,-2.56895,-2.54228,-2.51557,-2.48881,-2.462,-2.43514,-2.40823,-2.38127,-2.35425,-2.32718,-2.30004,-2.27285,-2.24559,-2.21826,-2.19087,-2.16341,-2.13587,-2.10826,-2.08057,-2.0528,-2.02494,-1.997,-1.96896,-1.94084,-1.91261,-1.88429,-1.85586,-1.82732,-1.79868,-1.76992,-1.74104,-1.71205,-1.68292,-1.65367,-1.62429,-1.59478,-1.56512,-1.53532,-1.50538,-1.47529,-1.44504,-1.41464,-1.38409,-1.35337,-1.32249,-1.29144,-1.26023,-1.22885,-1.1973,-1.16557,-1.13367,-1.10161,-1.06937,-1.03695,-1.00437,-0.971625,-0.938711,-0.905637,-0.872405,-0.839021,-0.805491,-0.771821,-0.738019,-0.704093,-0.670054,-0.635912,-0.601678,-0.567365,-0.532987,-0.498559,-0.464097,-0.429617,-0.395138,-0.360677,-0.326256,-0.291894,-0.257613,-0.223435,-0.189384,-0.155481,-0.121752,-0.0882205,-0.0549107,-0.0218477,0.0109439,0.0434391,0.0756134,0.107442,0.138902,0.169968,0.200617,0.230827,0.260577,0.289844,0.318608,0.346851,0.374552,0.401696,0.428265,0.454245,0.479621,0.504379,0.52851,0.552001,0.574844,0.597032,0.618556,0.639413,0.659598,0.679109,0.697944,0.716103,0.733588,0.7504,0.766545,0.782026,0.79685,0.811023,0.824555,0.837454,0.84973,0.861393,0.872457,0.882933,0.892833,0.902172,0.910962,0.919219,0.926956,0.934188,0.94093,0.947194,0.952997,0.958351,0.96327,0.967767,0.971854,0.975544,0.978846,0.981771,0.984329,0.986526,0.988371,0.989869,0.991025,0.991841,0.992321,0.992463,0.992267,0.99173,0.990846,0.989611,0.988014,0.986047,0.983696,0.980946,0.97778,0.97418,0.970123,0.965584,0.960536,0.954949,0.948788,0.942018,0.934598,0.926484,0.917629,0.907982,0.897488,0.886085,0.873711,0.860296,0.845768,0.830047,0.813051,0.794691,0.774873,0.7535,0.730468,0.705669,0.678993,0.650323,0.619542,0.586532,0.551173},
{-2.97822,-2.95213,-2.92601,-2.89985,-2.87365,-2.84742,-2.82116,-2.79486,-2.76852,-2.74214,-2.71573,-2.68927,-2.66278,-2.63624,-2.60966,-2.58304,-2.55638,-2.52966,-2.50291,-2.4761,-2.44924,-2.42233,-2.39537,-2.36835,-2.34127,-2.31414,-2.28694,-2.25968,-2.23235,-2.20495,-2.17748,-2.14994,-2.12232,-2.09463,-2.06684,-2.03898,-2.01103,-1.98298,-1.95484,-1.9266,-1.89826,-1.86982,-1.84127,-1.8126,-1.78382,-1.75492,-1.7259,-1.69675,-1.66747,-1.63806,-1.60851,-1.57881,-1.54898,-1.51899,-1.48885,-1.45856,-1.42811,-1.39749,-1.36671,-1.33576,-1.30465,-1.27336,-1.24189,-1.21025,-1.17844,-1.14644,-1.11427,-1.08191,-1.04938,-1.01667,-0.983789,-0.950731,-0.917503,-0.884109,-0.850553,-0.816841,-0.782979,-0.748973,-0.714833,-0.680567,-0.646187,-0.611702,-0.577125,-0.54247,-0.507752,-0.472986,-0.438188,-0.403376,-0.368569,-0.333788,-0.299051,-0.264382,-0.229801,-0.195333,-0.161001,-0.126829,-0.0928412,-0.0590636,-0.0255211,0.00776073,0.0407565,0.0734407,0.105788,0.137773,0.169372,0.20056,0.231314,0.26161,0.291427,0.320743,0.349537,0.377789,0.405482,0.432598,0.45912,0.485034,0.510325,0.53498,0.558989,0.582342,0.605029,0.627044,0.64838,0.669033,0.689,0.708278,0.726869,0.744771,0.761988,0.778523,0.79438,0.809566,0.824088,0.837953,0.851172,0.863753,0.875707,0.887048,0.897787,0.907936,0.917511,0.926525,0.934991,0.942926,0.950343,0.957258,0.963684,0.969637,0.975131,0.980179,0.984795,0.988991,0.99278,0.996173,0.99918,1.00181,1.00407,1.00598,1.00753,1.00872,1.00958,1.01009,1.01025,1.01007,1.00955,1.00867,1.00743,1.00583,1.00385,1.00149,0.998718,0.995529,0.9919,0.98781,0.983235,0.978147,0.972515,0.966308,0.959488,0.952015,0.943846,0.934934,0.925227,0.914672,0.903207,0.89077,0.877292,0.862701,0.846918,0.82986,0.81144,0.791564,0.770135,0.74705,0.722201,0.695478,0.666765,0.635944,0.602897,0.567503},
{-2.99203,-2.96595,-2.93984,-2.91369,-2.8875,-2.86128,-2.83502,-2.80872,-2.78239,-2.75601,-2.7296,-2.70315,-2.67666,-2.65013,-2.62356,-2.59694,-2.57027,-2.54357,-2.51681,-2.49,-2.46315,-2.43624,-2.40927,-2.38225,-2.35518,-2.32804,-2.30084,-2.27357,-2.24624,-2.21884,-2.19137,-2.16382,-2.1362,-2.10849,-2.08071,-2.05283,-2.02487,-1.99681,-1.96866,-1.94041,-1.91206,-1.8836,-1.85503,-1.82635,-1.79755,-1.76863,-1.73958,-1.71041,-1.6811,-1.65165,-1.62207,-1.59234,-1.56247,-1.53244,-1.50226,-1.47191,-1.44141,-1.41074,-1.3799,-1.34889,-1.31771,-1.28634,-1.2548,-1.22308,-1.19117,-1.15908,-1.1268,-1.09434,-1.06169,-1.02886,-0.995842,-0.962645,-0.929269,-0.895717,-0.861994,-0.828105,-0.794055,-0.759851,-0.725502,-0.691016,-0.656402,-0.621672,-0.586838,-0.551912,-0.51691,-0.481846,-0.446736,-0.411599,-0.376453,-0.341318,-0.306213,-0.271161,-0.236185,-0.201306,-0.16655,-0.131941,-0.0975036,-0.0632636,-0.0292469,0.00452049,0.0380123,0.0712023,0.104064,0.136573,0.168702,0.200426,0.231721,0.262563,0.292928,0.322794,0.352139,0.380943,0.409186,0.436849,0.463915,0.490368,0.516193,0.541377,0.565906,0.589771,0.612961,0.635469,0.657288,0.678413,0.698839,0.718565,0.73759,0.755914,0.773539,0.790468,0.806706,0.822257,0.83713,0.851333,0.864873,0.877762,0.890011,0.90163,0.912634,0.923035,0.932847,0.942085,0.950763,0.958895,0.966498,0.973585,0.980173,0.986276,0.991907,0.997083,1.00182,1.00612,1.01,1.01348,1.01657,1.01927,1.02159,1.02355,1.02514,1.02637,1.02725,1.02778,1.02796,1.02779,1.02726,1.02638,1.02513,1.02351,1.02151,1.01911,1.0163,1.01307,1.00939,1.00524,1.0006,0.995448,0.989744,0.983458,0.976554,0.968992,0.960729,0.951717,0.941906,0.931241,0.919663,0.907107,0.893507,0.878788,0.862874,0.845681,0.827123,0.807105,0.785531,0.762298,0.737299,0.710421,0.68155,0.650568,0.617355,0.581792},
{-3.00565,-2.97958,-2.95347,-2.92733,-2.90115,-2.87494,-2.84868,-2.82239,-2.79606,-2.7697,-2.74329,-2.71685,-2.69036,-2.66383,-2.63726,-2.61064,-2.58398,-2.55728,-2.53052,-2.50372,-2.47686,-2.44995,-2.42299,-2.39597,-2.36889,-2.34175,-2.31455,-2.28729,-2.25995,-2.23255,-2.20507,-2.17752,-2.14989,-2.12218,-2.09439,-2.06651,-2.03853,-2.01047,-1.98231,-1.95404,-1.92568,-1.8972,-1.86862,-1.83992,-1.8111,-1.78216,-1.75309,-1.72389,-1.69456,-1.66509,-1.63547,-1.60571,-1.5758,-1.54573,-1.51551,-1.48512,-1.45456,-1.42384,-1.39295,-1.36187,-1.33062,-1.29919,-1.26757,-1.23577,-1.20377,-1.17159,-1.13921,-1.10664,-1.07388,-1.04093,-1.00779,-0.974455,-0.940935,-0.90723,-0.873344,-0.839283,-0.80505,-0.770654,-0.736101,-0.701399,-0.666558,-0.631589,-0.596503,-0.561313,-0.526032,-0.490676,-0.455262,-0.419805,-0.384326,-0.348843,-0.313376,-0.277949,-0.242582,-0.207299,-0.172125,-0.137084,-0.102202,-0.0675047,-0.0330185,0.00122991,0.0352136,0.0689057,0.102279,0.135307,0.167964,0.200222,0.232057,0.263443,0.294356,0.324773,0.35467,0.384025,0.412819,0.441032,0.468644,0.495639,0.522001,0.547715,0.572769,0.597149,0.620847,0.643852,0.666158,0.687759,0.70865,0.728829,0.748294,0.767044,0.785082,0.802411,0.819034,0.834956,0.850186,0.86473,0.878599,0.891801,0.904348,0.916252,0.927526,0.938183,0.948238,0.957705,0.966598,0.974933,0.982726,0.989991,0.996745,1.003,1.00878,1.01408,1.01894,1.02335,1.02734,1.03091,1.03408,1.03685,1.03924,1.04125,1.04289,1.04417,1.04509,1.04564,1.04584,1.04569,1.04517,1.04429,1.04303,1.0414,1.03939,1.03697,1.03413,1.03087,1.02716,1.02297,1.01829,1.01309,1.00733,1.00099,0.994027,0.986402,0.978073,0.968993,0.959111,0.948372,0.936719,0.924086,0.910408,0.89561,0.879617,0.862345,0.843707,0.823611,0.80196,0.77865,0.753576,0.726625,0.697682,0.66663,0.633347,0.597714},
{-3.01908,-2.99302,-2.96692,-2.94079,-2.91462,-2.88841,-2.86216,-2.83588,-2.80955,-2.78319,-2.75679,-2.73035,-2.70387,-2.67735,-2.65078,-2.62417,-2.59751,-2.5708,-2.54405,-2.51725,-2.4904,-2.46349,-2.43653,-2.40951,-2.38243,-2.35529,-2.32809,-2.30082,-2.27348,-2.24608,-2.2186,-2.19104,-2.16341,-2.13569,-2.10789,-2.08,-2.05202,-2.02395,-1.99578,-1.96751,-1.93913,-1.91064,-1.88204,-1.85332,-1.82449,-1.79553,-1.76644,-1.73722,-1.70786,-1.67836,-1.64871,-1.61892,-1.58897,-1.55887,-1.5286,-1.49817,-1.46757,-1.4368,-1.40585,-1.37472,-1.3434,-1.3119,-1.28021,-1.24833,-1.21625,-1.18398,-1.15151,-1.11884,-1.08597,-1.0529,-1.01963,-0.986166,-0.952505,-0.918652,-0.884608,-0.850379,-0.81597,-0.781385,-0.746633,-0.711722,-0.676659,-0.641456,-0.606124,-0.570675,-0.535122,-0.499481,-0.463768,-0.427998,-0.392192,-0.356367,-0.320545,-0.284748,-0.248997,-0.213316,-0.17773,-0.142263,-0.106942,-0.0717925,-0.0368419,-0.00211721,0.032354,0.0665441,0.100425,0.13397,0.167151,0.199941,0.232314,0.264243,0.295703,0.326669,0.357117,0.387025,0.416371,0.445133,0.473293,0.500832,0.527733,0.553981,0.579561,0.60446,0.628668,0.652175,0.674972,0.697053,0.718413,0.739049,0.758957,0.778139,0.796594,0.814326,0.831339,0.847637,0.863227,0.878118,0.892318,0.905837,0.918687,0.930879,0.942426,0.953343,0.963643,0.973342,0.982453,0.990994,0.998979,1.00642,1.01334,1.01976,1.02568,1.03112,1.03609,1.04062,1.04471,1.04837,1.05162,1.05447,1.05692,1.05899,1.06068,1.062,1.06295,1.06353,1.06375,1.06361,1.0631,1.06221,1.06095,1.05931,1.05727,1.05483,1.05197,1.04867,1.04492,1.04069,1.03596,1.0307,1.02489,1.01848,1.01145,1.00376,0.995353,0.986195,0.976232,0.96541,0.95367,0.940949,0.927179,0.91229,0.896202,0.878835,0.860102,0.83991,0.818162,0.794756,0.769585,0.742538,0.713499,0.68235,0.648969,0.613237},
{-3.03233,-3.00628,-2.98019,-2.95406,-2.9279,-2.9017,-2.87546,-2.84918,-2.82286,-2.79651,-2.77011,-2.74368,-2.7172,-2.69068,-2.66412,-2.63751,-2.61085,-2.58415,-2.5574,-2.5306,-2.50375,-2.47684,-2.44988,-2.42286,-2.39579,-2.36865,-2.34144,-2.31418,-2.28684,-2.25943,-2.23195,-2.20439,-2.17675,-2.14903,-2.12122,-2.09333,-2.06534,-2.03726,-2.00908,-1.9808,-1.95241,-1.92391,-1.8953,-1.86657,-1.83771,-1.80873,-1.77963,-1.75038,-1.721,-1.69148,-1.6618,-1.63198,-1.602,-1.57186,-1.54156,-1.51108,-1.48044,-1.44962,-1.41861,-1.38743,-1.35605,-1.32448,-1.29272,-1.26076,-1.22861,-1.19625,-1.16368,-1.13092,-1.09794,-1.06476,-1.03137,-0.997781,-0.963984,-0.929986,-0.895789,-0.861397,-0.826815,-0.792047,-0.757102,-0.721985,-0.686707,-0.651276,-0.615703,-0.580001,-0.544182,-0.508261,-0.472255,-0.436179,-0.400051,-0.363891,-0.32772,-0.291559,-0.25543,-0.219357,-0.183364,-0.147477,-0.111722,-0.0761262,-0.0407161,-0.00551974,0.0294347,0.0641188,0.0985042,0.132562,0.166265,0.199585,0.232493,0.264963,0.296969,0.328484,0.359484,0.389944,0.419842,0.449156,0.477865,0.50595,0.533392,0.560176,0.586286,0.611708,0.63643,0.660442,0.683734,0.7063,0.728133,0.749229,0.769587,0.789204,0.808082,0.826223,0.84363,0.860308,0.876264,0.891506,0.906042,0.919883,0.93304,0.945525,0.957351,0.968531,0.979081,0.989015,0.99835,1.0071,1.01528,1.02291,1.03,1.03657,1.04264,1.04822,1.05332,1.05796,1.06215,1.06591,1.06925,1.07218,1.0747,1.07683,1.07857,1.07993,1.08092,1.08153,1.08177,1.08165,1.08114,1.08027,1.07901,1.07736,1.07531,1.07285,1.06996,1.06664,1.06285,1.05859,1.05382,1.04852,1.04265,1.0362,1.02912,1.02136,1.0129,1.00368,0.993658,0.982771,0.970965,0.958178,0.944342,0.929386,0.913232,0.8958,0.877003,0.856749,0.834941,0.811477,0.786251,0.75915,0.73006,0.698862,0.665434,0.629654},
{-3.0454,-3.01936,-2.99328,-2.96716,-2.941,-2.91481,-2.88858,-2.86231,-2.836,-2.80965,-2.78326,-2.75683,-2.73035,-2.70384,-2.67728,-2.65068,-2.62403,-2.59733,-2.57058,-2.54378,-2.51693,-2.49003,-2.46307,-2.43605,-2.40897,-2.38183,-2.35463,-2.32736,-2.30002,-2.27261,-2.24513,-2.21757,-2.18993,-2.1622,-2.13439,-2.10649,-2.0785,-2.05041,-2.02222,-1.99393,-1.96553,-1.93702,-1.90839,-1.87965,-1.85078,-1.82179,-1.79266,-1.7634,-1.73399,-1.70444,-1.67474,-1.64489,-1.61488,-1.58471,-1.55437,-1.52385,-1.49317,-1.4623,-1.43124,-1.4,-1.36857,-1.33694,-1.30511,-1.27308,-1.24085,-1.2084,-1.17575,-1.14289,-1.10981,-1.07652,-1.04302,-1.0093,-0.975375,-0.941237,-0.906891,-0.872341,-0.837591,-0.802645,-0.767511,-0.732195,-0.696706,-0.661052,-0.625245,-0.589295,-0.553216,-0.517022,-0.480729,-0.444352,-0.40791,-0.371421,-0.334907,-0.298388,-0.261887,-0.225428,-0.189035,-0.152734,-0.116551,-0.0805138,-0.0446495,-0.0089866,0.0264462,0.0616199,0.0965053,0.131073,0.165294,0.19914,0.232582,0.265591,0.298141,0.330204,0.361754,0.392766,0.423217,0.453082,0.482341,0.510973,0.538959,0.56628,0.592922,0.618869,0.644108,0.668627,0.692418,0.715471,0.737781,0.759342,0.780152,0.800209,0.819513,0.838065,0.85587,0.872932,0.889257,0.904853,0.919729,0.933894,0.947361,0.96014,0.972246,0.983693,0.994494,1.00467,1.01422,1.02318,1.03156,1.03937,1.04663,1.05336,1.05958,1.06529,1.07052,1.07527,1.07957,1.08342,1.08684,1.08983,1.09242,1.0946,1.09639,1.09779,1.09881,1.09944,1.0997,1.09958,1.09907,1.09819,1.09691,1.09524,1.09317,1.09067,1.08775,1.08438,1.08054,1.07622,1.07138,1.06601,1.06008,1.05354,1.04637,1.03853,1.02997,1.02065,1.01052,0.999526,0.987607,0.974701,0.960743,0.945661,0.929378,0.911813,0.892879,0.872485,0.850534,0.826924,0.801548,0.774294,0.745046,0.713686,0.68009,0.644136},
{-3.0583,-3.03226,-3.00619,-2.98008,-2.95393,-2.92775,-2.90152,-2.87526,-2.84896,-2.82261,-2.79623,-2.7698,-2.74334,-2.71683,-2.69027,-2.66367,-2.63703,-2.61033,-2.58359,-2.55679,-2.52994,-2.50304,-2.47608,-2.44907,-2.42199,-2.39485,-2.36765,-2.34038,-2.31304,-2.28563,-2.25814,-2.23058,-2.20294,-2.17521,-2.14739,-2.11949,-2.09149,-2.0634,-2.0352,-2.0069,-1.97849,-1.94997,-1.92133,-1.89258,-1.8637,-1.83468,-1.80554,-1.77626,-1.74683,-1.71726,-1.68754,-1.65766,-1.62762,-1.59741,-1.56704,-1.53649,-1.50576,-1.47485,-1.44375,-1.41245,-1.38096,-1.34928,-1.31738,-1.28528,-1.25297,-1.22045,-1.18771,-1.15476,-1.12158,-1.08819,-1.05457,-1.02074,-0.986681,-0.952407,-0.917916,-0.883212,-0.848298,-0.813179,-0.777861,-0.742351,-0.706656,-0.670785,-0.634748,-0.598556,-0.562223,-0.525761,-0.489187,-0.452515,-0.415764,-0.378953,-0.342101,-0.30523,-0.268363,-0.231524,-0.194736,-0.158026,-0.121421,-0.0849472,-0.0486335,-0.0125085,0.0233984,0.0590578,0.0944397,0.129514,0.164251,0.198621,0.232594,0.266141,0.299233,0.331844,0.363944,0.395509,0.426513,0.456932,0.486742,0.515923,0.544455,0.572317,0.599494,0.625969,0.651729,0.676761,0.701054,0.7246,0.747392,0.769423,0.79069,0.811192,0.830928,0.849898,0.868107,0.885558,0.902259,0.918215,0.933436,0.947932,0.961714,0.974795,0.987187,0.998906,1.00996,1.02038,1.03017,1.03934,1.04792,1.05592,1.06337,1.07026,1.07663,1.08248,1.08784,1.09271,1.09712,1.10107,1.10458,1.10766,1.11032,1.11257,1.11441,1.11586,1.11692,1.11759,1.11787,1.11777,1.11729,1.11641,1.11514,1.11347,1.11139,1.10888,1.10594,1.10255,1.09869,1.09434,1.08948,1.08407,1.0781,1.07153,1.06432,1.05643,1.04783,1.03847,1.02829,1.01725,1.00529,0.992341,0.978341,0.963218,0.946898,0.929298,0.910333,0.889911,0.867937,0.844307,0.818916,0.791653,0.7624,0.731038,0.697444,0.661493},
{-3.07102,-3.045,-3.01893,-2.99283,-2.96669,-2.94052,-2.9143,-2.88804,-2.86175,-2.83541,-2.80903,-2.78261,-2.75615,-2.72965,-2.7031,-2.6765,-2.64986,-2.62317,-2.59643,-2.56964,-2.54279,-2.51589,-2.48894,-2.46192,-2.43485,-2.40771,-2.38051,-2.35324,-2.3259,-2.29849,-2.271,-2.24344,-2.21579,-2.18806,-2.16024,-2.13233,-2.10433,-2.07623,-2.04803,-2.01972,-1.9913,-1.96277,-1.93412,-1.90536,-1.87646,-1.84744,-1.81828,-1.78898,-1.75953,-1.72994,-1.70019,-1.67029,-1.64022,-1.60999,-1.57958,-1.54899,-1.51822,-1.48727,-1.45612,-1.42478,-1.39324,-1.36149,-1.32954,-1.29737,-1.26499,-1.23239,-1.19957,-1.16653,-1.13326,-1.09976,-1.06604,-1.03208,-0.997905,-0.963499,-0.928868,-0.894015,-0.858942,-0.823655,-0.788158,-0.752458,-0.716562,-0.680479,-0.644219,-0.607791,-0.571209,-0.534485,-0.497635,-0.460675,-0.423621,-0.386493,-0.34931,-0.312094,-0.274867,-0.237653,-0.200477,-0.163364,-0.126341,-0.0894371,-0.0526793,-0.0160973,0.0202791,0.0564196,0.0922938,0.127871,0.16312,0.198011,0.232513,0.266595,0.300229,0.333385,0.366035,0.398152,0.429709,0.460681,0.491044,0.520775,0.549854,0.578259,0.605973,0.63298,0.659263,0.68481,0.70961,0.733652,0.756928,0.779433,0.801162,0.822112,0.842283,0.861676,0.880292,0.898137,0.915216,0.931536,0.947107,0.961937,0.976038,0.989423,1.00211,1.0141,1.02542,1.03608,1.0461,1.05549,1.06428,1.07247,1.08009,1.08715,1.09367,1.09967,1.10516,1.11015,1.11467,1.11872,1.12232,1.12548,1.12821,1.13052,1.13242,1.13391,1.13501,1.13571,1.13602,1.13593,1.13546,1.13459,1.13331,1.13163,1.12954,1.12702,1.12405,1.12063,1.11674,1.11235,1.10745,1.102,1.09598,1.08935,1.08209,1.07415,1.06549,1.05606,1.04582,1.03472,1.02269,1.00967,0.995606,0.980417,0.96403,0.946365,0.927335,0.906851,0.884815,0.861127,0.835678,0.808359,0.779051,0.747635,0.713987,0.677981},
{-3.08358,-3.05757,-3.03151,-3.00542,-2.97929,-2.95312,-2.92691,-2.90066,-2.87438,-2.84805,-2.82168,-2.79526,-2.76881,-2.74231,-2.71576,-2.68917,-2.66253,-2.63585,-2.60911,-2.58232,-2.55548,-2.52858,-2.50163,-2.47462,-2.44754,-2.42041,-2.39321,-2.36594,-2.3386,-2.31119,-2.2837,-2.25613,-2.22849,-2.20075,-2.17293,-2.14502,-2.11701,-2.08891,-2.0607,-2.03239,-2.00396,-1.97542,-1.94677,-1.91799,-1.88908,-1.86004,-1.83087,-1.80155,-1.77209,-1.74248,-1.71271,-1.68278,-1.65269,-1.62243,-1.59199,-1.56137,-1.53056,-1.49957,-1.46838,-1.43699,-1.4054,-1.37359,-1.34158,-1.30935,-1.2769,-1.24423,-1.21133,-1.1782,-1.14484,-1.11124,-1.07741,-1.04335,-1.00905,-0.974517,-0.93975,-0.904752,-0.869525,-0.834074,-0.798403,-0.762518,-0.726427,-0.690137,-0.653658,-0.617,-0.580174,-0.543194,-0.506075,-0.468831,-0.431481,-0.394042,-0.356534,-0.318978,-0.281397,-0.243814,-0.206255,-0.168745,-0.131311,-0.0939809,-0.056784,-0.0197499,0.0170914,0.0537088,0.0900714,0.126148,0.161906,0.197315,0.232343,0.266959,0.301132,0.334833,0.368032,0.400701,0.432811,0.464337,0.495254,0.525537,0.555165,0.584115,0.612369,0.63991,0.66672,0.692786,0.718096,0.742638,0.766404,0.789387,0.811582,0.832986,0.853598,0.873417,0.892447,0.91069,0.928153,0.944843,0.960767,0.975937,0.990363,1.00406,1.01703,1.02931,1.04089,1.0518,1.06206,1.07167,1.08067,1.08906,1.09686,1.1041,1.11078,1.11692,1.12254,1.12766,1.13229,1.13645,1.14014,1.14339,1.1462,1.14858,1.15053,1.15208,1.15322,1.15396,1.1543,1.15424,1.15379,1.15293,1.15166,1.14999,1.14789,1.14536,1.14239,1.13895,1.13504,1.13064,1.12571,1.12023,1.11418,1.10753,1.10023,1.09226,1.08357,1.07411,1.06384,1.0527,1.04064,1.0276,1.0135,0.998293,0.981887,0.964207,0.945168,0.924678,0.902643,0.87896,0.853524,0.826221,0.796937,0.765549,0.731932,0.695961},
{-3.09598,-3.06998,-3.04393,-3.01785,-2.99173,-2.96557,-2.93937,-2.91313,-2.88685,-2.86052,-2.83416,-2.80775,-2.7813,-2.75481,-2.72827,-2.70168,-2.67505,-2.64837,-2.62163,-2.59485,-2.56801,-2.54112,-2.51417,-2.48716,-2.46009,-2.43295,-2.40575,-2.37849,-2.35115,-2.32374,-2.29625,-2.26868,-2.24103,-2.2133,-2.18547,-2.15756,-2.12955,-2.10144,-2.07323,-2.04491,-2.01648,-1.98793,-1.95927,-1.93048,-1.90156,-1.87251,-1.84332,-1.81399,-1.78451,-1.75488,-1.72509,-1.69514,-1.66503,-1.63474,-1.60427,-1.57362,-1.54278,-1.51175,-1.48051,-1.44908,-1.41744,-1.38559,-1.35352,-1.32123,-1.28871,-1.25597,-1.22299,-1.18978,-1.15633,-1.12264,-1.08871,-1.05454,-1.02012,-0.985466,-0.950567,-0.915428,-0.880051,-0.844441,-0.808601,-0.772537,-0.736256,-0.699764,-0.663072,-0.626188,-0.589125,-0.551895,-0.514512,-0.476992,-0.43935,-0.401607,-0.36378,-0.325891,-0.287962,-0.250017,-0.21208,-0.174179,-0.136339,-0.0985894,-0.0609591,-0.0234781,0.0138229,0.0509125,0.0877589,0.12433,0.160593,0.196517,0.232068,0.267215,0.301926,0.336169,0.369915,0.403135,0.435798,0.467878,0.499348,0.530184,0.560361,0.589858,0.618654,0.64673,0.674069,0.700657,0.726479,0.751524,0.775782,0.799247,0.821911,0.843772,0.864827,0.885077,0.904523,0.923168,0.941018,0.95808,0.974362,0.989873,1.00463,1.01863,1.03191,1.04446,1.05631,1.06747,1.07797,1.08781,1.09701,1.1056,1.11358,1.12099,1.12783,1.13412,1.13987,1.14512,1.14986,1.15412,1.1579,1.16123,1.16411,1.16655,1.16856,1.17015,1.17133,1.1721,1.17246,1.17242,1.17197,1.17112,1.16985,1.16816,1.16605,1.16349,1.16049,1.15703,1.15308,1.14863,1.14366,1.13813,1.13203,1.12532,1.11796,1.10992,1.10116,1.09163,1.08129,1.07008,1.05794,1.04482,1.03066,1.01537,0.998882,0.981124,0.962006,0.941439,0.919326,0.895566,0.870052,0.842672,0.81331,0.781841,0.748142,0.712084},
{-3.10822,-3.08223,-3.0562,-3.03012,-3.00401,-2.97786,-2.95167,-2.92543,-2.89916,-2.87284,-2.84649,-2.82009,-2.79364,-2.76715,-2.74062,-2.71404,-2.68741,-2.66073,-2.634,-2.60722,-2.58039,-2.5535,-2.52655,-2.49955,-2.47248,-2.44535,-2.41815,-2.39088,-2.36354,-2.33613,-2.30865,-2.28108,-2.25343,-2.2257,-2.19787,-2.16995,-2.14194,-2.11383,-2.08561,-2.05729,-2.02885,-2.0003,-1.97163,-1.94283,-1.9139,-1.88484,-1.85564,-1.8263,-1.7968,-1.76716,-1.73735,-1.70738,-1.67724,-1.64692,-1.61643,-1.58575,-1.55487,-1.52381,-1.49254,-1.46106,-1.42938,-1.39747,-1.36535,-1.333,-1.30042,-1.26761,-1.23456,-1.20127,-1.16773,-1.13396,-1.09993,-1.06565,-1.03112,-0.996348,-0.961321,-0.926046,-0.890524,-0.854759,-0.818755,-0.782517,-0.74605,-0.709362,-0.672462,-0.635359,-0.598064,-0.560589,-0.522948,-0.485157,-0.447231,-0.409188,-0.371048,-0.332831,-0.294561,-0.256259,-0.217952,-0.179665,-0.141425,-0.103261,-0.065203,-0.0272803,0.0104754,0.0480324,0.0853582,0.12242,0.159185,0.19562,0.231691,0.267366,0.302612,0.337397,0.371689,0.405458,0.438674,0.471307,0.503332,0.534721,0.565449,0.595494,0.624833,0.653448,0.681319,0.70843,0.734768,0.760319,0.785074,0.809023,0.832161,0.854483,0.875986,0.89667,0.916536,0.935587,0.953829,0.971267,0.98791,1.00377,1.01885,1.03317,1.04675,1.05959,1.07171,1.08313,1.09386,1.10393,1.11335,1.12213,1.1303,1.13788,1.14488,1.15131,1.15721,1.16258,1.16743,1.17179,1.17567,1.17908,1.18203,1.18454,1.18661,1.18825,1.18946,1.19026,1.19065,1.19062,1.19018,1.18933,1.18806,1.18636,1.18423,1.18166,1.17863,1.17514,1.17115,1.16666,1.16164,1.15607,1.14991,1.14315,1.13573,1.12763,1.11881,1.10921,1.0988,1.08752,1.07532,1.06212,1.04788,1.03252,1.01596,0.998133,0.978943,0.958304,0.93612,0.912289,0.886705,0.859254,0.829819,0.798278,0.764502,0.728362},
{-3.12031,-3.09433,-3.06831,-3.04224,-3.01614,-2.99,-2.96381,-2.93759,-2.91132,-2.88501,-2.85866,-2.83227,-2.80583,-2.77935,-2.75282,-2.72624,-2.69962,-2.67295,-2.64622,-2.61945,-2.59262,-2.56573,-2.53879,-2.51179,-2.48472,-2.45759,-2.4304,-2.40313,-2.3758,-2.34839,-2.3209,-2.29333,-2.26569,-2.23795,-2.21012,-2.18221,-2.15419,-2.12608,-2.09786,-2.06953,-2.04109,-2.01253,-1.98385,-1.95505,-1.92611,-1.89704,-1.86783,-1.83847,-1.80896,-1.7793,-1.74948,-1.71949,-1.68933,-1.65899,-1.62847,-1.59776,-1.56686,-1.53576,-1.50445,-1.47293,-1.4412,-1.40925,-1.37708,-1.34467,-1.31204,-1.27916,-1.24604,-1.21267,-1.17906,-1.14519,-1.11107,-1.07669,-1.04206,-1.00717,-0.972015,-0.936608,-0.900946,-0.865031,-0.828867,-0.792459,-0.755812,-0.718933,-0.681831,-0.644513,-0.606991,-0.569278,-0.531385,-0.493328,-0.455123,-0.416787,-0.37834,-0.339802,-0.301195,-0.262543,-0.223871,-0.185204,-0.146569,-0.107997,-0.0695158,-0.0311566,0.00704912,0.045069,0.08287,0.120419,0.157681,0.194624,0.231213,0.267414,0.303193,0.338517,0.373354,0.407672,0.44144,0.474628,0.507207,0.53915,0.570431,0.601025,0.630911,0.660066,0.688472,0.716111,0.742968,0.769029,0.794284,0.818723,0.842338,0.865126,0.887081,0.908205,0.928496,0.947959,0.966597,0.984417,1.00143,1.01764,1.03306,1.0477,1.06158,1.07471,1.0871,1.09879,1.10977,1.12006,1.1297,1.13869,1.14705,1.15481,1.16197,1.16856,1.1746,1.18009,1.18507,1.18954,1.19351,1.19701,1.20004,1.20262,1.20475,1.20644,1.20771,1.20854,1.20896,1.20896,1.20854,1.2077,1.20643,1.20474,1.20261,1.20003,1.19699,1.19348,1.18947,1.18496,1.17992,1.17431,1.16813,1.16133,1.15388,1.14575,1.13689,1.12726,1.11681,1.1055,1.09326,1.08004,1.06577,1.05038,1.0338,1.01595,0.996744,0.976094,0.953903,0.93007,0.904488,0.877043,0.847618,0.816088,0.782325,0.746197},
{-3.13225,-3.10628,-3.08027,-3.05421,-3.02812,-3.00199,-2.97581,-2.94959,-2.92333,-2.89703,-2.87069,-2.8443,-2.81787,-2.7914,-2.76487,-2.73831,-2.71169,-2.68502,-2.6583,-2.63153,-2.6047,-2.57782,-2.55088,-2.52388,-2.49682,-2.46969,-2.4425,-2.41524,-2.38791,-2.3605,-2.33301,-2.30545,-2.2778,-2.25007,-2.22224,-2.19432,-2.16631,-2.13819,-2.10997,-2.08163,-2.05319,-2.02463,-1.99594,-1.96713,-1.93819,-1.90911,-1.87989,-1.85052,-1.821,-1.79132,-1.76149,-1.73148,-1.7013,-1.67094,-1.64039,-1.60966,-1.57873,-1.54759,-1.51625,-1.4847,-1.45293,-1.42094,-1.38871,-1.35625,-1.32356,-1.29062,-1.25743,-1.224,-1.1903,-1.15635,-1.12214,-1.08767,-1.05293,-1.01792,-0.982653,-0.947119,-0.91132,-0.87526,-0.838941,-0.802368,-0.765546,-0.728481,-0.691181,-0.653654,-0.615912,-0.577964,-0.539825,-0.501508,-0.46303,-0.424407,-0.385659,-0.346805,-0.307868,-0.268872,-0.22984,-0.190798,-0.151776,-0.1128,-0.0739013,-0.0351106,0.00354019,0.0420182,0.0802901,0.118322,0.156079,0.193526,0.230629,0.267353,0.303663,0.339525,0.374906,0.409772,0.444091,0.477833,0.510968,0.543466,0.575301,0.606447,0.63688,0.666579,0.695522,0.723691,0.751071,0.777647,0.803406,0.828338,0.852436,0.875694,0.898107,0.919675,0.940397,0.960275,0.979315,0.997522,1.0149,1.03147,1.04723,1.0622,1.07639,1.08982,1.10249,1.11444,1.12567,1.13621,1.14607,1.15527,1.16383,1.17176,1.1791,1.18585,1.19203,1.19766,1.20276,1.20734,1.21142,1.21502,1.21813,1.22079,1.22299,1.22474,1.22606,1.22695,1.2274,1.22744,1.22705,1.22623,1.22498,1.2233,1.22118,1.21861,1.21557,1.21206,1.20805,1.20354,1.19849,1.19288,1.18668,1.17988,1.17242,1.16428,1.15542,1.14578,1.13534,1.12403,1.1118,1.09859,1.08433,1.06897,1.05242,1.0346,1.01544,0.994842,0.972712,0.948947,0.923442,0.896083,0.866751,0.835321,0.801665,0.765647},
{-3.14404,-3.11808,-3.09208,-3.06604,-3.03995,-3.01383,-2.98766,-2.96145,-2.9352,-2.90891,-2.88258,-2.8562,-2.82977,-2.8033,-2.77679,-2.75022,-2.72361,-2.69695,-2.67023,-2.64347,-2.61665,-2.58977,-2.56283,-2.53584,-2.50878,-2.48166,-2.45447,-2.42721,-2.39988,-2.37247,-2.34499,-2.31743,-2.28978,-2.26205,-2.23422,-2.2063,-2.17829,-2.15017,-2.12194,-2.09361,-2.06516,-2.0366,-2.00791,-1.97909,-1.95014,-1.92105,-1.89182,-1.86245,-1.83292,-1.80323,-1.77337,-1.74335,-1.71315,-1.68277,-1.65221,-1.62145,-1.59049,-1.55933,-1.52796,-1.49637,-1.46456,-1.43252,-1.40025,-1.36774,-1.33499,-1.302,-1.26874,-1.23524,-1.20147,-1.16744,-1.13314,-1.09857,-1.06373,-1.02862,-0.993238,-0.95758,-0.921649,-0.885448,-0.848979,-0.812246,-0.775253,-0.738008,-0.700515,-0.662785,-0.624827,-0.586651,-0.548271,-0.5097,-0.470954,-0.43205,-0.393007,-0.353844,-0.314583,-0.275247,-0.235861,-0.196452,-0.157046,-0.117672,-0.0783612,-0.0391441,-5.30919e-05,0.0388786,0.0776169,0.116127,0.154375,0.192323,0.229938,0.267182,0.304021,0.34042,0.376342,0.411756,0.446627,0.480923,0.514613,0.547667,0.580058,0.611757,0.642741,0.672985,0.702469,0.731173,0.759079,0.786173,0.81244,0.837871,0.862456,0.886189,0.909065,0.931083,0.952241,0.972542,0.991989,1.01059,1.02835,1.04528,1.06139,1.07669,1.0912,1.10492,1.11789,1.13011,1.1416,1.15238,1.16247,1.17188,1.18064,1.18877,1.19628,1.2032,1.20953,1.21531,1.22054,1.22525,1.22944,1.23314,1.23635,1.23909,1.24137,1.2432,1.24459,1.24553,1.24604,1.24613,1.24578,1.245,1.24379,1.24214,1.24005,1.2375,1.2345,1.23101,1.22703,1.22253,1.21751,1.21193,1.20576,1.19898,1.19156,1.18345,1.17463,1.16505,1.15465,1.1434,1.13124,1.1181,1.10394,1.08867,1.07223,1.05453,1.0355,1.01505,0.993083,0.969495,0.944182,0.917031,0.887922,0.85673,0.823325,0.787571},
{-3.1557,-3.12975,-3.10375,-3.07772,-3.05165,-3.02553,-2.99937,-2.97317,-2.94693,-2.92065,-2.89432,-2.86795,-2.84153,-2.81507,-2.78856,-2.762,-2.73539,-2.70874,-2.68203,-2.65527,-2.62845,-2.60158,-2.57465,-2.54766,-2.5206,-2.49349,-2.4663,-2.43904,-2.41172,-2.38431,-2.35683,-2.32927,-2.30163,-2.27389,-2.24607,-2.21815,-2.19013,-2.16202,-2.13379,-2.10546,-2.07701,-2.04844,-2.01974,-1.99092,-1.96197,-1.93288,-1.90364,-1.87425,-1.84471,-1.81501,-1.78515,-1.75511,-1.72489,-1.6945,-1.66391,-1.63313,-1.60215,-1.57096,-1.53956,-1.50793,-1.47609,-1.44401,-1.4117,-1.37914,-1.34634,-1.31329,-1.27998,-1.24641,-1.21257,-1.17846,-1.14408,-1.10942,-1.07449,-1.03927,-1.00377,-0.967997,-0.931939,-0.895602,-0.858988,-0.822099,-0.784942,-0.74752,-0.709841,-0.671913,-0.633744,-0.595346,-0.556731,-0.517913,-0.478905,-0.439726,-0.400393,-0.360927,-0.321348,-0.281679,-0.241946,-0.202174,-0.162391,-0.122626,-0.0829086,-0.0432709,-0.00374522,0.0356347,0.0748345,0.113819,0.152552,0.190998,0.22912,0.266882,0.304246,0.341178,0.377641,0.4136,0.449021,0.48387,0.518115,0.551726,0.584672,0.616925,0.64846,0.679252,0.709278,0.738518,0.766953,0.794567,0.821346,0.847278,0.872353,0.896565,0.919907,0.942377,0.963975,0.984702,1.00456,1.02356,1.0417,1.05899,1.07545,1.09109,1.10592,1.11995,1.13321,1.1457,1.15745,1.16848,1.1788,1.18843,1.1974,1.20571,1.21341,1.22049,1.22698,1.2329,1.23827,1.24309,1.2474,1.2512,1.25451,1.25734,1.25969,1.26159,1.26304,1.26404,1.2646,1.26473,1.26443,1.26368,1.26251,1.26089,1.25882,1.2563,1.25331,1.24984,1.24587,1.2414,1.23639,1.23082,1.22467,1.21791,1.21051,1.20243,1.19364,1.18409,1.17373,1.16252,1.15041,1.13733,1.12323,1.10804,1.09168,1.07408,1.05516,1.03483,1.01299,0.989544,0.964387,0.937404,0.908476,0.877477,0.844275,0.808732},
{-3.16721,-3.14127,-3.11529,-3.08927,-3.0632,-3.0371,-3.01095,-2.98476,-2.95852,-2.93225,-2.90593,-2.87956,-2.85315,-2.8267,-2.80019,-2.77364,-2.74704,-2.72039,-2.69369,-2.66693,-2.64012,-2.61326,-2.58633,-2.55934,-2.53229,-2.50518,-2.478,-2.45075,-2.42342,-2.39602,-2.36854,-2.34099,-2.31334,-2.28561,-2.25779,-2.22987,-2.20186,-2.17374,-2.14551,-2.11718,-2.08873,-2.06016,-2.03146,-2.00264,-1.97368,-1.94458,-1.91534,-1.88594,-1.85639,-1.82668,-1.79681,-1.76676,-1.73653,-1.70611,-1.67551,-1.64471,-1.6137,-1.58249,-1.55106,-1.51941,-1.48753,-1.45542,-1.42306,-1.39046,-1.35761,-1.32451,-1.29114,-1.2575,-1.2236,-1.18942,-1.15496,-1.12021,-1.08519,-1.04987,-1.01427,-0.97838,-0.9422,-0.905732,-0.868977,-0.83194,-0.794623,-0.757031,-0.719172,-0.681052,-0.64268,-0.604067,-0.565223,-0.526164,-0.486902,-0.447455,-0.407841,-0.368078,-0.328189,-0.288196,-0.248123,-0.207997,-0.167845,-0.127696,-0.0875803,-0.0475297,-0.00757714,0.0322435,0.0718971,0.111348,0.15056,0.189496,0.228119,0.266392,0.304276,0.341735,0.378733,0.415232,0.451198,0.486595,0.521391,0.555553,0.589051,0.621855,0.653937,0.685273,0.715838,0.745611,0.774572,0.802703,0.829991,0.856421,0.881983,0.90667,0.930475,0.953395,0.975428,0.996575,1.01684,1.03623,1.05474,1.0724,1.0892,1.10517,1.12031,1.13464,1.14817,1.16093,1.17292,1.18418,1.19472,1.20455,1.21371,1.2222,1.23004,1.23727,1.24389,1.24993,1.2554,1.26032,1.2647,1.26857,1.27193,1.2748,1.27719,1.27911,1.28057,1.28157,1.28212,1.28223,1.28189,1.28111,1.27988,1.2782,1.27606,1.27346,1.27038,1.26682,1.26274,1.25815,1.25301,1.24731,1.24102,1.2341,1.22653,1.21828,1.2093,1.19955,1.18898,1.17755,1.16521,1.15188,1.13752,1.12206,1.10541,1.08751,1.06827,1.0476,1.0254,1.00158,0.976024,0.948616,0.919234,0.88775,0.85403,0.817932},
{-3.17858,-3.15266,-3.12669,-3.10067,-3.07462,-3.04852,-3.02239,-2.9962,-2.96998,-2.94371,-2.9174,-2.89104,-2.86464,-2.83819,-2.8117,-2.78515,-2.75856,-2.73191,-2.70522,-2.67847,-2.65166,-2.6248,-2.59788,-2.5709,-2.54385,-2.51674,-2.48957,-2.46232,-2.435,-2.4076,-2.38013,-2.35257,-2.32493,-2.2972,-2.26938,-2.24147,-2.21346,-2.18534,-2.15711,-2.12878,-2.10033,-2.07176,-2.04306,-2.01423,-1.98527,-1.95617,-1.92692,-1.89752,-1.86796,-1.83825,-1.80836,-1.7783,-1.74806,-1.71763,-1.68701,-1.65619,-1.62516,-1.59392,-1.56247,-1.53079,-1.49888,-1.46673,-1.43434,-1.4017,-1.3688,-1.33565,-1.30223,-1.26853,-1.23456,-1.20031,-1.16577,-1.13095,-1.09584,-1.06043,-1.02472,-0.98872,-0.952421,-0.915826,-0.878936,-0.841753,-0.804281,-0.766524,-0.728489,-0.690182,-0.651611,-0.612787,-0.573721,-0.534425,-0.494914,-0.455204,-0.415313,-0.37526,-0.335065,-0.294752,-0.254344,-0.213868,-0.173351,-0.132822,-0.0923118,-0.0518521,-0.011476,0.0287822,0.0688871,0.108802,0.148491,0.187916,0.227039,0.265821,0.304225,0.342212,0.379745,0.416786,0.453299,0.489247,0.524597,0.559315,0.593369,0.626728,0.659364,0.691249,0.72236,0.752673,0.782168,0.810826,0.83863,0.865568,0.891628,0.916801,0.941079,0.96446,0.986941,1.00852,1.02921,1.049,1.06791,1.08594,1.1031,1.11941,1.13488,1.14952,1.16335,1.17639,1.18866,1.20017,1.21094,1.221,1.23037,1.23906,1.24709,1.25449,1.26127,1.26746,1.27307,1.27812,1.28262,1.2866,1.29006,1.29302,1.2955,1.2975,1.29902,1.30009,1.3007,1.30086,1.30058,1.29984,1.29865,1.29701,1.29491,1.29234,1.28929,1.28576,1.28172,1.27716,1.27205,1.26638,1.26013,1.25325,1.24572,1.23752,1.22859,1.2189,1.2084,1.19704,1.18478,1.17155,1.15729,1.14193,1.12541,1.10765,1.08856,1.06805,1.04604,1.02241,0.997062,0.969878,0.940735,0.909504,0.876047,0.840223},
{-3.18982,-3.16391,-3.13795,-3.11195,-3.08591,-3.05982,-3.03369,-3.00752,-2.9813,-2.95505,-2.92874,-2.90239,-2.876,-2.84956,-2.82307,-2.79653,-2.76995,-2.74331,-2.71662,-2.68987,-2.66307,-2.63622,-2.6093,-2.58233,-2.55529,-2.52818,-2.50101,-2.47377,-2.44645,-2.41906,-2.39159,-2.36404,-2.3364,-2.30868,-2.28086,-2.25295,-2.22493,-2.19682,-2.1686,-2.14026,-2.11181,-2.08324,-2.05454,-2.02571,-1.99675,-1.96764,-1.93839,-1.90899,-1.87942,-1.8497,-1.8198,-1.78973,-1.75948,-1.72904,-1.69841,-1.66757,-1.63653,-1.60527,-1.57379,-1.54208,-1.51014,-1.47796,-1.44554,-1.41286,-1.37992,-1.34672,-1.31324,-1.27949,-1.24546,-1.21115,-1.17654,-1.14164,-1.10644,-1.07094,-1.03513,-0.999027,-0.962615,-0.925898,-0.888877,-0.851554,-0.813932,-0.776016,-0.73781,-0.699321,-0.660558,-0.621529,-0.582246,-0.54272,-0.502966,-0.463,-0.422838,-0.382501,-0.342007,-0.30138,-0.260644,-0.219825,-0.17895,-0.138048,-0.0971496,-0.0562871,-0.0154936,0.0251961,0.0657463,0.10612,0.146281,0.186189,0.225807,0.265095,0.304014,0.342526,0.380591,0.41817,0.455228,0.491725,0.527627,0.562899,0.597508,0.631422,0.664611,0.697048,0.728705,0.759559,0.789589,0.818774,0.847098,0.874545,0.901104,0.926765,0.95152,0.975365,0.998296,1.02031,1.04142,1.06162,1.08092,1.09933,1.11685,1.13351,1.14931,1.16426,1.1784,1.19172,1.20426,1.21602,1.22704,1.23732,1.2469,1.25579,1.26401,1.27158,1.27852,1.28486,1.2906,1.29578,1.3004,1.30448,1.30804,1.31109,1.31365,1.31572,1.31731,1.31844,1.3191,1.31931,1.31906,1.31836,1.3172,1.31559,1.31351,1.31097,1.30794,1.30442,1.3004,1.29585,1.29076,1.28511,1.27886,1.27201,1.2645,1.25632,1.24741,1.23775,1.22729,1.21597,1.20376,1.19058,1.17638,1.1611,1.14465,1.12698,1.10798,1.08759,1.06569,1.04219,1.01697,0.989935,0.960946,0.929875,0.896584,0.860928},
{-3.20094,-3.17503,-3.14909,-3.1231,-3.09707,-3.07099,-3.04487,-3.01871,-2.9925,-2.96625,-2.93996,-2.91361,-2.88723,-2.8608,-2.83431,-2.80778,-2.7812,-2.75457,-2.72789,-2.70115,-2.67436,-2.64751,-2.6206,-2.59363,-2.5666,-2.5395,-2.51233,-2.48509,-2.45778,-2.43039,-2.40293,-2.37538,-2.34775,-2.32003,-2.29221,-2.2643,-2.23629,-2.20818,-2.17996,-2.15163,-2.12318,-2.09461,-2.06591,-2.03708,-2.00812,-1.97901,-1.94975,-1.92035,-1.89078,-1.86105,-1.83115,-1.80107,-1.77081,-1.74036,-1.70971,-1.67886,-1.6478,-1.61652,-1.58502,-1.55329,-1.52132,-1.48912,-1.45666,-1.42394,-1.39096,-1.35772,-1.3242,-1.29039,-1.25631,-1.22193,-1.18725,-1.15227,-1.11699,-1.08141,-1.04551,-1.0093,-0.972782,-0.935948,-0.898801,-0.861343,-0.823577,-0.785506,-0.747135,-0.70847,-0.66952,-0.630292,-0.590797,-0.551048,-0.511057,-0.47084,-0.430415,-0.389799,-0.349012,-0.308078,-0.26702,-0.225864,-0.184637,-0.143368,-0.102087,-0.0608274,-0.0196222,0.0214937,0.0624842,0.103312,0.143939,0.184327,0.224436,0.264227,0.303658,0.342691,0.381286,0.419403,0.457003,0.494048,0.530502,0.566329,0.601493,0.635963,0.669707,0.702696,0.734902,0.7663,0.796867,0.826583,0.85543,0.883391,0.910454,0.936608,0.961845,0.986158,1.00955,1.03201,1.05354,1.07415,1.09385,1.11264,1.13054,1.14754,1.16368,1.17896,1.1934,1.20702,1.21983,1.23186,1.24312,1.25364,1.26343,1.27253,1.28094,1.28869,1.29581,1.3023,1.30819,1.31351,1.31825,1.32246,1.32612,1.32928,1.33193,1.33408,1.33575,1.33695,1.33769,1.33796,1.33777,1.33712,1.33602,1.33446,1.33243,1.32993,1.32695,1.32348,1.3195,1.315,1.30996,1.30437,1.29818,1.29139,1.28395,1.27584,1.26701,1.25744,1.24707,1.23586,1.22376,1.21071,1.19666,1.18153,1.16525,1.14776,1.12897,1.10878,1.08712,1.06387,1.03893,1.01217,0.983488,0.952737,0.91978,0.88447},
{-3.21192,-3.18603,-3.1601,-3.13412,-3.1081,-3.08203,-3.05592,-3.02977,-3.00357,-2.97733,-2.95104,-2.92471,-2.89833,-2.87191,-2.84544,-2.81891,-2.79234,-2.76572,-2.73904,-2.71231,-2.68552,-2.65868,-2.63178,-2.60481,-2.57778,-2.55069,-2.52353,-2.4963,-2.46899,-2.44161,-2.41415,-2.3866,-2.35898,-2.33126,-2.30345,-2.27554,-2.24754,-2.21943,-2.19121,-2.16288,-2.13443,-2.10586,-2.07717,-2.04834,-2.01937,-1.99027,-1.96101,-1.9316,-1.90203,-1.8723,-1.84239,-1.81231,-1.78204,-1.75158,-1.72092,-1.69005,-1.65898,-1.62769,-1.59617,-1.56442,-1.53243,-1.50019,-1.4677,-1.43495,-1.40194,-1.36865,-1.33509,-1.30124,-1.26709,-1.23266,-1.19792,-1.16287,-1.12751,-1.09185,-1.05586,-1.01956,-0.98293,-0.945984,-0.908716,-0.871129,-0.833223,-0.795004,-0.756474,-0.717639,-0.678508,-0.639087,-0.599388,-0.559421,-0.519201,-0.47874,-0.438058,-0.39717,-0.356099,-0.314865,-0.273492,-0.232006,-0.190434,-0.148805,-0.107149,-0.0654997,-0.0238897,0.0176456,0.0590696,0.100345,0.141433,0.182294,0.222888,0.263175,0.303114,0.342664,0.381784,0.420434,0.458573,0.496164,0.533166,0.569545,0.605263,0.640287,0.674584,0.708123,0.740877,0.772819,0.803924,0.834171,0.863541,0.892017,0.919584,0.946231,0.97195,0.996733,1.02058,1.04348,1.06544,1.08647,1.10657,1.12574,1.14401,1.16137,1.17784,1.19344,1.20819,1.22209,1.23518,1.24747,1.25898,1.26973,1.27974,1.28904,1.29764,1.30557,1.31284,1.31949,1.32552,1.33096,1.33583,1.34014,1.34391,1.34715,1.34988,1.35211,1.35385,1.3551,1.35589,1.35621,1.35606,1.35545,1.35438,1.35284,1.35083,1.34835,1.34539,1.34193,1.33797,1.33349,1.32846,1.32287,1.3167,1.30992,1.3025,1.2944,1.2856,1.27605,1.26571,1.25454,1.24248,1.22947,1.21547,1.2004,1.18419,1.16677,1.14805,1.12796,1.10639,1.08325,1.05841,1.03178,1.00321,0.972581,0.939746,0.904553},
{-3.22278,-3.1969,-3.17098,-3.14501,-3.119,-3.09295,-3.06685,-3.04071,-3.01452,-2.98829,-2.96201,-2.93569,-2.90932,-2.8829,-2.85644,-2.82992,-2.80336,-2.77674,-2.75007,-2.72335,-2.69657,-2.66973,-2.64283,-2.61588,-2.58885,-2.56177,-2.53461,-2.50738,-2.48008,-2.45271,-2.42525,-2.39771,-2.37009,-2.34238,-2.31457,-2.28667,-2.25867,-2.23057,-2.20235,-2.17403,-2.14558,-2.11701,-2.08832,-2.05949,-2.03053,-2.00142,-1.97217,-1.94276,-1.91319,-1.88345,-1.85354,-1.82345,-1.79317,-1.7627,-1.73204,-1.70116,-1.67008,-1.63877,-1.60723,-1.57546,-1.54345,-1.51119,-1.47868,-1.4459,-1.41285,-1.37953,-1.34592,-1.31202,-1.27783,-1.24334,-1.20854,-1.17342,-1.138,-1.10225,-1.06618,-1.02978,-0.993057,-0.956004,-0.91862,-0.880908,-0.842869,-0.804505,-0.765822,-0.726823,-0.687516,-0.647908,-0.60801,-0.567831,-0.527386,-0.486689,-0.445755,-0.404602,-0.363251,-0.321723,-0.280041,-0.238231,-0.19632,-0.154336,-0.112311,-0.070277,-0.0282673,0.0136825,0.0555355,0.0972538,0.138798,0.180129,0.221206,0.261987,0.30243,0.342495,0.382139,0.421321,0.459999,0.498134,0.535686,0.572617,0.608891,0.64447,0.679323,0.713417,0.746723,0.779212,0.81086,0.841643,0.871542,0.900538,0.928617,0.955765,0.981973,1.00723,1.03154,1.0549,1.0773,1.09875,1.11926,1.13883,1.15747,1.17519,1.19202,1.20795,1.22301,1.23722,1.2506,1.26316,1.27493,1.28593,1.29617,1.30569,1.3145,1.32262,1.33008,1.3369,1.3431,1.34869,1.3537,1.35814,1.36204,1.3654,1.36824,1.37057,1.37241,1.37377,1.37464,1.37505,1.37498,1.37446,1.37347,1.37201,1.37009,1.36769,1.36481,1.36145,1.35757,1.35318,1.34826,1.34277,1.33672,1.33005,1.32276,1.31481,1.30616,1.29677,1.28661,1.27563,1.26378,1.251,1.23724,1.22243,1.20651,1.1894,1.17102,1.15129,1.1301,1.10737,1.08298,1.05681,1.02874,0.998637,0.966352,0.931735},
{-3.23352,-3.20766,-3.18175,-3.15579,-3.12979,-3.10375,-3.07766,-3.05153,-3.02535,-2.99913,-2.97286,-2.94654,-2.92018,-2.89377,-2.86732,-2.84081,-2.81425,-2.78764,-2.76098,-2.73427,-2.70749,-2.68066,-2.65377,-2.62682,-2.59981,-2.57273,-2.54558,-2.51836,-2.49106,-2.46369,-2.43624,-2.40871,-2.38109,-2.35339,-2.32559,-2.29769,-2.2697,-2.24159,-2.21339,-2.18506,-2.15662,-2.12806,-2.09937,-2.07054,-2.04158,-2.01248,-1.98322,-1.95381,-1.92424,-1.8945,-1.86459,-1.8345,-1.80422,-1.77374,-1.74307,-1.71219,-1.68109,-1.64977,-1.61822,-1.58643,-1.5544,-1.52212,-1.48958,-1.45678,-1.4237,-1.39034,-1.3567,-1.32276,-1.28852,-1.25397,-1.21912,-1.18394,-1.14845,-1.11263,-1.07648,-1.03999,-1.00318,-0.96602,-0.928526,-0.890695,-0.852528,-0.814027,-0.775196,-0.736039,-0.696564,-0.656776,-0.616686,-0.576303,-0.535642,-0.494714,-0.453536,-0.412127,-0.370504,-0.32869,-0.286707,-0.244582,-0.20234,-0.160011,-0.117624,-0.0752137,-0.0328126,0.00954332,0.0518172,0.0939706,0.135964,0.177757,0.219308,0.260576,0.301517,0.34209,0.382252,0.421959,0.461171,0.499845,0.537942,0.575421,0.612245,0.648377,0.683782,0.718427,0.752281,0.785315,0.817502,0.84882,0.879245,0.908759,0.937347,0.964994,0.991689,1.01743,1.0422,1.066,1.08884,1.11071,1.13162,1.15158,1.1706,1.18869,1.20585,1.22212,1.23749,1.252,1.26566,1.27849,1.29051,1.30174,1.31221,1.32193,1.33093,1.33924,1.34687,1.35384,1.36018,1.36591,1.37104,1.3756,1.37959,1.38305,1.38598,1.38839,1.3903,1.39171,1.39264,1.3931,1.39308,1.39259,1.39164,1.39021,1.38831,1.38594,1.38309,1.37974,1.37588,1.37151,1.3666,1.36114,1.3551,1.34846,1.34119,1.33326,1.32464,1.31528,1.30516,1.29422,1.28241,1.26969,1.25598,1.24124,1.22539,1.20836,1.19007,1.17043,1.14934,1.12672,1.10243,1.07638,1.04843,1.01843,0.986259,0.951743},
{-3.24414,-3.21829,-3.19239,-3.16645,-3.14046,-3.11443,-3.08835,-3.06223,-3.03606,-3.00985,-2.98359,-2.95728,-2.93093,-2.90453,-2.87808,-2.85158,-2.82503,-2.79843,-2.77178,-2.74507,-2.71831,-2.69148,-2.6646,-2.63766,-2.61065,-2.58357,-2.55643,-2.52922,-2.50193,-2.47457,-2.44712,-2.4196,-2.39199,-2.36429,-2.33649,-2.3086,-2.28061,-2.25252,-2.22431,-2.196,-2.16756,-2.139,-2.11032,-2.0815,-2.05254,-2.02343,-1.99418,-1.96477,-1.9352,-1.90546,-1.87555,-1.84546,-1.81517,-1.7847,-1.75402,-1.72313,-1.69202,-1.66069,-1.62913,-1.59733,-1.56529,-1.53299,-1.50043,-1.4676,-1.43449,-1.4011,-1.36742,-1.33344,-1.29916,-1.26457,-1.22966,-1.19443,-1.15887,-1.12298,-1.08676,-1.05019,-1.01328,-0.976027,-0.938428,-0.900483,-0.862193,-0.82356,-0.784587,-0.745278,-0.705639,-0.665677,-0.625401,-0.58482,-0.543947,-0.502795,-0.46138,-0.419719,-0.377831,-0.335737,-0.29346,-0.251024,-0.208457,-0.165787,-0.123046,-0.0802639,-0.0374766,0.0052808,0.0479709,0.0905551,0.132993,0.175245,0.217268,0.259019,0.300456,0.341535,0.382213,0.422445,0.462189,0.501403,0.540045,0.578074,0.61545,0.652137,0.688097,0.723297,0.757703,0.791287,0.82402,0.855877,0.886835,0.916875,0.945979,0.974132,1.00132,1.02755,1.05279,1.07705,1.10034,1.12264,1.14397,1.16434,1.18374,1.2022,1.21972,1.23633,1.25204,1.26686,1.28081,1.29392,1.30621,1.3177,1.32841,1.33837,1.34759,1.3561,1.36392,1.37108,1.37759,1.38348,1.38876,1.39347,1.3976,1.40119,1.40424,1.40677,1.40879,1.41032,1.41136,1.41191,1.412,1.41161,1.41076,1.40943,1.40764,1.40537,1.40262,1.39938,1.39564,1.39139,1.38661,1.38128,1.37539,1.36891,1.3618,1.35405,1.34562,1.33648,1.32658,1.31588,1.30433,1.29189,1.27849,1.26408,1.24858,1.23193,1.21405,1.19484,1.17422,1.15209,1.12834,1.10285,1.0755,1.04614,1.01462,0.9808},
{-3.25464,-3.2288,-3.20292,-3.17699,-3.15101,-3.12499,-3.09892,-3.07281,-3.04666,-3.02045,-2.9942,-2.96791,-2.94156,-2.91517,-2.88873,-2.86224,-2.8357,-2.80911,-2.78246,-2.75576,-2.72901,-2.70219,-2.67532,-2.64838,-2.62138,-2.59431,-2.56718,-2.53997,-2.51269,-2.48533,-2.4579,-2.43038,-2.40277,-2.37508,-2.34729,-2.31941,-2.29143,-2.26334,-2.23514,-2.20683,-2.1784,-2.14984,-2.12116,-2.09235,-2.06339,-2.0343,-2.00505,-1.97564,-1.94607,-1.91634,-1.88642,-1.85633,-1.82605,-1.79557,-1.76488,-1.73399,-1.70288,-1.67154,-1.63997,-1.60816,-1.5761,-1.54379,-1.51121,-1.47836,-1.44523,-1.41181,-1.3781,-1.34409,-1.30976,-1.27513,-1.24017,-1.20489,-1.16927,-1.13332,-1.09702,-1.06038,-1.02338,-0.986039,-0.94834,-0.910288,-0.871881,-0.833123,-0.794014,-0.75456,-0.714765,-0.674635,-0.63418,-0.593409,-0.552333,-0.510965,-0.469321,-0.427417,-0.385272,-0.342906,-0.300343,-0.257606,-0.214723,-0.171722,-0.128633,-0.0854893,-0.0423245,0.000825503,0.0439231,0.0869295,0.129804,0.172506,0.214992,0.25722,0.299145,0.340723,0.381909,0.42266,0.462931,0.502678,0.541859,0.580432,0.618356,0.655593,0.692104,0.727854,0.762809,0.796939,0.830214,0.862608,0.894096,0.924659,0.954277,0.982935,1.01062,1.03732,1.06304,1.08776,1.11149,1.13422,1.15597,1.17673,1.19652,1.21535,1.23323,1.25017,1.2662,1.28133,1.29558,1.30896,1.32152,1.33325,1.34419,1.35437,1.36379,1.3725,1.3805,1.38783,1.3945,1.40053,1.40595,1.41078,1.41503,1.41873,1.42188,1.4245,1.42661,1.42822,1.42933,1.42996,1.43011,1.42978,1.42898,1.42771,1.42597,1.42376,1.42106,1.41787,1.41419,1.40999,1.40526,1.4,1.39416,1.38774,1.38071,1.37304,1.36469,1.35564,1.34584,1.33524,1.32381,1.3115,1.29824,1.28397,1.26864,1.25216,1.23445,1.21545,1.19504,1.17313,1.14961,1.12436,1.09725,1.06815,1.03689,1.00332},
{-3.26503,-3.23921,-3.21333,-3.18742,-3.16145,-3.13544,-3.10939,-3.08329,-3.05714,-3.03095,-3.00471,-2.97842,-2.95209,-2.9257,-2.89927,-2.87279,-2.84626,-2.81968,-2.79304,-2.76635,-2.7396,-2.71279,-2.68592,-2.65899,-2.632,-2.60494,-2.57781,-2.55062,-2.52334,-2.49599,-2.46857,-2.44105,-2.41346,-2.38577,-2.35799,-2.33011,-2.30214,-2.27406,-2.24586,-2.21756,-2.18914,-2.16059,-2.13191,-2.10311,-2.07416,-2.04506,-2.01582,-1.98642,-1.95685,-1.92712,-1.89721,-1.86712,-1.83684,-1.80636,-1.77567,-1.74478,-1.71366,-1.68232,-1.65074,-1.61892,-1.58685,-1.55452,-1.52193,-1.48906,-1.45591,-1.42247,-1.38873,-1.35468,-1.32033,-1.28565,-1.25065,-1.21532,-1.17965,-1.14363,-1.10727,-1.07055,-1.03348,-0.99605,-0.958258,-0.920103,-0.881585,-0.842706,-0.803468,-0.763874,-0.723928,-0.683638,-0.64301,-0.602054,-0.560781,-0.519204,-0.477337,-0.435196,-0.3928,-0.350169,-0.307326,-0.264294,-0.221101,-0.177775,-0.134345,-0.090845,-0.0473084,-0.00377117,0.0397289,0.0831526,0.126459,0.169607,0.212553,0.255253,0.297663,0.339737,0.381431,0.422698,0.463495,0.503775,0.543496,0.582613,0.621087,0.658875,0.695939,0.732243,0.767751,0.802432,0.836253,0.869189,0.901215,0.932306,0.962446,0.991616,1.0198,1.047,1.07319,1.09838,1.12256,1.14574,1.16791,1.18909,1.20928,1.22849,1.24673,1.26403,1.2804,1.29585,1.31041,1.32409,1.33692,1.34892,1.36012,1.37053,1.38019,1.38911,1.39732,1.40484,1.4117,1.41791,1.4235,1.42848,1.43289,1.43673,1.44002,1.44278,1.44502,1.44675,1.44799,1.44874,1.44902,1.44881,1.44814,1.447,1.44539,1.4433,1.44074,1.4377,1.43416,1.43012,1.42556,1.42047,1.41482,1.4086,1.40178,1.39434,1.38624,1.37745,1.36793,1.35764,1.34654,1.33458,1.32169,1.30784,1.29294,1.27693,1.25973,1.24126,1.22142,1.20012,1.17726,1.1527,1.12632,1.09799,1.06754,1.03482},
{-3.27531,-3.2495,-3.22364,-3.19773,-3.17178,-3.14578,-3.11974,-3.09365,-3.06751,-3.04133,-3.0151,-2.98882,-2.9625,-2.93613,-2.90971,-2.88323,-2.85671,-2.83014,-2.80351,-2.77682,-2.75008,-2.72328,-2.69642,-2.6695,-2.64252,-2.61547,-2.58835,-2.56116,-2.53389,-2.50655,-2.47913,-2.45163,-2.42404,-2.39636,-2.36859,-2.34072,-2.31275,-2.28468,-2.25649,-2.2282,-2.19978,-2.17124,-2.14257,-2.11377,-2.08483,-2.05574,-2.0265,-1.99711,-1.96755,-1.93782,-1.90792,-1.87783,-1.84755,-1.81707,-1.78638,-1.75549,-1.72437,-1.69303,-1.66144,-1.62962,-1.59754,-1.5652,-1.53259,-1.49971,-1.46654,-1.43308,-1.39932,-1.36525,-1.33086,-1.29615,-1.26111,-1.22573,-1.19001,-1.15394,-1.11752,-1.08073,-1.04359,-1.00607,-0.968192,-0.929941,-0.891319,-0.852326,-0.812965,-0.773238,-0.73315,-0.692705,-0.651913,-0.61078,-0.569318,-0.527539,-0.485457,-0.443088,-0.400449,-0.357562,-0.314448,-0.27113,-0.227636,-0.183993,-0.140231,-0.0963836,-0.0524838,-0.00856814,0.0353257,0.0791583,0.122889,0.166474,0.209872,0.253037,0.295924,0.338488,0.380682,0.42246,0.463776,0.504584,0.544838,0.584496,0.623514,0.66185,0.699464,0.736318,0.772377,0.807605,0.841972,0.875448,0.908008,0.939629,0.970289,0.999971,1.02866,1.05635,1.08302,1.10868,1.13331,1.15693,1.17953,1.20112,1.2217,1.2413,1.25991,1.27756,1.29426,1.31004,1.3249,1.33888,1.35199,1.36426,1.37571,1.38636,1.39624,1.40537,1.41378,1.42149,1.42853,1.43491,1.44066,1.4458,1.45035,1.45433,1.45775,1.46064,1.463,1.46485,1.4662,1.46706,1.46744,1.46734,1.46677,1.46574,1.46423,1.46226,1.45981,1.45688,1.45347,1.44956,1.44513,1.44018,1.43469,1.42863,1.42198,1.41472,1.40682,1.39824,1.38895,1.37891,1.36807,1.35639,1.34381,1.33028,1.31573,1.30009,1.28329,1.26525,1.24587,1.22505,1.20269,1.17867,1.15286,1.12511,1.09528,1.0632},
{-3.28548,-3.25968,-3.23383,-3.20794,-3.182,-3.15602,-3.12998,-3.1039,-3.07778,-3.05161,-3.02539,-2.99912,-2.97281,-2.94644,-2.92003,-2.89357,-2.86706,-2.84049,-2.81387,-2.78719,-2.76046,-2.73367,-2.70682,-2.67991,-2.65293,-2.62589,-2.59878,-2.5716,-2.54434,-2.51701,-2.4896,-2.4621,-2.43452,-2.40685,-2.37909,-2.35123,-2.32327,-2.2952,-2.26703,-2.23874,-2.21033,-2.1818,-2.15314,-2.12434,-2.09541,-2.06633,-2.0371,-2.00771,-1.97816,-1.94844,-1.91854,-1.88845,-1.85818,-1.8277,-1.79702,-1.76613,-1.73501,-1.70367,-1.67208,-1.64025,-1.60817,-1.57582,-1.54321,-1.51031,-1.47713,-1.44365,-1.40987,-1.37577,-1.34136,-1.30662,-1.27154,-1.23612,-1.20036,-1.16424,-1.12776,-1.09091,-1.0537,-1.01611,-0.978144,-0.939802,-0.901081,-0.861981,-0.822503,-0.78265,-0.742425,-0.701834,-0.660883,-0.61958,-0.577936,-0.535963,-0.493673,-0.451083,-0.40821,-0.365074,-0.321696,-0.2781,-0.234311,-0.190359,-0.146273,-0.102085,-0.0578293,-0.0135421,0.0307388,0.0749737,0.119121,0.163139,0.206983,0.250608,0.293967,0.337016,0.379706,0.421991,0.463823,0.505156,0.545943,0.586139,0.6257,0.664584,0.702748,0.740153,0.776762,0.812541,0.847455,0.881475,0.914573,0.946726,0.977911,1.00811,1.03731,1.06549,1.09265,1.11878,1.14388,1.16794,1.19098,1.21299,1.23398,1.25397,1.27296,1.29097,1.30802,1.32413,1.33932,1.3536,1.367,1.37955,1.39126,1.40216,1.41228,1.42165,1.43028,1.4382,1.44543,1.452,1.45793,1.46325,1.46796,1.4721,1.47568,1.47872,1.48123,1.48322,1.48472,1.48572,1.48625,1.4863,1.48588,1.48499,1.48364,1.48183,1.47954,1.47679,1.47355,1.46983,1.46561,1.46087,1.45561,1.44979,1.4434,1.43642,1.42881,1.42055,1.41159,1.40192,1.39147,1.38021,1.36808,1.35502,1.34099,1.3259,1.30969,1.29228,1.27356,1.25346,1.23186,1.20865,1.18369,1.15685,1.12797,1.09688},
{-3.29554,-3.26976,-3.24392,-3.21804,-3.19212,-3.16614,-3.14012,-3.11405,-3.08794,-3.06178,-3.03557,-3.00931,-2.98301,-2.95666,-2.93025,-2.9038,-2.8773,-2.85074,-2.82413,-2.79746,-2.77074,-2.74396,-2.71712,-2.69021,-2.66325,-2.63621,-2.60911,-2.58194,-2.55469,-2.52736,-2.49996,-2.47248,-2.4449,-2.41724,-2.38949,-2.36164,-2.33369,-2.30563,-2.27747,-2.24919,-2.22079,-2.19227,-2.16362,-2.13483,-2.10591,-2.07684,-2.04761,-2.01823,-1.98869,-1.95898,-1.92908,-1.89901,-1.86874,-1.83827,-1.80759,-1.7767,-1.74559,-1.71424,-1.68266,-1.65083,-1.61874,-1.58639,-1.55377,-1.52087,-1.48767,-1.45418,-1.42038,-1.38627,-1.35183,-1.31706,-1.28195,-1.2465,-1.21069,-1.17453,-1.138,-1.1011,-1.06382,-1.02616,-0.988122,-0.949696,-0.910883,-0.871682,-0.832095,-0.792123,-0.751769,-0.711038,-0.669937,-0.628472,-0.586655,-0.544495,-0.502007,-0.459204,-0.416105,-0.372729,-0.329096,-0.285231,-0.241158,-0.196906,-0.152505,-0.107986,-0.0633833,-0.0187336,0.0259252,0.0705535,0.11511,0.159551,0.203832,0.247908,0.291733,0.335259,0.378438,0.421223,0.463565,0.505416,0.54673,0.58746,0.62756,0.666986,0.705697,0.74365,0.780807,0.817133,0.852592,0.887154,0.92079,0.953474,0.985183,1.0159,1.0456,1.07428,1.10193,1.12854,1.1541,1.17861,1.20208,1.22451,1.24591,1.2663,1.28567,1.30405,1.32145,1.33789,1.3534,1.36798,1.38168,1.3945,1.40648,1.41764,1.428,1.43759,1.44644,1.45457,1.462,1.46876,1.47487,1.48036,1.48524,1.48954,1.49328,1.49646,1.49912,1.50126,1.50289,1.50404,1.5047,1.50489,1.50461,1.50387,1.50267,1.50101,1.49888,1.49629,1.49323,1.48969,1.48565,1.48112,1.47607,1.47048,1.46433,1.45761,1.45028,1.44231,1.43368,1.42434,1.41425,1.40338,1.39167,1.37906,1.36551,1.35093,1.33526,1.31843,1.30033,1.28089,1.25998,1.2375,1.21332,1.18729,1.15926,1.12906},
{-3.3055,-3.27973,-3.25391,-3.22804,-3.20213,-3.17616,-3.15015,-3.1241,-3.098,-3.07185,-3.04565,-3.0194,-2.99311,-2.96677,-2.94037,-2.91393,-2.88743,-2.86089,-2.83429,-2.80763,-2.78092,-2.75414,-2.72731,-2.70042,-2.67346,-2.64643,-2.61934,-2.59218,-2.56494,-2.53763,-2.51023,-2.48276,-2.45519,-2.42754,-2.3998,-2.37196,-2.34402,-2.31597,-2.28782,-2.25955,-2.23116,-2.20265,-2.17401,-2.14523,-2.11632,-2.08726,-2.05805,-2.02868,-1.99914,-1.96944,-1.93955,-1.90948,-1.87922,-1.84876,-1.81809,-1.78721,-1.7561,-1.72476,-1.69318,-1.66135,-1.62927,-1.59691,-1.56429,-1.53138,-1.49818,-1.46467,-1.43086,-1.39673,-1.36228,-1.32748,-1.29235,-1.25687,-1.22103,-1.18482,-1.14825,-1.11129,-1.07396,-1.03624,-0.998127,-0.959623,-0.920725,-0.88143,-0.84174,-0.801656,-0.76118,-0.720317,-0.679073,-0.637454,-0.595471,-0.553133,-0.510454,-0.467447,-0.42413,-0.380522,-0.336643,-0.292517,-0.248168,-0.203624,-0.158916,-0.114074,-0.0691329,-0.0241288,0.0209003,0.0659144,0.110872,0.155729,0.200441,0.244963,0.289246,0.333244,0.376907,0.420187,0.463034,0.505401,0.547238,0.588498,0.629135,0.669103,0.708358,0.746859,0.784565,0.821439,0.857445,0.89255,0.926726,0.959944,0.992182,1.02342,1.05363,1.08282,1.11096,1.13804,1.16407,1.18904,1.21296,1.23582,1.25764,1.27842,1.29818,1.31694,1.3347,1.35149,1.36732,1.38223,1.39623,1.40935,1.42161,1.43303,1.44365,1.45348,1.46257,1.47092,1.47857,1.48553,1.49185,1.49753,1.5026,1.50708,1.51099,1.51435,1.51718,1.51949,1.5213,1.52262,1.52345,1.52382,1.52372,1.52316,1.52215,1.52069,1.51877,1.51639,1.51356,1.51025,1.50647,1.5022,1.49743,1.49215,1.48632,1.47994,1.47298,1.4654,1.45718,1.44829,1.43869,1.42833,1.41716,1.40514,1.39221,1.3783,1.36335,1.34728,1.33,1.31142,1.29144,1.26994,1.24679,1.22186,1.19499,1.16601},
{-3.31535,-3.28959,-3.26379,-3.23793,-3.21203,-3.18608,-3.16009,-3.13404,-3.10795,-3.08181,-3.05563,-3.02939,-3.00311,-2.97678,-2.95039,-2.92396,-2.89747,-2.87094,-2.84435,-2.8177,-2.79099,-2.76423,-2.73741,-2.71053,-2.68358,-2.65656,-2.62948,-2.60232,-2.5751,-2.54779,-2.52041,-2.49294,-2.46539,-2.43775,-2.41002,-2.38219,-2.35426,-2.32622,-2.29808,-2.26982,-2.24144,-2.21294,-2.18431,-2.15555,-2.12665,-2.0976,-2.0684,-2.03904,-2.00952,-1.97982,-1.94995,-1.91989,-1.88964,-1.85919,-1.82853,-1.79765,-1.76655,-1.73522,-1.70364,-1.67182,-1.63974,-1.60739,-1.57476,-1.54185,-1.50864,-1.47513,-1.44131,-1.40717,-1.3727,-1.33789,-1.30274,-1.26723,-1.23136,-1.19512,-1.1585,-1.12151,-1.08412,-1.04634,-1.00817,-0.969593,-0.930616,-0.891234,-0.851449,-0.81126,-0.770671,-0.729684,-0.688306,-0.646542,-0.604401,-0.561894,-0.519033,-0.475832,-0.432307,-0.388477,-0.344361,-0.299984,-0.255369,-0.210543,-0.165538,-0.120383,-0.0751135,-0.0297649,0.0156245,0.0610147,0.106364,0.151628,0.196762,0.24172,0.286453,0.330914,0.375053,0.41882,0.462166,0.505041,0.547395,0.58918,0.630348,0.670853,0.710649,0.749693,0.787944,0.825363,0.861913,0.897561,0.932275,0.966026,0.998791,1.03055,1.06128,1.09096,1.1196,1.14716,1.17366,1.1991,1.22346,1.24675,1.26899,1.29018,1.31033,1.32946,1.34758,1.36472,1.38089,1.39612,1.41043,1.42384,1.43638,1.44808,1.45895,1.46904,1.47836,1.48694,1.4948,1.50198,1.5085,1.51437,1.51963,1.5243,1.5284,1.53194,1.53494,1.53743,1.53941,1.5409,1.54191,1.54246,1.54254,1.54217,1.54135,1.54009,1.53838,1.53622,1.53361,1.53055,1.52702,1.52302,1.51854,1.51355,1.50805,1.50201,1.49541,1.48823,1.48043,1.47198,1.46286,1.453,1.44238,1.43095,1.41863,1.40539,1.39114,1.37582,1.35934,1.34161,1.32253,1.30199,1.27985,1.25599,1.23025,1.20244},
{-3.3251,-3.29936,-3.27357,-3.24773,-3.22184,-3.1959,-3.16992,-3.14389,-3.11781,-3.09168,-3.0655,-3.03928,-3.01301,-2.98669,-2.96031,-2.93389,-2.90742,-2.88089,-2.85431,-2.82767,-2.80098,-2.77422,-2.74741,-2.72054,-2.6936,-2.66659,-2.63952,-2.61238,-2.58516,-2.55787,-2.53049,-2.50304,-2.4755,-2.44787,-2.42015,-2.39233,-2.36441,-2.33639,-2.30825,-2.28001,-2.25164,-2.22315,-2.19454,-2.16579,-2.1369,-2.10786,-2.07867,-2.04933,-2.01982,-1.99014,-1.96027,-1.93023,-1.89999,-1.86955,-1.8389,-1.80804,-1.77694,-1.74562,-1.71405,-1.68224,-1.65016,-1.61782,-1.58519,-1.55228,-1.51908,-1.48557,-1.45174,-1.41759,-1.38311,-1.34829,-1.31312,-1.27759,-1.24169,-1.20542,-1.16877,-1.13174,-1.09431,-1.05648,-1.01825,-0.979607,-0.940558,-0.901097,-0.861224,-0.820938,-0.780243,-0.73914,-0.697635,-0.655734,-0.613444,-0.570776,-0.527742,-0.484355,-0.44063,-0.396587,-0.352244,-0.307624,-0.262751,-0.217654,-0.17236,-0.126901,-0.0813116,-0.0356271,0.0101143,0.0558723,0.101605,0.147268,0.192817,0.238204,0.283381,0.328299,0.372908,0.417157,0.460997,0.504375,0.547243,0.589549,0.631246,0.672285,0.712621,0.752208,0.791004,0.828969,0.866064,0.902256,0.93751,0.971799,1.0051,1.03738,1.06862,1.09882,1.12795,1.15601,1.18299,1.20889,1.2337,1.25744,1.2801,1.30171,1.32226,1.34178,1.36028,1.37778,1.3943,1.40987,1.4245,1.43822,1.45106,1.46304,1.4742,1.48455,1.49412,1.50295,1.51106,1.51847,1.52521,1.53131,1.53679,1.54167,1.54598,1.54973,1.55294,1.55564,1.55784,1.55954,1.56077,1.56154,1.56185,1.56172,1.56115,1.56014,1.5587,1.55682,1.55451,1.55176,1.54856,1.54491,1.5408,1.5362,1.53112,1.52553,1.51941,1.51273,1.50547,1.49761,1.4891,1.47991,1.46999,1.45931,1.4478,1.43542,1.42209,1.40775,1.39232,1.37571,1.35782,1.33854,1.31775,1.29532,1.2711,1.2449},
{-3.33476,-3.30903,-3.28325,-3.25743,-3.23155,-3.20563,-3.17965,-3.15363,-3.12757,-3.10145,-3.07529,-3.04907,-3.02281,-2.9965,-2.97014,-2.94373,-2.91726,-2.89075,-2.86418,-2.83755,-2.81087,-2.78412,-2.75732,-2.73046,-2.70353,-2.67654,-2.64947,-2.62234,-2.59513,-2.56785,-2.54049,-2.51305,-2.48552,-2.4579,-2.43019,-2.40238,-2.37448,-2.34646,-2.31834,-2.29011,-2.26176,-2.23329,-2.20468,-2.17595,-2.14707,-2.11805,-2.08887,-2.05954,-2.03005,-2.00038,-1.97053,-1.9405,-1.91028,-1.87985,-1.84921,-1.81836,-1.78728,-1.75597,-1.72442,-1.69261,-1.66054,-1.62821,-1.59559,-1.56268,-1.52948,-1.49597,-1.46215,-1.428,-1.39351,-1.35868,-1.32349,-1.28795,-1.25203,-1.21574,-1.17906,-1.14199,-1.10453,-1.06665,-1.02837,-0.989674,-0.95056,-0.911027,-0.871073,-0.830699,-0.789906,-0.748695,-0.707072,-0.665042,-0.622613,-0.579794,-0.536596,-0.493032,-0.449118,-0.404871,-0.36031,-0.315458,-0.270338,-0.224978,-0.179406,-0.133653,-0.0877539,-0.0417435,0.00433997,0.0504561,0.0965629,0.142616,0.18857,0.234377,0.279989,0.325356,0.370428,0.415152,0.459479,0.503355,0.54673,0.589553,0.631774,0.673344,0.714216,0.754343,0.793682,0.832191,0.869831,0.906566,0.942362,0.977189,1.01102,1.04383,1.07559,1.1063,1.13594,1.16449,1.19195,1.21832,1.2436,1.26778,1.29089,1.31291,1.33388,1.35379,1.37268,1.39055,1.40743,1.42334,1.4383,1.45234,1.46549,1.47778,1.48922,1.49985,1.5097,1.51879,1.52715,1.53481,1.5418,1.54814,1.55386,1.55897,1.56351,1.56749,1.57093,1.57386,1.57629,1.57824,1.57972,1.58074,1.58131,1.58145,1.58115,1.58044,1.5793,1.57774,1.57577,1.57337,1.57055,1.56729,1.5636,1.55946,1.55485,1.54977,1.54418,1.53808,1.53144,1.52423,1.51642,1.50798,1.49886,1.48903,1.47843,1.46702,1.45473,1.4415,1.42726,1.41191,1.39537,1.37753,1.35828,1.33749,1.315,1.29066},
{-3.34431,-3.3186,-3.29284,-3.26703,-3.24116,-3.21525,-3.18929,-3.16329,-3.13723,-3.11113,-3.08498,-3.05877,-3.03252,-3.00622,-2.97987,-2.95347,-2.92702,-2.90051,-2.87395,-2.84734,-2.82066,-2.79393,-2.76714,-2.74029,-2.71337,-2.68639,-2.65934,-2.63221,-2.60502,-2.57775,-2.5504,-2.52297,-2.49545,-2.46784,-2.44015,-2.41235,-2.38446,-2.35646,-2.32835,-2.30013,-2.2718,-2.24334,-2.21475,-2.18603,-2.15717,-2.12816,-2.099,-2.06969,-2.0402,-2.01055,-1.98072,-1.95071,-1.9205,-1.89009,-1.85947,-1.82863,-1.79757,-1.76627,-1.73473,-1.70294,-1.67088,-1.63856,-1.60595,-1.57305,-1.53986,-1.50636,-1.47253,-1.43838,-1.4039,-1.36906,-1.33387,-1.29832,-1.26239,-1.22608,-1.18938,-1.15228,-1.11478,-1.07687,-1.03854,-0.999798,-0.960628,-0.921031,-0.881005,-0.840551,-0.799668,-0.758359,-0.716627,-0.674478,-0.631919,-0.588958,-0.545606,-0.501876,-0.457783,-0.413342,-0.368575,-0.323501,-0.278145,-0.232533,-0.186694,-0.140659,-0.0944606,-0.0481351,-0.00172043,0.0447432,0.0912136,0.137646,0.183995,0.230213,0.276251,0.322058,0.367583,0.412775,0.45758,0.501947,0.545823,0.589156,0.631896,0.673991,0.715394,0.756058,0.795937,0.834988,0.873171,0.910448,0.946785,0.982149,1.01651,1.04985,1.08214,1.11336,1.1435,1.17255,1.2005,1.22735,1.25309,1.27773,1.30128,1.32373,1.34511,1.36543,1.38471,1.40296,1.42021,1.43647,1.45178,1.46615,1.47962,1.49222,1.50396,1.51488,1.52502,1.53438,1.54302,1.55094,1.55819,1.56478,1.57075,1.57611,1.5809,1.58513,1.58883,1.59201,1.5947,1.59691,1.59865,1.59995,1.60081,1.60124,1.60125,1.60086,1.60006,1.59885,1.59725,1.59524,1.59284,1.59002,1.58679,1.58314,1.57906,1.57453,1.56955,1.56408,1.55811,1.55162,1.54457,1.53695,1.5287,1.51981,1.51021,1.49986,1.48871,1.47669,1.46374,1.44977,1.43471,1.41845,1.40089,1.38189,1.36132,1.33901},
{-3.35378,-3.32808,-3.30233,-3.27653,-3.25068,-3.22479,-3.19884,-3.17285,-3.1468,-3.12071,-3.09457,-3.06838,-3.04214,-3.01585,-2.98951,-2.96312,-2.93668,-2.91019,-2.88364,-2.85703,-2.83037,-2.80365,-2.77687,-2.75003,-2.72312,-2.69615,-2.66911,-2.642,-2.61482,-2.58756,-2.56022,-2.5328,-2.5053,-2.4777,-2.45002,-2.42224,-2.39436,-2.36638,-2.33828,-2.31008,-2.28176,-2.25331,-2.22474,-2.19603,-2.16719,-2.1382,-2.10906,-2.07976,-2.0503,-2.02066,-1.99085,-1.96085,-1.93066,-1.90027,-1.86967,-1.83885,-1.8078,-1.77652,-1.745,-1.71322,-1.68118,-1.64887,-1.61628,-1.5834,-1.55021,-1.51672,-1.48291,-1.44876,-1.41428,-1.37945,-1.34425,-1.30869,-1.27276,-1.23644,-1.19972,-1.1626,-1.12508,-1.08714,-1.04878,-1.00999,-0.970767,-0.931114,-0.891025,-0.850498,-0.809534,-0.768135,-0.726304,-0.684046,-0.641366,-0.598273,-0.554777,-0.510891,-0.466628,-0.422005,-0.37704,-0.331756,-0.286174,-0.240321,-0.194225,-0.147917,-0.10143,-0.0547996,-0.00806367,0.0387377,0.085562,0.132365,0.179101,0.22572,0.272175,0.318414,0.364386,0.410037,0.455316,0.500167,0.544539,0.588378,0.631632,0.67425,0.716182,0.75738,0.797798,0.837391,0.876117,0.913938,0.950818,0.986722,1.02162,1.05549,1.08831,1.12005,1.15071,1.18026,1.20871,1.23604,1.26226,1.28736,1.31136,1.33426,1.35607,1.37681,1.39649,1.41514,1.43277,1.4494,1.46507,1.4798,1.49361,1.50653,1.5186,1.52983,1.54027,1.54994,1.55887,1.56709,1.57462,1.5815,1.58775,1.5934,1.59847,1.60299,1.60697,1.61045,1.61344,1.61596,1.61802,1.61964,1.62084,1.62163,1.62201,1.622,1.6216,1.62082,1.61967,1.61813,1.61622,1.61394,1.61127,1.60821,1.60476,1.6009,1.59663,1.59192,1.58676,1.58113,1.57501,1.56836,1.56117,1.55339,1.54499,1.53592,1.52614,1.51559,1.5042,1.49192,1.47865,1.46431,1.44881,1.43202,1.41382,1.39406},
{-3.36314,-3.33746,-3.31173,-3.28594,-3.26011,-3.23423,-3.20829,-3.18231,-3.15628,-3.1302,-3.10407,-3.0779,-3.05167,-3.02539,-2.99906,-2.97269,-2.94625,-2.91977,-2.89323,-2.86664,-2.83999,-2.81328,-2.78651,-2.75968,-2.73278,-2.70583,-2.6788,-2.6517,-2.62453,-2.59728,-2.56996,-2.54255,-2.51506,-2.48748,-2.45981,-2.43205,-2.40418,-2.37621,-2.34814,-2.31995,-2.29164,-2.26321,-2.23466,-2.20597,-2.17714,-2.14817,-2.11905,-2.08977,-2.06032,-2.03071,-2.00092,-1.97094,-1.94077,-1.9104,-1.87981,-1.84902,-1.81799,-1.78673,-1.75523,-1.72347,-1.69145,-1.65916,-1.62658,-1.59372,-1.56055,-1.52707,-1.49327,-1.45913,-1.42466,-1.38983,-1.35465,-1.31909,-1.28315,-1.24682,-1.2101,-1.17297,-1.13542,-1.09746,-1.05907,-1.02025,-0.980986,-0.941285,-0.901141,-0.860551,-0.819517,-0.778038,-0.736117,-0.693759,-0.650969,-0.607755,-0.564126,-0.520095,-0.475674,-0.430879,-0.38573,-0.340246,-0.29445,-0.248368,-0.202028,-0.155459,-0.108696,-0.0617724,-0.0147271,0.0324001,0.0795669,0.126729,0.173839,0.22085,0.267712,0.314373,0.360782,0.406884,0.452626,0.497954,0.542814,0.587152,0.630914,0.674049,0.716506,0.758234,0.799187,0.839319,0.878587,0.91695,0.954372,0.990818,1.02626,1.06066,1.09401,1.12628,1.15745,1.18751,1.21646,1.24428,1.27098,1.29656,1.32102,1.34437,1.36662,1.38779,1.40788,1.42694,1.44496,1.46198,1.47802,1.49311,1.50728,1.52055,1.53295,1.54452,1.55528,1.56527,1.57451,1.58304,1.59088,1.59807,1.60463,1.61058,1.61596,1.62079,1.6251,1.6289,1.63222,1.63508,1.63749,1.63948,1.64105,1.64223,1.64302,1.64344,1.64349,1.64318,1.64251,1.6415,1.64015,1.63844,1.63639,1.63399,1.63124,1.62812,1.62463,1.62076,1.61649,1.61181,1.6067,1.60114,1.5951,1.58855,1.58146,1.5738,1.56551,1.55657,1.5469,1.53646,1.52517,1.51295,1.49971,1.48536,1.46978,1.45283},
{-3.37242,-3.34675,-3.32104,-3.29527,-3.26945,-3.24358,-3.21766,-3.19169,-3.16567,-3.1396,-3.11349,-3.08732,-3.06111,-3.03484,-3.00853,-2.98216,-2.95574,-2.92927,-2.90274,-2.87616,-2.84952,-2.82282,-2.79606,-2.76925,-2.74236,-2.71542,-2.6884,-2.66131,-2.63416,-2.60692,-2.57961,-2.55222,-2.52474,-2.49718,-2.46952,-2.44177,-2.41392,-2.38597,-2.35791,-2.32974,-2.30145,-2.27304,-2.2445,-2.21583,-2.18702,-2.15807,-2.12897,-2.09971,-2.07029,-2.04069,-2.01092,-1.98097,-1.95082,-1.92047,-1.88991,-1.85913,-1.82813,-1.79689,-1.76541,-1.73368,-1.70168,-1.66941,-1.63686,-1.60401,-1.57086,-1.5374,-1.50362,-1.4695,-1.43504,-1.40023,-1.36505,-1.3295,-1.29357,-1.25724,-1.22051,-1.18338,-1.14582,-1.10784,-1.06943,-1.03058,-0.991291,-0.951552,-0.911362,-0.870719,-0.829623,-0.788075,-0.746075,-0.703628,-0.660739,-0.617415,-0.573665,-0.5295,-0.484934,-0.43998,-0.394658,-0.348988,-0.302991,-0.256692,-0.21012,-0.163304,-0.116277,-0.0690731,-0.0217311,0.0257095,0.0732064,0.120715,0.168189,0.21558,0.262837,0.309909,0.356744,0.403287,0.449484,0.49528,0.54062,0.58545,0.629714,0.67336,0.716336,0.75859,0.800075,0.840743,0.88055,0.919455,0.957419,0.994406,1.03039,1.06533,1.09921,1.132,1.1637,1.19428,1.22373,1.25205,1.27925,1.3053,1.33023,1.35404,1.37674,1.39835,1.41888,1.43835,1.45678,1.4742,1.49063,1.5061,1.52064,1.53428,1.54704,1.55896,1.57007,1.5804,1.58998,1.59884,1.60702,1.61454,1.62143,1.62772,1.63344,1.63862,1.64327,1.64743,1.65112,1.65435,1.65716,1.65955,1.66154,1.66315,1.6644,1.66529,1.66584,1.66606,1.66595,1.66552,1.66478,1.66373,1.66237,1.6607,1.65872,1.65642,1.65381,1.65086,1.64758,1.64395,1.63996,1.63559,1.63082,1.62563,1.61999,1.61388,1.60725,1.60007,1.5923,1.58389,1.57477,1.56489,1.55416,1.5425,1.52982,1.516},
{-3.38161,-3.35596,-3.33025,-3.3045,-3.27869,-3.25284,-3.22693,-3.20098,-3.17497,-3.14892,-3.12281,-3.09666,-3.07046,-3.04421,-3.0179,-2.99155,-2.96514,-2.93868,-2.91216,-2.88559,-2.85897,-2.83228,-2.80554,-2.77873,-2.75186,-2.72492,-2.69792,-2.67085,-2.64371,-2.61649,-2.58919,-2.56181,-2.53435,-2.5068,-2.47916,-2.45142,-2.42359,-2.39566,-2.36761,-2.33946,-2.31119,-2.2828,-2.25428,-2.22563,-2.19684,-2.16791,-2.13883,-2.10959,-2.08019,-2.05062,-2.02087,-1.99094,-1.96082,-1.93049,-1.89996,-1.86921,-1.83823,-1.80702,-1.77557,-1.74386,-1.71189,-1.67964,-1.64711,-1.61429,-1.58117,-1.54773,-1.51397,-1.47987,-1.44543,-1.41064,-1.37547,-1.33994,-1.30401,-1.2677,-1.23098,-1.19384,-1.15628,-1.1183,-1.07987,-1.04101,-1.00169,-0.961922,-0.921696,-0.88101,-0.839863,-0.798254,-0.756186,-0.713661,-0.670684,-0.627261,-0.583401,-0.539114,-0.494413,-0.449313,-0.40383,-0.357984,-0.311798,-0.265295,-0.218503,-0.171451,-0.124172,-0.0766996,-0.0290724,0.0186703,0.0664862,0.114331,0.162158,0.209918,0.257561,0.305036,0.352289,0.399265,0.445909,0.492167,0.537981,0.583297,0.628059,0.672212,0.715704,0.758483,0.800499,0.841704,0.882051,0.9215,0.960009,0.997543,1.03407,1.06955,1.10397,1.1373,1.16953,1.20064,1.23061,1.25944,1.28714,1.31369,1.33911,1.3634,1.38657,1.40863,1.42961,1.44952,1.46838,1.48623,1.50307,1.51895,1.53389,1.54792,1.56107,1.57337,1.58486,1.59556,1.60551,1.61475,1.6233,1.6312,1.63847,1.64514,1.65125,1.65682,1.66188,1.66646,1.67057,1.67424,1.6775,1.68036,1.68285,1.68497,1.68675,1.68821,1.68934,1.69018,1.69072,1.69098,1.69096,1.69067,1.69012,1.6893,1.68822,1.68689,1.68529,1.68343,1.6813,1.6789,1.67621,1.67323,1.66994,1.66633,1.66237,1.65806,1.65336,1.64825,1.64269,1.63664,1.63007,1.62292,1.61514,1.60666,1.5974,1.58728},
{-3.39071,-3.36507,-3.33938,-3.31364,-3.28785,-3.26201,-3.23612,-3.21018,-3.18419,-3.15814,-3.13205,-3.10591,-3.07972,-3.05348,-3.02719,-3.00085,-2.97445,-2.948,-2.9215,-2.89494,-2.86833,-2.84166,-2.81492,-2.78813,-2.76127,-2.73435,-2.70736,-2.6803,-2.65317,-2.62597,-2.59868,-2.57132,-2.54387,-2.51634,-2.48872,-2.461,-2.43318,-2.40526,-2.37724,-2.3491,-2.32085,-2.29248,-2.26398,-2.23536,-2.20659,-2.17768,-2.14862,-2.11941,-2.09003,-2.06049,-2.03077,-2.00086,-1.97076,-1.94047,-1.90996,-1.87924,-1.84829,-1.81711,-1.78568,-1.754,-1.72206,-1.68985,-1.65735,-1.62456,-1.59146,-1.55805,-1.52432,-1.49025,-1.45583,-1.42106,-1.38592,-1.3504,-1.3145,-1.2782,-1.24149,-1.20436,-1.16681,-1.12882,-1.0904,-1.05152,-1.01219,-0.972405,-0.932153,-0.891434,-0.850247,-0.80859,-0.766465,-0.723874,-0.680822,-0.637313,-0.593356,-0.548961,-0.504139,-0.458906,-0.413276,-0.36727,-0.320909,-0.274216,-0.227219,-0.179946,-0.132429,-0.0847037,-0.0368059,0.0112244,0.0593451,0.107512,0.155678,0.203794,0.251811,0.299676,0.347334,0.394732,0.441814,0.488523,0.534802,0.580596,0.625848,0.670503,0.714506,0.757805,0.800348,0.842086,0.882973,0.922965,0.96202,1.0001,1.03717,1.07321,1.10817,1.14205,1.17481,1.20645,1.23695,1.26631,1.29452,1.32158,1.3475,1.37228,1.39593,1.41847,1.43992,1.46029,1.4796,1.49789,1.51517,1.53148,1.54684,1.56128,1.57485,1.58756,1.59946,1.61057,1.62093,1.63057,1.63953,1.64783,1.65552,1.66261,1.66915,1.67516,1.68067,1.6857,1.69029,1.69445,1.69821,1.7016,1.70463,1.70732,1.7097,1.71177,1.71356,1.71508,1.71634,1.71736,1.71814,1.71869,1.71902,1.71915,1.71907,1.71878,1.7183,1.71762,1.71675,1.71567,1.7144,1.71292,1.71123,1.70932,1.70718,1.7048,1.70217,1.69926,1.69606,1.69254,1.68868,1.68444,1.67978,1.67466,1.66903,1.66284}
};
//arrays dimensions are [z][energy], z=1 starts from index=0
//LS X coefficient (dE straggling) for A=atomic weight
double ls_X_coefficients_a[][200]=
{
{0.999131,0.999077,0.99902,0.998959,0.998896,0.998829,0.998758,0.998684,0.998606,0.998523,0.998436,0.998344,0.998247,0.998144,0.998037,0.997923,0.997803,0.997677,0.997544,0.997404,0.997256,0.9971,0.996936,0.996763,0.996581,0.996389,0.996187,0.995974,0.995749,0.995513,0.995264,0.995001,0.994725,0.994434,0.994127,0.993804,0.993465,0.993107,0.99273,0.992333,0.991915,0.991476,0.991013,0.990526,0.990014,0.989475,0.988907,0.988311,0.987683,0.987023,0.986328,0.985598,0.98483,0.984023,0.983175,0.982284,0.981347,0.980363,0.979329,0.978243,0.977103,0.975906,0.97465,0.973331,0.971948,0.970497,0.968975,0.967379,0.965707,0.963954,0.962119,0.960196,0.958184,0.956078,0.953874,0.95157,0.949161,0.946644,0.944014,0.941269,0.938405,0.935417,0.932302,0.929056,0.925676,0.922158,0.918498,0.914694,0.910743,0.906641,0.902385,0.897974,0.893405,0.888676,0.883786,0.878734,0.87352,0.868142,0.862602,0.8569,0.851037,0.845017,0.838841,0.832513,0.826037,0.819418,0.812662,0.805774,0.798763,0.791635,0.784399,0.777065,0.769643,0.762143,0.754577,0.746956,0.739293,0.731601,0.723893,0.716184,0.708485,0.700813,0.69318,0.685601,0.67809,0.67066,0.663323,0.656094,0.648984,0.642005,0.635167,0.62848,0.621954,0.615596,0.609414,0.603414,0.597601,0.591979,0.58655,0.581317,0.57628,0.571439,0.566792,0.562338,0.558072,0.553991,0.55009,0.546362,0.542801,0.5394,0.53615,0.533043,0.530069,0.52722,0.524484,0.52185,0.519308,0.516845,0.51445,0.512109,0.509809,0.507537,0.505278,0.503017,0.500738,0.498425,0.49606,0.493626,0.491102,0.48847,0.485706,0.482789,0.479693,0.476394,0.472863,0.46907,0.464985,0.460574,0.455801,0.45063,0.445021,0.438932,0.432321,0.42514,0.417349,0.4089,0.399748,0.389851,0.37917,0.367672,0.355335,0.342146,0.328114,0.31327,0.297676,0.281437,0.264712,0.247731,0.230813,0.214391},
{0.999536,0.999486,0.999433,0.999377,0.999317,0.999255,0.999188,0.999118,0.999045,0.998967,0.998884,0.998797,0.998705,0.998608,0.998506,0.998398,0.998284,0.998164,0.998037,0.997903,0.997761,0.997612,0.997455,0.997289,0.997114,0.996929,0.996734,0.996529,0.996312,0.996084,0.995843,0.99559,0.995322,0.99504,0.994743,0.99443,0.9941,0.993752,0.993385,0.992999,0.992593,0.992164,0.991713,0.991238,0.990738,0.990211,0.989657,0.989073,0.988459,0.987812,0.987132,0.986417,0.985664,0.984872,0.98404,0.983164,0.982244,0.981276,0.98026,0.979192,0.97807,0.976891,0.975654,0.974355,0.972991,0.97156,0.970059,0.968485,0.966834,0.965104,0.963291,0.961391,0.959402,0.95732,0.955141,0.952862,0.950479,0.947988,0.945385,0.942667,0.93983,0.93687,0.933783,0.930566,0.927216,0.923727,0.920098,0.916325,0.912405,0.908334,0.904111,0.899732,0.895196,0.890501,0.885644,0.880626,0.875445,0.870102,0.864596,0.858929,0.853101,0.847116,0.840975,0.834682,0.828241,0.821657,0.814936,0.808083,0.801106,0.794012,0.78681,0.779509,0.77212,0.764652,0.757118,0.749528,0.741895,0.734233,0.726554,0.718872,0.7112,0.703553,0.695945,0.688389,0.680899,0.673488,0.66617,0.658958,0.651862,0.644896,0.638069,0.631391,0.624871,0.618517,0.612336,0.606335,0.600517,0.594888,0.589448,0.584201,0.579146,0.574283,0.56961,0.565125,0.560824,0.556702,0.552753,0.548972,0.545352,0.541884,0.538559,0.535369,0.532303,0.52935,0.526501,0.523742,0.521061,0.518445,0.515881,0.513354,0.51085,0.508353,0.505846,0.503313,0.500736,0.498094,0.49537,0.49254,0.489584,0.486476,0.483193,0.479706,0.475988,0.472007,0.467733,0.46313,0.458162,0.452791,0.446976,0.440675,0.433846,0.426441,0.418417,0.409727,0.400325,0.390171,0.379226,0.367459,0.354848,0.341385,0.327081,0.311973,0.29613,0.279667,0.262754,0.245636,0.228653,0.212264,0.197081,0.183907},
{1.00011,1.00007,1.00002,0.999969,0.999915,0.999858,0.999797,0.999733,0.999665,0.999592,0.999516,0.999435,0.999349,0.999258,0.999162,0.99906,0.998953,0.998839,0.998719,0.998592,0.998457,0.998315,0.998165,0.998007,0.997839,0.997663,0.997476,0.997279,0.997071,0.996851,0.99662,0.996375,0.996117,0.995845,0.995558,0.995255,0.994935,0.994598,0.994243,0.993868,0.993473,0.993057,0.992618,0.992155,0.991668,0.991155,0.990614,0.990044,0.989445,0.988813,0.988148,0.987448,0.986711,0.985936,0.98512,0.984262,0.983359,0.98241,0.981412,0.980362,0.97926,0.978101,0.976884,0.975606,0.974264,0.972855,0.971376,0.969824,0.968197,0.966491,0.964702,0.962828,0.960864,0.958808,0.956656,0.954404,0.952048,0.949586,0.947012,0.944323,0.941516,0.938587,0.935531,0.932346,0.929027,0.925572,0.921976,0.918237,0.914351,0.910315,0.906127,0.901785,0.897285,0.892626,0.887807,0.882826,0.877683,0.872378,0.866911,0.861283,0.855495,0.849549,0.843448,0.837195,0.830794,0.824251,0.81757,0.810757,0.80382,0.796767,0.789606,0.782345,0.774996,0.767568,0.760073,0.752522,0.744929,0.737305,0.729664,0.722019,0.714385,0.706775,0.699202,0.691682,0.684226,0.67685,0.669566,0.662386,0.655323,0.648388,0.641591,0.634943,0.628453,0.622128,0.615975,0.610001,0.60421,0.598606,0.593192,0.587969,0.582939,0.5781,0.573451,0.568989,0.56471,0.560611,0.556686,0.552928,0.549331,0.545886,0.542585,0.539419,0.536378,0.533452,0.530629,0.527898,0.525247,0.522663,0.520132,0.51764,0.515174,0.512717,0.510254,0.507767,0.50524,0.502654,0.499989,0.497224,0.494337,0.491305,0.488104,0.484707,0.481087,0.477212,0.473053,0.468574,0.463741,0.458516,0.452859,0.446728,0.440079,0.432869,0.42505,0.416577,0.407403,0.397485,0.386783,0.37526,0.362892,0.349662,0.335574,0.320651,0.304949,0.288562,0.271635,0.254382,0.237102,0.220201,0.204232,0.189913},
{1.00081,1.00078,1.00074,1.0007,1.00065,1.0006,1.00055,1.00049,1.00043,1.00037,1.0003,1.00023,1.00015,1.00006,0.999976,0.999883,0.999783,0.999677,0.999565,0.999446,0.99932,0.999186,0.999044,0.998894,0.998736,0.998568,0.99839,0.998202,0.998003,0.997793,0.99757,0.997335,0.997087,0.996825,0.996548,0.996256,0.995947,0.995621,0.995277,0.994914,0.994531,0.994126,0.9937,0.99325,0.992776,0.992276,0.991749,0.991194,0.990608,0.989992,0.989342,0.988657,0.987936,0.987177,0.986378,0.985537,0.984652,0.983721,0.982742,0.981712,0.980629,0.97949,0.978293,0.977036,0.975715,0.974328,0.972872,0.971344,0.96974,0.968058,0.966294,0.964445,0.962507,0.960477,0.958352,0.956127,0.9538,0.951365,0.948821,0.946162,0.943385,0.940486,0.937462,0.934309,0.931023,0.927601,0.924039,0.920334,0.916483,0.912482,0.90833,0.904024,0.89956,0.894939,0.890158,0.885215,0.880111,0.874845,0.869417,0.863829,0.858081,0.852175,0.846115,0.839903,0.833543,0.827041,0.820401,0.81363,0.806735,0.799723,0.792603,0.785384,0.778076,0.77069,0.763236,0.755726,0.748173,0.74059,0.732989,0.725384,0.71779,0.710218,0.702685,0.695203,0.687785,0.680447,0.6732,0.666057,0.65903,0.652131,0.64537,0.638757,0.632302,0.626012,0.619894,0.613955,0.608198,0.602629,0.59725,0.592063,0.587069,0.582266,0.577654,0.57323,0.568991,0.564932,0.561049,0.557335,0.553783,0.550387,0.547137,0.544025,0.541042,0.538177,0.53542,0.53276,0.530185,0.527683,0.525241,0.522846,0.520485,0.518142,0.515803,0.513452,0.511073,0.508648,0.506158,0.503585,0.500909,0.498107,0.495156,0.492033,0.488711,0.485163,0.481358,0.477267,0.472854,0.468085,0.462922,0.457326,0.451254,0.444664,0.437509,0.429744,0.421322,0.412197,0.402323,0.391659,0.380169,0.367823,0.354604,0.340512,0.325566,0.309816,0.293349,0.276304,0.258884,0.241371,0.22416,0.207776},
{1.00159,1.00157,1.00154,1.00151,1.00148,1.00144,1.0014,1.00136,1.00131,1.00125,1.0012,1.00114,1.00107,1.001,1.00092,1.00084,1.00075,1.00065,1.00055,1.00044,1.00032,1.0002,1.00007,0.99993,0.999781,0.999623,0.999456,0.999278,0.999089,0.998889,0.998678,0.998453,0.998216,0.997964,0.997698,0.997417,0.99712,0.996805,0.996473,0.996121,0.99575,0.995359,0.994945,0.994508,0.994047,0.99356,0.993047,0.992505,0.991934,0.991332,0.990697,0.990028,0.989323,0.98858,0.987798,0.986974,0.986106,0.985193,0.984231,0.98322,0.982156,0.981037,0.97986,0.978623,0.977323,0.975958,0.974523,0.973017,0.971437,0.969778,0.968038,0.966213,0.964301,0.962296,0.960197,0.957999,0.955699,0.953293,0.950776,0.948146,0.945399,0.94253,0.939537,0.936415,0.933161,0.929771,0.926242,0.92257,0.918753,0.914787,0.910669,0.906398,0.901971,0.897386,0.892641,0.887736,0.882669,0.877441,0.872052,0.866502,0.860792,0.854926,0.848905,0.842733,0.836413,0.82995,0.823351,0.81662,0.809765,0.802793,0.795713,0.788534,0.781266,0.77392,0.766505,0.759035,0.751521,0.743977,0.736415,0.728848,0.721291,0.713757,0.706261,0.698815,0.691434,0.684131,0.676919,0.669811,0.662818,0.655953,0.649225,0.642646,0.636223,0.629965,0.623879,0.617971,0.612247,0.606709,0.601362,0.596206,0.591243,0.586473,0.581893,0.577502,0.573297,0.569273,0.565426,0.561749,0.558236,0.55488,0.551673,0.548606,0.545671,0.542857,0.540154,0.537552,0.535039,0.532604,0.530235,0.527919,0.525642,0.523392,0.521154,0.518912,0.516652,0.514357,0.51201,0.509593,0.507086,0.50447,0.501722,0.498821,0.495741,0.492457,0.488941,0.485164,0.481095,0.476699,0.471941,0.466784,0.461187,0.455109,0.448506,0.441333,0.433542,0.425087,0.41592,0.405996,0.395274,0.383714,0.371289,0.357979,0.343782,0.328717,0.312833,0.296217,0.279002,0.26139,0.243664,0.226215},
{1.00241,1.00241,1.0024,1.00238,1.00237,1.00235,1.00232,1.00229,1.00226,1.00222,1.00218,1.00213,1.00208,1.00202,1.00196,1.00189,1.00182,1.00174,1.00165,1.00155,1.00145,1.00134,1.00122,1.0011,1.00096,1.00081,1.00066,1.00049,1.00032,1.00013,0.999932,0.99972,0.999495,0.999256,0.999002,0.998734,0.998449,0.998147,0.997827,0.997489,0.997131,0.996752,0.996352,0.995929,0.995481,0.995009,0.994509,0.993982,0.993426,0.992839,0.992219,0.991566,0.990876,0.99015,0.989384,0.988577,0.987726,0.98683,0.985887,0.984894,0.983849,0.982749,0.981592,0.980375,0.979096,0.977752,0.976339,0.974855,0.973297,0.971661,0.969945,0.968144,0.966256,0.964277,0.962204,0.960032,0.957759,0.955379,0.952891,0.95029,0.947571,0.944732,0.941769,0.938678,0.935454,0.932096,0.928599,0.92496,0.921176,0.917244,0.913161,0.908924,0.904532,0.899983,0.895274,0.890405,0.885375,0.880184,0.874832,0.86932,0.863649,0.857821,0.851839,0.845705,0.839425,0.833001,0.826441,0.819749,0.812933,0.806001,0.798961,0.791821,0.784592,0.777284,0.769909,0.762477,0.755002,0.747495,0.73997,0.732441,0.724921,0.717424,0.709963,0.702553,0.695208,0.687939,0.680762,0.673687,0.666728,0.659896,0.653201,0.646654,0.640263,0.634037,0.627982,0.622105,0.616412,0.610905,0.605589,0.600464,0.595532,0.590793,0.586246,0.581888,0.577716,0.573727,0.569915,0.566275,0.5628,0.559485,0.55632,0.553298,0.55041,0.547646,0.544997,0.542453,0.540003,0.537635,0.535338,0.5331,0.530909,0.528751,0.526613,0.524482,0.522341,0.520177,0.517973,0.515711,0.513375,0.510946,0.508402,0.505724,0.502889,0.499872,0.496648,0.493189,0.489467,0.48545,0.481105,0.476396,0.471285,0.465734,0.459699,0.453138,0.446003,0.43825,0.429829,0.420693,0.410797,0.400096,0.388552,0.376133,0.36282,0.348606,0.333509,0.31757,0.300869,0.283537,0.265763,0.247821},
{1.00324,1.00326,1.00327,1.00328,1.00328,1.00328,1.00328,1.00327,1.00325,1.00324,1.00322,1.00319,1.00316,1.00312,1.00307,1.00302,1.00297,1.0029,1.00283,1.00276,1.00267,1.00258,1.00248,1.00237,1.00225,1.00212,1.00198,1.00183,1.00167,1.0015,1.00131,1.00111,1.0009,1.00068,1.00044,1.00019,0.999917,0.99963,0.999324,0.999,0.998657,0.998293,0.997907,0.997498,0.997065,0.996608,0.996123,0.995611,0.99507,0.994498,0.993895,0.993257,0.992584,0.991873,0.991124,0.990334,0.989501,0.988622,0.987697,0.986722,0.985695,0.984615,0.983477,0.98228,0.981021,0.979697,0.978305,0.976843,0.975307,0.973693,0.972,0.970223,0.968359,0.966404,0.964355,0.962209,0.959961,0.957608,0.955147,0.952573,0.949882,0.947072,0.944137,0.941075,0.937882,0.934554,0.931088,0.927481,0.923728,0.919828,0.915778,0.911575,0.907216,0.902701,0.898027,0.893193,0.888198,0.883043,0.877727,0.872251,0.866616,0.860824,0.854879,0.848782,0.842538,0.836152,0.829629,0.822974,0.816196,0.809301,0.802297,0.795194,0.788002,0.78073,0.773391,0.765995,0.758555,0.751084,0.743594,0.736099,0.728613,0.721149,0.713721,0.706343,0.699029,0.691792,0.684645,0.6776,0.67067,0.663866,0.657199,0.650679,0.644315,0.638114,0.632085,0.626233,0.620563,0.61508,0.609787,0.604684,0.599775,0.595058,0.590532,0.586195,0.582044,0.578075,0.574284,0.570666,0.567212,0.563918,0.560776,0.557776,0.554911,0.552172,0.549549,0.547031,0.544608,0.54227,0.540004,0.5378,0.535645,0.533525,0.531429,0.529343,0.527251,0.52514,0.522993,0.520794,0.518526,0.516171,0.513709,0.511119,0.508381,0.50547,0.502362,0.499029,0.495445,0.491578,0.487397,0.482866,0.477949,0.472607,0.466799,0.460482,0.453611,0.446139,0.438018,0.4292,0.419638,0.409286,0.398102,0.38605,0.373103,0.359247,0.344484,0.328841,0.312377,0.295194,0.277448,0.259364},
{1.00407,1.00411,1.00414,1.00417,1.0042,1.00422,1.00424,1.00426,1.00427,1.00428,1.00428,1.00427,1.00427,1.00425,1.00423,1.0042,1.00417,1.00413,1.00408,1.00402,1.00396,1.00389,1.00381,1.00372,1.00362,1.00351,1.00339,1.00326,1.00312,1.00297,1.0028,1.00263,1.00243,1.00223,1.00201,1.00177,1.00152,1.00125,1.00096,1.00065,1.00032,0.999977,0.999607,0.999215,0.998799,0.998358,0.99789,0.997395,0.99687,0.996315,0.995728,0.995107,0.994451,0.993758,0.993026,0.992253,0.991438,0.990578,0.989671,0.988715,0.987707,0.986645,0.985527,0.98435,0.983111,0.981808,0.980437,0.978996,0.977482,0.975891,0.97422,0.972466,0.970625,0.968695,0.96667,0.964549,0.962327,0.96,0.957565,0.955017,0.952354,0.949572,0.946666,0.943632,0.940469,0.937171,0.933735,0.930158,0.926437,0.922569,0.91855,0.91438,0.910054,0.905572,0.900931,0.896131,0.891171,0.88605,0.880769,0.875328,0.869729,0.863973,0.858063,0.852003,0.845795,0.839445,0.832958,0.826339,0.819597,0.812738,0.80577,0.798703,0.791546,0.78431,0.777006,0.769645,0.76224,0.754802,0.747346,0.739884,0.732431,0.724999,0.717603,0.710256,0.702972,0.695765,0.688647,0.681631,0.674729,0.667952,0.661311,0.654817,0.648478,0.642302,0.636296,0.630467,0.62482,0.619359,0.614087,0.609006,0.604117,0.59942,0.594914,0.590596,0.586464,0.582515,0.578743,0.575142,0.571708,0.568433,0.56531,0.56233,0.559485,0.556766,0.554164,0.551669,0.549269,0.546956,0.544716,0.54254,0.540414,0.538326,0.536264,0.534214,0.532162,0.530093,0.527993,0.525845,0.523633,0.521338,0.518941,0.516424,0.513763,0.510938,0.507923,0.504694,0.501221,0.497476,0.493427,0.489041,0.484281,0.47911,0.473487,0.467369,0.460713,0.453471,0.445596,0.43704,0.427754,0.417692,0.406808,0.395063,0.382426,0.368873,0.3544,0.339021,0.322778,0.305751,0.288069,0.269923},
{1.00487,1.00493,1.00499,1.00505,1.00511,1.00516,1.0052,1.00525,1.00528,1.00532,1.00535,1.00537,1.00539,1.0054,1.00541,1.00541,1.0054,1.00539,1.00537,1.00534,1.0053,1.00525,1.0052,1.00514,1.00506,1.00498,1.00488,1.00478,1.00466,1.00453,1.00439,1.00423,1.00406,1.00388,1.00368,1.00346,1.00323,1.00298,1.00271,1.00242,1.00212,1.00179,1.00144,1.00107,1.00067,1.00025,0.999797,0.99932,0.998814,0.998277,0.997708,0.997106,0.996468,0.995794,0.99508,0.994326,0.99353,0.992688,0.9918,0.990863,0.989875,0.988833,0.987735,0.986578,0.98536,0.984077,0.982728,0.981308,0.979815,0.978246,0.976598,0.974867,0.97305,0.971143,0.969142,0.967045,0.964848,0.962547,0.960137,0.957616,0.95498,0.952224,0.949346,0.946341,0.943205,0.939936,0.93653,0.932983,0.929292,0.925454,0.921467,0.917328,0.913034,0.908584,0.903976,0.899209,0.894282,0.889194,0.883947,0.87854,0.872974,0.867253,0.861377,0.855351,0.849178,0.842863,0.83641,0.829826,0.823118,0.816293,0.80936,0.802327,0.795204,0.788001,0.78073,0.773402,0.766029,0.758624,0.751199,0.743768,0.736345,0.728943,0.721577,0.714258,0.707003,0.699822,0.692731,0.685741,0.678863,0.672111,0.665494,0.659022,0.652704,0.646549,0.640564,0.634754,0.629125,0.623682,0.618426,0.613361,0.608487,0.603804,0.599311,0.595006,0.590886,0.586947,0.583185,0.579594,0.576168,0.572901,0.569785,0.566812,0.563973,0.561259,0.558661,0.55617,0.553774,0.551463,0.549225,0.54705,0.544924,0.542837,0.540774,0.538723,0.536669,0.534597,0.532494,0.530341,0.528124,0.525823,0.52342,0.520895,0.518226,0.515391,0.512366,0.509124,0.505639,0.501879,0.497815,0.493411,0.488632,0.48344,0.477794,0.471652,0.464968,0.457697,0.449789,0.441197,0.431872,0.421765,0.410833,0.399035,0.386336,0.372716,0.358166,0.342699,0.326356,0.309213,0.291397,0.273092},
{1.00564,1.00573,1.00582,1.00591,1.00599,1.00607,1.00615,1.00622,1.00629,1.00635,1.00641,1.00647,1.00652,1.00656,1.0066,1.00663,1.00665,1.00667,1.00668,1.00668,1.00667,1.00666,1.00663,1.0066,1.00655,1.0065,1.00643,1.00635,1.00626,1.00616,1.00605,1.00592,1.00578,1.00562,1.00544,1.00525,1.00505,1.00482,1.00458,1.00431,1.00403,1.00372,1.0034,1.00305,1.00267,1.00227,1.00184,1.00139,1.0009,1.00039,0.999841,0.999259,0.998642,0.997989,0.997296,0.996562,0.995786,0.994966,0.994099,0.993182,0.992215,0.991194,0.990117,0.988982,0.987785,0.986524,0.985197,0.983799,0.982329,0.980783,0.979158,0.97745,0.975657,0.973774,0.971798,0.969726,0.967554,0.965279,0.962895,0.960401,0.957791,0.955063,0.952213,0.949236,0.946129,0.942889,0.939512,0.935995,0.932335,0.928528,0.924572,0.920464,0.916202,0.911784,0.907209,0.902475,0.897581,0.892527,0.887313,0.88194,0.876409,0.870722,0.864881,0.858889,0.852751,0.84647,0.840052,0.833503,0.82683,0.82004,0.813141,0.806142,0.799053,0.791885,0.784648,0.777353,0.770013,0.76264,0.755248,0.747849,0.740458,0.733087,0.72575,0.718462,0.711236,0.704085,0.697021,0.690059,0.683209,0.676483,0.669892,0.663446,0.657153,0.651022,0.64506,0.639274,0.633668,0.628247,0.623014,0.61797,0.613118,0.608456,0.603984,0.5997,0.595601,0.591684,0.587943,0.584374,0.58097,0.577726,0.574633,0.571684,0.56887,0.566183,0.563613,0.56115,0.558785,0.556507,0.554305,0.552168,0.550083,0.54804,0.546025,0.544025,0.542028,0.540018,0.537981,0.535902,0.533764,0.53155,0.529242,0.526822,0.524267,0.521557,0.518668,0.515576,0.512254,0.508673,0.504803,0.500612,0.496065,0.491124,0.485752,0.479905,0.473541,0.466613,0.459074,0.450877,0.44197,0.432305,0.421836,0.410518,0.398311,0.385186,0.371125,0.356124,0.340206,0.323421,0.305862,0.287671},
{1.00638,1.0065,1.00661,1.00673,1.00684,1.00695,1.00706,1.00717,1.00727,1.00736,1.00746,1.00754,1.00763,1.0077,1.00777,1.00784,1.0079,1.00795,1.00799,1.00803,1.00806,1.00807,1.00808,1.00808,1.00807,1.00805,1.00802,1.00797,1.00792,1.00785,1.00776,1.00766,1.00755,1.00742,1.00728,1.00712,1.00694,1.00675,1.00653,1.00629,1.00604,1.00576,1.00546,1.00514,1.00479,1.00441,1.00401,1.00358,1.00312,1.00263,1.0021,1.00154,1.00095,1.00032,0.999648,0.998938,0.998184,0.997386,0.996541,0.995647,0.994702,0.993703,0.992649,0.991535,0.990361,0.989123,0.987818,0.986444,0.984996,0.983474,0.981872,0.980188,0.978418,0.97656,0.974609,0.972561,0.970414,0.968164,0.965807,0.963338,0.960755,0.958054,0.955231,0.952281,0.949203,0.945991,0.942643,0.939155,0.935524,0.931746,0.92782,0.923743,0.919512,0.915125,0.910581,0.905878,0.901016,0.895995,0.890813,0.885473,0.879974,0.87432,0.868512,0.862553,0.856448,0.8502,0.843815,0.837299,0.830659,0.823902,0.817035,0.810069,0.803012,0.795876,0.78867,0.781406,0.774097,0.766755,0.759393,0.752023,0.744661,0.737318,0.730009,0.722748,0.715548,0.708423,0.701385,0.694446,0.68762,0.680917,0.674348,0.667923,0.661651,0.65554,0.649597,0.643829,0.638241,0.632836,0.627619,0.622591,0.617752,0.613104,0.608645,0.604373,0.600286,0.596379,0.592649,0.589089,0.585695,0.582458,0.579373,0.576431,0.573624,0.570943,0.568379,0.565921,0.563561,0.561287,0.559089,0.556955,0.554874,0.552833,0.550821,0.548823,0.546828,0.544819,0.542784,0.540706,0.538569,0.536356,0.534049,0.531628,0.529074,0.526364,0.523475,0.520383,0.51706,0.513479,0.509609,0.505418,0.50087,0.495929,0.490556,0.484708,0.478343,0.471414,0.463874,0.455673,0.446763,0.437093,0.426617,0.415288,0.403067,0.389922,0.375833,0.360796,0.344828,0.327977,0.310329,0.292022},
{1.00708,1.00723,1.00737,1.00752,1.00766,1.0078,1.00794,1.00808,1.00821,1.00835,1.00847,1.0086,1.00871,1.00883,1.00893,1.00904,1.00913,1.00922,1.0093,1.00937,1.00944,1.0095,1.00954,1.00958,1.00961,1.00962,1.00963,1.00962,1.0096,1.00957,1.00952,1.00946,1.00938,1.00929,1.00918,1.00905,1.00891,1.00875,1.00856,1.00836,1.00814,1.00789,1.00762,1.00733,1.00701,1.00666,1.00629,1.00588,1.00545,1.00499,1.00449,1.00396,1.00339,1.00279,1.00214,1.00146,1.00073,0.999956,0.999136,0.998267,0.997346,0.996372,0.995342,0.994253,0.993103,0.991889,0.990608,0.989258,0.987835,0.986337,0.98476,0.9831,0.981356,0.979522,0.977597,0.975575,0.973454,0.97123,0.968898,0.966457,0.963901,0.961227,0.958431,0.955509,0.952459,0.949276,0.945956,0.942497,0.938896,0.935149,0.931253,0.927206,0.923005,0.91865,0.914137,0.909466,0.904636,0.899646,0.894496,0.889188,0.883722,0.878101,0.872325,0.8664,0.860327,0.854112,0.847761,0.841277,0.83467,0.827945,0.821111,0.814177,0.807153,0.800048,0.792874,0.785642,0.778363,0.771052,0.763719,0.75638,0.749046,0.741732,0.734452,0.727218,0.720046,0.712947,0.705935,0.699022,0.69222,0.685541,0.678996,0.672594,0.666344,0.660255,0.654333,0.648586,0.643018,0.637633,0.632435,0.627425,0.622605,0.617975,0.613534,0.609279,0.605209,0.60132,0.597606,0.594064,0.590687,0.587468,0.584401,0.581477,0.578689,0.576027,0.573483,0.571047,0.568709,0.566459,0.564286,0.562179,0.560127,0.558117,0.556138,0.554176,0.55222,0.550254,0.548265,0.546237,0.544155,0.542002,0.53976,0.537411,0.534935,0.532311,0.529516,0.526527,0.523317,0.519859,0.516123,0.512078,0.50769,0.502923,0.497739,0.492097,0.485955,0.479266,0.471983,0.464059,0.455444,0.446086,0.435939,0.424953,0.413086,0.400301,0.386571,0.371883,0.356242,0.339678,0.322257,0.304089},
{1.00774,1.00792,1.00809,1.00827,1.00844,1.00862,1.00879,1.00896,1.00913,1.00929,1.00946,1.00962,1.00977,1.00992,1.01007,1.01021,1.01034,1.01047,1.01059,1.01071,1.01081,1.01091,1.011,1.01107,1.01114,1.0112,1.01124,1.01128,1.0113,1.01131,1.0113,1.01128,1.01124,1.01119,1.01112,1.01103,1.01093,1.0108,1.01066,1.01049,1.0103,1.01009,1.00986,1.0096,1.00931,1.009,1.00866,1.00829,1.00789,1.00746,1.00699,1.00649,1.00595,1.00538,1.00476,1.0041,1.0034,1.00266,1.00187,1.00102,1.00013,0.999182,0.998178,0.997115,0.995991,0.994803,0.993548,0.992223,0.990826,0.989353,0.987802,0.986168,0.984449,0.982642,0.980742,0.978746,0.976652,0.974454,0.972149,0.969734,0.967205,0.964558,0.96179,0.958896,0.955874,0.952719,0.949428,0.945998,0.942425,0.938707,0.93484,0.930823,0.926653,0.922327,0.917845,0.913205,0.908405,0.903446,0.898328,0.893051,0.887617,0.882027,0.876283,0.870389,0.864348,0.858165,0.851844,0.845393,0.838816,0.832123,0.82532,0.818417,0.811423,0.804348,0.797203,0.790001,0.782752,0.775469,0.768164,0.760852,0.753546,0.746259,0.739005,0.731797,0.724649,0.717574,0.710585,0.703695,0.696916,0.690258,0.683733,0.677351,0.671121,0.66505,0.659146,0.653416,0.647864,0.642495,0.637311,0.632316,0.627509,0.622892,0.618462,0.614219,0.61016,0.606281,0.602577,0.599044,0.595675,0.592464,0.589404,0.586487,0.583705,0.58105,0.578511,0.57608,0.573747,0.571502,0.569333,0.567229,0.56518,0.563174,0.561198,0.559239,0.557285,0.555322,0.553335,0.551309,0.549229,0.547078,0.544839,0.542492,0.540018,0.537397,0.534605,0.531618,0.528411,0.524956,0.521224,0.517183,0.5128,0.508038,0.50286,0.497224,0.491087,0.484405,0.47713,0.469214,0.460605,0.451256,0.441114,0.430132,0.418266,0.405479,0.391742,0.377037,0.361369,0.344764,0.327283,0.309026},
{1.00837,1.00857,1.00877,1.00898,1.00919,1.00939,1.0096,1.0098,1.01001,1.01021,1.01041,1.0106,1.0108,1.01099,1.01117,1.01135,1.01153,1.0117,1.01186,1.01202,1.01216,1.0123,1.01244,1.01256,1.01267,1.01277,1.01286,1.01294,1.01301,1.01306,1.0131,1.01312,1.01313,1.01312,1.01309,1.01305,1.01299,1.0129,1.0128,1.01268,1.01253,1.01236,1.01216,1.01194,1.0117,1.01142,1.01112,1.01079,1.01042,1.01003,1.0096,1.00913,1.00863,1.00808,1.0075,1.00688,1.00621,1.00549,1.00473,1.00392,1.00306,1.00214,1.00116,1.00013,0.999033,0.997873,0.996646,0.99535,0.99398,0.992535,0.991011,0.989405,0.987713,0.985933,0.984061,0.982092,0.980025,0.977855,0.975578,0.973191,0.970689,0.96807,0.96533,0.962465,0.959471,0.956344,0.953082,0.949681,0.946138,0.942449,0.938613,0.934626,0.930485,0.92619,0.921738,0.917129,0.91236,0.907432,0.902345,0.897099,0.891696,0.886137,0.880425,0.874562,0.868553,0.862401,0.856112,0.849692,0.843146,0.836484,0.829712,0.822839,0.815876,0.808831,0.801716,0.794543,0.787323,0.780069,0.772793,0.765509,0.75823,0.750969,0.743741,0.736559,0.729436,0.722386,0.715422,0.708555,0.701799,0.695164,0.688661,0.6823,0.67609,0.670039,0.664155,0.658444,0.65291,0.647559,0.642393,0.637415,0.632625,0.628024,0.623611,0.619384,0.61534,0.611476,0.607788,0.60427,0.600917,0.597722,0.594678,0.591777,0.589012,0.586374,0.583854,0.581442,0.579128,0.576904,0.574757,0.572677,0.570654,0.568674,0.566728,0.564801,0.562881,0.560955,0.559009,0.557027,0.554996,0.552897,0.550716,0.548432,0.546028,0.543482,0.540773,0.537877,0.534769,0.531423,0.52781,0.5239,0.519658,0.515052,0.510042,0.504589,0.498651,0.492184,0.485141,0.477473,0.469131,0.460065,0.450223,0.439556,0.428017,0.415566,0.402167,0.387798,0.372452,0.356142,0.338911,0.320839},
{1.00895,1.00919,1.00942,1.00965,1.00989,1.01013,1.01037,1.0106,1.01084,1.01108,1.01132,1.01155,1.01178,1.01201,1.01224,1.01246,1.01268,1.01289,1.0131,1.0133,1.01349,1.01368,1.01385,1.01402,1.01418,1.01433,1.01447,1.01459,1.01471,1.01481,1.01489,1.01497,1.01502,1.01506,1.01508,1.01509,1.01507,1.01503,1.01498,1.0149,1.0148,1.01467,1.01452,1.01435,1.01414,1.01391,1.01365,1.01336,1.01304,1.01268,1.01229,1.01186,1.01139,1.01089,1.01034,1.00975,1.00912,1.00844,1.00771,1.00694,1.00611,1.00522,1.00428,1.00327,1.00221,1.00108,0.999885,0.998618,0.997278,0.995863,0.994368,0.992791,0.991128,0.989376,0.987532,0.985593,0.983553,0.981411,0.979163,0.976804,0.974331,0.971741,0.969029,0.966192,0.963227,0.960129,0.956896,0.953524,0.950009,0.94635,0.942543,0.938585,0.934474,0.930209,0.925787,0.921207,0.916469,0.911571,0.906514,0.901299,0.895926,0.890397,0.884715,0.878883,0.872903,0.866782,0.860523,0.854132,0.847617,0.840983,0.834241,0.827397,0.820462,0.813446,0.806359,0.799214,0.792021,0.784793,0.777544,0.770285,0.763032,0.755796,0.748592,0.741433,0.734334,0.727306,0.720363,0.713517,0.706781,0.700166,0.693681,0.687339,0.681146,0.675112,0.669244,0.663547,0.658028,0.652691,0.647538,0.642572,0.637793,0.633203,0.6288,0.624582,0.620548,0.616692,0.613011,0.6095,0.606153,0.602963,0.599924,0.597028,0.594266,0.591631,0.589113,0.586703,0.584391,0.582167,0.58002,0.577939,0.575914,0.573933,0.571984,0.570053,0.568129,0.566198,0.564246,0.562258,0.560219,0.558113,0.555922,0.553628,0.551212,0.548653,0.54593,0.543019,0.539895,0.536531,0.532899,0.528967,0.524703,0.520071,0.515034,0.509552,0.503582,0.497081,0.490001,0.482293,0.473909,0.464796,0.454903,0.444181,0.432583,0.420066,0.406596,0.392149,0.376715,0.360307,0.342966,0.324768},
{1.00951,1.00977,1.01003,1.01029,1.01056,1.01083,1.0111,1.01137,1.01164,1.01192,1.01219,1.01246,1.01273,1.013,1.01327,1.01353,1.01379,1.01405,1.0143,1.01455,1.01479,1.01502,1.01525,1.01546,1.01567,1.01587,1.01606,1.01623,1.0164,1.01655,1.01669,1.01681,1.01692,1.01701,1.01708,1.01714,1.01717,1.01719,1.01718,1.01715,1.0171,1.01703,1.01693,1.0168,1.01664,1.01646,1.01625,1.016,1.01572,1.01541,1.01506,1.01468,1.01426,1.01379,1.01329,1.01274,1.01215,1.01151,1.01082,1.01008,1.00928,1.00843,1.00753,1.00656,1.00553,1.00443,1.00327,1.00204,1.00073,0.999346,0.997883,0.996338,0.994706,0.992985,0.991172,0.989263,0.987254,0.985142,0.982923,0.980594,0.978151,0.97559,0.972908,0.970101,0.967165,0.964097,0.960893,0.957551,0.954067,0.950437,0.94666,0.942732,0.938651,0.934416,0.930024,0.925474,0.920766,0.915899,0.910872,0.905687,0.900345,0.894846,0.889195,0.883392,0.877443,0.871352,0.865122,0.858762,0.852276,0.845672,0.838959,0.832144,0.825238,0.81825,0.811191,0.804073,0.796908,0.789707,0.782484,0.775251,0.768023,0.760812,0.753633,0.746498,0.739422,0.732417,0.725496,0.718672,0.711957,0.705362,0.698898,0.692574,0.686401,0.680385,0.674534,0.668855,0.663353,0.658031,0.652894,0.647943,0.64318,0.638604,0.634215,0.630011,0.62599,0.622148,0.61848,0.614983,0.611649,0.608473,0.605447,0.602564,0.599817,0.597196,0.594693,0.592298,0.590002,0.587795,0.585666,0.583605,0.5816,0.579641,0.577715,0.57581,0.573913,0.572012,0.570093,0.56814,0.566139,0.564075,0.56193,0.559686,0.557325,0.554827,0.55217,0.549332,0.546287,0.543011,0.539473,0.535646,0.531496,0.526988,0.522087,0.516753,0.510944,0.504616,0.497724,0.490219,0.482051,0.473169,0.463522,0.453059,0.441731,0.429493,0.416307,0.402142,0.386984,0.370834,0.353718,0.335699},
{1.01003,1.01031,1.0106,1.01089,1.01119,1.01149,1.01179,1.0121,1.0124,1.01271,1.01302,1.01333,1.01364,1.01395,1.01426,1.01457,1.01487,1.01517,1.01547,1.01576,1.01605,1.01633,1.01661,1.01687,1.01713,1.01738,1.01762,1.01785,1.01807,1.01827,1.01847,1.01864,1.0188,1.01895,1.01908,1.01919,1.01928,1.01935,1.0194,1.01942,1.01943,1.01941,1.01936,1.01928,1.01918,1.01905,1.01889,1.01869,1.01847,1.0182,1.0179,1.01757,1.01719,1.01678,1.01632,1.01581,1.01526,1.01467,1.01402,1.01332,1.01257,1.01176,1.01089,1.00996,1.00897,1.00791,1.00678,1.00559,1.00431,1.00297,1.00154,1.00003,0.998427,0.996739,0.994958,0.993081,0.991104,0.989023,0.986836,0.984538,0.982125,0.979595,0.976943,0.974166,0.971261,0.968223,0.965049,0.961737,0.958282,0.954683,0.950935,0.947037,0.942986,0.93878,0.934418,0.929898,0.92522,0.920382,0.915385,0.91023,0.904917,0.899448,0.893825,0.888052,0.882132,0.876069,0.869869,0.863536,0.857079,0.850503,0.843817,0.83703,0.830151,0.823189,0.816157,0.809065,0.801925,0.794749,0.78755,0.780342,0.773137,0.765949,0.758792,0.751679,0.744623,0.737638,0.730737,0.723932,0.717235,0.710658,0.70421,0.697903,0.691744,0.685743,0.679906,0.67424,0.66875,0.66344,0.658314,0.653373,0.648619,0.644052,0.639671,0.635474,0.631459,0.627623,0.62396,0.620466,0.617135,0.613961,0.610937,0.608056,0.605308,0.602686,0.600181,0.597784,0.595484,0.593272,0.591137,0.589069,0.587057,0.585088,0.583151,0.581234,0.579324,0.577407,0.575471,0.573499,0.571478,0.56939,0.56722,0.564948,0.562557,0.560025,0.557331,0.554452,0.551364,0.548039,0.544449,0.540565,0.536352,0.531777,0.526803,0.521389,0.515494,0.509074,0.502082,0.494469,0.486185,0.477178,0.467398,0.456793,0.445313,0.432915,0.419558,0.405215,0.38987,0.373524,0.356208,0.337981},
{1.01052,1.01083,1.01114,1.01146,1.01179,1.01211,1.01245,1.01279,1.01313,1.01347,1.01382,1.01416,1.01451,1.01486,1.01521,1.01556,1.01591,1.01625,1.0166,1.01694,1.01727,1.0176,1.01793,1.01825,1.01856,1.01886,1.01916,1.01944,1.01971,1.01997,1.02022,1.02046,1.02068,1.02088,1.02107,1.02123,1.02138,1.02151,1.02162,1.0217,1.02177,1.0218,1.02181,1.0218,1.02175,1.02168,1.02157,1.02143,1.02126,1.02105,1.0208,1.02052,1.0202,1.01983,1.01942,1.01897,1.01847,1.01792,1.01732,1.01666,1.01596,1.01519,1.01437,1.01348,1.01253,1.01151,1.01042,1.00927,1.00803,1.00672,1.00533,1.00385,1.00229,1.00064,0.998894,0.997051,0.995107,0.99306,0.990906,0.98864,0.98626,0.983762,0.981142,0.978397,0.975522,0.972515,0.969373,0.966091,0.962667,0.959097,0.95538,0.951512,0.947491,0.943315,0.938983,0.934493,0.929844,0.925035,0.920068,0.914942,0.909658,0.904218,0.898624,0.892879,0.886988,0.880953,0.87478,0.868476,0.862046,0.855497,0.848838,0.842077,0.835224,0.828288,0.821281,0.814213,0.807097,0.799945,0.79277,0.785584,0.778401,0.771235,0.764098,0.757005,0.749969,0.743004,0.736121,0.729333,0.722653,0.716091,0.709659,0.703366,0.697221,0.691233,0.685408,0.679753,0.674273,0.668973,0.663855,0.658922,0.654175,0.649614,0.645238,0.641046,0.637034,0.6332,0.629538,0.626045,0.622714,0.619538,0.616511,0.613625,0.610872,0.608244,0.605731,0.603324,0.601013,0.598788,0.596639,0.594554,0.592523,0.590534,0.588574,0.586631,0.584693,0.582745,0.580773,0.578763,0.5767,0.574566,0.572344,0.570017,0.567564,0.564965,0.562197,0.559238,0.556061,0.55264,0.548946,0.544947,0.54061,0.535899,0.530778,0.525204,0.519137,0.512529,0.505336,0.497505,0.488988,0.479732,0.469686,0.458797,0.447018,0.434305,0.42062,0.405936,0.390241,0.373542,0.355872,0.337302},
{1.01099,1.01132,1.01165,1.012,1.01235,1.01271,1.01307,1.01344,1.01381,1.01419,1.01457,1.01496,1.01534,1.01573,1.01612,1.01652,1.01691,1.0173,1.01769,1.01808,1.01846,1.01884,1.01922,1.01959,1.01996,1.02031,1.02066,1.021,1.02133,1.02165,1.02196,1.02225,1.02253,1.0228,1.02304,1.02327,1.02348,1.02367,1.02384,1.02399,1.02412,1.02421,1.02429,1.02433,1.02435,1.02433,1.02429,1.02421,1.0241,1.02395,1.02376,1.02353,1.02327,1.02296,1.02261,1.02221,1.02176,1.02126,1.02071,1.02011,1.01945,1.01874,1.01796,1.01712,1.01622,1.01524,1.0142,1.01309,1.0119,1.01063,1.00928,1.00784,1.00632,1.00471,1.003,1.00119,0.999286,0.997275,0.995156,0.992926,0.990581,0.988118,0.985532,0.98282,0.979979,0.977005,0.973895,0.970646,0.967254,0.963717,0.960032,0.956195,0.952206,0.948062,0.94376,0.939301,0.934683,0.929905,0.924968,0.919872,0.914618,0.909208,0.903644,0.897929,0.892067,0.886062,0.879918,0.873642,0.86724,0.86072,0.854088,0.847355,0.840529,0.83362,0.82664,0.819598,0.812508,0.805381,0.79823,0.791069,0.78391,0.776767,0.769653,0.762583,0.755569,0.748624,0.741762,0.734995,0.728335,0.721793,0.715379,0.709105,0.702978,0.697008,0.6912,0.685563,0.6801,0.674816,0.669715,0.664798,0.660067,0.655521,0.651161,0.646985,0.642989,0.639171,0.635527,0.63205,0.628736,0.625578,0.62257,0.619704,0.616972,0.614365,0.611875,0.609492,0.607207,0.605011,0.602892,0.60084,0.598844,0.596892,0.594974,0.593076,0.591187,0.589293,0.58738,0.585434,0.583441,0.581384,0.579247,0.577011,0.57466,0.572172,0.569526,0.5667,0.563669,0.560408,0.556889,0.553081,0.548954,0.544472,0.539599,0.534297,0.528523,0.522235,0.515386,0.507928,0.49981,0.490981,0.481389,0.470982,0.459708,0.447521,0.434377,0.420241,0.405092,0.38892,0.371741,0.353599},
{1.01142,1.01178,1.01214,1.01251,1.01288,1.01327,1.01366,1.01406,1.01447,1.01488,1.01529,1.01571,1.01614,1.01657,1.017,1.01743,1.01787,1.0183,1.01874,1.01918,1.01961,1.02004,1.02047,1.02089,1.02131,1.02172,1.02213,1.02253,1.02292,1.0233,1.02366,1.02402,1.02436,1.02469,1.025,1.02529,1.02557,1.02582,1.02606,1.02627,1.02646,1.02663,1.02676,1.02687,1.02696,1.02701,1.02703,1.02701,1.02696,1.02688,1.02675,1.02659,1.02639,1.02614,1.02584,1.0255,1.02512,1.02468,1.02418,1.02364,1.02303,1.02237,1.02165,1.02086,1.02001,1.01908,1.01809,1.01702,1.01588,1.01465,1.01335,1.01196,1.01048,1.0089,1.00724,1.00547,1.00361,1.00163,0.999554,0.997362,0.995054,0.992627,0.990077,0.9874,0.984594,0.981655,0.978579,0.975363,0.972005,0.9685,0.964847,0.961043,0.957086,0.952973,0.948703,0.944275,0.939688,0.934941,0.930034,0.924968,0.919744,0.914363,0.908829,0.903143,0.897309,0.891332,0.885217,0.878968,0.872594,0.8661,0.859496,0.852789,0.845989,0.839105,0.83215,0.825133,0.818067,0.810964,0.803836,0.796697,0.789561,0.782439,0.775347,0.768297,0.761303,0.754377,0.747534,0.740786,0.734143,0.727618,0.721221,0.714963,0.708852,0.702896,0.697103,0.69148,0.68603,0.680759,0.675671,0.670766,0.666046,0.661513,0.657164,0.652998,0.649013,0.645206,0.641571,0.638104,0.6348,0.631653,0.628654,0.625798,0.623076,0.62048,0.618,0.615629,0.613356,0.611171,0.609065,0.607026,0.605044,0.603108,0.601206,0.599326,0.597456,0.595583,0.593692,0.591771,0.589805,0.587777,0.585672,0.583472,0.581159,0.578713,0.576114,0.573339,0.570365,0.567165,0.563713,0.55998,0.555934,0.551541,0.546765,0.541569,0.535911,0.529748,0.523036,0.515724,0.507765,0.499106,0.489695,0.47948,0.468409,0.456432,0.443504,0.429587,0.414654,0.39869,0.381701,0.363719},
{1.01184,1.01221,1.01259,1.01299,1.01339,1.0138,1.01422,1.01465,1.01508,1.01553,1.01598,1.01643,1.0169,1.01736,1.01783,1.01831,1.01879,1.01927,1.01975,1.02023,1.02072,1.0212,1.02168,1.02216,1.02263,1.0231,1.02356,1.02402,1.02447,1.02491,1.02533,1.02575,1.02616,1.02655,1.02693,1.02729,1.02763,1.02795,1.02825,1.02854,1.02879,1.02903,1.02924,1.02942,1.02957,1.02969,1.02978,1.02983,1.02985,1.02983,1.02978,1.02968,1.02954,1.02936,1.02913,1.02885,1.02853,1.02815,1.02772,1.02723,1.02669,1.02608,1.02542,1.02468,1.02388,1.02302,1.02207,1.02106,1.01997,1.01879,1.01753,1.01619,1.01475,1.01323,1.01161,1.00988,1.00806,1.00613,1.00409,1.00194,0.999669,0.99728,0.994767,0.992128,0.989358,0.986455,0.983414,0.980233,0.976909,0.973438,0.969818,0.966047,0.962122,0.958041,0.953802,0.949405,0.944848,0.940132,0.935255,0.930218,0.925024,0.919672,0.914166,0.908508,0.902702,0.896752,0.890664,0.884442,0.878094,0.871626,0.865047,0.858364,0.851589,0.844729,0.837797,0.830803,0.823759,0.816677,0.80957,0.802452,0.795335,0.788233,0.781159,0.774126,0.767149,0.760241,0.753413,0.746679,0.740051,0.73354,0.727156,0.72091,0.71481,0.708865,0.703081,0.697467,0.692025,0.686762,0.681679,0.67678,0.672066,0.667536,0.66319,0.659027,0.655043,0.651235,0.6476,0.644132,0.640825,0.637673,0.634669,0.631807,0.629077,0.626471,0.623981,0.621597,0.61931,0.61711,0.614986,0.612927,0.610923,0.608963,0.607033,0.605123,0.60322,0.601309,0.599379,0.597413,0.595398,0.593316,0.591152,0.588887,0.586504,0.58398,0.581296,0.578429,0.575353,0.572043,0.568471,0.564606,0.560416,0.555868,0.550923,0.545543,0.539686,0.533309,0.526364,0.518802,0.510574,0.501627,0.491908,0.481365,0.469945,0.457602,0.444289,0.429973,0.414627,0.398242,0.38083,0.362431},
{1.01223,1.01262,1.01302,1.01344,1.01387,1.0143,1.01475,1.01521,1.01567,1.01615,1.01663,1.01712,1.01762,1.01812,1.01863,1.01915,1.01967,1.02019,1.02072,1.02125,1.02178,1.02232,1.02285,1.02338,1.02391,1.02443,1.02495,1.02547,1.02598,1.02648,1.02697,1.02745,1.02792,1.02838,1.02883,1.02925,1.02967,1.03006,1.03043,1.03079,1.03112,1.03142,1.0317,1.03195,1.03218,1.03237,1.03253,1.03266,1.03275,1.03281,1.03282,1.0328,1.03273,1.03262,1.03246,1.03225,1.03199,1.03168,1.03132,1.0309,1.03042,1.02988,1.02927,1.0286,1.02786,1.02705,1.02617,1.02521,1.02417,1.02305,1.02184,1.02055,1.01917,1.01769,1.01612,1.01444,1.01266,1.01078,1.00878,1.00667,1.00445,1.0021,0.999626,0.997027,0.994296,0.99143,0.988427,0.985283,0.981995,0.978559,0.974975,0.971238,0.967346,0.963299,0.959093,0.954728,0.950203,0.945518,0.940672,0.935666,0.930501,0.925179,0.919702,0.914073,0.908295,0.902373,0.896312,0.890117,0.883795,0.877354,0.8708,0.864142,0.857391,0.850555,0.843646,0.836675,0.829653,0.822593,0.815508,0.80841,0.801313,0.79423,0.787175,0.780161,0.773201,0.766309,0.759498,0.75278,0.746167,0.73967,0.733299,0.727066,0.720979,0.715045,0.709273,0.703669,0.698238,0.692983,0.68791,0.683019,0.678312,0.673789,0.669449,0.665292,0.661313,0.65751,0.653879,0.650414,0.64711,0.643961,0.64096,0.638098,0.635369,0.632764,0.630274,0.627889,0.6256,0.623398,0.621271,0.619209,0.617201,0.615236,0.613301,0.611385,0.609475,0.607556,0.605617,0.603642,0.601615,0.599522,0.597345,0.595066,0.592667,0.590127,0.587425,0.584537,0.58144,0.578107,0.57451,0.570618,0.566399,0.56182,0.556841,0.551426,0.54553,0.539111,0.532122,0.524513,0.516234,0.507232,0.497455,0.48685,0.475364,0.462948,0.449559,0.435159,0.419723,0.403239,0.385718,0.367198},
{1.0126,1.01301,1.01343,1.01387,1.01432,1.01478,1.01525,1.01574,1.01623,1.01674,1.01725,1.01777,1.01831,1.01885,1.0194,1.01995,1.02051,1.02108,1.02165,1.02223,1.02281,1.02339,1.02398,1.02456,1.02514,1.02573,1.02631,1.02688,1.02745,1.02801,1.02857,1.02912,1.02966,1.03018,1.03069,1.03119,1.03168,1.03214,1.03259,1.03301,1.03342,1.0338,1.03416,1.03448,1.03478,1.03505,1.03529,1.0355,1.03567,1.0358,1.03589,1.03594,1.03595,1.03591,1.03583,1.03569,1.03551,1.03527,1.03498,1.03462,1.03421,1.03374,1.0332,1.0326,1.03192,1.03118,1.03035,1.02945,1.02848,1.02741,1.02627,1.02503,1.0237,1.02228,1.02075,1.01913,1.0174,1.01557,1.01362,1.01155,1.00937,1.00707,1.00464,1.00208,0.999395,0.99657,0.993607,0.990501,0.987251,0.983853,0.980305,0.976604,0.972748,0.968735,0.964563,0.960232,0.955739,0.951086,0.946272,0.941297,0.936163,0.930871,0.925423,0.919823,0.914073,0.908179,0.902145,0.895977,0.889682,0.883266,0.876737,0.870104,0.863377,0.856565,0.849679,0.84273,0.83573,0.828691,0.821626,0.814548,0.80747,0.800406,0.793369,0.786372,0.779429,0.772554,0.765758,0.759055,0.752455,0.745972,0.739615,0.733394,0.727318,0.721396,0.715634,0.710039,0.704617,0.699371,0.694306,0.689422,0.684722,0.680205,0.675871,0.671719,0.667744,0.663946,0.660318,0.656856,0.653554,0.650406,0.647406,0.644545,0.641816,0.63921,0.636718,0.634331,0.63204,0.629834,0.627703,0.625637,0.623623,0.621652,0.61971,0.617785,0.615866,0.613937,0.611987,0.609999,0.607959,0.605851,0.603657,0.601361,0.598942,0.596381,0.593656,0.590743,0.587619,0.584256,0.580627,0.576701,0.572445,0.567826,0.562805,0.557342,0.551397,0.544925,0.537879,0.530208,0.521864,0.512793,0.502941,0.492256,0.480685,0.468179,0.454693,0.440189,0.424641,0.408038,0.390388,0.371728},
{1.01295,1.01338,1.01382,1.01428,1.01475,1.01523,1.01573,1.01624,1.01676,1.01729,1.01784,1.0184,1.01896,1.01954,1.02012,1.02072,1.02132,1.02193,1.02255,1.02317,1.0238,1.02443,1.02507,1.0257,1.02634,1.02698,1.02762,1.02825,1.02888,1.02951,1.03013,1.03075,1.03135,1.03195,1.03253,1.0331,1.03365,1.03419,1.03472,1.03522,1.0357,1.03616,1.03659,1.037,1.03738,1.03773,1.03805,1.03833,1.03858,1.03879,1.03897,1.0391,1.03918,1.03923,1.03922,1.03917,1.03906,1.0389,1.03868,1.0384,1.03807,1.03767,1.0372,1.03667,1.03606,1.03539,1.03463,1.0338,1.03288,1.03189,1.0308,1.02962,1.02835,1.02699,1.02552,1.02395,1.02228,1.0205,1.0186,1.01659,1.01445,1.0122,1.00982,1.00731,1.00466,1.00188,0.998959,0.995895,0.992686,0.989328,0.985818,0.982155,0.978336,0.974359,0.970223,0.965927,0.961469,0.956849,0.952068,0.947125,0.942022,0.936761,0.931344,0.925773,0.920053,0.914187,0.908181,0.90204,0.895771,0.889381,0.882878,0.87627,0.869567,0.862779,0.855916,0.84899,0.842012,0.834994,0.82795,0.820892,0.813834,0.806788,0.799769,0.79279,0.785865,0.779005,0.772225,0.765537,0.758953,0.752484,0.74614,0.739932,0.733869,0.727958,0.722208,0.716625,0.711213,0.705977,0.700921,0.696047,0.691356,0.686848,0.682522,0.678378,0.674411,0.67062,0.666999,0.663545,0.66025,0.657109,0.654116,0.651262,0.64854,0.645941,0.643456,0.641077,0.638794,0.636596,0.634473,0.632416,0.630412,0.62845,0.626519,0.624606,0.622699,0.620785,0.618849,0.616877,0.614855,0.612767,0.610595,0.608322,0.605929,0.603397,0.600703,0.597826,0.59474,0.59142,0.587837,0.583962,0.579763,0.575205,0.570252,0.564864,0.559001,0.552617,0.545667,0.538101,0.529869,0.520919,0.511196,0.500648,0.489221,0.476865,0.463533,0.449184,0.43379,0.417332,0.399813,0.38126},
{1.01328,1.01373,1.01419,1.01466,1.01515,1.01566,1.01618,1.01671,1.01726,1.01782,1.0184,1.01899,1.01959,1.0202,1.02082,1.02145,1.0221,1.02275,1.02341,1.02408,1.02475,1.02543,1.02612,1.02681,1.0275,1.02819,1.02889,1.02958,1.03028,1.03097,1.03165,1.03233,1.03301,1.03367,1.03433,1.03497,1.0356,1.03621,1.03681,1.03739,1.03795,1.03849,1.03901,1.03949,1.03996,1.04039,1.04079,1.04116,1.04149,1.04179,1.04204,1.04226,1.04243,1.04256,1.04264,1.04266,1.04264,1.04256,1.04242,1.04223,1.04197,1.04165,1.04126,1.0408,1.04027,1.03967,1.03899,1.03822,1.03738,1.03645,1.03543,1.03432,1.03311,1.03181,1.03041,1.0289,1.02728,1.02555,1.02371,1.02175,1.01967,1.01747,1.01514,1.01268,1.01008,1.00734,1.00447,1.00145,0.998281,0.994964,0.991496,0.987872,0.984092,0.980154,0.976054,0.971794,0.967371,0.962786,0.958038,0.953128,0.948058,0.942828,0.937441,0.9319,0.926209,0.920372,0.914394,0.90828,0.902038,0.895673,0.889195,0.882612,0.875932,0.869167,0.862326,0.855421,0.848464,0.841467,0.834443,0.827404,0.820363,0.813336,0.806334,0.799371,0.792461,0.785616,0.778851,0.772176,0.765605,0.759148,0.752816,0.746619,0.740566,0.734665,0.728924,0.723349,0.717946,0.712718,0.707669,0.702801,0.698115,0.693612,0.689292,0.685151,0.681188,0.6774,0.673782,0.670329,0.667036,0.663897,0.660904,0.658049,0.655327,0.652726,0.65024,0.647859,0.645572,0.643371,0.641244,0.639181,0.637172,0.635203,0.633265,0.631344,0.629428,0.627503,0.625556,0.623572,0.621537,0.619433,0.617246,0.614955,0.612544,0.60999,0.607274,0.604373,0.601261,0.597912,0.594299,0.590391,0.586157,0.581561,0.576566,0.571135,0.565224,0.55879,0.551786,0.544162,0.535869,0.526853,0.517061,0.506438,0.494932,0.482491,0.469069,0.454624,0.439125,0.422556,0.404916,0.386232},
{1.0136,1.01406,1.01454,1.01503,1.01554,1.01607,1.01661,1.01717,1.01774,1.01833,1.01893,1.01955,1.02018,1.02083,1.02148,1.02215,1.02284,1.02353,1.02423,1.02494,1.02566,1.02639,1.02713,1.02787,1.02862,1.02937,1.03012,1.03088,1.03163,1.03238,1.03313,1.03388,1.03462,1.03536,1.03609,1.0368,1.03751,1.0382,1.03888,1.03954,1.04018,1.0408,1.04139,1.04197,1.04251,1.04303,1.04352,1.04398,1.0444,1.04478,1.04512,1.04543,1.04569,1.0459,1.04607,1.04618,1.04624,1.04625,1.0462,1.04609,1.04592,1.04568,1.04537,1.045,1.04455,1.04402,1.04342,1.04273,1.04196,1.04111,1.04016,1.03912,1.03798,1.03675,1.03541,1.03396,1.03241,1.03074,1.02896,1.02706,1.02504,1.02289,1.02061,1.0182,1.01566,1.01297,1.01014,1.00717,1.00405,1.00078,0.997353,0.993772,0.990033,0.986135,0.982075,0.977852,0.973467,0.968918,0.964205,0.95933,0.954292,0.949095,0.94374,0.93823,0.932569,0.926762,0.920812,0.914726,0.908511,0.902173,0.89572,0.889161,0.882506,0.875764,0.868946,0.862063,0.855127,0.848151,0.841146,0.834126,0.827105,0.820095,0.81311,0.806163,0.799269,0.79244,0.785689,0.779029,0.772471,0.766026,0.759707,0.753521,0.74748,0.74159,0.735859,0.730294,0.7249,0.719681,0.71464,0.709781,0.705103,0.700608,0.696294,0.69216,0.688204,0.684423,0.680811,0.677364,0.674077,0.670944,0.667956,0.665108,0.662391,0.659797,0.657317,0.654942,0.652662,0.650468,0.648348,0.646293,0.644291,0.642332,0.640403,0.638492,0.636587,0.634674,0.63274,0.630771,0.628751,0.626665,0.624496,0.622227,0.619838,0.617311,0.614623,0.611752,0.608675,0.605364,0.601793,0.597931,0.593747,0.589207,0.584275,0.57891,0.573074,0.56672,0.559804,0.552276,0.544085,0.535181,0.525507,0.515011,0.503639,0.491337,0.478059,0.46376,0.448406,0.431976,0.414463,0.395886},
{1.0139,1.01438,1.01487,1.01538,1.01591,1.01645,1.01702,1.0176,1.0182,1.01881,1.01944,1.02009,1.02075,1.02142,1.02212,1.02282,1.02354,1.02427,1.02502,1.02577,1.02654,1.02732,1.0281,1.0289,1.0297,1.0305,1.03131,1.03213,1.03294,1.03376,1.03457,1.03539,1.0362,1.03701,1.03781,1.0386,1.03938,1.04015,1.0409,1.04164,1.04237,1.04307,1.04375,1.04441,1.04505,1.04565,1.04623,1.04677,1.04729,1.04776,1.0482,1.04859,1.04894,1.04925,1.04951,1.04971,1.04987,1.04996,1.05,1.04998,1.0499,1.04975,1.04953,1.04924,1.04888,1.04843,1.04791,1.04731,1.04662,1.04584,1.04497,1.04401,1.04294,1.04178,1.04051,1.03914,1.03765,1.03605,1.03433,1.0325,1.03053,1.02844,1.02622,1.02387,1.02138,1.01875,1.01597,1.01305,1.00998,1.00675,1.00337,0.999835,0.99614,0.992283,0.988264,0.984082,0.979735,0.975223,0.970547,0.965707,0.960704,0.955541,0.950218,0.94474,0.939109,0.933331,0.92741,0.921352,0.915164,0.908852,0.902424,0.89589,0.889258,0.882539,0.875743,0.868881,0.861966,0.855009,0.848023,0.841022,0.834017,0.827024,0.820055,0.813124,0.806244,0.799428,0.792691,0.786042,0.779496,0.773063,0.766754,0.760578,0.754546,0.748664,0.742941,0.737384,0.731996,0.726783,0.721748,0.716893,0.71222,0.707729,0.703418,0.699288,0.695334,0.691554,0.687944,0.684498,0.681211,0.678077,0.675089,0.672239,0.66952,0.666923,0.664439,0.66206,0.659775,0.657575,0.655449,0.653387,0.651377,0.649409,0.64747,0.645548,0.643631,0.641704,0.639756,0.63777,0.635733,0.633628,0.631438,0.629146,0.626733,0.624178,0.621461,0.618559,0.615447,0.6121,0.608488,0.604584,0.600353,0.595763,0.590777,0.585355,0.579456,0.573035,0.566048,0.558443,0.550172,0.54118,0.531414,0.520819,0.509342,0.496929,0.483533,0.469109,0.453623,0.437052,0.419391,0.400656},
{1.01419,1.01468,1.01519,1.01571,1.01626,1.01682,1.01741,1.01801,1.01863,1.01927,1.01992,1.0206,1.02129,1.022,1.02272,1.02346,1.02422,1.02499,1.02577,1.02657,1.02738,1.0282,1.02904,1.02988,1.03073,1.0316,1.03246,1.03334,1.03421,1.03509,1.03597,1.03686,1.03774,1.03861,1.03949,1.04035,1.04121,1.04206,1.04289,1.04372,1.04452,1.04531,1.04608,1.04683,1.04755,1.04825,1.04892,1.04955,1.05016,1.05073,1.05126,1.05175,1.05219,1.0526,1.05295,1.05325,1.0535,1.0537,1.05383,1.05391,1.05392,1.05386,1.05373,1.05353,1.05326,1.05291,1.05247,1.05196,1.05135,1.05066,1.04987,1.04899,1.048,1.04692,1.04573,1.04443,1.04301,1.04148,1.03984,1.03807,1.03617,1.03414,1.03199,1.02969,1.02726,1.02468,1.02196,1.01909,1.01607,1.0129,1.00957,1.00608,1.00243,0.998623,0.994648,0.990507,0.986202,0.98173,0.977092,0.97229,0.967323,0.962195,0.956906,0.951461,0.945863,0.940116,0.934225,0.928196,0.922036,0.915751,0.90935,0.902841,0.896234,0.889538,0.882765,0.875925,0.869031,0.862094,0.855128,0.848145,0.841159,0.834183,0.827231,0.820316,0.813451,0.80665,0.799926,0.793292,0.786758,0.780337,0.77404,0.767876,0.761854,0.755983,0.75027,0.744722,0.739343,0.734139,0.729112,0.724266,0.7196,0.715117,0.710814,0.706691,0.702744,0.698972,0.695369,0.69193,0.68865,0.685524,0.682543,0.679702,0.676991,0.674403,0.671928,0.669559,0.667284,0.665095,0.66298,0.660931,0.658935,0.656981,0.655058,0.653153,0.651255,0.64935,0.647424,0.645464,0.643454,0.641379,0.639222,0.636967,0.634594,0.632084,0.629415,0.626567,0.623514,0.620231,0.616692,0.612865,0.608721,0.604226,0.599342,0.594034,0.588258,0.581973,0.575131,0.567685,0.559585,0.550778,0.54121,0.530827,0.519573,0.507395,0.494243,0.480071,0.46484,0.448522,0.431105,0.412593},
{1.01447,1.01497,1.01549,1.01603,1.01659,1.01717,1.01778,1.0184,1.01904,1.0197,1.02038,1.02108,1.0218,1.02254,1.0233,1.02407,1.02486,1.02567,1.02649,1.02733,1.02819,1.02906,1.02994,1.03083,1.03174,1.03265,1.03357,1.0345,1.03544,1.03639,1.03733,1.03828,1.03923,1.04018,1.04112,1.04206,1.043,1.04393,1.04484,1.04575,1.04664,1.04752,1.04837,1.04921,1.05002,1.05081,1.05158,1.05231,1.05301,1.05367,1.0543,1.05489,1.05543,1.05594,1.05639,1.05679,1.05714,1.05743,1.05767,1.05784,1.05795,1.05799,1.05796,1.05786,1.05768,1.05742,1.05708,1.05666,1.05614,1.05554,1.05484,1.05404,1.05314,1.05214,1.05103,1.04981,1.04847,1.04702,1.04544,1.04374,1.04192,1.03996,1.03787,1.03564,1.03327,1.03075,1.02809,1.02528,1.02232,1.0192,1.01592,1.01248,1.00888,1.00512,1.00119,0.997091,0.992828,0.988398,0.9838,0.979036,0.974107,0.969015,0.963761,0.958349,0.952783,0.947067,0.941206,0.935206,0.929074,0.922816,0.91644,0.909956,0.903373,0.8967,0.889948,0.883129,0.876255,0.869337,0.862389,0.855423,0.848453,0.841492,0.834555,0.827653,0.820801,0.814013,0.8073,0.800676,0.794152,0.78774,0.781451,0.775294,0.769279,0.763414,0.757707,0.752163,0.746789,0.741588,0.736564,0.73172,0.727056,0.722573,0.71827,0.714146,0.710198,0.706423,0.702816,0.699374,0.69609,0.692957,0.68997,0.687121,0.684401,0.681803,0.679317,0.676935,0.674646,0.672442,0.67031,0.668242,0.666225,0.664248,0.6623,0.660368,0.658439,0.656501,0.654539,0.652539,0.650486,0.648364,0.646156,0.643844,0.641409,0.638832,0.636091,0.633163,0.630024,0.626647,0.623005,0.619068,0.614803,0.610177,0.605153,0.599691,0.59375,0.587287,0.580253,0.572601,0.56428,0.555236,0.545415,0.534762,0.523223,0.510744,0.497274,0.48277,0.467193,0.450518,0.432735,0.413854},
{1.01473,1.01524,1.01578,1.01633,1.01691,1.01751,1.01813,1.01877,1.01943,1.02011,1.02082,1.02155,1.02229,1.02306,1.02385,1.02465,1.02548,1.02632,1.02719,1.02807,1.02896,1.02987,1.0308,1.03174,1.0327,1.03367,1.03465,1.03564,1.03663,1.03764,1.03865,1.03966,1.04068,1.0417,1.04272,1.04374,1.04475,1.04576,1.04676,1.04774,1.04872,1.04969,1.05063,1.05156,1.05247,1.05335,1.05421,1.05504,1.05583,1.0566,1.05733,1.05802,1.05866,1.05927,1.05982,1.06033,1.06078,1.06118,1.06152,1.06179,1.06201,1.06215,1.06222,1.06222,1.06214,1.06199,1.06174,1.06142,1.061,1.06049,1.05988,1.05918,1.05837,1.05745,1.05643,1.05529,1.05404,1.05267,1.05117,1.04955,1.0478,1.04591,1.04389,1.04173,1.03943,1.03698,1.03438,1.03163,1.02873,1.02566,1.02244,1.01906,1.01551,1.0118,1.00792,1.00387,0.999651,0.995265,0.99071,0.985987,0.981097,0.976043,0.970826,0.96545,0.959918,0.954235,0.948406,0.942436,0.936333,0.930103,0.923754,0.917296,0.910737,0.904088,0.897359,0.890561,0.883708,0.87681,0.86988,0.862932,0.855979,0.849035,0.842112,0.835225,0.828387,0.821611,0.814911,0.808298,0.801785,0.795384,0.789104,0.782956,0.776949,0.771092,0.765392,0.759855,0.754487,0.749291,0.744273,0.739433,0.734773,0.730294,0.725995,0.721874,0.717929,0.714156,0.710552,0.707111,0.703828,0.700697,0.697711,0.694862,0.692142,0.689544,0.687058,0.684675,0.682386,0.68018,0.678048,0.675977,0.673959,0.67198,0.670029,0.668095,0.666163,0.664222,0.662256,0.660253,0.658196,0.656069,0.653857,0.65154,0.649101,0.646519,0.643773,0.64084,0.637696,0.634314,0.630667,0.626725,0.622455,0.617825,0.612796,0.607331,0.601387,0.59492,0.587885,0.580232,0.57191,0.562866,0.553045,0.542393,0.530855,0.518376,0.504906,0.490398,0.474815,0.458128,0.440323,0.421409},
{1.01499,1.01551,1.01606,1.01662,1.01721,1.01783,1.01846,1.01912,1.0198,1.02051,1.02124,1.02199,1.02276,1.02355,1.02437,1.02521,1.02607,1.02695,1.02785,1.02877,1.0297,1.03066,1.03163,1.03262,1.03363,1.03465,1.03568,1.03673,1.03778,1.03885,1.03992,1.04101,1.04209,1.04318,1.04427,1.04537,1.04646,1.04754,1.04863,1.0497,1.05076,1.05181,1.05285,1.05387,1.05487,1.05585,1.05681,1.05773,1.05863,1.0595,1.06033,1.06112,1.06187,1.06258,1.06325,1.06386,1.06442,1.06492,1.06537,1.06575,1.06607,1.06632,1.0665,1.06661,1.06664,1.06658,1.06644,1.06622,1.0659,1.06549,1.06499,1.06438,1.06366,1.06284,1.06191,1.06086,1.0597,1.05841,1.057,1.05546,1.05379,1.05198,1.05004,1.04795,1.04572,1.04334,1.04081,1.03813,1.03528,1.03228,1.02912,1.02579,1.0223,1.01864,1.01481,1.01081,1.00665,1.00231,0.997795,0.993116,0.988267,0.983253,0.978074,0.972735,0.967238,0.961589,0.955792,0.949854,0.94378,0.937578,0.931257,0.924825,0.918291,0.911665,0.904958,0.898183,0.891349,0.88447,0.877559,0.870628,0.863691,0.856762,0.849853,0.84298,0.836154,0.82939,0.822701,0.816098,0.809594,0.803201,0.796929,0.790788,0.784788,0.778936,0.773241,0.767708,0.762344,0.757151,0.752135,0.747297,0.742638,0.73816,0.73386,0.729739,0.725792,0.722017,0.71841,0.714966,0.711679,0.708543,0.70555,0.702695,0.699968,0.697361,0.694866,0.692472,0.690171,0.687952,0.685805,0.683719,0.681683,0.679685,0.677713,0.675756,0.673799,0.67183,0.669835,0.667798,0.665706,0.663541,0.661286,0.658923,0.656434,0.653798,0.650992,0.647995,0.64478,0.641323,0.637594,0.633563,0.629197,0.624462,0.619321,0.613734,0.607659,0.601052,0.593866,0.58605,0.577554,0.568325,0.558307,0.547445,0.535683,0.522969,0.509251,0.494484,0.47863,0.461662,0.443568,0.424359},
{1.01523,1.01577,1.01632,1.0169,1.0175,1.01813,1.01878,1.01946,1.02016,1.02089,1.02163,1.02241,1.02321,1.02403,1.02487,1.02574,1.02663,1.02754,1.02848,1.02944,1.03041,1.03141,1.03243,1.03347,1.03452,1.03559,1.03668,1.03778,1.0389,1.04002,1.04116,1.04231,1.04346,1.04462,1.04579,1.04695,1.04812,1.04929,1.05045,1.05161,1.05276,1.0539,1.05503,1.05614,1.05724,1.05832,1.05937,1.0604,1.0614,1.06237,1.06331,1.06421,1.06507,1.06588,1.06666,1.06738,1.06805,1.06867,1.06922,1.06972,1.07015,1.07051,1.0708,1.07102,1.07116,1.07121,1.07119,1.07107,1.07086,1.07055,1.07015,1.06964,1.06903,1.06831,1.06747,1.06652,1.06545,1.06426,1.06294,1.06149,1.0599,1.05818,1.05631,1.05431,1.05215,1.04985,1.04739,1.04477,1.042,1.03906,1.03597,1.0327,1.02927,1.02566,1.02189,1.01795,1.01383,1.00954,1.00507,1.00044,0.995636,0.990664,0.985526,0.980225,0.974766,0.969152,0.963389,0.957484,0.951441,0.945269,0.938976,0.932571,0.926063,0.919462,0.912778,0.906024,0.899212,0.892353,0.88546,0.878547,0.871627,0.864713,0.857819,0.850959,0.844147,0.837395,0.830716,0.824124,0.817629,0.811245,0.804981,0.798848,0.792854,0.787009,0.781319,0.775791,0.770431,0.765242,0.760229,0.755394,0.750738,0.746261,0.741962,0.737841,0.733895,0.73012,0.726512,0.723067,0.719778,0.71664,0.713645,0.710786,0.708055,0.705444,0.702944,0.700545,0.698237,0.696011,0.693857,0.691762,0.689717,0.687708,0.685726,0.683756,0.681786,0.679802,0.677791,0.675738,0.673627,0.671441,0.669165,0.666779,0.664264,0.6616,0.658765,0.655735,0.652486,0.648992,0.645223,0.641149,0.636737,0.631953,0.626759,0.621115,0.61498,0.608309,0.601054,0.593165,0.584592,0.57528,0.565174,0.55422,0.54236,0.529542,0.515715,0.500831,0.484854,0.467755,0.449522,0.430164},
{1.01547,1.01601,1.01658,1.01717,1.01778,1.01842,1.01909,1.01978,1.0205,1.02124,1.02201,1.02281,1.02363,1.02448,1.02535,1.02625,1.02717,1.02811,1.02908,1.03008,1.03109,1.03213,1.0332,1.03428,1.03538,1.0365,1.03764,1.0388,1.03997,1.04116,1.04236,1.04357,1.04479,1.04602,1.04726,1.0485,1.04975,1.05099,1.05224,1.05348,1.05472,1.05595,1.05717,1.05838,1.05957,1.06075,1.0619,1.06303,1.06414,1.06521,1.06626,1.06726,1.06823,1.06916,1.07005,1.07088,1.07167,1.0724,1.07307,1.07368,1.07423,1.07471,1.07512,1.07545,1.0757,1.07587,1.07596,1.07595,1.07586,1.07566,1.07537,1.07497,1.07447,1.07385,1.07312,1.07227,1.0713,1.0702,1.06897,1.06761,1.06612,1.06449,1.06271,1.06079,1.05871,1.05649,1.05411,1.05157,1.04887,1.046,1.04297,1.03977,1.0364,1.03286,1.02915,1.02526,1.02119,1.01696,1.01254,1.00796,1.0032,0.998272,0.993177,0.987918,0.982497,0.976921,0.971195,0.965323,0.959313,0.953172,0.946909,0.940532,0.93405,0.927474,0.920815,0.914084,0.907293,0.900454,0.89358,0.886685,0.879782,0.872884,0.866005,0.859159,0.852359,0.845619,0.838952,0.83237,0.825885,0.819509,0.813253,0.807127,0.801141,0.795301,0.789617,0.784094,0.778738,0.773554,0.768544,0.763712,0.759058,0.754583,0.750286,0.746166,0.74222,0.738446,0.734838,0.731392,0.728102,0.724963,0.721966,0.719106,0.716372,0.713758,0.711255,0.708852,0.70654,0.70431,0.70215,0.70005,0.697998,0.695983,0.693993,0.692015,0.690036,0.688043,0.686022,0.683957,0.681834,0.679635,0.677345,0.674944,0.672413,0.669732,0.666879,0.66383,0.660561,0.657044,0.653251,0.649153,0.644715,0.639903,0.634679,0.629005,0.622837,0.616131,0.60884,0.600914,0.5923,0.582947,0.572797,0.561796,0.549888,0.537018,0.523135,0.508192,0.49215,0.47498,0.456667,0.437219},
{1.0157,1.01625,1.01682,1.01742,1.01805,1.0187,1.01938,1.02009,1.02082,1.02159,1.02238,1.02319,1.02404,1.02491,1.0258,1.02673,1.02768,1.02866,1.02966,1.03069,1.03175,1.03283,1.03393,1.03506,1.0362,1.03738,1.03857,1.03978,1.04101,1.04225,1.04351,1.04479,1.04608,1.04738,1.04869,1.05001,1.05133,1.05266,1.05398,1.05531,1.05664,1.05796,1.05927,1.06057,1.06186,1.06314,1.06439,1.06563,1.06684,1.06802,1.06917,1.07029,1.07137,1.07242,1.07342,1.07437,1.07527,1.07612,1.07691,1.07765,1.07831,1.07891,1.07944,1.07989,1.08026,1.08055,1.08076,1.08087,1.08089,1.08081,1.08063,1.08035,1.07996,1.07945,1.07883,1.07809,1.07722,1.07623,1.0751,1.07384,1.07244,1.0709,1.06922,1.06738,1.0654,1.06326,1.06096,1.0585,1.05588,1.05309,1.05013,1.047,1.04369,1.04022,1.03657,1.03274,1.02873,1.02455,1.02019,1.01566,1.01095,1.00607,1.00102,0.995801,0.990422,0.984886,0.979196,0.97336,0.967384,0.961276,0.955043,0.948694,0.94224,0.93569,0.929055,0.922347,0.915578,0.908759,0.901904,0.895027,0.88814,0.881258,0.874393,0.86756,0.860773,0.854044,0.847387,0.840814,0.834338,0.82797,0.821721,0.815601,0.80962,0.803785,0.798105,0.792585,0.787232,0.78205,0.777041,0.77221,0.767556,0.763081,0.758783,0.754661,0.750714,0.746936,0.743325,0.739875,0.73658,0.733435,0.730433,0.727565,0.724824,0.722201,0.719688,0.717275,0.714952,0.712708,0.710534,0.708419,0.70635,0.704317,0.702307,0.700307,0.698305,0.696286,0.694237,0.692142,0.689986,0.687751,0.685422,0.682979,0.680402,0.677671,0.674764,0.671656,0.668324,0.664739,0.660872,0.656693,0.652169,0.647264,0.641941,0.636158,0.629875,0.623045,0.61562,0.607552,0.598787,0.589271,0.578949,0.567765,0.555664,0.54259,0.528492,0.513324,0.497046,0.479631,0.461065,0.441356},
{1.01592,1.01648,1.01706,1.01767,1.0183,1.01897,1.01966,1.02038,1.02114,1.02191,1.02272,1.02356,1.02442,1.02532,1.02624,1.02719,1.02817,1.02918,1.03022,1.03128,1.03237,1.03349,1.03463,1.0358,1.037,1.03822,1.03946,1.04072,1.04201,1.04331,1.04463,1.04597,1.04733,1.0487,1.05008,1.05147,1.05287,1.05427,1.05568,1.0571,1.05851,1.05992,1.06133,1.06272,1.06411,1.06549,1.06684,1.06818,1.0695,1.07079,1.07206,1.07329,1.07449,1.07565,1.07676,1.07784,1.07886,1.07983,1.08075,1.0816,1.08239,1.08311,1.08377,1.08434,1.08484,1.08525,1.08558,1.08582,1.08596,1.08601,1.08595,1.08578,1.08551,1.08512,1.08461,1.08398,1.08322,1.08234,1.08132,1.08017,1.07887,1.07743,1.07585,1.07411,1.07221,1.07016,1.06795,1.06558,1.06304,1.06033,1.05745,1.05439,1.05116,1.04775,1.04417,1.04041,1.03646,1.03234,1.02804,1.02356,1.0189,1.01407,1.00907,1.0039,0.998565,0.99307,0.987421,0.981623,0.975683,0.969609,0.963408,0.957091,0.950666,0.944143,0.937534,0.93085,0.924104,0.917307,0.910473,0.903614,0.896745,0.889879,0.88303,0.876212,0.869438,0.862721,0.856075,0.849513,0.843047,0.836688,0.830447,0.824335,0.81836,0.812532,0.806857,0.801342,0.795994,0.790815,0.785811,0.780982,0.776332,0.771859,0.767563,0.763444,0.759498,0.755722,0.752112,0.748663,0.745369,0.742225,0.739222,0.736355,0.733614,0.730992,0.728478,0.726065,0.723742,0.721498,0.719324,0.717208,0.715139,0.713106,0.711096,0.709096,0.707094,0.705075,0.703026,0.700932,0.698776,0.696543,0.694215,0.691774,0.6892,0.686473,0.68357,0.680467,0.677141,0.673563,0.669705,0.665536,0.661024,0.656133,0.650825,0.645061,0.638799,0.631992,0.624594,0.616555,0.607823,0.598344,0.588062,0.576921,0.564865,0.551839,0.537791,0.522672,0.506443,0.489071,0.470541,0.450855},
{1.01613,1.0167,1.01729,1.0179,1.01855,1.01923,1.01993,1.02067,1.02143,1.02223,1.02305,1.02391,1.02479,1.02571,1.02666,1.02763,1.02864,1.02968,1.03075,1.03184,1.03297,1.03412,1.03531,1.03652,1.03776,1.03902,1.04032,1.04163,1.04297,1.04433,1.04571,1.04711,1.04853,1.04997,1.05142,1.05289,1.05436,1.05585,1.05734,1.05884,1.06034,1.06184,1.06334,1.06483,1.06632,1.06779,1.06926,1.0707,1.07213,1.07353,1.07491,1.07625,1.07757,1.07885,1.08008,1.08128,1.08242,1.08352,1.08456,1.08554,1.08646,1.08731,1.08809,1.08879,1.08942,1.08996,1.09042,1.09079,1.09106,1.09123,1.09129,1.09125,1.0911,1.09083,1.09045,1.08994,1.0893,1.08853,1.08762,1.08658,1.08539,1.08406,1.08257,1.08094,1.07914,1.07719,1.07507,1.07279,1.07033,1.06771,1.06491,1.06193,1.05878,1.05545,1.05193,1.04824,1.04436,1.0403,1.03606,1.03164,1.02704,1.02226,1.01731,1.01219,1.0069,1.00145,0.995839,0.99008,0.984178,0.978139,0.971972,0.965686,0.959291,0.952797,0.946214,0.939555,0.932832,0.926057,0.919242,0.912403,0.905551,0.898701,0.891867,0.885062,0.8783,0.871595,0.86496,0.858407,0.851949,0.845597,0.839363,0.833256,0.827287,0.821462,0.815791,0.810279,0.804933,0.799756,0.794752,0.789924,0.785272,0.780799,0.776502,0.77238,0.768431,0.764652,0.761037,0.757584,0.754285,0.751135,0.748126,0.745251,0.742502,0.73987,0.737347,0.734923,0.732587,0.730331,0.728142,0.726011,0.723925,0.721873,0.719843,0.717821,0.715795,0.713751,0.711674,0.709549,0.707361,0.705092,0.702725,0.700242,0.697623,0.694846,0.69189,0.68873,0.685341,0.681696,0.677765,0.673518,0.668922,0.66394,0.658534,0.652666,0.646291,0.639364,0.631837,0.62366,0.614781,0.605145,0.594697,0.58338,0.571138,0.557916,0.543661,0.528326,0.51187,0.494262,0.475488,0.455549},
{1.01634,1.01691,1.01751,1.01813,1.01879,1.01947,1.02019,1.02094,1.02172,1.02253,1.02337,1.02424,1.02515,1.02608,1.02705,1.02805,1.02909,1.03015,1.03125,1.03238,1.03354,1.03473,1.03596,1.03721,1.03849,1.0398,1.04114,1.04251,1.0439,1.04532,1.04676,1.04822,1.0497,1.05121,1.05273,1.05427,1.05582,1.05738,1.05896,1.06054,1.06213,1.06372,1.06531,1.0669,1.06848,1.07006,1.07163,1.07318,1.07471,1.07623,1.07772,1.07918,1.08062,1.08201,1.08337,1.08469,1.08596,1.08719,1.08835,1.08947,1.09051,1.0915,1.09241,1.09325,1.09401,1.09469,1.09527,1.09577,1.09618,1.09648,1.09668,1.09677,1.09674,1.0966,1.09634,1.09596,1.09544,1.09479,1.09401,1.09308,1.09201,1.09079,1.08941,1.08788,1.08619,1.08434,1.08232,1.08013,1.07777,1.07524,1.07252,1.06963,1.06656,1.06331,1.05987,1.05625,1.05244,1.04845,1.04427,1.03991,1.03537,1.03065,1.02575,1.02068,1.01544,1.01004,1.00448,0.998761,0.992898,0.986898,0.980767,0.974515,0.968151,0.961687,0.955132,0.9485,0.941801,0.935048,0.928256,0.921436,0.914603,0.90777,0.900951,0.894161,0.887413,0.88072,0.874096,0.867553,0.861104,0.854761,0.848534,0.842434,0.83647,0.830651,0.824985,0.819477,0.814134,0.80896,0.803958,0.799132,0.794482,0.790009,0.785713,0.781591,0.777642,0.773862,0.770247,0.766792,0.763492,0.76034,0.757329,0.754451,0.751699,0.749065,0.746538,0.74411,0.74177,0.739509,0.737315,0.735179,0.733087,0.731029,0.728992,0.726963,0.72493,0.722877,0.720791,0.718657,0.716459,0.71418,0.711802,0.709307,0.706676,0.703886,0.700916,0.697742,0.694338,0.690677,0.68673,0.682466,0.677852,0.672852,0.667428,0.66154,0.655145,0.648198,0.640651,0.632453,0.623553,0.613895,0.603425,0.592085,0.57982,0.566572,0.552291,0.536926,0.520436,0.502789,0.483968,0.463971},
{1.01654,1.01712,1.01772,1.01835,1.01902,1.01971,1.02044,1.0212,1.02199,1.02281,1.02367,1.02456,1.02548,1.02644,1.02743,1.02846,1.02951,1.03061,1.03173,1.0329,1.03409,1.03532,1.03658,1.03787,1.03919,1.04055,1.04193,1.04335,1.04479,1.04627,1.04776,1.04929,1.05084,1.05241,1.054,1.05561,1.05723,1.05888,1.06053,1.0622,1.06387,1.06555,1.06724,1.06892,1.07061,1.07228,1.07395,1.07561,1.07726,1.07889,1.08049,1.08207,1.08363,1.08515,1.08663,1.08808,1.08948,1.09083,1.09213,1.09337,1.09456,1.09567,1.09672,1.0977,1.0986,1.09941,1.10014,1.10077,1.10131,1.10175,1.10209,1.10231,1.10242,1.10242,1.10229,1.10203,1.10165,1.10113,1.10046,1.09966,1.09871,1.0976,1.09635,1.09493,1.09335,1.0916,1.08969,1.0876,1.08534,1.0829,1.08028,1.07748,1.0745,1.07133,1.06797,1.06443,1.06069,1.05677,1.05267,1.04837,1.0439,1.03924,1.0344,1.02938,1.02419,1.01884,1.01332,1.00765,1.00183,0.995871,0.989778,0.983561,0.977231,0.970798,0.964273,0.957668,0.950995,0.944266,0.937496,0.930696,0.923882,0.917067,0.910265,0.903489,0.896754,0.890074,0.883461,0.876928,0.870489,0.864153,0.857934,0.85184,0.845882,0.840067,0.834405,0.8289,0.82356,0.818388,0.813388,0.808563,0.803914,0.799441,0.795144,0.791022,0.787071,0.78329,0.779673,0.776215,0.772912,0.769757,0.766742,0.76386,0.761104,0.758464,0.755932,0.753497,0.751151,0.748883,0.746682,0.744536,0.742436,0.740368,0.73832,0.73628,0.734234,0.732168,0.730069,0.727919,0.725705,0.723408,0.721012,0.718497,0.715843,0.713031,0.710036,0.706836,0.703404,0.699714,0.695735,0.691438,0.686788,0.68175,0.676287,0.670357,0.663918,0.656924,0.649327,0.641078,0.632124,0.62241,0.61188,0.600477,0.588146,0.574829,0.560474,0.545032,0.528458,0.510722,0.491803,0.4717},
{1.01674,1.01732,1.01792,1.01856,1.01923,1.01994,1.02067,1.02144,1.02225,1.02309,1.02396,1.02486,1.0258,1.02678,1.02779,1.02884,1.02992,1.03104,1.0322,1.03339,1.03461,1.03587,1.03717,1.0385,1.03987,1.04127,1.0427,1.04416,1.04566,1.04718,1.04874,1.05032,1.05193,1.05356,1.05522,1.0569,1.05861,1.06032,1.06206,1.06381,1.06557,1.06734,1.06912,1.0709,1.07268,1.07446,1.07624,1.07801,1.07976,1.0815,1.08323,1.08493,1.0866,1.08824,1.08986,1.09143,1.09296,1.09444,1.09588,1.09726,1.09858,1.09984,1.10102,1.10214,1.10318,1.10414,1.105,1.10578,1.10647,1.10705,1.10752,1.10789,1.10814,1.10828,1.10828,1.10817,1.10791,1.10752,1.10699,1.10632,1.10549,1.10452,1.10338,1.10208,1.10062,1.09899,1.09718,1.0952,1.09305,1.09071,1.08819,1.08549,1.08259,1.07951,1.07624,1.07278,1.06913,1.06528,1.06125,1.05703,1.05262,1.04802,1.04324,1.03829,1.03315,1.02785,1.02239,1.01676,1.01099,1.00507,0.999015,0.992836,0.986541,0.980142,0.973648,0.967071,0.960425,0.953722,0.946975,0.940198,0.933403,0.926607,0.919821,0.913061,0.906341,0.899673,0.893072,0.88655,0.88012,0.873793,0.867581,0.861494,0.855542,0.849733,0.844074,0.838574,0.833237,0.828067,0.823069,0.818246,0.813598,0.809125,0.804829,0.800706,0.796756,0.792973,0.789355,0.785896,0.782591,0.779433,0.776416,0.773532,0.770773,0.76813,0.765594,0.763156,0.760805,0.758533,0.756327,0.754176,0.75207,0.749997,0.747943,0.745896,0.743843,0.74177,0.739663,0.737505,0.735282,0.732976,0.73057,0.728045,0.725381,0.722558,0.719552,0.71634,0.712896,0.709193,0.705202,0.700892,0.696229,0.691178,0.685701,0.679758,0.673305,0.666298,0.658689,0.650428,0.641461,0.631736,0.621195,0.609781,0.597439,0.584111,0.569743,0.554287,0.537696,0.519938,0.500989,0.480846},
{1.01693,1.01751,1.01812,1.01877,1.01945,1.02016,1.0209,1.02168,1.0225,1.02335,1.02423,1.02515,1.02611,1.02711,1.02814,1.02921,1.03031,1.03146,1.03264,1.03386,1.03511,1.03641,1.03774,1.03911,1.04051,1.04195,1.04343,1.04494,1.04649,1.04806,1.04967,1.05132,1.05299,1.05469,1.05641,1.05816,1.05994,1.06173,1.06355,1.06538,1.06723,1.06909,1.07096,1.07283,1.07472,1.0766,1.07848,1.08035,1.08222,1.08408,1.08592,1.08774,1.08953,1.0913,1.09304,1.09475,1.09641,1.09803,1.0996,1.10112,1.10258,1.10398,1.10531,1.10657,1.10775,1.10886,1.10987,1.1108,1.11163,1.11236,1.11298,1.11349,1.11389,1.11417,1.11432,1.11434,1.11423,1.11398,1.11359,1.11305,1.11236,1.11151,1.1105,1.10933,1.10799,1.10648,1.10479,1.10292,1.10088,1.09865,1.09623,1.09363,1.09084,1.08785,1.08467,1.0813,1.07773,1.07396,1.07001,1.06586,1.06152,1.05699,1.05228,1.04739,1.04231,1.03707,1.03166,1.02608,1.02035,1.01448,1.00847,1.00233,0.996073,0.989708,0.983247,0.976701,0.970083,0.963407,0.956684,0.949929,0.943155,0.936378,0.92961,0.922866,0.916159,0.909505,0.902915,0.896404,0.889983,0.883664,0.87746,0.871379,0.865432,0.859627,0.853973,0.848475,0.84314,0.837972,0.832975,0.828152,0.823504,0.819031,0.814733,0.810609,0.806656,0.802871,0.799249,0.795787,0.792478,0.789316,0.786293,0.783404,0.780638,0.777989,0.775445,0.773,0.770641,0.768359,0.766143,0.763982,0.761865,0.759778,0.757711,0.75565,0.753582,0.751492,0.749367,0.74719,0.744946,0.742618,0.740188,0.737637,0.734946,0.732093,0.729056,0.72581,0.72233,0.718589,0.714557,0.710203,0.705493,0.700392,0.694863,0.688864,0.682352,0.675283,0.667607,0.659276,0.650236,0.640432,0.629809,0.61831,0.605877,0.592454,0.577986,0.562423,0.545721,0.527844,0.508769,0.48849},
{1.01712,1.0177,1.01832,1.01897,1.01965,1.02037,1.02112,1.02191,1.02274,1.0236,1.0245,1.02543,1.02641,1.02742,1.02847,1.02956,1.03069,1.03185,1.03306,1.03431,1.03559,1.03692,1.03828,1.03969,1.04113,1.04261,1.04413,1.04569,1.04728,1.04891,1.05058,1.05228,1.05401,1.05577,1.05756,1.05938,1.06123,1.0631,1.06499,1.06691,1.06884,1.07079,1.07275,1.07472,1.0767,1.07869,1.08067,1.08266,1.08464,1.08661,1.08857,1.09051,1.09243,1.09432,1.09619,1.09803,1.09983,1.10158,1.10329,1.10495,1.10656,1.1081,1.10958,1.11099,1.11232,1.11357,1.11474,1.11581,1.1168,1.11768,1.11845,1.11911,1.11966,1.12009,1.12039,1.12056,1.1206,1.12049,1.12024,1.11985,1.11929,1.11858,1.11771,1.11667,1.11546,1.11407,1.11251,1.11076,1.10884,1.10672,1.10442,1.10192,1.09923,1.09634,1.09326,1.08998,1.0865,1.08282,1.07895,1.07488,1.07062,1.06617,1.06152,1.05669,1.05168,1.0465,1.04114,1.03562,1.02994,1.02412,1.01815,1.01206,1.00584,0.99951,0.993084,0.98657,0.979983,0.973334,0.966637,0.959906,0.953154,0.946397,0.939647,0.93292,0.926229,0.919588,0.913011,0.90651,0.900099,0.89379,0.887592,0.881518,0.875577,0.869777,0.864127,0.858632,0.8533,0.848134,0.843138,0.838316,0.833668,0.829194,0.824896,0.82077,0.816816,0.813028,0.809405,0.805939,0.802627,0.799461,0.796435,0.79354,0.79077,0.788115,0.785566,0.783114,0.780748,0.778459,0.776235,0.774066,0.771939,0.769843,0.767766,0.765693,0.763613,0.761511,0.759371,0.75718,0.754921,0.752576,0.750129,0.747559,0.744848,0.741974,0.738914,0.735644,0.732139,0.728371,0.72431,0.719926,0.715186,0.710052,0.704488,0.698452,0.691903,0.684794,0.677077,0.668702,0.659617,0.649767,0.639096,0.627546,0.61506,0.601582,0.587056,0.571431,0.554662,0.536713,0.517559,0.497191},
{1.0173,1.01789,1.01851,1.01916,1.01985,1.02057,1.02133,1.02213,1.02297,1.02384,1.02475,1.0257,1.02669,1.02771,1.02878,1.02989,1.03104,1.03223,1.03346,1.03474,1.03605,1.03741,1.0388,1.04024,1.04172,1.04325,1.04481,1.04641,1.04805,1.04973,1.05145,1.0532,1.05499,1.05681,1.05867,1.06056,1.06248,1.06442,1.0664,1.06839,1.07041,1.07245,1.0745,1.07657,1.07865,1.08073,1.08282,1.08492,1.08701,1.08909,1.09117,1.09323,1.09528,1.0973,1.0993,1.10127,1.10321,1.1051,1.10695,1.10876,1.11051,1.1122,1.11382,1.11538,1.11687,1.11827,1.11959,1.12083,1.12196,1.123,1.12393,1.12475,1.12546,1.12604,1.1265,1.12682,1.12701,1.12706,1.12696,1.1267,1.1263,1.12573,1.125,1.12409,1.12302,1.12177,1.12033,1.11872,1.11691,1.11492,1.11273,1.11034,1.10776,1.10498,1.102,1.09882,1.09544,1.09185,1.08807,1.08408,1.0799,1.07553,1.07096,1.0662,1.06125,1.05613,1.05083,1.04537,1.03975,1.03397,1.02805,1.022,1.01583,1.00954,1.00315,0.996669,0.990113,0.983493,0.976823,0.970117,0.963388,0.956652,0.949921,0.943211,0.936536,0.929909,0.923344,0.916855,0.910453,0.904152,0.897962,0.891894,0.885958,0.880162,0.874515,0.869023,0.863692,0.858527,0.853531,0.848708,0.844059,0.839584,0.835282,0.831154,0.827195,0.823404,0.819775,0.816304,0.812986,0.809813,0.806779,0.803877,0.801097,0.798433,0.795874,0.79341,0.791032,0.78873,0.786492,0.784307,0.782164,0.780051,0.777954,0.775861,0.773758,0.771631,0.769466,0.767246,0.764957,0.762579,0.760097,0.757489,0.754737,0.751819,0.748712,0.745391,0.741831,0.738004,0.733881,0.729429,0.724616,0.719405,0.713758,0.707635,0.700991,0.693781,0.685958,0.67747,0.668265,0.658288,0.647482,0.63579,0.623154,0.609518,0.594827,0.579029,0.562078,0.543939,0.524586,0.50401},
{1.01748,1.01807,1.01869,1.01935,1.02004,1.02077,1.02154,1.02234,1.02319,1.02407,1.02499,1.02595,1.02696,1.028,1.02908,1.03021,1.03138,1.03259,1.03385,1.03515,1.03649,1.03787,1.0393,1.04078,1.04229,1.04385,1.04545,1.0471,1.04879,1.05052,1.05228,1.05409,1.05594,1.05783,1.05975,1.0617,1.06369,1.06571,1.06776,1.06983,1.07194,1.07406,1.0762,1.07837,1.08054,1.08273,1.08493,1.08713,1.08933,1.09153,1.09373,1.09591,1.09809,1.10024,1.10237,1.10447,1.10655,1.10858,1.11058,1.11253,1.11442,1.11627,1.11805,1.11976,1.1214,1.12296,1.12444,1.12583,1.12713,1.12833,1.12942,1.1304,1.13127,1.13201,1.13263,1.13311,1.13346,1.13366,1.13372,1.13362,1.13337,1.13295,1.13236,1.13161,1.13068,1.12956,1.12827,1.12678,1.12511,1.12324,1.12117,1.11891,1.11644,1.11378,1.1109,1.10783,1.10455,1.10106,1.09737,1.09347,1.08938,1.08508,1.08059,1.07591,1.07103,1.06598,1.06075,1.05534,1.04978,1.04406,1.03819,1.03219,1.02606,1.01981,1.01346,1.00702,1.00049,0.993905,0.987264,0.980584,0.97388,0.967165,0.960455,0.953764,0.947105,0.940493,0.933942,0.927465,0.921074,0.914782,0.9086,0.902539,0.896609,0.890818,0.885175,0.879686,0.874357,0.869194,0.864199,0.859376,0.854726,0.85025,0.845947,0.841816,0.837855,0.83406,0.830428,0.826953,0.82363,0.820452,0.817413,0.814504,0.811718,0.809046,0.806479,0.804008,0.801621,0.799309,0.797061,0.794865,0.792709,0.790583,0.788472,0.786364,0.784246,0.782102,0.779918,0.777679,0.775368,0.772969,0.770462,0.767829,0.765049,0.762102,0.758963,0.755609,0.752014,0.748149,0.743986,0.739491,0.734633,0.729374,0.723676,0.717499,0.710799,0.70353,0.695644,0.68709,0.677816,0.667765,0.656883,0.645112,0.632392,0.618669,0.603885,0.58799,0.570937,0.552688,0.533218,0.512516},
{1.01765,1.01824,1.01887,1.01953,1.02023,1.02096,1.02173,1.02255,1.0234,1.02429,1.02522,1.0262,1.02721,1.02827,1.02937,1.03051,1.0317,1.03294,1.03421,1.03554,1.03691,1.03832,1.03978,1.04128,1.04284,1.04443,1.04608,1.04776,1.04949,1.05127,1.05309,1.05495,1.05686,1.0588,1.06078,1.0628,1.06486,1.06695,1.06908,1.07123,1.07342,1.07563,1.07786,1.08012,1.08239,1.08468,1.08698,1.08929,1.09161,1.09393,1.09624,1.09855,1.10085,1.10313,1.10539,1.10764,1.10985,1.11203,1.11417,1.11626,1.11831,1.12031,1.12224,1.12411,1.12591,1.12763,1.12928,1.13083,1.13229,1.13366,1.13491,1.13606,1.13709,1.138,1.13879,1.13944,1.13995,1.14031,1.14053,1.14059,1.1405,1.14024,1.1398,1.1392,1.13842,1.13745,1.1363,1.13495,1.13341,1.13168,1.12974,1.1276,1.12526,1.12271,1.11996,1.11699,1.11382,1.11043,1.10684,1.10304,1.09904,1.09483,1.09042,1.08581,1.08102,1.07603,1.07087,1.06553,1.06003,1.05436,1.04855,1.0426,1.03651,1.03031,1.024,1.0176,1.01111,1.00456,0.997945,0.991293,0.984615,0.977924,0.971235,0.964563,0.957922,0.951325,0.944788,0.938323,0.931943,0.92566,0.919487,0.913432,0.907507,0.901721,0.896081,0.890595,0.885267,0.880104,0.87511,0.870286,0.865634,0.861155,0.85685,0.852715,0.84875,0.84495,0.841312,0.83783,0.8345,0.831314,0.828267,0.825349,0.822553,0.81987,0.817292,0.814807,0.812407,0.81008,0.807815,0.805602,0.803429,0.801282,0.79915,0.797018,0.794875,0.792704,0.790491,0.78822,0.785876,0.783439,0.780893,0.778218,0.775393,0.772396,0.769205,0.765794,0.762137,0.758207,0.753974,0.749404,0.744465,0.73912,0.73333,0.727055,0.72025,0.712869,0.704864,0.696185,0.686777,0.676585,0.665553,0.653624,0.640738,0.62684,0.611873,0.595785,0.578531,0.560072,0.540383,0.519453},
{1.01782,1.01841,1.01904,1.0197,1.02041,1.02115,1.02192,1.02274,1.0236,1.0245,1.02544,1.02643,1.02746,1.02853,1.02964,1.03081,1.03201,1.03326,1.03456,1.03591,1.0373,1.03874,1.04023,1.04177,1.04336,1.04499,1.04667,1.0484,1.05017,1.052,1.05386,1.05578,1.05774,1.05974,1.06178,1.06387,1.066,1.06816,1.07036,1.07259,1.07486,1.07716,1.07948,1.08183,1.0842,1.08659,1.089,1.09141,1.09384,1.09627,1.09871,1.10114,1.10356,1.10598,1.10838,1.11075,1.11311,1.11543,1.11772,1.11996,1.12216,1.12431,1.12641,1.12844,1.1304,1.13229,1.13409,1.13582,1.13745,1.13898,1.14041,1.14173,1.14293,1.14401,1.14497,1.14579,1.14647,1.147,1.14739,1.14762,1.14769,1.14759,1.14732,1.14687,1.14624,1.14543,1.14442,1.14323,1.14183,1.14024,1.13844,1.13644,1.13422,1.1318,1.12916,1.12631,1.12325,1.11998,1.11649,1.11279,1.10888,1.10477,1.10045,1.09593,1.09121,1.08631,1.08121,1.07595,1.07051,1.0649,1.05915,1.05325,1.04722,1.04106,1.0348,1.02843,1.02199,1.01547,1.00889,1.00227,0.995616,0.98895,0.982285,0.975633,0.969011,0.962432,0.95591,0.949458,0.94309,0.936818,0.930654,0.924607,0.918689,0.912908,0.907272,0.901789,0.896465,0.891303,0.886309,0.881486,0.876833,0.872354,0.868046,0.863909,0.859941,0.856137,0.852495,0.849009,0.845674,0.842483,0.839429,0.836505,0.833701,0.831011,0.828424,0.82593,0.82352,0.821183,0.818907,0.816682,0.814495,0.812335,0.810188,0.808041,0.80588,0.803691,0.801458,0.799167,0.7968,0.79434,0.791768,0.789065,0.786211,0.783183,0.779959,0.776513,0.772819,0.768849,0.764573,0.759959,0.754972,0.749577,0.743734,0.737402,0.730538,0.723096,0.715026,0.706277,0.696797,0.68653,0.67542,0.663407,0.650436,0.636446,0.621384,0.605196,0.587837,0.569267,0.549458,0.528399},
{1.01799,1.01858,1.01921,1.01988,1.02058,1.02132,1.02211,1.02293,1.0238,1.02471,1.02566,1.02665,1.02769,1.02878,1.02991,1.03108,1.03231,1.03358,1.0349,1.03627,1.03768,1.03915,1.04067,1.04224,1.04385,1.04552,1.04724,1.04901,1.05082,1.05269,1.05461,1.05657,1.05859,1.06064,1.06275,1.0649,1.06709,1.06932,1.0716,1.07391,1.07626,1.07864,1.08105,1.08349,1.08596,1.08845,1.09096,1.09348,1.09602,1.09857,1.10113,1.10368,1.10623,1.10878,1.11131,1.11383,1.11632,1.11879,1.12122,1.12362,1.12598,1.12829,1.13054,1.13273,1.13486,1.13691,1.13889,1.14078,1.14259,1.14429,1.1459,1.14739,1.14877,1.15003,1.15116,1.15216,1.15301,1.15372,1.15428,1.15469,1.15492,1.15499,1.15489,1.15461,1.15414,1.15349,1.15264,1.1516,1.15036,1.14891,1.14725,1.14539,1.14331,1.14102,1.13851,1.13579,1.13285,1.12969,1.12631,1.12272,1.11891,1.11489,1.11067,1.10624,1.10161,1.09678,1.09177,1.08657,1.0812,1.07566,1.06997,1.06413,1.05815,1.05204,1.04583,1.03951,1.0331,1.02662,1.02007,1.01349,1.00686,1.00022,0.993583,0.986954,0.980352,0.97379,0.967284,0.960846,0.95449,0.948229,0.942073,0.936034,0.930122,0.924346,0.918714,0.913233,0.90791,0.90275,0.897755,0.89293,0.888276,0.883793,0.879482,0.875341,0.871367,0.867558,0.863909,0.860415,0.857072,0.853872,0.850808,0.847873,0.845058,0.842354,0.839754,0.837245,0.834819,0.832464,0.83017,0.827925,0.825716,0.823532,0.82136,0.819186,0.816996,0.814775,0.812508,0.81018,0.807773,0.80527,0.802653,0.7999,0.796993,0.793907,0.790621,0.787109,0.783343,0.779297,0.774938,0.770236,0.765155,0.759658,0.753707,0.74726,0.740272,0.732698,0.724488,0.715591,0.705953,0.69552,0.684233,0.672034,0.658866,0.644671,0.629392,0.612978,0.595382,0.576566,0.556502,0.535177},
{1.01816,1.01875,1.01938,1.02004,1.02075,1.0215,1.02228,1.02311,1.02399,1.0249,1.02586,1.02686,1.02791,1.02901,1.03015,1.03135,1.03259,1.03388,1.03522,1.0366,1.03805,1.03954,1.04108,1.04268,1.04433,1.04603,1.04778,1.04959,1.05145,1.05336,1.05532,1.05734,1.0594,1.06152,1.06368,1.06589,1.06815,1.07045,1.0728,1.07519,1.07761,1.08008,1.08258,1.08511,1.08767,1.09026,1.09288,1.09551,1.09816,1.10082,1.1035,1.10618,1.10886,1.11153,1.1142,1.11685,1.11949,1.12211,1.12469,1.12724,1.12976,1.13222,1.13464,1.137,1.13929,1.14152,1.14367,1.14574,1.14771,1.1496,1.15138,1.15306,1.15462,1.15606,1.15737,1.15855,1.15959,1.16048,1.16122,1.1618,1.16221,1.16246,1.16253,1.16242,1.16213,1.16164,1.16096,1.16007,1.15899,1.15769,1.15619,1.15447,1.15254,1.15039,1.14801,1.14542,1.1426,1.13957,1.13631,1.13283,1.12913,1.12522,1.12109,1.11676,1.11222,1.10748,1.10255,1.09743,1.09213,1.08666,1.08103,1.07525,1.06933,1.06328,1.05712,1.05084,1.04448,1.03804,1.03153,1.02498,1.01839,1.01178,1.00517,0.99856,0.99198,0.985438,0.978949,0.972527,0.966185,0.959936,0.953791,0.947761,0.941857,0.936087,0.930461,0.924984,0.919665,0.914506,0.909513,0.904689,0.900034,0.895551,0.891238,0.887094,0.883118,0.879305,0.875652,0.872155,0.868806,0.8656,0.86253,0.859588,0.856766,0.854055,0.851446,0.848929,0.846493,0.844128,0.841823,0.839566,0.837345,0.835147,0.83296,0.83077,0.828564,0.826325,0.82404,0.821692,0.819264,0.816738,0.814096,0.811318,0.808383,0.805268,0.801951,0.798405,0.794605,0.790522,0.786124,0.781381,0.776256,0.770714,0.764715,0.758217,0.751177,0.743548,0.73528,0.726323,0.716622,0.706123,0.694768,0.682498,0.669256,0.654984,0.639624,0.623125,0.605439,0.586527,0.566359,0.544922},
{1.01832,1.01891,1.01954,1.02021,1.02091,1.02166,1.02245,1.02329,1.02417,1.02509,1.02606,1.02707,1.02813,1.02924,1.03039,1.0316,1.03285,1.03416,1.03552,1.03693,1.03839,1.03991,1.04148,1.0431,1.04478,1.04651,1.0483,1.05015,1.05205,1.054,1.05601,1.05807,1.06019,1.06236,1.06458,1.06685,1.06917,1.07154,1.07396,1.07642,1.07893,1.08147,1.08406,1.08668,1.08934,1.09203,1.09475,1.09749,1.10025,1.10303,1.10582,1.10862,1.11143,1.11424,1.11704,1.11983,1.12261,1.12538,1.12811,1.13082,1.13349,1.13612,1.1387,1.14122,1.14369,1.14609,1.14841,1.15066,1.15282,1.15489,1.15685,1.15871,1.16046,1.16208,1.16358,1.16495,1.16617,1.16725,1.16818,1.16894,1.16954,1.16997,1.17022,1.17029,1.17017,1.16986,1.16935,1.16863,1.16771,1.16658,1.16523,1.16367,1.16188,1.15988,1.15765,1.15519,1.15251,1.1496,1.14646,1.1431,1.13952,1.13572,1.1317,1.12746,1.12302,1.11837,1.11353,1.10849,1.10327,1.09788,1.09232,1.0866,1.08074,1.07475,1.06864,1.06242,1.0561,1.0497,1.04323,1.03672,1.03016,1.02358,1.01699,1.01041,1.00385,0.997333,0.990862,0.984456,0.978127,0.97189,0.965755,0.959733,0.953836,0.948072,0.942449,0.936976,0.931657,0.926499,0.921505,0.916679,0.912022,0.907534,0.903216,0.899067,0.895084,0.891264,0.887602,0.884095,0.880735,0.877518,0.874435,0.87148,0.868643,0.865915,0.863289,0.860752,0.858296,0.855908,0.853579,0.851296,0.849047,0.846819,0.8446,0.842375,0.84013,0.83785,0.835521,0.833124,0.830645,0.828063,0.825361,0.822517,0.819512,0.816322,0.812924,0.809291,0.805396,0.801211,0.796705,0.791844,0.786594,0.780917,0.774774,0.768122,0.760917,0.753111,0.744656,0.735499,0.725587,0.714862,0.703269,0.690748,0.677241,0.66269,0.647038,0.630233,0.61223,0.592987,0.572479,0.550691},
{1.01848,1.01907,1.0197,1.02036,1.02107,1.02183,1.02262,1.02346,1.02434,1.02527,1.02624,1.02726,1.02833,1.02945,1.03062,1.03184,1.03311,1.03443,1.03581,1.03723,1.03872,1.04026,1.04185,1.0435,1.04521,1.04698,1.0488,1.05068,1.05262,1.05461,1.05666,1.05877,1.06094,1.06316,1.06544,1.06777,1.07016,1.07259,1.07508,1.07762,1.0802,1.08283,1.0855,1.08821,1.09096,1.09375,1.09657,1.09941,1.10229,1.10518,1.10809,1.11102,1.11395,1.11689,1.11983,1.12277,1.12569,1.1286,1.13149,1.13435,1.13718,1.13997,1.14272,1.14542,1.14806,1.15063,1.15314,1.15556,1.15791,1.16016,1.16231,1.16436,1.1663,1.16811,1.1698,1.17136,1.17278,1.17405,1.17517,1.17612,1.17691,1.17753,1.17797,1.17822,1.17829,1.17816,1.17782,1.17728,1.17654,1.17557,1.17439,1.17299,1.17136,1.16951,1.16743,1.16512,1.16257,1.1598,1.1568,1.15356,1.1501,1.14641,1.14251,1.13838,1.13404,1.12949,1.12473,1.11979,1.11465,1.10933,1.10385,1.09821,1.09241,1.08648,1.08042,1.07426,1.06799,1.06164,1.05521,1.04873,1.04221,1.03567,1.02911,1.02256,1.01603,1.00953,1.00308,0.996687,0.990375,0.984151,0.978028,0.972017,0.966128,0.960371,0.954754,0.949285,0.94397,0.938814,0.933822,0.928995,0.924337,0.919848,0.915528,0.911375,0.907388,0.903562,0.899895,0.896381,0.893015,0.88979,0.886698,0.883733,0.880886,0.878148,0.875509,0.872959,0.870489,0.868086,0.865741,0.86344,0.861172,0.858924,0.856683,0.854435,0.852165,0.849859,0.8475,0.845073,0.84256,0.839943,0.837203,0.834319,0.83127,0.828033,0.824585,0.820898,0.816947,0.812701,0.80813,0.8032,0.797877,0.792121,0.785895,0.779155,0.771857,0.763952,0.755393,0.746126,0.736097,0.725251,0.713529,0.700873,0.687224,0.672525,0.656718,0.639751,0.621577,0.602156,0.581461,0.559477},
{1.01864,1.01922,1.01985,1.02052,1.02123,1.02198,1.02278,1.02362,1.02451,1.02544,1.02642,1.02745,1.02853,1.02966,1.03083,1.03207,1.03335,1.03469,1.03608,1.03753,1.03903,1.04059,1.04221,1.04389,1.04562,1.04742,1.04927,1.05119,1.05316,1.0552,1.05729,1.05945,1.06166,1.06394,1.06627,1.06866,1.0711,1.07361,1.07616,1.07877,1.08143,1.08414,1.0869,1.0897,1.09254,1.09542,1.09834,1.10129,1.10428,1.10728,1.11031,1.11336,1.11643,1.1195,1.12257,1.12565,1.12872,1.13178,1.13482,1.13784,1.14083,1.14379,1.1467,1.14957,1.15238,1.15514,1.15782,1.16044,1.16297,1.16541,1.16775,1.16999,1.17212,1.17414,1.17602,1.17778,1.17939,1.18086,1.18218,1.18333,1.18432,1.18513,1.18577,1.18621,1.18647,1.18652,1.18637,1.18602,1.18545,1.18466,1.18365,1.18242,1.18096,1.17926,1.17734,1.17518,1.17278,1.17015,1.16729,1.16419,1.16085,1.15729,1.1535,1.14949,1.14525,1.1408,1.13615,1.1313,1.12625,1.12102,1.11561,1.11004,1.10432,1.09845,1.09246,1.08635,1.08013,1.07383,1.06745,1.06101,1.05453,1.04802,1.0415,1.03497,1.02847,1.02199,1.01556,1.00919,1.0029,0.996686,0.990575,0.984574,0.978694,0.972945,0.967334,0.961869,0.956556,0.951402,0.946409,0.941582,0.936922,0.93243,0.928105,0.923948,0.919954,0.916122,0.912447,0.908924,0.905548,0.902312,0.899208,0.89623,0.893369,0.890615,0.887959,0.885392,0.882902,0.880478,0.87811,0.875785,0.873491,0.871214,0.868942,0.866661,0.864355,0.86201,0.85961,0.857139,0.854578,0.851909,0.849113,0.846169,0.843055,0.839749,0.836226,0.83246,0.828422,0.824084,0.819414,0.814379,0.808942,0.803066,0.79671,0.789832,0.782387,0.774326,0.7656,0.756157,0.745941,0.734897,0.722966,0.71009,0.69621,0.681268,0.665206,0.647973,0.629522,0.609814,0.58882,0.566528},
{1.01879,1.01938,1.02,1.02067,1.02138,1.02214,1.02293,1.02378,1.02467,1.02561,1.02659,1.02763,1.02871,1.02985,1.03104,1.03228,1.03358,1.03493,1.03634,1.0378,1.03933,1.04091,1.04255,1.04425,1.04601,1.04784,1.04972,1.05167,1.05368,1.05576,1.05789,1.06009,1.06235,1.06468,1.06706,1.06951,1.07202,1.07458,1.07721,1.07989,1.08262,1.08541,1.08825,1.09114,1.09407,1.09705,1.10007,1.10313,1.10622,1.10934,1.11249,1.11566,1.11885,1.12205,1.12526,1.12848,1.13169,1.1349,1.1381,1.14128,1.14443,1.14755,1.15064,1.15368,1.15667,1.15961,1.16248,1.16528,1.168,1.17063,1.17317,1.17561,1.17794,1.18015,1.18224,1.1842,1.18602,1.18769,1.18921,1.19057,1.19176,1.19277,1.19361,1.19425,1.1947,1.19495,1.195,1.19483,1.19445,1.19385,1.19302,1.19196,1.19067,1.18915,1.18739,1.18539,1.18315,1.18067,1.17795,1.17499,1.17179,1.16836,1.16469,1.16079,1.15668,1.15234,1.14779,1.14303,1.13808,1.13294,1.12761,1.12212,1.11647,1.11068,1.10475,1.0987,1.09254,1.08629,1.07996,1.07357,1.06713,1.06066,1.05417,1.04768,1.0412,1.03475,1.02834,1.02199,1.01572,1.00952,1.00343,0.997438,0.991568,0.985827,0.980223,0.974763,0.969455,0.964303,0.959312,0.954485,0.949824,0.945329,0.941002,0.93684,0.932842,0.929004,0.925322,0.921791,0.918406,0.915161,0.912047,0.909057,0.906183,0.903415,0.900745,0.898161,0.895654,0.893212,0.890823,0.888477,0.886159,0.883857,0.881558,0.879248,0.876911,0.874533,0.872096,0.869586,0.866983,0.864269,0.861425,0.85843,0.855261,0.851895,0.848309,0.844474,0.840364,0.835948,0.831194,0.82607,0.820538,0.814561,0.808098,0.801106,0.793539,0.785349,0.776487,0.7669,0.756531,0.745327,0.733227,0.720173,0.706105,0.690967,0.6747,0.657253,0.638579,0.618637,0.597401,0.574856},
{1.01894,1.01953,1.02015,1.02082,1.02153,1.02228,1.02308,1.02393,1.02482,1.02576,1.02676,1.0278,1.02889,1.03004,1.03123,1.03249,1.0338,1.03516,1.03658,1.03807,1.03961,1.04121,1.04287,1.0446,1.04638,1.04824,1.05015,1.05213,1.05418,1.05629,1.05847,1.06071,1.06302,1.06539,1.06783,1.07033,1.07289,1.07552,1.07821,1.08096,1.08377,1.08664,1.08956,1.09253,1.09556,1.09863,1.10175,1.10491,1.10811,1.11134,1.11461,1.1179,1.12122,1.12455,1.1279,1.13126,1.13462,1.13798,1.14133,1.14467,1.14798,1.15127,1.15453,1.15775,1.16092,1.16404,1.1671,1.17008,1.173,1.17583,1.17856,1.1812,1.18374,1.18615,1.18845,1.19062,1.19264,1.19452,1.19625,1.19782,1.19922,1.20044,1.20148,1.20233,1.20299,1.20344,1.20369,1.20372,1.20353,1.20312,1.20248,1.2016,1.20049,1.19915,1.19756,1.19572,1.19365,1.19132,1.18876,1.18594,1.18289,1.17959,1.17606,1.17229,1.16829,1.16407,1.15963,1.15498,1.15012,1.14507,1.13984,1.13443,1.12886,1.12314,1.11728,1.1113,1.1052,1.09901,1.09273,1.08639,1.07999,1.07356,1.0671,1.06065,1.0542,1.04778,1.04139,1.03507,1.02881,1.02263,1.01655,1.01057,1.00471,0.998977,0.993379,0.987924,0.982618,0.977467,0.972476,0.967647,0.962983,0.958484,0.954151,0.949982,0.945975,0.942128,0.938435,0.934892,0.931494,0.928233,0.925103,0.922095,0.919201,0.916412,0.913719,0.91111,0.908576,0.906105,0.903685,0.901304,0.898949,0.896608,0.894266,0.891909,0.889522,0.887089,0.884594,0.882021,0.87935,0.876562,0.873639,0.870558,0.867297,0.863832,0.860139,0.856189,0.851955,0.847406,0.84251,0.837232,0.831536,0.825383,0.818731,0.811537,0.803755,0.795336,0.78623,0.776382,0.765738,0.754241,0.741831,0.728451,0.71404,0.698541,0.681897,0.664057,0.644973,0.624609,0.602937,0.579948},
{1.0191,1.01967,1.0203,1.02096,1.02167,1.02243,1.02323,1.02408,1.02497,1.02592,1.02691,1.02796,1.02906,1.03021,1.03142,1.03268,1.034,1.03538,1.03682,1.03831,1.03987,1.04149,1.04318,1.04492,1.04674,1.04862,1.05056,1.05257,1.05465,1.0568,1.05901,1.0613,1.06365,1.06607,1.06856,1.07112,1.07374,1.07643,1.07918,1.082,1.08488,1.08782,1.09083,1.09389,1.097,1.10017,1.10338,1.10665,1.10995,1.1133,1.11668,1.1201,1.12354,1.127,1.13049,1.13399,1.13749,1.141,1.14451,1.14801,1.15149,1.15495,1.15838,1.16178,1.16513,1.16843,1.17168,1.17486,1.17797,1.181,1.18394,1.18678,1.18952,1.19215,1.19466,1.19704,1.19928,1.20137,1.20332,1.2051,1.20671,1.20815,1.20941,1.21047,1.21134,1.212,1.21245,1.21269,1.21271,1.21249,1.21205,1.21137,1.21045,1.20928,1.20788,1.20622,1.20431,1.20216,1.19975,1.19709,1.19419,1.19103,1.18764,1.18401,1.18014,1.17604,1.17171,1.16717,1.16243,1.15748,1.15234,1.14703,1.14154,1.1359,1.13012,1.1242,1.11817,1.11204,1.10582,1.09953,1.09318,1.08679,1.08038,1.07396,1.06755,1.06116,1.0548,1.0485,1.04227,1.03611,1.03005,1.02409,1.01824,1.01252,1.00693,1.00149,0.996189,0.991045,0.986059,0.981234,0.976573,0.972077,0.967745,0.963576,0.95957,0.955721,0.952027,0.948482,0.945081,0.941817,0.938683,0.935671,0.932773,0.929979,0.92728,0.924666,0.922125,0.919647,0.91722,0.914832,0.912469,0.91012,0.907769,0.905403,0.903006,0.900563,0.898058,0.895474,0.892792,0.889993,0.887058,0.883965,0.880692,0.877215,0.873509,0.869547,0.865301,0.86074,0.855832,0.850543,0.844836,0.838673,0.832012,0.824811,0.817022,0.808598,0.799488,0.789639,0.778996,0.767502,0.755097,0.741724,0.727322,0.711834,0.695201,0.677371,0.658297,0.637937,0.616265,0.593264},
{1.01924,1.01982,1.02044,1.0211,1.02181,1.02257,1.02337,1.02422,1.02511,1.02606,1.02706,1.02811,1.02922,1.03038,1.03159,1.03287,1.0342,1.03559,1.03704,1.03855,1.04012,1.04176,1.04347,1.04523,1.04707,1.04897,1.05095,1.05299,1.0551,1.05728,1.05954,1.06186,1.06425,1.06672,1.06926,1.07187,1.07455,1.0773,1.08011,1.083,1.08595,1.08897,1.09205,1.09519,1.09839,1.10165,1.10497,1.10833,1.11174,1.1152,1.1187,1.12224,1.1258,1.1294,1.13302,1.13666,1.14031,1.14397,1.14764,1.15129,1.15494,1.15857,1.16218,1.16575,1.16929,1.17278,1.17622,1.17959,1.1829,1.18613,1.18928,1.19233,1.19528,1.19812,1.20084,1.20344,1.2059,1.20822,1.21038,1.21238,1.21422,1.21588,1.21736,1.21864,1.21972,1.2206,1.22127,1.22172,1.22195,1.22194,1.2217,1.22122,1.22049,1.21952,1.2183,1.21683,1.2151,1.21312,1.21088,1.20838,1.20564,1.20264,1.19939,1.19589,1.19216,1.18819,1.18399,1.17957,1.17493,1.17009,1.16506,1.15984,1.15444,1.14888,1.14318,1.13734,1.13138,1.12531,1.11915,1.11291,1.10662,1.10028,1.09391,1.08753,1.08115,1.07479,1.06847,1.06219,1.05598,1.04985,1.0438,1.03785,1.03202,1.02631,1.02073,1.01529,1.01,1.00486,0.999877,0.995053,0.990391,0.985892,0.981557,0.977384,0.97337,0.969514,0.965811,0.962256,0.958844,0.955567,0.952419,0.949392,0.946477,0.943665,0.940946,0.93831,0.935746,0.933243,0.930788,0.92837,0.925975,0.923591,0.921203,0.918797,0.916357,0.913868,0.911313,0.908674,0.905934,0.903073,0.900071,0.896905,0.893555,0.889994,0.886199,0.882141,0.877791,0.87312,0.868094,0.862679,0.856837,0.85053,0.843715,0.83635,0.828387,0.819778,0.810471,0.800413,0.789549,0.777822,0.765171,0.751539,0.736865,0.721091,0.70416,0.686019,0.666621,0.645926,0.623906,0.600548},
{1.01939,1.01996,1.02058,1.02124,1.02195,1.0227,1.0235,1.02435,1.02525,1.0262,1.02721,1.02826,1.02937,1.03054,1.03176,1.03304,1.03438,1.03578,1.03724,1.03877,1.04036,1.04202,1.04374,1.04553,1.04739,1.04931,1.05131,1.05338,1.05553,1.05774,1.06003,1.06239,1.06483,1.06734,1.06993,1.07259,1.07532,1.07813,1.08101,1.08396,1.08698,1.09007,1.09323,1.09646,1.09975,1.1031,1.1065,1.10997,1.11349,1.11705,1.12067,1.12432,1.12802,1.13175,1.1355,1.13928,1.14308,1.14689,1.15071,1.15453,1.15834,1.16214,1.16592,1.16968,1.1734,1.17708,1.18071,1.18429,1.1878,1.19123,1.19459,1.19785,1.20102,1.20408,1.20702,1.20984,1.21252,1.21506,1.21745,1.21968,1.22175,1.22363,1.22534,1.22685,1.22816,1.22926,1.23015,1.23082,1.23126,1.23147,1.23144,1.23117,1.23065,1.22988,1.22886,1.22758,1.22603,1.22423,1.22217,1.21985,1.21727,1.21443,1.21133,1.20799,1.2044,1.20056,1.1965,1.1922,1.18768,1.18296,1.17803,1.17291,1.16761,1.16214,1.15652,1.15076,1.14488,1.13888,1.13278,1.12661,1.12037,1.11408,1.10776,1.10142,1.09508,1.08876,1.08247,1.07622,1.07004,1.06392,1.0579,1.05197,1.04616,1.04046,1.03489,1.02946,1.02418,1.01905,1.01407,1.00925,1.00459,1.00009,0.995752,0.991577,0.987561,0.983702,0.979994,0.976433,0.973014,0.96973,0.966573,0.963536,0.960611,0.957787,0.955055,0.952405,0.949826,0.947307,0.944835,0.942398,0.939983,0.937577,0.935166,0.932735,0.930268,0.927751,0.925165,0.922494,0.919719,0.916821,0.913778,0.910571,0.907175,0.903567,0.89972,0.895608,0.891201,0.886469,0.881378,0.875894,0.86998,0.863596,0.856702,0.849251,0.841199,0.832496,0.823092,0.812931,0.801959,0.790119,0.777351,0.763596,0.748794,0.732886,0.715815,0.697529,0.677978,0.657122,0.634933,0.611395},
{1.01954,1.0201,1.02072,1.02138,1.02208,1.02283,1.02363,1.02448,1.02538,1.02634,1.02734,1.0284,1.02952,1.03069,1.03192,1.03321,1.03456,1.03597,1.03744,1.03898,1.04058,1.04225,1.04399,1.0458,1.04768,1.04964,1.05166,1.05376,1.05593,1.05818,1.0605,1.0629,1.06538,1.06794,1.07057,1.07328,1.07606,1.07893,1.08187,1.08488,1.08797,1.09114,1.09437,1.09768,1.10105,1.10449,1.10799,1.11156,1.11518,1.11886,1.12258,1.12636,1.13018,1.13403,1.13793,1.14185,1.14579,1.14975,1.15372,1.1577,1.16168,1.16566,1.16961,1.17355,1.17746,1.18133,1.18516,1.18893,1.19265,1.19629,1.19986,1.20334,1.20672,1.21,1.21317,1.21621,1.21913,1.2219,1.22452,1.22698,1.22928,1.2314,1.23334,1.23508,1.23662,1.23796,1.23908,1.23998,1.24064,1.24107,1.24127,1.24121,1.2409,1.24034,1.23952,1.23844,1.23709,1.23548,1.2336,1.23146,1.22905,1.22638,1.22345,1.22026,1.21682,1.21313,1.2092,1.20504,1.20065,1.19604,1.19122,1.18621,1.18101,1.17564,1.17011,1.16444,1.15863,1.1527,1.14668,1.14057,1.13439,1.12815,1.12188,1.11559,1.10929,1.10301,1.09675,1.09053,1.08438,1.07829,1.07229,1.06638,1.06058,1.0549,1.04934,1.04392,1.03864,1.03352,1.02854,1.02372,1.01906,1.01456,1.01022,1.00604,1.00202,0.998155,0.994438,0.990867,0.987437,0.984139,0.980968,0.977916,0.974972,0.972129,0.969377,0.966704,0.9641,0.961554,0.959053,0.956585,0.954136,0.951694,0.949243,0.946769,0.944257,0.94169,0.939051,0.936323,0.933487,0.930522,0.927409,0.924125,0.920648,0.916952,0.913011,0.908798,0.904283,0.899435,0.894221,0.888605,0.88255,0.876016,0.868961,0.86134,0.853106,0.844211,0.834602,0.824226,0.813025,0.800944,0.787922,0.773899,0.758817,0.742615,0.725237,0.70663,0.686745,0.665545,0.642998,0.619092},
{1.01968,1.02024,1.02085,1.02151,1.02221,1.02296,1.02376,1.02461,1.02551,1.02647,1.02747,1.02854,1.02965,1.03083,1.03207,1.03336,1.03472,1.03614,1.03762,1.03918,1.04079,1.04248,1.04424,1.04606,1.04796,1.04994,1.05199,1.05411,1.05631,1.05859,1.06095,1.06339,1.0659,1.0685,1.07118,1.07394,1.07677,1.07969,1.08269,1.08577,1.08893,1.09216,1.09547,1.09885,1.10231,1.10584,1.10944,1.1131,1.11682,1.12061,1.12445,1.12834,1.13228,1.13627,1.14029,1.14435,1.14844,1.15256,1.15669,1.16083,1.16497,1.16912,1.17325,1.17737,1.18147,1.18553,1.18956,1.19354,1.19746,1.20131,1.20509,1.20879,1.2124,1.2159,1.2193,1.22257,1.22572,1.22873,1.23159,1.23429,1.23682,1.23919,1.24136,1.24335,1.24513,1.2467,1.24806,1.24919,1.25009,1.25076,1.25117,1.25134,1.25126,1.25091,1.25031,1.24943,1.24829,1.24688,1.2452,1.24324,1.24102,1.23852,1.23576,1.23274,1.22945,1.22592,1.22213,1.21811,1.21385,1.20937,1.20467,1.19978,1.19469,1.18942,1.18399,1.1784,1.17268,1.16683,1.16088,1.15484,1.14872,1.14255,1.13633,1.13009,1.12384,1.1176,1.11138,1.1052,1.09907,1.09301,1.08703,1.08115,1.07537,1.0697,1.06416,1.05875,1.05349,1.04837,1.0434,1.03858,1.03393,1.02943,1.02509,1.02091,1.01689,1.01302,1.0093,1.00572,1.00228,0.998978,0.995798,0.992735,0.989781,0.986926,0.984159,0.981472,0.978852,0.976288,0.973769,0.97128,0.96881,0.966344,0.963868,0.961367,0.958826,0.956228,0.953556,0.950793,0.947919,0.944914,0.941758,0.938428,0.934902,0.931153,0.927157,0.922886,0.918309,0.913395,0.908111,0.902421,0.896288,0.889671,0.88253,0.874818,0.866488,0.857492,0.847778,0.83729,0.825975,0.813772,0.800624,0.78647,0.77125,0.754905,0.737377,0.718614,0.698567,0.677194,0.654468,0.63037},
{1.01982,1.02038,1.02099,1.02164,1.02234,1.02309,1.02388,1.02473,1.02563,1.02659,1.0276,1.02866,1.02978,1.03097,1.03221,1.03351,1.03487,1.0363,1.0378,1.03936,1.04099,1.04269,1.04446,1.04631,1.04823,1.05022,1.05229,1.05444,1.05667,1.05898,1.06137,1.06384,1.0664,1.06904,1.07176,1.07456,1.07745,1.08042,1.08348,1.08662,1.08984,1.09314,1.09653,1.09999,1.10353,1.10714,1.11083,1.11459,1.11841,1.12231,1.12626,1.13027,1.13433,1.13845,1.14261,1.14681,1.15104,1.1553,1.15959,1.16389,1.16821,1.17252,1.17684,1.18114,1.18543,1.18968,1.19391,1.19809,1.20222,1.20629,1.21029,1.21421,1.21804,1.22177,1.2254,1.22891,1.2323,1.23554,1.23865,1.24159,1.24437,1.24698,1.2494,1.25163,1.25366,1.25548,1.25709,1.25846,1.2596,1.26051,1.26116,1.26156,1.26171,1.26159,1.2612,1.26055,1.25962,1.25841,1.25693,1.25518,1.25314,1.25083,1.24825,1.2454,1.24228,1.23891,1.23528,1.2314,1.22728,1.22294,1.21837,1.21359,1.20862,1.20346,1.19813,1.19264,1.18701,1.18125,1.17538,1.16941,1.16336,1.15725,1.15109,1.1449,1.1387,1.13251,1.12633,1.12018,1.11409,1.10806,1.10211,1.09625,1.09049,1.08485,1.07932,1.07393,1.06867,1.06356,1.0586,1.0538,1.04915,1.04465,1.04031,1.03613,1.03211,1.02824,1.02451,1.02093,1.01749,1.01418,1.01099,1.00792,1.00495,1.00208,0.999305,0.996604,0.993969,0.991388,0.98885,0.986342,0.983851,0.981363,0.978863,0.976336,0.973767,0.971139,0.968436,0.965638,0.962728,0.959684,0.956487,0.953114,0.949541,0.945743,0.941695,0.937368,0.932732,0.927756,0.922406,0.916647,0.910441,0.903748,0.896526,0.888729,0.880311,0.871223,0.861411,0.850822,0.839401,0.827088,0.813825,0.799552,0.784207,0.767733,0.75007,0.731166,0.710971,0.689443,0.666552,0.64228},
{1.01996,1.02052,1.02112,1.02176,1.02246,1.02321,1.024,1.02485,1.02575,1.02671,1.02772,1.02878,1.02991,1.03109,1.03234,1.03364,1.03502,1.03645,1.03796,1.03953,1.04117,1.04289,1.04467,1.04654,1.04847,1.05049,1.05258,1.05476,1.05701,1.05935,1.06177,1.06428,1.06687,1.06954,1.07231,1.07516,1.07809,1.08112,1.08423,1.08743,1.09071,1.09408,1.09754,1.10108,1.1047,1.1084,1.11218,1.11603,1.11996,1.12395,1.12802,1.13214,1.13633,1.14057,1.14486,1.1492,1.15358,1.15799,1.16243,1.1669,1.17138,1.17587,1.18036,1.18485,1.18933,1.19378,1.1982,1.20259,1.20693,1.21122,1.21544,1.21958,1.22364,1.22761,1.23147,1.23522,1.23885,1.24234,1.24569,1.24889,1.25192,1.25478,1.25746,1.25994,1.26223,1.2643,1.26615,1.26778,1.26917,1.27032,1.27122,1.27186,1.27225,1.27236,1.27221,1.27178,1.27107,1.27008,1.26881,1.26726,1.26543,1.26332,1.26092,1.25825,1.25531,1.2521,1.24864,1.24491,1.24095,1.23674,1.23231,1.22766,1.22281,1.21777,1.21255,1.20716,1.20162,1.19595,1.19017,1.18428,1.1783,1.17226,1.16616,1.16003,1.15389,1.14774,1.14161,1.13551,1.12945,1.12345,1.11753,1.1117,1.10597,1.10034,1.09484,1.08946,1.08422,1.07912,1.07417,1.06937,1.06472,1.06023,1.0559,1.05172,1.0477,1.04382,1.0401,1.03651,1.03306,1.02974,1.02655,1.02347,1.02049,1.01762,1.01482,1.01211,1.00946,1.00686,1.00431,1.00178,0.999272,0.996762,0.994239,0.991687,0.989092,0.986436,0.983703,0.980873,0.977929,0.974849,0.971613,0.968199,0.964583,0.960739,0.956642,0.952264,0.947573,0.94254,0.93713,0.931308,0.925035,0.918273,0.910977,0.903104,0.894606,0.885434,0.875536,0.864857,0.853342,0.840932,0.827568,0.813189,0.797736,0.781149,0.763368,0.744341,0.724017,0.702353,0.679317,0.65489},
{1.0201,1.02065,1.02125,1.02189,1.02258,1.02332,1.02412,1.02496,1.02586,1.02682,1.02783,1.0289,1.03002,1.03121,1.03246,1.03377,1.03515,1.03659,1.03811,1.03969,1.04134,1.04307,1.04487,1.04675,1.0487,1.05074,1.05285,1.05505,1.05733,1.05969,1.06214,1.06468,1.06731,1.07002,1.07283,1.07572,1.07871,1.08178,1.08495,1.0882,1.09155,1.09499,1.09851,1.10212,1.10582,1.10961,1.11347,1.11742,1.12145,1.12555,1.12972,1.13396,1.13827,1.14264,1.14706,1.15153,1.15606,1.16062,1.16522,1.16984,1.17449,1.17915,1.18383,1.1885,1.19317,1.19782,1.20244,1.20704,1.21159,1.21609,1.22054,1.22491,1.2292,1.2334,1.23751,1.2415,1.24538,1.24912,1.25272,1.25617,1.25946,1.26258,1.26551,1.26826,1.2708,1.27313,1.27525,1.27713,1.27878,1.28018,1.28134,1.28223,1.28286,1.28322,1.28331,1.28311,1.28264,1.28187,1.28082,1.27949,1.27786,1.27595,1.27375,1.27128,1.26852,1.26549,1.26219,1.25863,1.25482,1.25076,1.24648,1.24196,1.23724,1.23232,1.22721,1.22193,1.2165,1.21093,1.20523,1.19942,1.19353,1.18756,1.18153,1.17546,1.16937,1.16327,1.15719,1.15113,1.14511,1.13915,1.13327,1.12746,1.12175,1.11615,1.11066,1.1053,1.10007,1.09499,1.09004,1.08525,1.08061,1.07612,1.07179,1.06761,1.06358,1.0597,1.05597,1.05238,1.04892,1.04559,1.04238,1.03929,1.0363,1.0334,1.03059,1.02786,1.02518,1.02256,1.01998,1.01742,1.01488,1.01233,1.00977,1.00718,1.00454,1.00184,0.999054,0.99617,0.993167,0.990025,0.986722,0.983236,0.979543,0.975617,0.971433,0.96696,0.96217,0.957031,0.951507,0.945564,0.939164,0.932265,0.924825,0.916798,0.908139,0.898795,0.888716,0.877847,0.86613,0.853509,0.839923,0.825313,0.809616,0.792774,0.774728,0.755423,0.73481,0.712847,0.689499,0.664749},
{1.02024,1.02078,1.02137,1.02201,1.0227,1.02344,1.02423,1.02507,1.02597,1.02692,1.02793,1.029,1.03013,1.03132,1.03258,1.03389,1.03528,1.03673,1.03825,1.03984,1.0415,1.04324,1.04505,1.04694,1.04892,1.05097,1.0531,1.05532,1.05763,1.06002,1.0625,1.06506,1.06772,1.07048,1.07332,1.07626,1.07929,1.08241,1.08563,1.08894,1.09235,1.09585,1.09944,1.10313,1.10691,1.11077,1.11472,1.11876,1.12289,1.12709,1.13137,1.13573,1.14015,1.14464,1.1492,1.15381,1.15847,1.16319,1.16794,1.17273,1.17754,1.18238,1.18723,1.19209,1.19695,1.20179,1.20663,1.21143,1.2162,1.22092,1.22559,1.23019,1.23472,1.23916,1.24351,1.24775,1.25187,1.25587,1.25973,1.26344,1.26699,1.27038,1.27358,1.27659,1.2794,1.282,1.28438,1.28653,1.28844,1.29011,1.29153,1.29268,1.29356,1.29418,1.29451,1.29456,1.29432,1.2938,1.29298,1.29187,1.29046,1.28876,1.28677,1.28449,1.28193,1.27908,1.27597,1.27258,1.26893,1.26504,1.2609,1.25653,1.25194,1.24715,1.24217,1.23701,1.23168,1.22621,1.22061,1.21489,1.20908,1.20319,1.19723,1.19123,1.1852,1.17917,1.17313,1.16712,1.16115,1.15523,1.14938,1.1436,1.13792,1.13234,1.12688,1.12154,1.11633,1.11126,1.10633,1.10155,1.09691,1.09243,1.0881,1.08393,1.0799,1.07602,1.07229,1.06869,1.06523,1.0619,1.05868,1.05558,1.05258,1.04967,1.04685,1.0441,1.04141,1.03877,1.03617,1.03359,1.03103,1.02846,1.02588,1.02326,1.02059,1.01786,1.01504,1.01212,1.00909,1.0059,1.00256,0.999031,0.995292,0.991317,0.987081,0.982554,0.977706,0.972506,0.966919,0.960908,0.954437,0.947464,0.939947,0.93184,0.923096,0.913665,0.903494,0.89253,0.880715,0.867992,0.8543,0.839579,0.823768,0.806807,0.788638,0.769205,0.748457,0.726351,0.702853,0.677941},
{1.02038,1.02091,1.0215,1.02213,1.02281,1.02355,1.02434,1.02518,1.02607,1.02703,1.02804,1.02911,1.03023,1.03143,1.03268,1.034,1.03539,1.03685,1.03837,1.03997,1.04165,1.04339,1.04522,1.04713,1.04911,1.05118,1.05333,1.05557,1.0579,1.06032,1.06282,1.06542,1.06811,1.0709,1.07378,1.07676,1.07983,1.08301,1.08627,1.08964,1.09311,1.09667,1.10033,1.10409,1.10794,1.11189,1.11593,1.12006,1.12427,1.12858,1.13297,1.13743,1.14198,1.14659,1.15128,1.15602,1.16083,1.16569,1.17059,1.17554,1.18053,1.18554,1.19057,1.19561,1.20066,1.20571,1.21074,1.21576,1.22074,1.22568,1.23058,1.23541,1.24018,1.24487,1.24946,1.25395,1.25833,1.26259,1.26671,1.27069,1.27451,1.27816,1.28163,1.28491,1.288,1.29087,1.29352,1.29595,1.29814,1.30007,1.30176,1.30318,1.30433,1.3052,1.30579,1.3061,1.30611,1.30582,1.30524,1.30437,1.30319,1.30171,1.29993,1.29786,1.2955,1.29285,1.28992,1.28671,1.28324,1.27951,1.27553,1.27131,1.26687,1.26221,1.25736,1.25232,1.24711,1.24175,1.23625,1.23063,1.2249,1.21909,1.21321,1.20728,1.20132,1.19534,1.18936,1.1834,1.17747,1.17159,1.16578,1.16004,1.15438,1.14883,1.14339,1.13807,1.13287,1.12781,1.12289,1.11812,1.11349,1.10901,1.10468,1.10051,1.09648,1.09259,1.08885,1.08524,1.08177,1.07842,1.07518,1.07206,1.06904,1.06611,1.06326,1.06048,1.05776,1.05509,1.05245,1.04983,1.04722,1.04461,1.04197,1.0393,1.03657,1.03377,1.03089,1.0279,1.02478,1.02151,1.01807,1.01444,1.0106,1.00651,1.00215,0.997489,0.9925,0.98715,0.981402,0.975221,0.968567,0.9614,0.953676,0.94535,0.936373,0.926695,0.916262,0.905021,0.892914,0.879883,0.865866,0.850805,0.834637,0.817301,0.798741,0.778901,0.757731,0.735187,0.711237,0.68586},
{1.02051,1.02104,1.02162,1.02225,1.02293,1.02366,1.02444,1.02528,1.02617,1.02712,1.02813,1.0292,1.03033,1.03152,1.03278,1.03411,1.0355,1.03696,1.03849,1.0401,1.04178,1.04354,1.04538,1.04729,1.04929,1.05138,1.05355,1.05581,1.05816,1.0606,1.06313,1.06576,1.06848,1.0713,1.07422,1.07723,1.08035,1.08357,1.08689,1.09031,1.09383,1.09745,1.10118,1.10501,1.10893,1.11296,1.11708,1.1213,1.12561,1.13001,1.13451,1.13908,1.14374,1.14848,1.15329,1.15818,1.16312,1.16813,1.17319,1.1783,1.18345,1.18863,1.19384,1.19907,1.20432,1.20956,1.2148,1.22003,1.22523,1.2304,1.23552,1.24059,1.2456,1.25053,1.25537,1.26012,1.26476,1.26928,1.27367,1.27791,1.282,1.28593,1.28968,1.29325,1.29661,1.29977,1.3027,1.30541,1.30787,1.31009,1.31205,1.31375,1.31517,1.31632,1.31717,1.31774,1.31801,1.31798,1.31765,1.31702,1.31608,1.31483,1.31328,1.31143,1.30928,1.30683,1.3041,1.30108,1.29779,1.29424,1.29043,1.28637,1.28208,1.27757,1.27285,1.26794,1.26285,1.25761,1.25221,1.24669,1.24107,1.23534,1.22955,1.22369,1.2178,1.21189,1.20597,1.20007,1.19419,1.18836,1.18258,1.17688,1.17126,1.16574,1.16032,1.15502,1.14985,1.14481,1.1399,1.13514,1.13052,1.12605,1.12173,1.11756,1.11353,1.10964,1.1059,1.10229,1.09881,1.09545,1.09221,1.08907,1.08604,1.0831,1.08023,1.07743,1.0747,1.072,1.06934,1.0667,1.06406,1.06142,1.05875,1.05604,1.05328,1.05044,1.04751,1.04448,1.04131,1.03799,1.0345,1.03081,1.0269,1.02275,1.01832,1.01358,1.00852,1.00308,0.997248,0.990974,0.984222,0.976951,0.969119,0.960678,0.951581,0.941777,0.931212,0.919833,0.907582,0.8944,0.880227,0.865001,0.848662,0.83115,0.812405,0.792371,0.770999,0.748245,0.724074,0.698464},
{1.02065,1.02117,1.02174,1.02236,1.02304,1.02376,1.02454,1.02538,1.02627,1.02721,1.02822,1.02929,1.03042,1.03161,1.03287,1.0342,1.03559,1.03706,1.0386,1.04021,1.0419,1.04367,1.04552,1.04745,1.04946,1.05156,1.05375,1.05602,1.05839,1.06085,1.06341,1.06607,1.06882,1.07167,1.07462,1.07768,1.08084,1.0841,1.08746,1.09094,1.09451,1.0982,1.10199,1.10588,1.10988,1.11398,1.11819,1.12249,1.1269,1.1314,1.13599,1.14068,1.14545,1.15031,1.15525,1.16027,1.16535,1.17051,1.17572,1.18099,1.1863,1.19166,1.19705,1.20246,1.2079,1.21334,1.21879,1.22423,1.22965,1.23504,1.2404,1.2457,1.25095,1.25613,1.26123,1.26623,1.27114,1.27592,1.28058,1.2851,1.28947,1.29368,1.29772,1.30156,1.30522,1.30866,1.31188,1.31488,1.31763,1.32014,1.32239,1.32437,1.32607,1.3275,1.32863,1.32947,1.33001,1.33024,1.33017,1.32979,1.32909,1.32809,1.32677,1.32515,1.32322,1.32099,1.31846,1.31564,1.31254,1.30917,1.30553,1.30165,1.29752,1.29316,1.28858,1.28381,1.27885,1.27373,1.26845,1.26304,1.25751,1.25188,1.24617,1.2404,1.23458,1.22874,1.22289,1.21704,1.21121,1.20543,1.1997,1.19403,1.18845,1.18296,1.17757,1.17229,1.16714,1.16211,1.15722,1.15247,1.14786,1.1434,1.13908,1.1349,1.13087,1.12698,1.12323,1.11961,1.11612,1.11275,1.10949,1.10634,1.10328,1.10031,1.09742,1.09459,1.09182,1.08909,1.08639,1.08371,1.08103,1.07834,1.07561,1.07285,1.07002,1.06712,1.06412,1.06101,1.05776,1.05435,1.05076,1.04697,1.04296,1.03868,1.03413,1.02926,1.02405,1.01847,1.01247,1.00602,0.999088,0.991623,0.983583,0.974922,0.965591,0.95554,0.944715,0.93306,0.920518,0.90703,0.892535,0.876972,0.860279,0.842396,0.823265,0.80283,0.78104,0.757853,0.733234,0.707165},
{1.02078,1.0213,1.02186,1.02247,1.02314,1.02386,1.02464,1.02547,1.02636,1.0273,1.02831,1.02937,1.0305,1.0317,1.03296,1.03428,1.03568,1.03715,1.0387,1.04031,1.04201,1.04379,1.04564,1.04758,1.04961,1.05172,1.05393,1.05622,1.05861,1.06109,1.06367,1.06635,1.06913,1.07202,1.075,1.07809,1.08129,1.0846,1.08801,1.09153,1.09516,1.0989,1.10275,1.10671,1.11078,1.11496,1.11924,1.12363,1.12813,1.13273,1.13742,1.14222,1.1471,1.15208,1.15715,1.16229,1.16752,1.17282,1.17818,1.18361,1.18909,1.19462,1.20019,1.20579,1.21142,1.21706,1.22271,1.22837,1.23401,1.23963,1.24521,1.25076,1.25625,1.26168,1.26704,1.27231,1.27748,1.28253,1.28747,1.29227,1.29692,1.30142,1.30574,1.30988,1.31383,1.31757,1.32109,1.32438,1.32743,1.33023,1.33277,1.33505,1.33704,1.33876,1.34018,1.3413,1.34211,1.34262,1.34282,1.3427,1.34226,1.34151,1.34044,1.33905,1.33736,1.33535,1.33304,1.33043,1.32753,1.32435,1.3209,1.31719,1.31323,1.30903,1.30462,1.29999,1.29517,1.29017,1.28502,1.27972,1.2743,1.26878,1.26316,1.25748,1.25174,1.24597,1.24019,1.2344,1.22864,1.22291,1.21722,1.2116,1.20606,1.2006,1.19525,1.19,1.18487,1.17987,1.175,1.17026,1.16566,1.16121,1.1569,1.15273,1.1487,1.14481,1.14106,1.13744,1.13394,1.13056,1.1273,1.12413,1.12106,1.11808,1.11517,1.11233,1.10954,1.10679,1.10406,1.10135,1.09864,1.09592,1.09316,1.09036,1.08749,1.08455,1.0815,1.07834,1.07504,1.07157,1.06793,1.06407,1.05999,1.05565,1.05102,1.04607,1.04078,1.0351,1.02901,1.02246,1.01542,1.00784,0.999685,0.990901,0.981442,0.971255,0.960288,0.948485,0.935788,0.922139,0.907475,0.891737,0.874861,0.856788,0.837458,0.816816,0.794811,0.771398,0.746543,0.720225},
{1.02091,1.02142,1.02198,1.02258,1.02325,1.02396,1.02473,1.02556,1.02644,1.02738,1.02839,1.02945,1.03058,1.03177,1.03303,1.03436,1.03576,1.03724,1.03878,1.04041,1.04211,1.04389,1.04576,1.04771,1.04974,1.05187,1.05409,1.0564,1.0588,1.06131,1.06391,1.06662,1.06942,1.07233,1.07535,1.07848,1.08171,1.08506,1.08852,1.09209,1.09577,1.09957,1.10348,1.1075,1.11164,1.11589,1.12025,1.12473,1.12931,1.134,1.1388,1.1437,1.1487,1.15379,1.15898,1.16426,1.16962,1.17506,1.18058,1.18616,1.19181,1.19751,1.20325,1.20904,1.21486,1.22071,1.22657,1.23243,1.23829,1.24414,1.24996,1.25575,1.26149,1.26718,1.27279,1.27832,1.28376,1.2891,1.29431,1.2994,1.30434,1.30913,1.31374,1.31818,1.32243,1.32647,1.33029,1.33389,1.33724,1.34035,1.34319,1.34577,1.34807,1.35007,1.35179,1.3532,1.35431,1.3551,1.35557,1.35573,1.35556,1.35507,1.35425,1.35311,1.35166,1.34989,1.3478,1.34541,1.34273,1.33975,1.3365,1.33297,1.32919,1.32516,1.3209,1.31643,1.31176,1.3069,1.30187,1.2967,1.29139,1.28597,1.28046,1.27487,1.26922,1.26353,1.25782,1.2521,1.2464,1.24073,1.2351,1.22952,1.22402,1.2186,1.21328,1.20806,1.20296,1.19798,1.19313,1.18841,1.18382,1.17938,1.17507,1.17091,1.16688,1.16299,1.15924,1.15561,1.15211,1.14872,1.14544,1.14226,1.13918,1.13617,1.13324,1.13037,1.12755,1.12477,1.12202,1.11927,1.11652,1.11375,1.11095,1.1081,1.10518,1.10218,1.09907,1.09584,1.09247,1.08893,1.0852,1.08126,1.07709,1.07265,1.06791,1.06285,1.05744,1.05164,1.04541,1.03872,1.03153,1.02379,1.01546,1.0065,0.996854,0.986469,0.975293,0.96327,0.950343,0.936451,0.921534,0.90553,0.888377,0.870014,0.850382,0.829426,0.807093,0.78334,0.758133,0.731449},
{1.02104,1.02154,1.02209,1.02269,1.02335,1.02406,1.02482,1.02564,1.02652,1.02746,1.02846,1.02952,1.03065,1.03184,1.0331,1.03443,1.03583,1.03731,1.03886,1.04049,1.04219,1.04398,1.04586,1.04782,1.04986,1.052,1.05423,1.05656,1.05898,1.0615,1.06413,1.06685,1.06969,1.07263,1.07568,1.07884,1.08211,1.08549,1.08899,1.09261,1.09634,1.10019,1.10416,1.10825,1.11245,1.11677,1.12121,1.12577,1.13044,1.13522,1.14012,1.14512,1.15023,1.15544,1.16075,1.16616,1.17166,1.17724,1.1829,1.18864,1.19445,1.20032,1.20625,1.21222,1.21824,1.22428,1.23035,1.23643,1.24251,1.24859,1.25465,1.26068,1.26667,1.27261,1.27848,1.28428,1.29,1.29561,1.30111,1.30648,1.31172,1.3168,1.32172,1.32646,1.33102,1.33537,1.3395,1.34341,1.34707,1.35049,1.35365,1.35654,1.35914,1.36146,1.36348,1.36519,1.36659,1.36768,1.36844,1.36888,1.36899,1.36877,1.36822,1.36734,1.36614,1.36461,1.36277,1.36061,1.35814,1.35538,1.35233,1.349,1.34541,1.34156,1.33747,1.33316,1.32864,1.32393,1.31904,1.314,1.30881,1.30351,1.2981,1.29261,1.28705,1.28145,1.27582,1.27018,1.26454,1.25893,1.25336,1.24783,1.24238,1.237,1.23172,1.22654,1.22146,1.21651,1.21168,1.20698,1.20241,1.19798,1.19368,1.18952,1.1855,1.18162,1.17786,1.17423,1.17072,1.16732,1.16404,1.16085,1.15775,1.15473,1.15178,1.14889,1.14605,1.14324,1.14045,1.13767,1.13489,1.13208,1.12924,1.12635,1.12338,1.12033,1.11717,1.11388,1.11044,1.10684,1.10304,1.09903,1.09477,1.09024,1.08541,1.08026,1.07474,1.06883,1.06249,1.05568,1.04836,1.04049,1.03202,1.0229,1.0131,1.00255,0.991199,0.978994,0.965876,0.951785,0.936659,0.920438,0.903058,0.884459,0.864582,0.843369,0.820769,0.796738,0.77124,0.744252},
{1.02117,1.02166,1.0222,1.0228,1.02345,1.02415,1.02491,1.02572,1.0266,1.02753,1.02853,1.02959,1.03071,1.0319,1.03316,1.03449,1.0359,1.03737,1.03893,1.04056,1.04227,1.04406,1.04594,1.04791,1.04997,1.05212,1.05436,1.0567,1.05914,1.06168,1.06432,1.06707,1.06993,1.07289,1.07597,1.07916,1.08247,1.08589,1.08943,1.09309,1.09688,1.10078,1.1048,1.10895,1.11322,1.11761,1.12212,1.12676,1.13151,1.13639,1.14138,1.14648,1.1517,1.15703,1.16246,1.16799,1.17362,1.17935,1.18516,1.19106,1.19703,1.20307,1.20917,1.21533,1.22154,1.22778,1.23406,1.24035,1.24666,1.25296,1.25926,1.26553,1.27177,1.27797,1.28411,1.29018,1.29617,1.30207,1.30786,1.31352,1.31906,1.32444,1.32967,1.33472,1.33959,1.34425,1.3487,1.35293,1.35692,1.36065,1.36413,1.36734,1.37026,1.37289,1.37523,1.37725,1.37896,1.38035,1.38141,1.38215,1.38255,1.38261,1.38234,1.38173,1.38079,1.37952,1.37792,1.376,1.37377,1.37123,1.36839,1.36527,1.36187,1.35822,1.35431,1.35017,1.34581,1.34126,1.33652,1.33161,1.32655,1.32137,1.31608,1.31069,1.30524,1.29973,1.29418,1.28862,1.28305,1.27751,1.272,1.26653,1.26113,1.2558,1.25055,1.24541,1.24037,1.23544,1.23063,1.22595,1.2214,1.21699,1.21271,1.20856,1.20454,1.20066,1.1969,1.19327,1.18976,1.18635,1.18306,1.17985,1.17674,1.17371,1.17074,1.16783,1.16496,1.16213,1.15931,1.1565,1.15368,1.15084,1.14796,1.14502,1.142,1.1389,1.13568,1.13234,1.12884,1.12516,1.1213,1.1172,1.11286,1.10825,1.10333,1.09808,1.09246,1.08644,1.07998,1.07305,1.0656,1.05759,1.04898,1.03972,1.02975,1.01904,1.00751,0.995128,0.98182,0.96753,0.952197,0.93576,0.918154,0.899321,0.879198,0.85773,0.834865,0.810557,0.78477,0.75748},
{1.0213,1.02178,1.02232,1.0229,1.02354,1.02424,1.02499,1.0258,1.02667,1.0276,1.02859,1.02965,1.03077,1.03196,1.03322,1.03455,1.03595,1.03743,1.03898,1.04062,1.04233,1.04413,1.04602,1.04799,1.05006,1.05222,1.05447,1.05682,1.05928,1.06183,1.06449,1.06726,1.07014,1.07313,1.07624,1.07946,1.0828,1.08626,1.08984,1.09354,1.09737,1.10133,1.1054,1.10961,1.11394,1.1184,1.12299,1.1277,1.13254,1.1375,1.14258,1.14779,1.15311,1.15855,1.1641,1.16976,1.17552,1.18139,1.18735,1.1934,1.19953,1.20574,1.21202,1.21836,1.22476,1.2312,1.23768,1.24419,1.25072,1.25726,1.26379,1.27031,1.27681,1.28327,1.28967,1.29602,1.30229,1.30847,1.31455,1.32052,1.32635,1.33205,1.33758,1.34295,1.34814,1.35312,1.3579,1.36245,1.36676,1.37083,1.37464,1.37817,1.38142,1.38438,1.38704,1.38939,1.39141,1.39312,1.39449,1.39553,1.39623,1.39659,1.3966,1.39628,1.39561,1.3946,1.39326,1.3916,1.38961,1.3873,1.38469,1.38179,1.3786,1.37514,1.37142,1.36746,1.36328,1.35889,1.3543,1.34954,1.34462,1.33957,1.3344,1.32913,1.32378,1.31836,1.31291,1.30743,1.30195,1.29647,1.29103,1.28562,1.28027,1.27499,1.2698,1.26469,1.25969,1.25479,1.25001,1.24536,1.24083,1.23643,1.23216,1.22803,1.22402,1.22014,1.21639,1.21276,1.20924,1.20583,1.20253,1.19932,1.19619,1.19314,1.19016,1.18723,1.18434,1.18148,1.17864,1.1758,1.17295,1.17007,1.16715,1.16417,1.16111,1.15796,1.15469,1.15129,1.14773,1.144,1.14006,1.1359,1.13148,1.12679,1.12179,1.11644,1.11073,1.10461,1.09805,1.091,1.08343,1.0753,1.06656,1.05716,1.04706,1.03619,1.02452,1.01197,0.998491,0.984025,0.968509,0.951881,0.934077,0.915037,0.8947,0.873008,0.849909,0.825356,0.799313,0.771754},
{1.02143,1.0219,1.02243,1.023,1.02364,1.02433,1.02507,1.02588,1.02674,1.02766,1.02865,1.0297,1.03082,1.03201,1.03327,1.03459,1.03599,1.03747,1.03903,1.04066,1.04238,1.04419,1.04608,1.04806,1.05013,1.0523,1.05456,1.05693,1.05939,1.06197,1.06464,1.06743,1.07033,1.07335,1.07648,1.07973,1.0831,1.0866,1.09021,1.09396,1.09783,1.10183,1.10596,1.11023,1.11462,1.11914,1.1238,1.12859,1.1335,1.13855,1.14373,1.14903,1.15446,1.16001,1.16567,1.17146,1.17735,1.18335,1.18946,1.19566,1.20195,1.20833,1.21478,1.22131,1.2279,1.23454,1.24123,1.24796,1.25471,1.26148,1.26825,1.27501,1.28176,1.28848,1.29516,1.30178,1.30833,1.3148,1.32118,1.32745,1.33359,1.3396,1.34545,1.35114,1.35665,1.36196,1.36707,1.37195,1.37661,1.38101,1.38515,1.38902,1.39261,1.3959,1.39889,1.40157,1.40393,1.40596,1.40765,1.409,1.41001,1.41067,1.41099,1.41096,1.41057,1.40985,1.40878,1.40737,1.40563,1.40357,1.4012,1.39852,1.39555,1.3923,1.38878,1.38501,1.38101,1.37679,1.37237,1.36776,1.36299,1.35807,1.35303,1.34788,1.34264,1.33733,1.33197,1.32659,1.32118,1.31579,1.31041,1.30507,1.29978,1.29455,1.2894,1.28434,1.27937,1.27451,1.26976,1.26513,1.26062,1.25624,1.25199,1.24786,1.24386,1.23998,1.23623,1.2326,1.22907,1.22566,1.22234,1.21912,1.21597,1.2129,1.20989,1.20693,1.20402,1.20112,1.19824,1.19536,1.19247,1.18954,1.18656,1.18353,1.18041,1.17719,1.17385,1.17037,1.16673,1.16291,1.15888,1.15461,1.15009,1.14529,1.14016,1.13469,1.12884,1.12257,1.11585,1.10865,1.10091,1.09259,1.08366,1.07406,1.06374,1.05265,1.04073,1.02793,1.0142,0.999456,0.983653,0.966725,0.948608,0.92924,0.908562,0.886515,0.863046,0.83811,0.811668,0.783695},
{1.02156,1.02202,1.02253,1.0231,1.02373,1.02441,1.02515,1.02595,1.0268,1.02772,1.02871,1.02975,1.03087,1.03205,1.03331,1.03463,1.03603,1.03751,1.03906,1.0407,1.04242,1.04423,1.04612,1.04811,1.05019,1.05237,1.05464,1.05701,1.05949,1.06208,1.06477,1.06758,1.0705,1.07354,1.07669,1.07997,1.08337,1.0869,1.09055,1.09434,1.09825,1.1023,1.10648,1.1108,1.11525,1.11984,1.12456,1.12942,1.13442,1.13955,1.14482,1.15022,1.15574,1.1614,1.16718,1.17309,1.17911,1.18525,1.1915,1.19785,1.2043,1.21084,1.21747,1.22418,1.23096,1.2378,1.2447,1.25164,1.25861,1.26561,1.27262,1.27964,1.28664,1.29362,1.30057,1.30747,1.31431,1.32107,1.32775,1.33432,1.34078,1.3471,1.35328,1.35929,1.36513,1.37078,1.37623,1.38145,1.38644,1.39119,1.39568,1.3999,1.40383,1.40747,1.4108,1.41382,1.41652,1.41888,1.4209,1.42259,1.42392,1.4249,1.42552,1.42579,1.42571,1.42527,1.42448,1.42335,1.42188,1.42007,1.41795,1.41551,1.41276,1.40973,1.40643,1.40286,1.39905,1.39501,1.39076,1.38631,1.3817,1.37693,1.37202,1.367,1.36188,1.35668,1.35143,1.34614,1.34083,1.33552,1.33021,1.32494,1.31972,1.31455,1.30945,1.30444,1.29951,1.29469,1.28998,1.28537,1.28089,1.27653,1.27229,1.26818,1.26419,1.26033,1.25658,1.25295,1.24942,1.246,1.24268,1.23945,1.23629,1.2332,1.23018,1.2272,1.22426,1.22134,1.21843,1.21552,1.21259,1.20962,1.20661,1.20352,1.20035,1.19708,1.19369,1.19015,1.18645,1.18255,1.17845,1.17411,1.16951,1.16461,1.1594,1.15383,1.14787,1.1415,1.13466,1.12733,1.11947,1.11102,1.10195,1.0922,1.08172,1.07047,1.05839,1.04541,1.03149,1.01656,1.00056,0.983424,0.965091,0.945499,0.924587,0.902297,0.878574,0.853373,0.826653,0.798388},
{1.02168,1.02213,1.02264,1.0232,1.02382,1.02449,1.02522,1.02601,1.02686,1.02778,1.02875,1.0298,1.03091,1.03209,1.03334,1.03466,1.03606,1.03754,1.03909,1.04073,1.04245,1.04426,1.04616,1.04815,1.05023,1.05242,1.0547,1.05708,1.05957,1.06217,1.06488,1.0677,1.07064,1.0737,1.07688,1.08018,1.08361,1.08717,1.09086,1.09468,1.09864,1.10273,1.10696,1.11133,1.11584,1.12049,1.12528,1.13021,1.13528,1.14049,1.14585,1.15134,1.15697,1.16273,1.16862,1.17465,1.1808,1.18707,1.19346,1.19996,1.20657,1.21328,1.22008,1.22697,1.23394,1.24098,1.24808,1.25523,1.26243,1.26966,1.27691,1.28418,1.29144,1.29868,1.3059,1.31308,1.32021,1.32727,1.33425,1.34113,1.3479,1.35454,1.36105,1.36739,1.37357,1.37956,1.38535,1.39092,1.39627,1.40137,1.40621,1.41078,1.41507,1.41906,1.42275,1.42612,1.42916,1.43187,1.43423,1.43625,1.43792,1.43922,1.44017,1.44076,1.44098,1.44084,1.44035,1.4395,1.4383,1.43677,1.4349,1.43271,1.43021,1.42741,1.42432,1.42097,1.41736,1.41351,1.40944,1.40517,1.40071,1.3961,1.39133,1.38645,1.38146,1.37638,1.37124,1.36605,1.36083,1.35561,1.35039,1.34519,1.34003,1.33493,1.32989,1.32492,1.32004,1.31526,1.31058,1.30601,1.30156,1.29722,1.293,1.2889,1.28492,1.28107,1.27732,1.27369,1.27016,1.26674,1.2634,1.26016,1.25699,1.25388,1.25083,1.24783,1.24486,1.24191,1.23896,1.23601,1.23303,1.23002,1.22695,1.22381,1.22059,1.21725,1.21379,1.21017,1.20639,1.20241,1.19822,1.19378,1.18907,1.18407,1.17873,1.17304,1.16695,1.16044,1.15346,1.14598,1.13794,1.12932,1.12007,1.11013,1.09945,1.08799,1.07568,1.06247,1.04831,1.03312,1.01686,0.999442,0.980819,0.960925,0.939698,0.917079,0.893015,0.867457,0.840366,0.811716},
{1.02181,1.02225,1.02274,1.02329,1.0239,1.02457,1.02529,1.02607,1.02692,1.02783,1.0288,1.02984,1.03094,1.03212,1.03336,1.03468,1.03608,1.03755,1.03911,1.04075,1.04247,1.04428,1.04618,1.04817,1.05026,1.05245,1.05474,1.05713,1.05963,1.06224,1.06497,1.06781,1.07076,1.07384,1.07704,1.08037,1.08382,1.08741,1.09113,1.09499,1.09898,1.10312,1.10739,1.11181,1.11638,1.12108,1.12594,1.13094,1.13609,1.14138,1.14682,1.1524,1.15812,1.16399,1.17,1.17614,1.18241,1.18882,1.19534,1.20199,1.20875,1.21563,1.2226,1.22967,1.23683,1.24406,1.25137,1.25874,1.26616,1.27362,1.28111,1.28862,1.29614,1.30366,1.31115,1.31861,1.32603,1.33339,1.34067,1.34786,1.35495,1.36192,1.36876,1.37544,1.38196,1.3883,1.39444,1.40037,1.40607,1.41153,1.41673,1.42167,1.42632,1.43068,1.43473,1.43846,1.44186,1.44492,1.44764,1.45001,1.45202,1.45367,1.45495,1.45586,1.4564,1.45658,1.45639,1.45584,1.45493,1.45368,1.45208,1.45015,1.4479,1.44534,1.44249,1.43935,1.43595,1.43231,1.42843,1.42434,1.42006,1.41561,1.411,1.40626,1.4014,1.39645,1.39143,1.38635,1.38124,1.37611,1.37098,1.36586,1.36078,1.35574,1.35076,1.34585,1.34102,1.33628,1.33164,1.32711,1.32268,1.31837,1.31418,1.3101,1.30613,1.30229,1.29855,1.29492,1.2914,1.28797,1.28463,1.28137,1.27819,1.27507,1.272,1.26897,1.26598,1.263,1.26002,1.25703,1.25402,1.25096,1.24785,1.24466,1.24138,1.23798,1.23446,1.23078,1.22692,1.22287,1.21859,1.21407,1.20927,1.20416,1.19873,1.19292,1.18672,1.18009,1.17298,1.16536,1.15718,1.14841,1.139,1.12889,1.11804,1.1064,1.0939,1.0805,1.06613,1.05073,1.03423,1.01659,0.997722,0.977574,0.956083,0.93319,0.908839,0.882982,0.855578,0.826599},
{1.02193,1.02236,1.02285,1.02339,1.02399,1.02464,1.02536,1.02613,1.02697,1.02787,1.02884,1.02987,1.03097,1.03214,1.03338,1.0347,1.03609,1.03756,1.03912,1.04075,1.04248,1.04429,1.04619,1.04819,1.05028,1.05247,1.05477,1.05717,1.05968,1.0623,1.06503,1.06788,1.07086,1.07395,1.07717,1.08052,1.084,1.08762,1.09137,1.09526,1.09929,1.10347,1.10779,1.11225,1.11687,1.12163,1.12655,1.13162,1.13684,1.14221,1.14773,1.1534,1.15922,1.16519,1.1713,1.17756,1.18395,1.19049,1.19715,1.20394,1.21086,1.21789,1.22503,1.23228,1.23963,1.24706,1.25457,1.26215,1.26979,1.27749,1.28522,1.29298,1.30076,1.30854,1.31631,1.32406,1.33177,1.33942,1.34701,1.35452,1.36194,1.36924,1.37641,1.38344,1.3903,1.39699,1.40349,1.40978,1.41585,1.42167,1.42725,1.43255,1.43758,1.44231,1.44673,1.45083,1.4546,1.45804,1.46112,1.46385,1.46621,1.46821,1.46984,1.47109,1.47196,1.47246,1.47259,1.47235,1.47175,1.47078,1.46947,1.46781,1.46582,1.46352,1.46091,1.45801,1.45483,1.4514,1.44772,1.44383,1.43973,1.43545,1.431,1.42641,1.4217,1.41689,1.41199,1.40703,1.40202,1.39699,1.39196,1.38693,1.38192,1.37696,1.37204,1.36719,1.36242,1.35773,1.35314,1.34864,1.34425,1.33996,1.33579,1.33173,1.32779,1.32395,1.32022,1.3166,1.31307,1.30964,1.3063,1.30303,1.29983,1.2967,1.29361,1.29056,1.28753,1.28452,1.28151,1.27849,1.27543,1.27233,1.26917,1.26593,1.26259,1.25913,1.25554,1.25178,1.24785,1.24372,1.23935,1.23473,1.22984,1.22463,1.21908,1.21316,1.20683,1.20006,1.19282,1.18505,1.17672,1.16779,1.15821,1.14792,1.13689,1.12505,1.11235,1.09873,1.08414,1.0685,1.05177,1.03387,1.01474,0.994316,0.972539,0.949348,0.924686,0.898504,0.870762,0.841428},
{1.02205,1.02247,1.02295,1.02348,1.02407,1.02471,1.02542,1.02619,1.02702,1.02791,1.02887,1.0299,1.03099,1.03215,1.03339,1.03471,1.03609,1.03756,1.03911,1.04075,1.04247,1.04428,1.04619,1.04818,1.05028,1.05248,1.05478,1.05718,1.0597,1.06233,1.06507,1.06794,1.07092,1.07404,1.07728,1.08065,1.08415,1.08779,1.09157,1.09549,1.09956,1.10377,1.10814,1.11265,1.11732,1.12214,1.12711,1.13224,1.13753,1.14297,1.14858,1.15433,1.16025,1.16631,1.17253,1.1789,1.18542,1.19208,1.19888,1.20581,1.21288,1.22007,1.22738,1.23481,1.24234,1.24996,1.25768,1.26547,1.27334,1.28126,1.28923,1.29724,1.30528,1.31333,1.32137,1.32941,1.33741,1.34537,1.35327,1.3611,1.36884,1.37648,1.38399,1.39136,1.39858,1.40563,1.41249,1.41915,1.42559,1.43179,1.43775,1.44343,1.44884,1.45395,1.45875,1.46324,1.46739,1.4712,1.47466,1.47776,1.48049,1.48285,1.48484,1.48644,1.48766,1.4885,1.48896,1.48904,1.48875,1.48809,1.48707,1.48569,1.48398,1.48194,1.47959,1.47693,1.47399,1.47078,1.46732,1.46363,1.45972,1.45562,1.45135,1.44692,1.44236,1.43769,1.43293,1.42809,1.42321,1.41829,1.41335,1.40841,1.40349,1.39861,1.39376,1.38898,1.38427,1.37963,1.37508,1.37063,1.36627,1.36202,1.35788,1.35384,1.34991,1.34609,1.34238,1.33876,1.33524,1.3318,1.32846,1.32518,1.32197,1.31882,1.31572,1.31265,1.3096,1.30656,1.30352,1.30046,1.29736,1.29422,1.29101,1.28771,1.28432,1.2808,1.27714,1.27332,1.26932,1.2651,1.26066,1.25595,1.25096,1.24565,1.24,1.23397,1.22752,1.22063,1.21325,1.20535,1.19688,1.1878,1.17805,1.1676,1.1564,1.14438,1.13149,1.11767,1.10288,1.08703,1.07007,1.05194,1.03257,1.0119,0.989863,0.966399,0.941454,0.914976,0.886922,0.857261},
{1.02217,1.02258,1.02304,1.02357,1.02415,1.02478,1.02548,1.02624,1.02706,1.02795,1.0289,1.02992,1.031,1.03216,1.0334,1.0347,1.03609,1.03755,1.0391,1.04073,1.04245,1.04426,1.04617,1.04817,1.05026,1.05246,1.05477,1.05718,1.0597,1.06234,1.0651,1.06797,1.07097,1.0741,1.07735,1.08074,1.08427,1.08793,1.09174,1.09569,1.09979,1.10404,1.10844,1.113,1.11772,1.12259,1.12762,1.13281,1.13817,1.14368,1.14936,1.1552,1.16121,1.16737,1.17369,1.18017,1.1868,1.19359,1.20052,1.2076,1.21481,1.22216,1.22964,1.23724,1.24495,1.25277,1.26069,1.26869,1.27678,1.28493,1.29314,1.3014,1.3097,1.31801,1.32634,1.33466,1.34296,1.35122,1.35944,1.36759,1.37566,1.38363,1.39149,1.39921,1.40679,1.41421,1.42144,1.42847,1.43529,1.44187,1.44821,1.45429,1.46008,1.46558,1.47078,1.47566,1.4802,1.4844,1.48824,1.49173,1.49484,1.49757,1.49993,1.50189,1.50347,1.50466,1.50546,1.50588,1.50591,1.50557,1.50485,1.50378,1.50236,1.50059,1.49851,1.49611,1.49341,1.49044,1.4872,1.48372,1.48002,1.47611,1.47202,1.46776,1.46336,1.45884,1.45422,1.44952,1.44476,1.43995,1.43512,1.43028,1.42545,1.42065,1.41588,1.41117,1.40651,1.40193,1.39744,1.39303,1.38871,1.38449,1.38038,1.37637,1.37246,1.36865,1.36494,1.36133,1.35781,1.35438,1.35102,1.34774,1.34451,1.34134,1.33822,1.33512,1.33204,1.32897,1.32588,1.32278,1.31964,1.31644,1.31317,1.30982,1.30636,1.30277,1.29903,1.29513,1.29103,1.28672,1.28217,1.27736,1.27225,1.26682,1.26104,1.25487,1.24828,1.24123,1.23369,1.22562,1.21697,1.2077,1.19776,1.1871,1.17567,1.16342,1.15029,1.13623,1.12116,1.10504,1.0878,1.06937,1.04969,1.02869,1.00631,0.982493,0.957178,0.930315,0.901859,0.871778},
{1.02229,1.02269,1.02314,1.02365,1.02422,1.02485,1.02554,1.02629,1.0271,1.02798,1.02892,1.02993,1.03101,1.03217,1.03339,1.0347,1.03608,1.03754,1.03908,1.04071,1.04243,1.04424,1.04614,1.04814,1.05024,1.05244,1.05474,1.05716,1.05969,1.06233,1.06509,1.06798,1.07099,1.07413,1.0774,1.08081,1.08435,1.08804,1.09187,1.09585,1.09998,1.10427,1.10871,1.11331,1.11807,1.12299,1.12808,1.13333,1.13875,1.14433,1.15009,1.15601,1.1621,1.16836,1.17478,1.18137,1.18811,1.19502,1.20208,1.2093,1.21666,1.22416,1.2318,1.23957,1.24747,1.25548,1.2636,1.27181,1.28012,1.2885,1.29695,1.30546,1.31402,1.3226,1.3312,1.33981,1.34841,1.35698,1.36551,1.37399,1.38239,1.3907,1.39891,1.40699,1.41493,1.42272,1.43032,1.43774,1.44494,1.45192,1.45865,1.46512,1.47132,1.47722,1.48282,1.4881,1.49304,1.49764,1.50188,1.50576,1.50927,1.51239,1.51512,1.51747,1.51941,1.52097,1.52212,1.52289,1.52326,1.52325,1.52286,1.52209,1.52097,1.5195,1.51769,1.51556,1.51312,1.5104,1.5074,1.50414,1.50065,1.49695,1.49305,1.48897,1.48475,1.48039,1.47592,1.47136,1.46673,1.46205,1.45733,1.4526,1.44787,1.44315,1.43847,1.43383,1.42925,1.42473,1.42029,1.41593,1.41166,1.40749,1.4034,1.39942,1.39554,1.39175,1.38806,1.38446,1.38095,1.37752,1.37416,1.37087,1.36764,1.36446,1.36132,1.3582,1.3551,1.352,1.34888,1.34575,1.34257,1.33933,1.33601,1.33261,1.32909,1.32545,1.32165,1.31768,1.31351,1.30912,1.30449,1.29959,1.2944,1.28887,1.28298,1.27671,1.27,1.26284,1.25518,1.24697,1.23818,1.22877,1.21868,1.20786,1.19627,1.18386,1.17055,1.1563,1.14105,1.12473,1.10728,1.08864,1.06873,1.04751,1.02489,1.00082,0.975241,0.948102,0.919356,0.888969},
{1.02241,1.02279,1.02324,1.02374,1.02429,1.02491,1.02559,1.02633,1.02714,1.028,1.02894,1.02994,1.03102,1.03216,1.03338,1.03468,1.03605,1.03751,1.03905,1.04067,1.04239,1.04419,1.04609,1.04809,1.05019,1.05239,1.0547,1.05712,1.05965,1.0623,1.06507,1.06797,1.07099,1.07414,1.07742,1.08085,1.08441,1.08812,1.09197,1.09598,1.10014,1.10446,1.10893,1.11357,1.11837,1.12334,1.12848,1.13379,1.13927,1.14492,1.15075,1.15675,1.16293,1.16927,1.17579,1.18248,1.18934,1.19637,1.20356,1.21091,1.21841,1.22607,1.23387,1.24181,1.24989,1.25809,1.2664,1.27483,1.28335,1.29196,1.30065,1.30941,1.31822,1.32708,1.33596,1.34485,1.35375,1.36263,1.37148,1.38028,1.38902,1.39768,1.40624,1.41468,1.42299,1.43115,1.43914,1.44694,1.45454,1.46191,1.46905,1.47592,1.48253,1.48884,1.49485,1.50054,1.50589,1.5109,1.51556,1.51984,1.52375,1.52727,1.5304,1.53313,1.53546,1.53739,1.53892,1.54004,1.54077,1.5411,1.54104,1.5406,1.5398,1.53863,1.53711,1.53526,1.5331,1.53063,1.52787,1.52486,1.52159,1.5181,1.5144,1.51052,1.50648,1.50229,1.49798,1.49357,1.48908,1.48453,1.47994,1.47532,1.47069,1.46607,1.46148,1.45692,1.45241,1.44796,1.44358,1.43928,1.43506,1.43092,1.42688,1.42293,1.41907,1.4153,1.41163,1.40804,1.40454,1.40111,1.39775,1.39446,1.39122,1.38802,1.38486,1.38172,1.37859,1.37546,1.37232,1.36914,1.36592,1.36263,1.35927,1.35581,1.35223,1.34852,1.34465,1.34061,1.33636,1.33189,1.32717,1.32217,1.31687,1.31124,1.30524,1.29884,1.29201,1.28471,1.2769,1.26855,1.25961,1.25003,1.23977,1.22878,1.217,1.20439,1.19088,1.17642,1.16095,1.1444,1.12672,1.10783,1.08766,1.06617,1.04327,1.01891,0.993024,0.965565,0.936483,0.905742},
{1.02253,1.0229,1.02333,1.02382,1.02437,1.02497,1.02564,1.02637,1.02717,1.02803,1.02895,1.02995,1.03101,1.03215,1.03336,1.03465,1.03602,1.03747,1.03901,1.04063,1.04234,1.04414,1.04604,1.04803,1.05013,1.05233,1.05464,1.05706,1.0596,1.06225,1.06503,1.06793,1.07096,1.07412,1.07742,1.08085,1.08443,1.08816,1.09204,1.09607,1.10025,1.1046,1.10911,1.11379,1.11863,1.12365,1.12883,1.1342,1.13974,1.14545,1.15135,1.15743,1.16368,1.17012,1.17673,1.18352,1.19049,1.19764,1.20495,1.21243,1.22008,1.22788,1.23584,1.24395,1.2522,1.26059,1.2691,1.27773,1.28648,1.29532,1.30424,1.31325,1.32232,1.33144,1.3406,1.34979,1.35898,1.36817,1.37734,1.38647,1.39555,1.40456,1.41347,1.42228,1.43096,1.4395,1.44788,1.45607,1.46407,1.47185,1.47939,1.48668,1.4937,1.50044,1.50687,1.51298,1.51876,1.52419,1.52926,1.53397,1.53829,1.54222,1.54576,1.54889,1.55162,1.55394,1.55585,1.55735,1.55844,1.55913,1.55942,1.55932,1.55884,1.55799,1.55678,1.55523,1.55334,1.55115,1.54865,1.54589,1.54286,1.53959,1.53611,1.53243,1.52858,1.52457,1.52044,1.51619,1.51184,1.50743,1.50297,1.49847,1.49396,1.48945,1.48495,1.48048,1.47605,1.47167,1.46736,1.46311,1.45895,1.45486,1.45086,1.44694,1.44311,1.43938,1.43572,1.43215,1.42866,1.42524,1.42188,1.41859,1.41534,1.41214,1.40896,1.40581,1.40266,1.3995,1.39633,1.39312,1.38986,1.38653,1.38312,1.37961,1.37598,1.37221,1.36828,1.36417,1.35985,1.3553,1.3505,1.34542,1.34003,1.3343,1.3282,1.32169,1.31475,1.30734,1.29941,1.29093,1.28185,1.27213,1.26173,1.25058,1.23865,1.22587,1.2122,1.19756,1.18191,1.16517,1.14728,1.12819,1.10781,1.08609,1.06297,1.03836,1.01223,0.984503,0.95514,0.924101},
{1.02264,1.023,1.02342,1.0239,1.02443,1.02503,1.02569,1.02641,1.02719,1.02804,1.02896,1.02995,1.031,1.03213,1.03334,1.03462,1.03598,1.03743,1.03896,1.04057,1.04228,1.04407,1.04597,1.04796,1.05006,1.05226,1.05457,1.05699,1.05953,1.06218,1.06496,1.06787,1.0709,1.07407,1.07738,1.08083,1.08443,1.08817,1.09207,1.09612,1.10033,1.1047,1.10925,1.11396,1.11884,1.1239,1.12913,1.13455,1.14014,1.14592,1.15188,1.15803,1.16437,1.17089,1.17759,1.18448,1.19156,1.19882,1.20625,1.21386,1.22165,1.2296,1.23772,1.24599,1.25442,1.26299,1.27169,1.28053,1.28948,1.29855,1.30771,1.31697,1.32629,1.33568,1.34512,1.3546,1.36409,1.3736,1.38309,1.39255,1.40197,1.41132,1.4206,1.42977,1.43883,1.44776,1.45653,1.46512,1.47352,1.48171,1.48967,1.49739,1.50483,1.51199,1.51885,1.5254,1.53161,1.53747,1.54298,1.54811,1.55286,1.55722,1.56118,1.56473,1.56786,1.57059,1.57289,1.57478,1.57625,1.57731,1.57796,1.57821,1.57807,1.57755,1.57666,1.57542,1.57383,1.57192,1.5697,1.56719,1.56441,1.56138,1.55813,1.55466,1.55101,1.5472,1.54324,1.53916,1.53497,1.53071,1.52638,1.52201,1.51762,1.51322,1.50882,1.50444,1.5001,1.4958,1.49156,1.48737,1.48326,1.47922,1.47527,1.47139,1.46759,1.46388,1.46025,1.45669,1.45321,1.44979,1.44644,1.44314,1.43989,1.43667,1.43348,1.4303,1.42712,1.42394,1.42072,1.41747,1.41417,1.41079,1.40733,1.40376,1.40006,1.39622,1.39221,1.38802,1.38361,1.37897,1.37407,1.36888,1.36338,1.35753,1.3513,1.34467,1.33759,1.33002,1.32194,1.3133,1.30405,1.29416,1.28356,1.27223,1.26009,1.2471,1.2332,1.21834,1.20244,1.18546,1.16731,1.14794,1.12729,1.10527,1.08184,1.05691,1.03044,1.00236,0.972629,0.941199},
{1.02276,1.0231,1.02351,1.02397,1.0245,1.02508,1.02573,1.02644,1.02721,1.02805,1.02896,1.02994,1.03099,1.03211,1.03331,1.03458,1.03594,1.03737,1.03889,1.0405,1.0422,1.044,1.04589,1.04788,1.04997,1.05217,1.05447,1.05689,1.05943,1.06209,1.06487,1.06778,1.07082,1.074,1.07732,1.08078,1.08439,1.08815,1.09206,1.09613,1.10037,1.10477,1.10934,1.11408,1.119,1.12409,1.12937,1.13484,1.14049,1.14632,1.15235,1.15857,1.16498,1.17158,1.17838,1.18536,1.19254,1.19991,1.20746,1.2152,1.22312,1.23121,1.23948,1.24792,1.25652,1.26527,1.27417,1.28321,1.29238,1.30167,1.31106,1.32056,1.33015,1.3398,1.34952,1.35929,1.36908,1.37889,1.38871,1.3985,1.40826,1.41797,1.42761,1.43716,1.4466,1.45591,1.46508,1.47408,1.48289,1.4915,1.49989,1.50803,1.51591,1.5235,1.5308,1.53779,1.54444,1.55075,1.5567,1.56227,1.56746,1.57226,1.57665,1.58063,1.58419,1.58733,1.59004,1.59233,1.5942,1.59564,1.59667,1.59729,1.5975,1.59733,1.59677,1.59584,1.59457,1.59295,1.59102,1.58879,1.58627,1.58349,1.58047,1.57723,1.57379,1.57018,1.56641,1.56251,1.55849,1.55438,1.5502,1.54597,1.5417,1.53742,1.53313,1.52885,1.5246,1.52038,1.51622,1.5121,1.50805,1.50407,1.50015,1.49632,1.49256,1.48887,1.48526,1.48173,1.47826,1.47485,1.4715,1.4682,1.46493,1.4617,1.45849,1.45529,1.45209,1.44887,1.44562,1.44233,1.43898,1.43555,1.43203,1.4284,1.42464,1.42072,1.41664,1.41236,1.40787,1.40313,1.39813,1.39284,1.38722,1.38125,1.3749,1.36813,1.3609,1.3532,1.34496,1.33615,1.32673,1.31666,1.30588,1.29435,1.28201,1.26881,1.25469,1.23959,1.22345,1.20622,1.18781,1.16817,1.14723,1.12492,1.10117,1.07593,1.04912,1.02068,0.990576,0.958752},
{1.02287,1.0232,1.0236,1.02405,1.02456,1.02513,1.02577,1.02647,1.02723,1.02806,1.02896,1.02993,1.03097,1.03208,1.03327,1.03453,1.03588,1.03731,1.03882,1.04043,1.04212,1.04391,1.04579,1.04778,1.04986,1.05206,1.05436,1.05678,1.05932,1.06198,1.06476,1.06768,1.07072,1.0739,1.07723,1.0807,1.08432,1.08809,1.09202,1.09611,1.10036,1.10479,1.10938,1.11415,1.11911,1.12424,1.12956,1.13507,1.14077,1.14666,1.15275,1.15904,1.16552,1.1722,1.17908,1.18616,1.19344,1.20091,1.20858,1.21644,1.22449,1.23273,1.24115,1.24974,1.25851,1.26744,1.27653,1.28577,1.29515,1.30466,1.31429,1.32403,1.33387,1.34379,1.35379,1.36385,1.37394,1.38407,1.3942,1.40433,1.41444,1.4245,1.4345,1.44443,1.45425,1.46396,1.47353,1.48294,1.49217,1.50121,1.51002,1.5186,1.52692,1.53497,1.54272,1.55015,1.55726,1.56402,1.57042,1.57645,1.58209,1.58734,1.59217,1.59659,1.60059,1.60416,1.6073,1.61001,1.61228,1.61413,1.61554,1.61654,1.61713,1.61731,1.6171,1.61652,1.61556,1.61426,1.61263,1.61068,1.60844,1.60592,1.60315,1.60015,1.59694,1.59354,1.58997,1.58626,1.58242,1.57848,1.57446,1.57037,1.56624,1.56208,1.55791,1.55374,1.54958,1.54546,1.54137,1.53733,1.53335,1.52942,1.52556,1.52177,1.51805,1.5144,1.51082,1.50731,1.50386,1.50046,1.49712,1.49382,1.49055,1.48732,1.48409,1.48088,1.47765,1.47441,1.47113,1.4678,1.46441,1.46093,1.45736,1.45368,1.44986,1.44588,1.44173,1.43737,1.4328,1.42798,1.42289,1.4175,1.41178,1.40571,1.39924,1.39235,1.38501,1.37717,1.3688,1.35985,1.35029,1.34006,1.32912,1.31742,1.30491,1.29153,1.27722,1.26193,1.24559,1.22814,1.20952,1.18966,1.16848,1.14592,1.12192,1.09641,1.06932,1.04059,1.01017,0.978008},
{1.02298,1.0233,1.02368,1.02412,1.02462,1.02518,1.02581,1.02649,1.02725,1.02806,1.02895,1.02991,1.03094,1.03204,1.03322,1.03448,1.03581,1.03723,1.03874,1.04034,1.04202,1.0438,1.04568,1.04766,1.04974,1.05193,1.05424,1.05665,1.05919,1.06185,1.06463,1.06754,1.07059,1.07378,1.07711,1.08059,1.08421,1.088,1.09194,1.09604,1.10032,1.10476,1.10938,1.11418,1.11917,1.12434,1.12969,1.13525,1.14099,1.14694,1.15309,1.15943,1.16599,1.17274,1.1797,1.18687,1.19425,1.20182,1.2096,1.21758,1.22576,1.23414,1.2427,1.25146,1.26039,1.2695,1.27877,1.28821,1.2978,1.30752,1.31739,1.32737,1.33746,1.34765,1.35793,1.36827,1.37867,1.3891,1.39956,1.41003,1.42048,1.4309,1.44127,1.45157,1.46179,1.47189,1.48187,1.4917,1.50136,1.51082,1.52008,1.5291,1.53787,1.54637,1.55458,1.56248,1.57005,1.57728,1.58414,1.59064,1.59674,1.60245,1.60775,1.61262,1.61707,1.62108,1.62466,1.6278,1.6305,1.63276,1.63458,1.63598,1.63695,1.63751,1.63766,1.63742,1.63681,1.63584,1.63452,1.63287,1.63092,1.62868,1.62617,1.62342,1.62045,1.61727,1.61392,1.61041,1.60676,1.603,1.59914,1.59521,1.59122,1.5872,1.58315,1.5791,1.57505,1.57102,1.56703,1.56307,1.55916,1.5553,1.5515,1.54777,1.54409,1.54048,1.53694,1.53345,1.53002,1.52664,1.52331,1.52002,1.51676,1.51352,1.51029,1.50706,1.50382,1.50055,1.49725,1.49389,1.49047,1.48695,1.48334,1.47961,1.47574,1.4717,1.46749,1.46307,1.45843,1.45354,1.44837,1.4429,1.4371,1.43093,1.42437,1.41738,1.40994,1.40199,1.3935,1.38444,1.37475,1.3644,1.35333,1.34149,1.32884,1.31531,1.30086,1.28541,1.26891,1.2513,1.23251,1.21247,1.19111,1.16837,1.14417,1.11844,1.09113,1.06217,1.0315,0.999069},
{1.02309,1.0234,1.02376,1.02419,1.02468,1.02523,1.02584,1.02651,1.02725,1.02806,1.02894,1.02988,1.0309,1.032,1.03316,1.03441,1.03574,1.03715,1.03865,1.04024,1.04191,1.04369,1.04556,1.04753,1.04961,1.05179,1.05409,1.0565,1.05904,1.06169,1.06447,1.06739,1.07044,1.07363,1.07696,1.08044,1.08408,1.08787,1.09182,1.09594,1.10023,1.1047,1.10934,1.11416,1.11917,1.12438,1.12977,1.13536,1.14116,1.14715,1.15335,1.15976,1.16638,1.17321,1.18025,1.1875,1.19496,1.20264,1.21053,1.21863,1.22693,1.23544,1.24415,1.25305,1.26215,1.27143,1.28089,1.29052,1.30031,1.31026,1.32035,1.33057,1.34092,1.35137,1.36192,1.37255,1.38325,1.394,1.40478,1.41558,1.42638,1.43717,1.44791,1.45859,1.4692,1.47971,1.4901,1.50035,1.51043,1.52034,1.53004,1.53951,1.54874,1.5577,1.56638,1.57475,1.5828,1.5905,1.59785,1.60482,1.6114,1.61759,1.62336,1.6287,1.63361,1.63809,1.64212,1.64571,1.64884,1.65153,1.65378,1.65559,1.65696,1.65791,1.65844,1.65857,1.65831,1.65768,1.65669,1.65536,1.65372,1.65177,1.64954,1.64705,1.64433,1.64139,1.63826,1.63497,1.63152,1.62795,1.62427,1.62051,1.61667,1.6128,1.60888,1.60496,1.60103,1.59711,1.59321,1.58934,1.58551,1.58173,1.578,1.57432,1.5707,1.56714,1.56364,1.56019,1.55679,1.55344,1.55012,1.54685,1.5436,1.54036,1.53713,1.5339,1.53065,1.52738,1.52406,1.52068,1.51723,1.5137,1.51005,1.50629,1.50238,1.4983,1.49405,1.48959,1.48489,1.47995,1.47472,1.46919,1.46333,1.4571,1.45047,1.44341,1.43589,1.42787,1.41931,1.41016,1.4004,1.38996,1.3788,1.36688,1.35414,1.34053,1.32599,1.31045,1.29387,1.27616,1.25728,1.23714,1.21568,1.19284,1.16853,1.1427,1.11527,1.08617,1.05536,1.02277},
{1.0232,1.02349,1.02385,1.02426,1.02473,1.02527,1.02587,1.02653,1.02726,1.02805,1.02892,1.02985,1.03086,1.03194,1.0331,1.03434,1.03566,1.03706,1.03855,1.04012,1.04179,1.04356,1.04542,1.04739,1.04946,1.05164,1.05393,1.05634,1.05886,1.06151,1.06429,1.06721,1.07026,1.07345,1.07678,1.08027,1.08391,1.08771,1.09167,1.0958,1.10011,1.10459,1.10925,1.11409,1.11913,1.12436,1.12979,1.13542,1.14125,1.14729,1.15355,1.16001,1.16669,1.17359,1.1807,1.18804,1.19559,1.20337,1.21136,1.21957,1.22799,1.23663,1.24548,1.25454,1.26379,1.27324,1.28288,1.2927,1.3027,1.31286,1.32317,1.33364,1.34423,1.35495,1.36577,1.37669,1.38769,1.39875,1.40985,1.42099,1.43214,1.44328,1.4544,1.46546,1.47647,1.48738,1.49818,1.50886,1.51938,1.52973,1.53988,1.54982,1.55951,1.56895,1.5781,1.58695,1.59548,1.60368,1.61151,1.61897,1.62605,1.63272,1.63897,1.6448,1.65019,1.65514,1.65964,1.66369,1.66728,1.67041,1.6731,1.67533,1.67712,1.67848,1.6794,1.67992,1.68003,1.67975,1.67911,1.67811,1.67678,1.67514,1.6732,1.67099,1.66853,1.66585,1.66296,1.65988,1.65665,1.65328,1.64979,1.6462,1.64254,1.63881,1.63504,1.63125,1.62744,1.62363,1.61984,1.61607,1.61233,1.60863,1.60497,1.60136,1.59779,1.59428,1.59082,1.58741,1.58404,1.58072,1.57743,1.57416,1.57092,1.56769,1.56447,1.56123,1.55797,1.55468,1.55135,1.54795,1.54448,1.54091,1.53723,1.53343,1.52947,1.52536,1.52105,1.51653,1.51178,1.50678,1.50149,1.49589,1.48995,1.48365,1.47694,1.4698,1.4622,1.45409,1.44544,1.4362,1.42634,1.4158,1.40455,1.39252,1.37968,1.36596,1.3513,1.33566,1.31896,1.30114,1.28213,1.26187,1.24029,1.21731,1.19286,1.16688,1.13929,1.11003,1.07904,1.04625},
{1.02331,1.02359,1.02392,1.02432,1.02478,1.02531,1.02589,1.02654,1.02726,1.02804,1.02889,1.02982,1.03081,1.03188,1.03303,1.03426,1.03557,1.03696,1.03844,1.04,1.04166,1.04342,1.04527,1.04723,1.04929,1.05146,1.05375,1.05615,1.05867,1.06132,1.06409,1.067,1.07005,1.07324,1.07658,1.08006,1.08371,1.08751,1.09148,1.09562,1.09994,1.10443,1.10911,1.11398,1.11904,1.12429,1.12975,1.13541,1.14129,1.14737,1.15367,1.16019,1.16693,1.17389,1.18107,1.18849,1.19612,1.20399,1.21208,1.2204,1.22894,1.23771,1.24669,1.25589,1.2653,1.27491,1.28473,1.29474,1.30493,1.3153,1.32584,1.33653,1.34737,1.35835,1.36944,1.38065,1.39194,1.40331,1.41474,1.42621,1.43771,1.44921,1.46069,1.47215,1.48354,1.49486,1.50609,1.51719,1.52815,1.53894,1.54955,1.55995,1.57012,1.58003,1.58967,1.59901,1.60803,1.61672,1.62505,1.63301,1.64058,1.64775,1.6545,1.66082,1.6667,1.67213,1.67711,1.68163,1.68569,1.68928,1.69242,1.69509,1.69731,1.69908,1.70041,1.70132,1.70181,1.70191,1.70162,1.70096,1.69996,1.69863,1.69699,1.69506,1.69288,1.69045,1.6878,1.68496,1.68194,1.67878,1.67548,1.67207,1.66857,1.665,1.66137,1.65771,1.65402,1.65032,1.64663,1.64295,1.63929,1.63565,1.63205,1.62849,1.62498,1.6215,1.61807,1.61467,1.61131,1.60799,1.6047,1.60142,1.59816,1.5949,1.59164,1.58836,1.58505,1.5817,1.5783,1.57483,1.57127,1.56761,1.56384,1.55993,1.55586,1.55161,1.54717,1.54251,1.5376,1.53243,1.52696,1.52117,1.51503,1.50852,1.50158,1.49421,1.48635,1.47797,1.46904,1.4595,1.44933,1.43846,1.42686,1.41447,1.40124,1.38712,1.37204,1.35595,1.33878,1.32047,1.30094,1.28014,1.25799,1.23442,1.20935,1.18272,1.15445,1.12447,1.09272,1.05914},
{1.02341,1.02368,1.024,1.02439,1.02483,1.02534,1.02591,1.02655,1.02725,1.02802,1.02886,1.02978,1.03076,1.03182,1.03295,1.03417,1.03546,1.03684,1.03831,1.03987,1.04152,1.04326,1.04511,1.04706,1.04911,1.05127,1.05355,1.05594,1.05846,1.0611,1.06387,1.06677,1.06982,1.073,1.07634,1.07983,1.08347,1.08728,1.09126,1.0954,1.09973,1.10423,1.10892,1.11381,1.11889,1.12417,1.12965,1.13535,1.14125,1.14738,1.15372,1.16029,1.16708,1.1741,1.18136,1.18884,1.19656,1.20452,1.21271,1.22113,1.22978,1.23867,1.24778,1.25712,1.26668,1.27646,1.28645,1.29664,1.30703,1.31761,1.32836,1.33929,1.35038,1.36161,1.37297,1.38446,1.39605,1.40773,1.41948,1.43129,1.44314,1.455,1.46686,1.4787,1.4905,1.50223,1.51388,1.52541,1.53682,1.54807,1.55914,1.57001,1.58066,1.59106,1.60119,1.61103,1.62055,1.62975,1.63859,1.64707,1.65515,1.66283,1.6701,1.67693,1.68332,1.68925,1.69473,1.69974,1.70428,1.70835,1.71195,1.71509,1.71775,1.71996,1.72172,1.72305,1.72394,1.72442,1.72451,1.72422,1.72356,1.72256,1.72125,1.71963,1.71774,1.71559,1.7132,1.71061,1.70783,1.70489,1.7018,1.69859,1.69527,1.69188,1.68841,1.6849,1.68135,1.67779,1.67421,1.67064,1.66708,1.66354,1.66003,1.65654,1.65309,1.64968,1.6463,1.64295,1.63963,1.63634,1.63308,1.62982,1.62658,1.62333,1.62008,1.6168,1.61349,1.61013,1.60672,1.60323,1.59965,1.59597,1.59216,1.58822,1.58411,1.57983,1.57534,1.57063,1.56567,1.56045,1.55492,1.54907,1.54287,1.53629,1.52929,1.52184,1.51391,1.50546,1.49645,1.48684,1.47658,1.46563,1.45395,1.44148,1.42817,1.41396,1.39879,1.38262,1.36536,1.34696,1.32735,1.30646,1.28421,1.26054,1.23537,1.20863,1.18023,1.15012,1.11823,1.08448},
{1.02352,1.02377,1.02408,1.02445,1.02488,1.02537,1.02593,1.02655,1.02724,1.028,1.02883,1.02973,1.0307,1.03174,1.03287,1.03407,1.03535,1.03672,1.03818,1.03972,1.04136,1.0431,1.04493,1.04687,1.04891,1.05106,1.05333,1.05572,1.05822,1.06086,1.06362,1.06652,1.06956,1.07274,1.07607,1.07956,1.0832,1.08701,1.09099,1.09514,1.09947,1.10399,1.10869,1.11359,1.11869,1.12399,1.12949,1.13522,1.14115,1.14731,1.1537,1.16031,1.16716,1.17424,1.18155,1.18911,1.1969,1.20494,1.21322,1.22174,1.23051,1.23951,1.24875,1.25823,1.26794,1.27787,1.28803,1.2984,1.30898,1.31976,1.33073,1.34189,1.35321,1.3647,1.37633,1.3881,1.39998,1.41197,1.42404,1.43619,1.44838,1.46061,1.47284,1.48507,1.49727,1.50942,1.52149,1.53346,1.54532,1.55703,1.56857,1.57992,1.59105,1.60194,1.61258,1.62293,1.63297,1.64268,1.65204,1.66104,1.66965,1.67786,1.68565,1.693,1.69991,1.70637,1.71236,1.71787,1.72292,1.72748,1.73156,1.73517,1.7383,1.74097,1.74317,1.74492,1.74623,1.74712,1.7476,1.74768,1.74739,1.74674,1.74576,1.74446,1.74287,1.74102,1.73891,1.73658,1.73405,1.73134,1.72847,1.72547,1.72235,1.71914,1.71585,1.71249,1.70909,1.70566,1.70222,1.69876,1.69531,1.69186,1.68844,1.68503,1.68165,1.6783,1.67497,1.67168,1.6684,1.66514,1.6619,1.65867,1.65544,1.65221,1.64895,1.64567,1.64236,1.63899,1.63555,1.63204,1.62843,1.62472,1.62087,1.61689,1.61273,1.6084,1.60386,1.59909,1.59407,1.58877,1.58317,1.57725,1.57097,1.5643,1.55721,1.54967,1.54164,1.53309,1.52398,1.51426,1.5039,1.49284,1.48104,1.46845,1.45502,1.44068,1.42539,1.40908,1.39169,1.37316,1.3534,1.33236,1.30997,1.28613,1.26079,1.23387,1.20528,1.17496,1.14283,1.10884},
{1.02362,1.02385,1.02415,1.0245,1.02492,1.0254,1.02594,1.02655,1.02723,1.02797,1.02879,1.02967,1.03063,1.03166,1.03277,1.03396,1.03524,1.03659,1.03803,1.03957,1.04119,1.04292,1.04474,1.04667,1.0487,1.05084,1.0531,1.05547,1.05797,1.06059,1.06335,1.06624,1.06927,1.07245,1.07578,1.07926,1.0829,1.08671,1.09069,1.09484,1.09918,1.1037,1.10841,1.11332,1.11843,1.12375,1.12928,1.13502,1.14099,1.14718,1.1536,1.16026,1.16715,1.17428,1.18166,1.18928,1.19715,1.20526,1.21363,1.22225,1.23112,1.24023,1.2496,1.2592,1.26905,1.27914,1.28946,1.30001,1.31078,1.32176,1.33294,1.34432,1.35588,1.36762,1.37952,1.39156,1.40374,1.41603,1.42843,1.44091,1.45345,1.46604,1.47865,1.49127,1.50387,1.51643,1.52893,1.54135,1.55365,1.56583,1.57784,1.58968,1.6013,1.6127,1.62384,1.63471,1.64528,1.65552,1.66541,1.67495,1.6841,1.69284,1.70117,1.70906,1.71651,1.72349,1.73001,1.73605,1.74161,1.74669,1.75127,1.75537,1.75898,1.76212,1.76478,1.76698,1.76873,1.77004,1.77093,1.77141,1.7715,1.77122,1.77058,1.76962,1.76836,1.76681,1.76499,1.76294,1.76068,1.75822,1.75559,1.7528,1.7499,1.74688,1.74377,1.74059,1.73735,1.73407,1.73076,1.72743,1.72409,1.72076,1.71743,1.71411,1.71081,1.70753,1.70427,1.70103,1.69781,1.6946,1.69139,1.6882,1.68499,1.68177,1.67854,1.67527,1.67195,1.66858,1.66514,1.66162,1.658,1.65427,1.65041,1.64639,1.64221,1.63784,1.63327,1.62846,1.6234,1.61806,1.61242,1.60645,1.60011,1.59339,1.58625,1.57866,1.57058,1.56197,1.5528,1.54303,1.53261,1.52149,1.50964,1.49699,1.4835,1.46912,1.45377,1.43742,1.41998,1.40139,1.38159,1.3605,1.33805,1.31417,1.28877,1.26179,1.23313,1.20273,1.17051,1.1364},
{1.02372,1.02394,1.02422,1.02456,1.02496,1.02542,1.02595,1.02655,1.02721,1.02794,1.02874,1.02961,1.03056,1.03158,1.03267,1.03385,1.03511,1.03645,1.03788,1.0394,1.04101,1.04272,1.04453,1.04645,1.04847,1.0506,1.05284,1.05521,1.05769,1.06031,1.06305,1.06593,1.06896,1.07213,1.07545,1.07892,1.08256,1.08637,1.09034,1.0945,1.09883,1.10336,1.10808,1.113,1.11812,1.12345,1.129,1.13476,1.14075,1.14697,1.15343,1.16012,1.16706,1.17424,1.18167,1.18935,1.19729,1.20548,1.21393,1.22264,1.2316,1.24083,1.25031,1.26004,1.27003,1.28026,1.29074,1.30146,1.31241,1.32358,1.33498,1.34658,1.35837,1.37036,1.38251,1.39483,1.4073,1.4199,1.43261,1.44542,1.45831,1.47125,1.48424,1.49725,1.51026,1.52323,1.53616,1.54902,1.56178,1.57443,1.58692,1.59924,1.61137,1.62328,1.63494,1.64633,1.65742,1.6682,1.67864,1.68872,1.69842,1.70771,1.71659,1.72504,1.73303,1.74056,1.74762,1.7542,1.76029,1.76589,1.77099,1.7756,1.77971,1.78333,1.78647,1.78914,1.79134,1.79309,1.7944,1.79529,1.79577,1.79587,1.79561,1.795,1.79407,1.79283,1.79133,1.78957,1.78757,1.78537,1.78299,1.78044,1.77775,1.77494,1.77202,1.76902,1.76594,1.76281,1.75965,1.75645,1.75323,1.75001,1.74678,1.74355,1.74034,1.73713,1.73393,1.73075,1.72757,1.7244,1.72123,1.71806,1.71487,1.71166,1.70843,1.70516,1.70184,1.69846,1.695,1.69146,1.68781,1.68404,1.68013,1.67608,1.67184,1.66742,1.66278,1.65791,1.65278,1.64737,1.64165,1.63559,1.62917,1.62236,1.61512,1.60743,1.59924,1.59053,1.58124,1.57135,1.56081,1.54957,1.53759,1.52481,1.51119,1.49666,1.48118,1.46467,1.44708,1.42834,1.40837,1.38711,1.36448,1.34041,1.31482,1.28762,1.25874,1.22809,1.1956,1.16119},
{1.02382,1.02402,1.02428,1.02461,1.025,1.02545,1.02596,1.02654,1.02719,1.0279,1.02869,1.02954,1.03047,1.03148,1.03256,1.03372,1.03497,1.0363,1.03771,1.03922,1.04082,1.04252,1.04431,1.04621,1.04822,1.05034,1.05257,1.05492,1.0574,1.06,1.06273,1.0656,1.06862,1.07178,1.07509,1.07856,1.08219,1.08599,1.08996,1.09411,1.09845,1.10297,1.1077,1.11262,1.11775,1.12309,1.12865,1.13444,1.14045,1.1467,1.15318,1.15991,1.16688,1.17411,1.18159,1.18933,1.19732,1.20559,1.21411,1.22291,1.23197,1.24129,1.25089,1.26074,1.27086,1.28124,1.29187,1.30276,1.31388,1.32525,1.33684,1.34866,1.36069,1.37291,1.38533,1.39792,1.41067,1.42357,1.4366,1.44974,1.46297,1.47628,1.48965,1.50304,1.51645,1.52985,1.54322,1.55652,1.56974,1.58286,1.59584,1.60866,1.62129,1.63371,1.6459,1.65783,1.66946,1.68079,1.69179,1.70242,1.71268,1.72254,1.73199,1.741,1.74956,1.75765,1.76527,1.77241,1.77905,1.78519,1.79083,1.79596,1.80059,1.80472,1.80836,1.81151,1.81418,1.81639,1.81814,1.81946,1.82036,1.82086,1.82099,1.82075,1.82017,1.81928,1.8181,1.81665,1.81495,1.81303,1.81091,1.80861,1.80616,1.80357,1.80086,1.79805,1.79516,1.79221,1.7892,1.78615,1.78307,1.77997,1.77687,1.77375,1.77063,1.76752,1.7644,1.76129,1.75818,1.75507,1.75196,1.74883,1.74569,1.74252,1.73932,1.73608,1.73278,1.72942,1.72598,1.72244,1.7188,1.71504,1.71114,1.70708,1.70285,1.69842,1.69378,1.6889,1.68376,1.67834,1.67261,1.66654,1.66012,1.6533,1.64606,1.63836,1.63017,1.62146,1.61218,1.6023,1.59178,1.58056,1.5686,1.55585,1.54226,1.52778,1.51234,1.49589,1.47837,1.45969,1.43981,1.41864,1.3961,1.37213,1.34663,1.31953,1.29075,1.26019,1.22779,1.19345},
{1.02392,1.0241,1.02435,1.02466,1.02503,1.02546,1.02596,1.02653,1.02716,1.02786,1.02863,1.02947,1.03039,1.03138,1.03244,1.03359,1.03482,1.03614,1.03754,1.03903,1.04062,1.0423,1.04408,1.04596,1.04796,1.05006,1.05228,1.05462,1.05708,1.05967,1.06239,1.06525,1.06825,1.0714,1.0747,1.07816,1.08178,1.08557,1.08954,1.09369,1.09802,1.10254,1.10726,1.11219,1.11733,1.12268,1.12825,1.13404,1.14007,1.14634,1.15285,1.15961,1.16662,1.17388,1.18141,1.1892,1.19725,1.20558,1.21418,1.22305,1.2322,1.24163,1.25132,1.2613,1.27154,1.28206,1.29284,1.30388,1.31518,1.32673,1.33852,1.35055,1.3628,1.37526,1.38793,1.40079,1.41382,1.42702,1.44035,1.45382,1.4674,1.48107,1.4948,1.50859,1.5224,1.53622,1.55002,1.56377,1.57745,1.59104,1.6045,1.61782,1.63097,1.64391,1.65663,1.66909,1.68128,1.69316,1.70472,1.71592,1.72675,1.73719,1.74721,1.7568,1.76593,1.7746,1.78279,1.7905,1.7977,1.8044,1.81059,1.81626,1.82142,1.82608,1.83022,1.83387,1.83703,1.83971,1.84193,1.84369,1.84502,1.84594,1.84646,1.84661,1.8464,1.84586,1.84501,1.84388,1.84249,1.84086,1.83901,1.83697,1.83476,1.8324,1.8299,1.8273,1.82459,1.82181,1.81896,1.81606,1.81312,1.81015,1.80716,1.80414,1.80112,1.79809,1.79505,1.79201,1.78895,1.78589,1.78282,1.77973,1.77661,1.77346,1.77027,1.76703,1.76373,1.76036,1.7569,1.75334,1.74968,1.74588,1.74194,1.73784,1.73356,1.72907,1.72437,1.71943,1.71422,1.70873,1.70292,1.69677,1.69026,1.68335,1.67601,1.66822,1.65993,1.65111,1.64172,1.63172,1.62107,1.60973,1.59765,1.58477,1.57105,1.55643,1.54085,1.52426,1.50658,1.48775,1.4677,1.44636,1.42364,1.39948,1.37378,1.34646,1.31744,1.28663,1.25394,1.21929},
{1.02402,1.02418,1.02441,1.0247,1.02506,1.02548,1.02596,1.02651,1.02712,1.02781,1.02856,1.02939,1.03029,1.03127,1.03232,1.03345,1.03466,1.03596,1.03735,1.03883,1.0404,1.04206,1.04383,1.0457,1.04768,1.04977,1.05197,1.05429,1.05674,1.05931,1.06202,1.06486,1.06785,1.07099,1.07428,1.07772,1.08134,1.08512,1.08908,1.09321,1.09754,1.10206,1.10678,1.11171,1.11684,1.1222,1.12778,1.13358,1.13963,1.14591,1.15244,1.15922,1.16626,1.17356,1.18113,1.18897,1.19708,1.20546,1.21413,1.22308,1.23231,1.24182,1.25162,1.26171,1.27207,1.28272,1.29364,1.30484,1.31631,1.32804,1.34002,1.35225,1.36472,1.37742,1.39034,1.40346,1.41677,1.43026,1.44391,1.4577,1.47162,1.48564,1.49975,1.51393,1.52814,1.54238,1.55661,1.57081,1.58496,1.59903,1.61298,1.62681,1.64047,1.65394,1.6672,1.68022,1.69296,1.70541,1.71754,1.72933,1.74074,1.75177,1.76238,1.77256,1.78229,1.79155,1.80034,1.80863,1.81641,1.82369,1.83045,1.83668,1.8424,1.8476,1.85228,1.85645,1.86012,1.86329,1.86599,1.86823,1.87001,1.87137,1.87231,1.87286,1.87304,1.87288,1.87239,1.8716,1.87054,1.86922,1.86766,1.8659,1.86395,1.86184,1.85958,1.8572,1.8547,1.85212,1.84945,1.84672,1.84394,1.84112,1.83826,1.83538,1.83247,1.82955,1.82661,1.82366,1.82069,1.8177,1.8147,1.81167,1.80861,1.80551,1.80237,1.79917,1.79591,1.79257,1.78914,1.78561,1.78197,1.77819,1.77427,1.77018,1.76591,1.76145,1.75676,1.75183,1.74663,1.74115,1.73536,1.72923,1.72273,1.71585,1.70853,1.70076,1.69251,1.68373,1.67438,1.66443,1.65384,1.64257,1.63055,1.61776,1.60413,1.58961,1.57414,1.55767,1.54012,1.52143,1.50154,1.48036,1.45781,1.43383,1.40832,1.3812,1.35238,1.32176,1.28926,1.25479},
{1.02411,1.02426,1.02447,1.02475,1.02508,1.02549,1.02595,1.02649,1.02709,1.02776,1.02849,1.0293,1.03019,1.03115,1.03218,1.0333,1.0345,1.03578,1.03715,1.03861,1.04017,1.04182,1.04357,1.04542,1.04738,1.04945,1.05164,1.05395,1.05638,1.05893,1.06163,1.06445,1.06743,1.07055,1.07382,1.07726,1.08086,1.08463,1.08857,1.0927,1.09702,1.10153,1.10625,1.11117,1.1163,1.12166,1.12724,1.13305,1.1391,1.1454,1.15195,1.15875,1.16582,1.17315,1.18075,1.18863,1.19678,1.20523,1.21395,1.22297,1.23228,1.24188,1.25177,1.26196,1.27244,1.28321,1.29427,1.30562,1.31724,1.32914,1.34131,1.35374,1.36643,1.37935,1.39251,1.40589,1.41947,1.43325,1.4472,1.46132,1.47557,1.48995,1.50443,1.51899,1.53361,1.54826,1.56292,1.57758,1.59219,1.60673,1.62118,1.63551,1.6497,1.6637,1.6775,1.69107,1.70438,1.71741,1.73012,1.74249,1.7545,1.76612,1.77734,1.78812,1.79845,1.80832,1.81771,1.8266,1.83498,1.84285,1.85019,1.857,1.86329,1.86904,1.87427,1.87898,1.88317,1.88686,1.89006,1.89278,1.89503,1.89684,1.89822,1.89919,1.89977,1.9,1.89988,1.89944,1.89872,1.89772,1.89647,1.895,1.89332,1.89146,1.88945,1.88729,1.88501,1.88262,1.88014,1.87758,1.87496,1.87228,1.86956,1.8668,1.86401,1.86119,1.85834,1.85547,1.85258,1.84966,1.84671,1.84373,1.84071,1.83765,1.83453,1.83136,1.82811,1.82478,1.82135,1.81782,1.81416,1.81037,1.80643,1.80232,1.79803,1.79353,1.7888,1.78383,1.7786,1.77307,1.76723,1.76105,1.7545,1.74756,1.74019,1.73236,1.72404,1.7152,1.70579,1.69578,1.68513,1.67378,1.66171,1.64885,1.63516,1.62057,1.60504,1.5885,1.57089,1.55214,1.53217,1.51092,1.48831,1.46424,1.43864,1.41142,1.38248,1.35173,1.31907,1.28441},
{1.0242,1.02434,1.02453,1.02479,1.02511,1.02549,1.02594,1.02646,1.02704,1.02769,1.02842,1.02921,1.03008,1.03102,1.03204,1.03314,1.03432,1.03559,1.03694,1.03838,1.03992,1.04155,1.04329,1.04512,1.04707,1.04912,1.05129,1.05358,1.05599,1.05853,1.06121,1.06402,1.06697,1.07008,1.07334,1.07675,1.08034,1.08409,1.08803,1.09214,1.09645,1.10095,1.10566,1.11057,1.1157,1.12105,1.12663,1.13245,1.13851,1.14481,1.15137,1.15819,1.16528,1.17263,1.18027,1.18818,1.19638,1.20487,1.21365,1.22273,1.23211,1.2418,1.25178,1.26206,1.27265,1.28354,1.29473,1.30622,1.318,1.33007,1.34241,1.35504,1.36793,1.38108,1.39447,1.4081,1.42196,1.43602,1.45027,1.4647,1.47929,1.49402,1.50887,1.52381,1.53883,1.5539,1.569,1.58411,1.59918,1.61421,1.62916,1.644,1.65871,1.67326,1.68761,1.70174,1.71563,1.72924,1.74254,1.75551,1.76813,1.78037,1.7922,1.8036,1.81456,1.82505,1.83505,1.84456,1.85356,1.86204,1.86999,1.8774,1.88428,1.89062,1.89642,1.90169,1.90643,1.91065,1.91437,1.91759,1.92034,1.92262,1.92446,1.92588,1.9269,1.92753,1.92781,1.92775,1.92738,1.92673,1.92581,1.92465,1.92327,1.92169,1.91994,1.91803,1.91599,1.91382,1.91155,1.90919,1.90675,1.90424,1.90168,1.89907,1.89642,1.89373,1.891,1.88824,1.88545,1.88263,1.87977,1.87687,1.87393,1.87094,1.86788,1.86477,1.86157,1.85829,1.85492,1.85143,1.84782,1.84407,1.84017,1.8361,1.83184,1.82738,1.8227,1.81777,1.81257,1.80709,1.8013,1.79517,1.78868,1.78179,1.77449,1.76673,1.75849,1.74974,1.74043,1.73052,1.71998,1.70877,1.69683,1.68412,1.67059,1.65619,1.64085,1.62452,1.60713,1.58862,1.56892,1.54794,1.52561,1.50185,1.47656,1.44967,1.42106,1.39065,1.35833,1.324},
{1.02429,1.02441,1.02458,1.02482,1.02513,1.0255,1.02593,1.02643,1.02699,1.02763,1.02833,1.02911,1.02996,1.03089,1.03189,1.03297,1.03414,1.03538,1.03672,1.03815,1.03966,1.04128,1.04299,1.04481,1.04674,1.04877,1.05092,1.05319,1.05558,1.05811,1.06076,1.06355,1.06649,1.06958,1.07282,1.07622,1.07978,1.08352,1.08744,1.09154,1.09583,1.10032,1.10501,1.10992,1.11504,1.12039,1.12596,1.13178,1.13784,1.14414,1.15071,1.15754,1.16464,1.17202,1.17968,1.18762,1.19586,1.20439,1.21323,1.22236,1.23181,1.24156,1.25163,1.262,1.27269,1.28369,1.29501,1.30663,1.31855,1.33078,1.3433,1.35611,1.3692,1.38257,1.39619,1.41007,1.42418,1.43852,1.45307,1.46781,1.48273,1.4978,1.51301,1.52834,1.54376,1.55925,1.57478,1.59033,1.60587,1.62138,1.63683,1.65219,1.66742,1.68251,1.69742,1.71212,1.72659,1.74078,1.75469,1.76827,1.7815,1.79436,1.80682,1.81885,1.83044,1.84157,1.85221,1.86235,1.87198,1.88109,1.88966,1.89769,1.90517,1.91211,1.9185,1.92435,1.92965,1.93443,1.93869,1.94244,1.94569,1.94847,1.95079,1.95267,1.95413,1.95519,1.95588,1.95621,1.95622,1.95592,1.95535,1.95451,1.95344,1.95216,1.95068,1.94903,1.94723,1.9453,1.94324,1.94109,1.93884,1.93651,1.93411,1.93165,1.92914,1.92658,1.92398,1.92133,1.91865,1.91592,1.91314,1.91032,1.90745,1.90452,1.90153,1.89847,1.89532,1.89208,1.88875,1.88529,1.88171,1.87799,1.87412,1.87007,1.86584,1.8614,1.85673,1.85182,1.84665,1.84118,1.83541,1.8293,1.82284,1.81598,1.80871,1.80099,1.79279,1.78407,1.77481,1.76496,1.75449,1.74335,1.73149,1.71887,1.70544,1.69114,1.67592,1.65972,1.64247,1.6241,1.60456,1.58375,1.56159,1.53802,1.51292,1.48622,1.4578,1.42758,1.39543,1.36126},
{1.02438,1.02448,1.02464,1.02486,1.02514,1.02549,1.02591,1.02639,1.02694,1.02756,1.02824,1.029,1.02984,1.03074,1.03173,1.03279,1.03394,1.03517,1.03649,1.03789,1.03939,1.04099,1.04268,1.04448,1.04639,1.0484,1.05053,1.05278,1.05515,1.05765,1.06029,1.06306,1.06598,1.06904,1.07226,1.07564,1.07919,1.08291,1.08681,1.09089,1.09516,1.09964,1.10432,1.10921,1.11432,1.11965,1.12522,1.13103,1.13708,1.14339,1.14996,1.1568,1.16391,1.1713,1.17898,1.18695,1.19522,1.20379,1.21266,1.22185,1.23135,1.24117,1.25131,1.26178,1.27256,1.28367,1.2951,1.30684,1.31891,1.33129,1.34397,1.35696,1.37025,1.38382,1.39767,1.41179,1.42616,1.44077,1.45561,1.47065,1.4859,1.50131,1.51688,1.53259,1.5484,1.5643,1.58027,1.59627,1.61228,1.62827,1.64422,1.66009,1.67586,1.6915,1.70697,1.72224,1.7373,1.75209,1.76661,1.78081,1.79467,1.80816,1.82126,1.83394,1.84618,1.85796,1.86925,1.88005,1.89032,1.90008,1.90929,1.91795,1.92607,1.93362,1.94062,1.94707,1.95297,1.95832,1.96314,1.96744,1.97123,1.97452,1.97734,1.97971,1.98163,1.98315,1.98427,1.98502,1.98543,1.98551,1.9853,1.98481,1.98407,1.9831,1.98192,1.98056,1.97902,1.97734,1.97552,1.97359,1.97155,1.96942,1.96721,1.96492,1.96257,1.96017,1.95771,1.95519,1.95263,1.95002,1.94735,1.94464,1.94186,1.93902,1.93612,1.93313,1.93006,1.9269,1.92363,1.92025,1.91674,1.91308,1.90927,1.90529,1.90112,1.89674,1.89215,1.88731,1.88221,1.87682,1.87113,1.86511,1.85874,1.85199,1.84482,1.83722,1.82915,1.82058,1.81147,1.80178,1.79148,1.78053,1.76888,1.75649,1.7433,1.72926,1.71432,1.69842,1.68149,1.66347,1.64428,1.62386,1.60212,1.57897,1.55432,1.52808,1.50015,1.47041,1.43877,1.4051},
{1.02447,1.02455,1.02469,1.02489,1.02516,1.02549,1.02589,1.02635,1.02688,1.02748,1.02815,1.02889,1.02971,1.03059,1.03156,1.03261,1.03373,1.03494,1.03624,1.03763,1.03911,1.04068,1.04236,1.04414,1.04602,1.04801,1.05012,1.05235,1.0547,1.05718,1.05979,1.06254,1.06544,1.06848,1.07168,1.07503,1.07856,1.08226,1.08613,1.09019,1.09445,1.0989,1.10356,1.10844,1.11353,1.11885,1.12441,1.13021,1.13625,1.14256,1.14913,1.15597,1.16308,1.17048,1.17818,1.18616,1.19446,1.20306,1.21197,1.2212,1.23075,1.24063,1.25084,1.26138,1.27225,1.28345,1.29499,1.30685,1.31905,1.33157,1.34442,1.35758,1.37105,1.38482,1.39888,1.41323,1.42785,1.44273,1.45785,1.4732,1.48876,1.50451,1.52043,1.53651,1.55271,1.56903,1.58542,1.60187,1.61834,1.63482,1.65126,1.66765,1.68396,1.70014,1.71618,1.73203,1.74767,1.76308,1.77821,1.79303,1.80753,1.82167,1.83542,1.84875,1.86165,1.87409,1.88605,1.89751,1.90846,1.91887,1.92874,1.93806,1.94682,1.95501,1.96264,1.96971,1.97621,1.98216,1.98756,1.99243,1.99677,2.0006,2.00394,2.00681,2.00923,2.01121,2.01279,2.01397,2.01479,2.01528,2.01544,2.01532,2.01492,2.01428,2.01342,2.01235,2.01109,2.00967,2.0081,2.0064,2.00459,2.00266,2.00064,1.99854,1.99637,1.99412,1.99181,1.98943,1.987,1.98451,1.98196,1.97935,1.97667,1.97393,1.97111,1.96821,1.96522,1.96213,1.95893,1.95561,1.95216,1.94857,1.94482,1.9409,1.93679,1.93248,1.92795,1.92317,1.91814,1.91283,1.90721,1.90128,1.89499,1.88832,1.88126,1.87377,1.86581,1.85736,1.84839,1.83885,1.82872,1.81794,1.80648,1.79428,1.78131,1.76751,1.75282,1.73719,1.72056,1.70285,1.68399,1.66391,1.64254,1.61977,1.59552,1.5697,1.54219,1.51288,1.48167,1.44842},
{1.02456,1.02461,1.02473,1.02492,1.02517,1.02548,1.02586,1.0263,1.02682,1.0274,1.02805,1.02877,1.02957,1.03044,1.03138,1.03241,1.03352,1.03471,1.03599,1.03735,1.03881,1.04037,1.04202,1.04377,1.04564,1.04761,1.04969,1.0519,1.05422,1.05668,1.05927,1.06199,1.06486,1.06788,1.07105,1.07439,1.07789,1.08156,1.08541,1.08945,1.09368,1.09811,1.10275,1.10761,1.11268,1.11798,1.12352,1.12931,1.13534,1.14164,1.1482,1.15504,1.16215,1.16956,1.17726,1.18526,1.19357,1.20219,1.21113,1.2204,1.23,1.23993,1.2502,1.2608,1.27175,1.28304,1.29468,1.30666,1.31898,1.33163,1.34463,1.35795,1.3716,1.38556,1.39984,1.41441,1.42927,1.4444,1.4598,1.47544,1.49131,1.50739,1.52367,1.54011,1.5567,1.57342,1.59024,1.60713,1.62407,1.64103,1.65798,1.67489,1.69172,1.70846,1.72506,1.7415,1.75774,1.77376,1.78951,1.80498,1.82012,1.83491,1.84932,1.86333,1.87691,1.89003,1.90267,1.91481,1.92644,1.93753,1.94808,1.95807,1.9675,1.97636,1.98464,1.99234,1.99948,2.00605,2.01205,2.01751,2.02243,2.02683,2.03071,2.03411,2.03704,2.03951,2.04156,2.04321,2.04447,2.04538,2.04595,2.04621,2.04618,2.04589,2.04536,2.04461,2.04366,2.04252,2.04123,2.03978,2.03821,2.03651,2.03471,2.03281,2.03083,2.02876,2.02662,2.02441,2.02213,2.01979,2.01737,2.01489,2.01234,2.00972,2.00701,2.00422,2.00134,1.99835,1.99525,1.99204,1.98869,1.9852,1.98155,1.97773,1.97373,1.96952,1.9651,1.96045,1.95554,1.95035,1.94487,1.93908,1.93295,1.92645,1.91956,1.91225,1.9045,1.89627,1.88753,1.87825,1.86838,1.85789,1.84674,1.83488,1.82227,1.80885,1.79457,1.77938,1.76321,1.74599,1.72767,1.70815,1.68736,1.66521,1.64162,1.61647,1.58967,1.5611,1.53064,1.49815},
{1.02464,1.02468,1.02478,1.02494,1.02517,1.02547,1.02583,1.02625,1.02675,1.02731,1.02794,1.02864,1.02942,1.03027,1.0312,1.0322,1.03329,1.03446,1.03572,1.03706,1.0385,1.04003,1.04166,1.0434,1.04523,1.04718,1.04924,1.05142,1.05373,1.05616,1.05872,1.06142,1.06426,1.06725,1.0704,1.07371,1.07718,1.08082,1.08465,1.08866,1.09287,1.09727,1.10189,1.10672,1.11177,1.11705,1.12257,1.12833,1.13435,1.14063,1.14718,1.15401,1.16112,1.16852,1.17622,1.18423,1.19255,1.20119,1.21016,1.21945,1.22909,1.23906,1.24938,1.26005,1.27107,1.28244,1.29416,1.30624,1.31868,1.33146,1.34459,1.35807,1.37188,1.38603,1.4005,1.41529,1.43038,1.44576,1.46143,1.47735,1.49353,1.50993,1.52655,1.54335,1.56033,1.57745,1.59469,1.61202,1.62942,1.64685,1.6643,1.68172,1.6991,1.71639,1.73356,1.75058,1.76743,1.78406,1.80044,1.81655,1.83234,1.8478,1.86289,1.87757,1.89184,1.90565,1.91899,1.93183,1.94415,1.95594,1.96718,1.97787,1.98798,1.99751,2.00647,2.01483,2.02262,2.02983,2.03646,2.04253,2.04805,2.05303,2.05748,2.06143,2.06489,2.06788,2.07043,2.07255,2.07427,2.07562,2.07662,2.07728,2.07764,2.07772,2.07754,2.07712,2.07649,2.07566,2.07465,2.07347,2.07215,2.0707,2.06913,2.06745,2.06567,2.0638,2.06184,2.0598,2.05768,2.05549,2.05323,2.05089,2.04847,2.04597,2.04339,2.04071,2.03794,2.03507,2.03208,2.02897,2.02573,2.02235,2.01881,2.0151,2.01121,2.00712,2.00281,1.99828,1.9935,1.98845,1.98311,1.97747,1.9715,1.96517,1.95847,1.95136,1.94382,1.93581,1.92731,1.91829,1.9087,1.89851,1.88768,1.87616,1.86391,1.85089,1.83703,1.82229,1.80659,1.78988,1.77209,1.75314,1.73295,1.71143,1.68849,1.66403,1.63794,1.61011,1.5804,1.54868},
{1.02472,1.02474,1.02482,1.02497,1.02518,1.02545,1.02579,1.0262,1.02667,1.02721,1.02783,1.02851,1.02927,1.0301,1.031,1.03199,1.03305,1.0342,1.03544,1.03676,1.03818,1.03968,1.04129,1.043,1.04481,1.04674,1.04877,1.05093,1.0532,1.05561,1.05814,1.06081,1.06363,1.06659,1.06971,1.07298,1.07643,1.08004,1.08384,1.08782,1.092,1.09638,1.10096,1.10576,1.11079,1.11604,1.12154,1.12728,1.13328,1.13954,1.14607,1.15288,1.15998,1.16737,1.17507,1.18308,1.1914,1.20005,1.20903,1.21835,1.22801,1.23802,1.24839,1.25911,1.27019,1.28163,1.29344,1.30561,1.31815,1.33105,1.34431,1.35793,1.3719,1.38622,1.40088,1.41588,1.43119,1.44682,1.46274,1.47894,1.49541,1.51213,1.52908,1.54624,1.56359,1.58111,1.59876,1.61653,1.63439,1.6523,1.67025,1.68819,1.7061,1.72394,1.74169,1.7593,1.77675,1.794,1.81103,1.82778,1.84424,1.86037,1.87615,1.89153,1.90649,1.92101,1.93506,1.94861,1.96166,1.97416,1.98612,1.99752,2.00834,2.01857,2.02822,2.03727,2.04574,2.05361,2.06089,2.0676,2.07375,2.07933,2.08438,2.08891,2.09293,2.09646,2.09953,2.10216,2.10437,2.10619,2.10764,2.10873,2.10951,2.10999,2.11018,2.11013,2.10984,2.10933,2.10864,2.10776,2.10672,2.10554,2.10423,2.10279,2.10124,2.09959,2.09784,2.096,2.09408,2.09208,2.08999,2.08782,2.08557,2.08323,2.08081,2.07829,2.07567,2.07295,2.07011,2.06716,2.06407,2.06084,2.05746,2.05391,2.05019,2.04628,2.04215,2.03781,2.03323,2.02839,2.02328,2.01788,2.01215,2.0061,1.99968,1.99287,1.98565,1.97799,1.96986,1.96123,1.95206,1.94232,1.93197,1.92097,1.90927,1.89683,1.8836,1.86952,1.85453,1.83858,1.82158,1.80348,1.78418,1.76361,1.74167,1.71826,1.69327,1.66658,1.63807,1.60759},
{1.0248,1.0248,1.02486,1.02499,1.02518,1.02543,1.02575,1.02614,1.02659,1.02711,1.02771,1.02837,1.0291,1.02991,1.0308,1.03176,1.03281,1.03393,1.03515,1.03645,1.03784,1.03932,1.0409,1.04259,1.04438,1.04627,1.04828,1.05041,1.05266,1.05503,1.05754,1.06018,1.06296,1.0659,1.06898,1.07223,1.07564,1.07922,1.08299,1.08694,1.09108,1.09542,1.09998,1.10475,1.10974,1.11496,1.12043,1.12614,1.13211,1.13835,1.14486,1.15165,1.15873,1.16611,1.1738,1.1818,1.19012,1.19877,1.20776,1.21709,1.22677,1.23681,1.24721,1.25797,1.2691,1.28061,1.29249,1.30474,1.31737,1.33038,1.34376,1.35752,1.37164,1.38612,1.40096,1.41615,1.43168,1.44753,1.4637,1.48017,1.49693,1.51396,1.53124,1.54875,1.56646,1.58437,1.60243,1.62063,1.63894,1.65733,1.67577,1.69423,1.71267,1.73107,1.74939,1.7676,1.78566,1.80354,1.8212,1.83861,1.85575,1.87256,1.88903,1.90512,1.92079,1.93603,1.95081,1.9651,1.97887,1.99211,2.00481,2.01693,2.02848,2.03944,2.0498,2.05957,2.06873,2.07729,2.08525,2.09263,2.09942,2.10564,2.11131,2.11644,2.12105,2.12515,2.12877,2.13193,2.13466,2.13697,2.13889,2.14045,2.14166,2.14256,2.14316,2.14349,2.14357,2.14342,2.14306,2.1425,2.14177,2.14088,2.13985,2.13868,2.13738,2.13598,2.13447,2.13285,2.13115,2.12935,2.12747,2.1255,2.12344,2.12129,2.11905,2.11671,2.11428,2.11174,2.10909,2.10632,2.10342,2.10038,2.09719,2.09385,2.09033,2.08664,2.08274,2.07864,2.07431,2.06973,2.0649,2.05979,2.05438,2.04865,2.04258,2.03615,2.02933,2.0221,2.01442,2.00627,1.99762,1.98843,1.97867,1.9683,1.95727,1.94554,1.93306,1.91979,1.90566,1.89062,1.8746,1.85752,1.83932,1.8199,1.79918,1.77705,1.75342,1.72815,1.70112,1.67218},
{1.02488,1.02485,1.0249,1.025,1.02517,1.02541,1.02571,1.02607,1.02651,1.02701,1.02758,1.02822,1.02894,1.02972,1.03059,1.03153,1.03255,1.03365,1.03484,1.03612,1.03748,1.03894,1.0405,1.04216,1.04392,1.04579,1.04777,1.04987,1.05209,1.05443,1.0569,1.05952,1.06227,1.06517,1.06822,1.07143,1.07481,1.07836,1.08209,1.086,1.09011,1.09442,1.09893,1.10367,1.10862,1.11381,1.11925,1.12493,1.13087,1.13707,1.14355,1.15032,1.15737,1.16473,1.1724,1.18039,1.1887,1.19735,1.20633,1.21567,1.22536,1.23542,1.24584,1.25664,1.26781,1.27937,1.29131,1.30364,1.31635,1.32945,1.34294,1.35682,1.37108,1.38572,1.40072,1.4161,1.43182,1.4479,1.46431,1.48103,1.49807,1.51539,1.53299,1.55084,1.56891,1.5872,1.60566,1.62429,1.64305,1.6619,1.68083,1.6998,1.71877,1.73773,1.75662,1.77542,1.79409,1.8126,1.83091,1.84899,1.8668,1.88431,1.90148,1.91828,1.93468,1.95066,1.96617,1.9812,1.99573,2.00972,2.02317,2.03605,2.04834,2.06005,2.07115,2.08165,2.09153,2.10081,2.10947,2.11754,2.125,2.13189,2.1382,2.14396,2.14918,2.15388,2.15808,2.1618,2.16507,2.1679,2.17032,2.17237,2.17405,2.17539,2.17642,2.17716,2.17763,2.17786,2.17786,2.17765,2.17725,2.17668,2.17595,2.17507,2.17405,2.17292,2.17166,2.1703,2.16884,2.16728,2.16562,2.16387,2.16203,2.1601,2.15807,2.15594,2.15372,2.15139,2.14895,2.1464,2.14372,2.1409,2.13795,2.13485,2.13158,2.12814,2.12452,2.12069,2.11666,2.1124,2.10789,2.10313,2.09809,2.09275,2.0871,2.08111,2.07476,2.06802,2.06088,2.0533,2.04525,2.0367,2.02763,2.01798,2.00773,1.99683,1.98524,1.9729,1.95977,1.94579,1.93089,1.91501,1.89807,1.88,1.8607,1.84007,1.81802,1.79442,1.76914,1.74204},
{1.02495,1.02491,1.02493,1.02501,1.02516,1.02538,1.02566,1.026,1.02642,1.0269,1.02745,1.02807,1.02876,1.02952,1.03037,1.03128,1.03228,1.03336,1.03453,1.03578,1.03712,1.03855,1.04008,1.04171,1.04344,1.04528,1.04724,1.0493,1.05149,1.0538,1.05624,1.05882,1.06154,1.0644,1.06742,1.07059,1.07393,1.07745,1.08114,1.08501,1.08908,1.09335,1.09783,1.10252,1.10744,1.11259,1.11798,1.12363,1.12953,1.1357,1.14214,1.14888,1.1559,1.16323,1.17088,1.17884,1.18714,1.19577,1.20475,1.21408,1.22378,1.23384,1.24428,1.2551,1.2663,1.2779,1.28989,1.30228,1.31507,1.32826,1.34185,1.35583,1.37022,1.38499,1.40016,1.4157,1.43162,1.4479,1.46454,1.48151,1.49881,1.51643,1.53433,1.5525,1.57093,1.58959,1.60845,1.6275,1.64669,1.66601,1.68543,1.70491,1.72441,1.74392,1.76339,1.78278,1.80207,1.82121,1.84017,1.85892,1.87742,1.89562,1.91351,1.93104,1.94818,1.96491,1.98118,1.99698,2.01227,2.02704,2.04125,2.05491,2.06798,2.08045,2.09232,2.10357,2.11421,2.12422,2.13362,2.1424,2.15058,2.15816,2.16515,2.17157,2.17743,2.18276,2.18757,2.19188,2.19572,2.19911,2.20207,2.20463,2.2068,2.20863,2.21012,2.21131,2.21221,2.21285,2.21324,2.21341,2.21338,2.21316,2.21276,2.21221,2.21151,2.21068,2.20972,2.20865,2.20746,2.20618,2.20479,2.20331,2.20173,2.20006,2.19829,2.19643,2.19446,2.1924,2.19023,2.18795,2.18555,2.18303,2.18038,2.17758,2.17464,2.17154,2.16827,2.16481,2.16117,2.15732,2.15324,2.14894,2.14438,2.13955,2.13444,2.12903,2.12329,2.11721,2.11076,2.10391,2.09665,2.08894,2.08075,2.07205,2.0628,2.05297,2.04252,2.0314,2.01956,2.00695,1.99351,1.97918,1.96389,1.94757,1.93014,1.91149,1.89153,1.87015,1.84722,1.82261},
{1.02503,1.02496,1.02496,1.02502,1.02515,1.02535,1.0256,1.02593,1.02632,1.02678,1.02731,1.0279,1.02857,1.02932,1.03014,1.03103,1.032,1.03306,1.0342,1.03542,1.03674,1.03814,1.03965,1.04125,1.04295,1.04476,1.04668,1.04872,1.05087,1.05315,1.05556,1.0581,1.06078,1.06361,1.06658,1.06972,1.07302,1.07649,1.08014,1.08397,1.088,1.09223,1.09666,1.10131,1.10618,1.11129,1.11664,1.12224,1.1281,1.13423,1.14063,1.14733,1.15432,1.16161,1.16922,1.17716,1.18543,1.19404,1.203,1.21232,1.22201,1.23207,1.24252,1.25335,1.26458,1.2762,1.28823,1.30067,1.31352,1.32678,1.34045,1.35454,1.36903,1.38394,1.39925,1.41495,1.43105,1.44752,1.46437,1.48158,1.49914,1.51702,1.53522,1.55371,1.57248,1.5915,1.61075,1.63021,1.64983,1.66961,1.68951,1.70949,1.72952,1.74957,1.76961,1.7896,1.8095,1.82928,1.8489,1.86832,1.88751,1.90642,1.92503,1.9433,1.96119,1.97867,1.99572,2.01229,2.02837,2.04393,2.05894,2.07339,2.08725,2.10052,2.11317,2.12521,2.13662,2.14741,2.15756,2.16709,2.176,2.1843,2.192,2.19911,2.20565,2.21164,2.21709,2.22203,2.22647,2.23044,2.23397,2.23708,2.23979,2.24213,2.24411,2.24578,2.24714,2.24822,2.24904,2.24962,2.24999,2.25015,2.25012,2.24993,2.24958,2.24909,2.24846,2.24771,2.24684,2.24586,2.24478,2.2436,2.24232,2.24095,2.23948,2.23792,2.23626,2.23451,2.23266,2.2307,2.22863,2.22645,2.22415,2.22173,2.21916,2.21646,2.21361,2.21059,2.20741,2.20404,2.20048,2.19671,2.19272,2.1885,2.18403,2.1793,2.17428,2.16896,2.16332,2.15733,2.15099,2.14425,2.13709,2.12949,2.12142,2.11284,2.10371,2.094,2.08366,2.07264,2.0609,2.04838,2.03502,2.02075,2.00548,1.98915,1.97165,1.95289,1.93274,1.91108},
{1.0251,1.02501,1.02499,1.02503,1.02514,1.02531,1.02555,1.02585,1.02622,1.02666,1.02716,1.02774,1.02838,1.0291,1.0299,1.03077,1.03172,1.03275,1.03386,1.03506,1.03635,1.03772,1.0392,1.04077,1.04244,1.04422,1.04611,1.04811,1.05023,1.05247,1.05484,1.05735,1.05999,1.06278,1.06571,1.06881,1.07207,1.07549,1.0791,1.08289,1.08687,1.09105,1.09543,1.10003,1.10486,1.10992,1.11522,1.12077,1.12658,1.13266,1.13902,1.14567,1.15262,1.15987,1.16744,1.17534,1.18357,1.19215,1.20109,1.21039,1.22006,1.23011,1.24055,1.25138,1.26262,1.27426,1.28632,1.2988,1.31169,1.32501,1.33876,1.35293,1.36752,1.38254,1.39797,1.41382,1.43008,1.44674,1.46379,1.48122,1.49901,1.51716,1.53564,1.55444,1.57353,1.5929,1.61253,1.63238,1.65243,1.67266,1.69302,1.7135,1.73405,1.75465,1.77525,1.79583,1.81635,1.83676,1.85704,1.87713,1.89702,1.91665,1.93599,1.955,1.97365,1.99191,2.00974,2.02711,2.04399,2.06035,2.07618,2.09144,2.10612,2.1202,2.13367,2.14652,2.15873,2.17031,2.18126,2.19157,2.20124,2.2103,2.21874,2.22657,2.23382,2.2405,2.24663,2.25222,2.25731,2.2619,2.26604,2.26973,2.273,2.27589,2.27841,2.28058,2.28244,2.284,2.28529,2.28632,2.28712,2.2877,2.28809,2.28829,2.28833,2.28821,2.28796,2.28757,2.28706,2.28643,2.2857,2.28487,2.28393,2.28291,2.28179,2.28058,2.27929,2.2779,2.27642,2.27484,2.27317,2.27139,2.26951,2.26752,2.26542,2.26319,2.26084,2.25834,2.25571,2.25291,2.24996,2.24684,2.24353,2.24002,2.23631,2.23238,2.22821,2.22379,2.21911,2.21414,2.20887,2.20328,2.19734,2.19103,2.18433,2.17721,2.16964,2.16158,2.153,2.14385,2.1341,2.1237,2.1126,2.10072,2.08802,2.07441,2.05982,2.04415,2.02731,2.00917},
{1.02517,1.02506,1.02502,1.02504,1.02512,1.02527,1.02548,1.02577,1.02611,1.02653,1.02701,1.02756,1.02818,1.02888,1.02965,1.0305,1.03142,1.03242,1.03351,1.03468,1.03594,1.03729,1.03873,1.04027,1.04191,1.04365,1.04551,1.04747,1.04956,1.05176,1.0541,1.05656,1.05916,1.06191,1.0648,1.06785,1.07107,1.07445,1.078,1.08174,1.08567,1.0898,1.09414,1.09869,1.10346,1.10847,1.11371,1.11921,1.12497,1.131,1.1373,1.1439,1.15079,1.158,1.16552,1.17337,1.18156,1.1901,1.199,1.20827,1.21791,1.22794,1.23836,1.24919,1.26042,1.27207,1.28414,1.29664,1.30957,1.32294,1.33674,1.35098,1.36566,1.38078,1.39633,1.41231,1.42872,1.44554,1.46278,1.48041,1.49843,1.51682,1.53557,1.55467,1.57408,1.59379,1.61378,1.63402,1.65449,1.67515,1.69598,1.71695,1.73802,1.75916,1.78033,1.8015,1.82263,1.84368,1.86461,1.88539,1.90598,1.92633,1.94641,1.96619,1.98561,2.00466,2.02329,2.04147,2.05917,2.07637,2.09303,2.10913,2.12466,2.13959,2.1539,2.16759,2.18064,2.19305,2.20482,2.21594,2.22642,2.23627,2.24549,2.25409,2.26209,2.26951,2.27635,2.28265,2.28841,2.29368,2.29846,2.30278,2.30667,2.31015,2.31324,2.31598,2.31838,2.32047,2.32227,2.3238,2.32508,2.32614,2.32699,2.32764,2.32812,2.32844,2.32861,2.32864,2.32855,2.32834,2.32802,2.3276,2.32709,2.32648,2.32579,2.32501,2.32416,2.32322,2.3222,2.3211,2.31991,2.31865,2.31729,2.31585,2.31432,2.31269,2.31096,2.30912,2.30718,2.30511,2.30292,2.30061,2.29815,2.29554,2.29278,2.28986,2.28675,2.28346,2.27998,2.27628,2.27235,2.26819,2.26376,2.25906,2.25407,2.24877,2.24312,2.23712,2.23072,2.2239,2.21663,2.20887,2.20058,2.19171,2.18221,2.17203,2.1611,2.14935,2.1367,2.12306},
{1.02524,1.02511,1.02504,1.02504,1.0251,1.02523,1.02542,1.02568,1.026,1.02639,1.02685,1.02738,1.02798,1.02865,1.0294,1.03021,1.03111,1.03209,1.03315,1.03429,1.03552,1.03684,1.03825,1.03976,1.04136,1.04307,1.04489,1.04682,1.04887,1.05104,1.05333,1.05575,1.05831,1.06101,1.06386,1.06686,1.07003,1.07336,1.07687,1.08055,1.08443,1.0885,1.09278,1.09728,1.10199,1.10694,1.11213,1.11757,1.12326,1.12923,1.13548,1.14201,1.14885,1.156,1.16346,1.17126,1.1794,1.18789,1.19674,1.20597,1.21557,1.22557,1.23596,1.24676,1.25798,1.26962,1.2817,1.29421,1.30716,1.32055,1.3344,1.34869,1.36344,1.37864,1.39429,1.41038,1.42692,1.4439,1.4613,1.47912,1.49735,1.51598,1.53498,1.55435,1.57406,1.5941,1.61443,1.63505,1.65592,1.67701,1.69829,1.71974,1.74131,1.76298,1.78471,1.80647,1.82821,1.8499,1.87149,1.89295,1.91424,1.93532,1.95615,1.97669,1.9969,2.01675,2.03619,2.05521,2.07375,2.09179,2.10931,2.12628,2.14268,2.15847,2.17366,2.18822,2.20214,2.21542,2.22805,2.24002,2.25134,2.26202,2.27206,2.28147,2.29026,2.29845,2.30606,2.3131,2.3196,2.32557,2.33105,2.33605,2.34059,2.34472,2.34844,2.35178,2.35478,2.35745,2.35981,2.36189,2.36371,2.36529,2.36666,2.36782,2.3688,2.36961,2.37026,2.37078,2.37116,2.37143,2.37159,2.37166,2.37163,2.37151,2.37132,2.37105,2.37071,2.3703,2.36982,2.36928,2.36868,2.36802,2.36729,2.3665,2.36565,2.36473,2.36374,2.36269,2.36156,2.36036,2.35908,2.35771,2.35626,2.35471,2.35307,2.35133,2.34948,2.34751,2.34542,2.3432,2.34085,2.33834,2.33568,2.33286,2.32985,2.32664,2.32324,2.3196,2.31573,2.3116,2.30718,2.30246,2.29741,2.292,2.28619,2.27995,2.27324,2.266,2.25819,2.24974}
};
//LS X coefficient for A=atomic weight * 1.05
double ls_X_coefficients_ahi[][200]=
{
{0.999129,0.999075,0.999018,0.998958,0.998894,0.998827,0.998757,0.998682,0.998604,0.998521,0.998434,0.998341,0.998244,0.998142,0.998034,0.997921,0.997801,0.997675,0.997542,0.997401,0.997254,0.997098,0.996934,0.996761,0.996578,0.996386,0.996184,0.995971,0.995746,0.99551,0.99526,0.994998,0.994721,0.99443,0.994124,0.993801,0.993461,0.993103,0.992726,0.992329,0.991911,0.991471,0.991008,0.990521,0.990009,0.98947,0.988902,0.988305,0.987677,0.987017,0.986322,0.985592,0.984824,0.984017,0.983169,0.982277,0.98134,0.980356,0.979322,0.978236,0.977096,0.975898,0.974642,0.973323,0.971939,0.970488,0.968966,0.96737,0.965698,0.963945,0.962109,0.960186,0.958174,0.956067,0.953863,0.951559,0.949149,0.946632,0.944002,0.941257,0.938392,0.935404,0.932288,0.929042,0.925662,0.922143,0.918484,0.914679,0.910727,0.906625,0.902369,0.897957,0.893388,0.888659,0.883768,0.878716,0.873501,0.868122,0.862581,0.856879,0.851016,0.844995,0.838818,0.83249,0.826013,0.819394,0.812637,0.805749,0.798736,0.791608,0.784371,0.777036,0.769613,0.762112,0.754545,0.746923,0.739259,0.731566,0.723857,0.716146,0.708447,0.700773,0.693139,0.685559,0.678046,0.670614,0.663276,0.656045,0.648933,0.641951,0.635111,0.628422,0.621893,0.615533,0.609348,0.603345,0.597528,0.591902,0.586469,0.581232,0.57619,0.571344,0.566692,0.562231,0.557959,0.553871,0.549962,0.546226,0.542656,0.539244,0.535984,0.532865,0.529878,0.527014,0.524263,0.521612,0.519052,0.516569,0.514151,0.511786,0.509459,0.507158,0.504867,0.50257,0.500253,0.497897,0.495486,0.493001,0.490422,0.487728,0.484898,0.481908,0.478732,0.475345,0.471718,0.467821,0.463622,0.459087,0.45418,0.448863,0.443096,0.436836,0.430039,0.422662,0.41466,0.405986,0.396596,0.386449,0.375509,0.363744,0.351135,0.337677,0.323383,0.308294,0.292485,0.276076,0.259248,0.242255,0.225451,0.209311},
{0.999535,0.999484,0.999431,0.999375,0.999315,0.999253,0.999186,0.999116,0.999042,0.998964,0.998882,0.998795,0.998703,0.998606,0.998503,0.998395,0.998281,0.998161,0.998034,0.997899,0.997758,0.997609,0.997451,0.997285,0.99711,0.996925,0.99673,0.996525,0.996308,0.99608,0.995839,0.995585,0.995318,0.995035,0.994738,0.994425,0.994095,0.993747,0.99338,0.992994,0.992587,0.992159,0.991707,0.991232,0.990732,0.990205,0.98965,0.989066,0.988452,0.987805,0.987125,0.986409,0.985656,0.984864,0.984032,0.983156,0.982235,0.981268,0.980251,0.979183,0.97806,0.976882,0.975644,0.974344,0.972981,0.971549,0.970048,0.968473,0.966822,0.965092,0.963278,0.961379,0.95939,0.957307,0.955128,0.952848,0.950464,0.947973,0.94537,0.942651,0.939814,0.936853,0.933766,0.930549,0.927198,0.923709,0.92008,0.916306,0.912385,0.908314,0.90409,0.899711,0.895174,0.890478,0.885621,0.880603,0.875421,0.870077,0.864571,0.858902,0.853074,0.847088,0.840946,0.834653,0.828211,0.821626,0.814904,0.80805,0.801072,0.793977,0.786775,0.779473,0.772082,0.764614,0.757078,0.749487,0.741853,0.734189,0.726509,0.718825,0.711152,0.703503,0.695893,0.688335,0.680843,0.67343,0.66611,0.658895,0.651798,0.644828,0.637998,0.631317,0.624794,0.618437,0.612253,0.606247,0.600425,0.594791,0.589346,0.584094,0.579033,0.574163,0.569484,0.564991,0.560681,0.55655,0.552592,0.548801,0.545169,0.541688,0.53835,0.535145,0.532062,0.529092,0.526223,0.523443,0.520739,0.518097,0.515505,0.512948,0.510411,0.507877,0.50533,0.502753,0.500128,0.497434,0.494651,0.491759,0.488733,0.485551,0.482184,0.478608,0.474791,0.470703,0.466312,0.461581,0.456475,0.450954,0.444977,0.438502,0.431484,0.423878,0.415638,0.406719,0.397077,0.38667,0.375462,0.363425,0.350541,0.336808,0.322243,0.306894,0.290844,0.274221,0.25722,0.240113,0.223273,0.207206,0.192579,0.180267},
{1.00011,1.00007,1.00002,0.999967,0.999913,0.999856,0.999795,0.999731,0.999663,0.99959,0.999514,0.999432,0.999347,0.999256,0.999159,0.999058,0.99895,0.998836,0.998716,0.998589,0.998454,0.998312,0.998162,0.998003,0.997836,0.997659,0.997472,0.997275,0.997067,0.996848,0.996616,0.996371,0.996113,0.99584,0.995553,0.99525,0.99493,0.994593,0.994238,0.993863,0.993468,0.993051,0.992612,0.99215,0.991662,0.991149,0.990608,0.990038,0.989438,0.988806,0.988141,0.987441,0.986704,0.985928,0.985112,0.984254,0.983351,0.982401,0.981403,0.980354,0.979251,0.978092,0.976875,0.975596,0.974253,0.972844,0.971365,0.969814,0.968186,0.966479,0.96469,0.962816,0.960852,0.958796,0.956643,0.954391,0.952035,0.949571,0.946997,0.944308,0.941501,0.938571,0.935515,0.932329,0.929011,0.925555,0.921959,0.918219,0.914332,0.910296,0.906108,0.901764,0.897264,0.892604,0.887785,0.882804,0.87766,0.872355,0.866887,0.861258,0.855469,0.849522,0.84342,0.837167,0.830766,0.824221,0.817539,0.810726,0.803788,0.796734,0.789571,0.78231,0.774959,0.767531,0.760034,0.752483,0.744888,0.737263,0.72962,0.721974,0.714338,0.706726,0.699152,0.69163,0.684173,0.676795,0.669508,0.662326,0.65526,0.648323,0.641523,0.634873,0.628379,0.62205,0.615894,0.609916,0.604121,0.598512,0.593093,0.587866,0.582829,0.577984,0.573328,0.568859,0.564573,0.560465,0.55653,0.552762,0.549154,0.545697,0.542383,0.539202,0.536146,0.533202,0.53036,0.527609,0.524935,0.522326,0.519768,0.517247,0.514748,0.512256,0.509754,0.507225,0.504652,0.502014,0.499293,0.496467,0.493513,0.490408,0.487127,0.483642,0.479926,0.475947,0.471674,0.467071,0.462104,0.456732,0.450917,0.444615,0.437782,0.430374,0.422343,0.413645,0.404232,0.394064,0.383099,0.371307,0.358663,0.345158,0.330801,0.315625,0.299696,0.283123,0.266073,0.248783,0.231583,0.214922,0.199405,0.185812},
{1.00081,1.00078,1.00074,1.00069,1.00065,1.0006,1.00055,1.00049,1.00043,1.00037,1.0003,1.00022,1.00015,1.00006,0.999974,0.99988,0.999781,0.999675,0.999563,0.999443,0.999317,0.999183,0.999042,0.998892,0.998733,0.998565,0.998387,0.998198,0.997999,0.997789,0.997567,0.997332,0.997083,0.996821,0.996544,0.996252,0.995943,0.995617,0.995272,0.994909,0.994526,0.994122,0.993695,0.993245,0.992771,0.992271,0.991744,0.991188,0.990602,0.989986,0.989336,0.988651,0.98793,0.987171,0.986372,0.98553,0.984645,0.983714,0.982734,0.981704,0.980621,0.979482,0.978285,0.977027,0.975706,0.974319,0.972863,0.971334,0.96973,0.968048,0.966283,0.964434,0.962496,0.960466,0.95834,0.956115,0.953787,0.951353,0.948808,0.946148,0.943371,0.940472,0.937448,0.934294,0.931008,0.927585,0.924023,0.920318,0.916466,0.912465,0.908312,0.904005,0.899542,0.89492,0.890138,0.885195,0.88009,0.874824,0.869395,0.863806,0.858058,0.852151,0.84609,0.839878,0.833517,0.827014,0.820374,0.813602,0.806706,0.799693,0.792572,0.785353,0.778044,0.770656,0.763201,0.75569,0.748136,0.740552,0.73295,0.725344,0.717748,0.710175,0.70264,0.695156,0.687737,0.680397,0.673148,0.666003,0.658974,0.652072,0.645309,0.638694,0.632236,0.625943,0.619821,0.613878,0.608118,0.602545,0.597162,0.59197,0.58697,0.582162,0.577544,0.573113,0.568867,0.564801,0.560909,0.557186,0.553624,0.550217,0.546955,0.54383,0.540833,0.537952,0.535179,0.5325,0.529905,0.52738,0.524914,0.522493,0.520102,0.517727,0.515353,0.512964,0.510543,0.508071,0.505531,0.502903,0.500166,0.497297,0.494274,0.491071,0.487662,0.484019,0.480111,0.475906,0.47137,0.466467,0.461159,0.455405,0.449163,0.442388,0.435036,0.427059,0.418412,0.409047,0.398922,0.387995,0.376232,0.363608,0.35011,0.335744,0.320537,0.304551,0.287887,0.270702,0.253226,0.23577,0.218769,0.202799},
{1.00159,1.00157,1.00154,1.00151,1.00148,1.00144,1.0014,1.00135,1.00131,1.00125,1.0012,1.00113,1.00107,1.00099,1.00092,1.00083,1.00074,1.00065,1.00055,1.00044,1.00032,1.0002,1.00007,0.999927,0.999778,0.999621,0.999453,0.999275,0.999086,0.998886,0.998674,0.99845,0.998212,0.997961,0.997695,0.997413,0.997116,0.996801,0.996469,0.996117,0.995746,0.995354,0.99494,0.994503,0.994042,0.993555,0.993042,0.9925,0.991929,0.991327,0.990692,0.990023,0.989317,0.988574,0.987792,0.986967,0.9861,0.985186,0.984224,0.983213,0.982148,0.981029,0.979852,0.978615,0.977315,0.975949,0.974515,0.973009,0.971428,0.969769,0.968028,0.966203,0.964291,0.962286,0.960187,0.957988,0.955688,0.953281,0.950765,0.948134,0.945387,0.942518,0.939524,0.936402,0.933147,0.929757,0.926227,0.922555,0.918737,0.914771,0.910653,0.906382,0.901954,0.897368,0.892623,0.887718,0.88265,0.877422,0.872032,0.866481,0.860771,0.854904,0.848883,0.84271,0.836389,0.829926,0.823326,0.816594,0.809739,0.802766,0.795686,0.788506,0.781237,0.773889,0.766474,0.759003,0.751488,0.743943,0.736379,0.728811,0.721253,0.713718,0.70622,0.698773,0.69139,0.684085,0.676872,0.669762,0.662767,0.6559,0.64917,0.642588,0.636163,0.629902,0.623813,0.617902,0.612174,0.606633,0.601281,0.596121,0.591154,0.586378,0.581793,0.577396,0.573185,0.569154,0.565298,0.561613,0.558091,0.554725,0.551508,0.548429,0.54548,0.542652,0.539934,0.537315,0.534784,0.532329,0.529937,0.527597,0.525294,0.523014,0.520744,0.518468,0.516169,0.513832,0.511439,0.508971,0.506409,0.503731,0.500917,0.497943,0.494783,0.491412,0.487801,0.48392,0.479736,0.475216,0.470324,0.465021,0.459265,0.453016,0.446228,0.438855,0.430851,0.422169,0.412761,0.402583,0.391595,0.37976,0.367053,0.35346,0.338985,0.323655,0.30753,0.290711,0.273351,0.255675,0.237998,0.22075},
{1.00241,1.00241,1.0024,1.00238,1.00237,1.00234,1.00232,1.00229,1.00226,1.00222,1.00218,1.00213,1.00208,1.00202,1.00196,1.00189,1.00182,1.00173,1.00165,1.00155,1.00145,1.00134,1.00122,1.00109,1.00096,1.00081,1.00066,1.00049,1.00032,1.00013,0.999929,0.999717,0.999492,0.999253,0.998999,0.99873,0.998445,0.998144,0.997824,0.997485,0.997127,0.996749,0.996348,0.995925,0.995477,0.995004,0.994505,0.993978,0.993421,0.992834,0.992214,0.991561,0.990871,0.990144,0.989378,0.988571,0.98772,0.986824,0.985881,0.984888,0.983842,0.982742,0.981585,0.980368,0.979089,0.977744,0.976331,0.974847,0.973289,0.971653,0.969936,0.968136,0.966247,0.964268,0.962194,0.960022,0.957749,0.955369,0.952881,0.950279,0.94756,0.944721,0.941757,0.938666,0.935442,0.932084,0.928586,0.924947,0.921162,0.91723,0.913146,0.908909,0.904517,0.899967,0.895258,0.890389,0.885358,0.880167,0.874815,0.869302,0.86363,0.857802,0.851819,0.845685,0.839404,0.83298,0.826419,0.819726,0.81291,0.805977,0.798936,0.791795,0.784566,0.777257,0.76988,0.762448,0.754972,0.747464,0.739938,0.732408,0.724887,0.717389,0.709927,0.702516,0.695168,0.687899,0.680719,0.673643,0.666683,0.659848,0.653152,0.646602,0.640209,0.63398,0.627923,0.622043,0.616346,0.610837,0.605516,0.600388,0.595452,0.590708,0.586156,0.581792,0.577615,0.573619,0.5698,0.566153,0.56267,0.559345,0.556171,0.553138,0.550238,0.547462,0.544799,0.54224,0.539773,0.537386,0.53507,0.53281,0.530595,0.528411,0.526244,0.524081,0.521906,0.519703,0.517457,0.51515,0.512763,0.510279,0.507675,0.504931,0.502023,0.498926,0.495615,0.492062,0.488236,0.484106,0.479637,0.474794,0.469537,0.463828,0.457622,0.450875,0.443542,0.435575,0.426927,0.417549,0.407398,0.39643,0.384609,0.371906,0.358306,0.343809,0.328441,0.312252,0.295339,0.277848,0.259994,0.242079},
{1.00324,1.00326,1.00327,1.00328,1.00328,1.00328,1.00327,1.00327,1.00325,1.00324,1.00321,1.00319,1.00315,1.00312,1.00307,1.00302,1.00296,1.0029,1.00283,1.00275,1.00267,1.00258,1.00247,1.00236,1.00224,1.00211,1.00198,1.00183,1.00167,1.00149,1.00131,1.00111,1.0009,1.00068,1.00044,1.00018,0.999914,0.999626,0.999321,0.998997,0.998654,0.998289,0.997903,0.997494,0.997062,0.996604,0.996119,0.995607,0.995066,0.994494,0.99389,0.993252,0.992579,0.991868,0.991119,0.990328,0.989495,0.988617,0.987691,0.986716,0.985689,0.984608,0.983471,0.982273,0.981014,0.97969,0.978298,0.976836,0.975299,0.973686,0.971992,0.970214,0.96835,0.966395,0.964346,0.9622,0.959952,0.957599,0.955137,0.952562,0.949872,0.947061,0.944126,0.941064,0.93787,0.934542,0.931076,0.927468,0.923715,0.919815,0.915764,0.911561,0.907202,0.902686,0.898011,0.893177,0.888182,0.883026,0.87771,0.872233,0.866598,0.860806,0.85486,0.848762,0.842518,0.836131,0.829608,0.822953,0.816173,0.809277,0.802273,0.79517,0.787977,0.780704,0.773364,0.765968,0.758527,0.751054,0.743564,0.736068,0.72858,0.721115,0.713686,0.706307,0.698992,0.691753,0.684604,0.677558,0.670627,0.663821,0.657152,0.65063,0.644263,0.63806,0.632028,0.626173,0.620501,0.615014,0.609717,0.604612,0.599698,0.594976,0.590446,0.586103,0.581947,0.577972,0.574175,0.570549,0.567088,0.563785,0.560633,0.557623,0.554747,0.551996,0.549359,0.546827,0.544388,0.542032,0.539748,0.537522,0.535344,0.533199,0.531076,0.528959,0.526834,0.524686,0.522499,0.520256,0.51794,0.515532,0.513012,0.510359,0.507551,0.504563,0.501372,0.497948,0.494264,0.490289,0.485988,0.481328,0.47627,0.470775,0.464802,0.458306,0.451242,0.443562,0.435219,0.426165,0.416353,0.405738,0.394279,0.381944,0.368707,0.354563,0.339517,0.323608,0.306907,0.28953,0.271654,0.253533},
{1.00407,1.00411,1.00414,1.00417,1.0042,1.00422,1.00424,1.00426,1.00427,1.00428,1.00428,1.00427,1.00426,1.00425,1.00423,1.0042,1.00417,1.00413,1.00408,1.00402,1.00396,1.00389,1.00381,1.00372,1.00362,1.00351,1.00339,1.00326,1.00312,1.00297,1.0028,1.00262,1.00243,1.00222,1.002,1.00177,1.00151,1.00124,1.00095,1.00065,1.00032,0.999973,0.999604,0.999212,0.998795,0.998354,0.997886,0.997391,0.996866,0.996311,0.995724,0.995103,0.994446,0.993753,0.993021,0.992248,0.991433,0.990573,0.989665,0.988709,0.987701,0.986639,0.985521,0.984344,0.983105,0.981801,0.980431,0.978989,0.977475,0.975883,0.974212,0.972458,0.970617,0.968686,0.966662,0.96454,0.962318,0.959991,0.957555,0.955008,0.952344,0.949561,0.946655,0.943622,0.940457,0.937159,0.933723,0.930146,0.926424,0.922556,0.918537,0.914366,0.91004,0.905558,0.900917,0.896116,0.891156,0.886034,0.880753,0.875311,0.869712,0.863955,0.858045,0.851984,0.845776,0.839425,0.832937,0.826318,0.819575,0.812715,0.805747,0.798679,0.791522,0.784285,0.77698,0.769618,0.762212,0.754774,0.747317,0.739854,0.732399,0.724966,0.717569,0.710221,0.702936,0.695727,0.688608,0.68159,0.674686,0.667908,0.661266,0.654769,0.648428,0.642249,0.636242,0.63041,0.62476,0.619296,0.614021,0.608936,0.604043,0.599342,0.594831,0.590508,0.586371,0.582416,0.578637,0.57503,0.571588,0.568305,0.565172,0.562182,0.559327,0.556596,0.553981,0.551472,0.549057,0.546727,0.544469,0.542272,0.540124,0.538012,0.535923,0.533844,0.531759,0.529656,0.527517,0.525326,0.523067,0.520721,0.518269,0.51569,0.512962,0.510063,0.506968,0.50365,0.500081,0.49623,0.492066,0.487555,0.482658,0.477339,0.471555,0.465263,0.458418,0.450974,0.442883,0.434095,0.424563,0.414241,0.403085,0.391057,0.378131,0.364286,0.349523,0.333865,0.317366,0.300119,0.282271,0.264037},
{1.00487,1.00493,1.00499,1.00505,1.0051,1.00516,1.0052,1.00525,1.00528,1.00532,1.00535,1.00537,1.00539,1.0054,1.00541,1.00541,1.0054,1.00539,1.00537,1.00534,1.0053,1.00525,1.0052,1.00513,1.00506,1.00498,1.00488,1.00477,1.00466,1.00453,1.00438,1.00423,1.00406,1.00387,1.00367,1.00346,1.00323,1.00298,1.00271,1.00242,1.00211,1.00179,1.00144,1.00106,1.00066,1.00024,0.999793,0.999316,0.99881,0.998273,0.997704,0.997102,0.996464,0.995789,0.995075,0.994321,0.993525,0.992683,0.991795,0.990858,0.989869,0.988827,0.987729,0.986572,0.985353,0.984071,0.982721,0.981301,0.979808,0.978239,0.97659,0.974859,0.973041,0.971134,0.969134,0.967037,0.964839,0.962537,0.960128,0.957606,0.95497,0.952214,0.949335,0.94633,0.943194,0.939925,0.936518,0.932971,0.929279,0.925441,0.921454,0.917314,0.91302,0.90857,0.903961,0.899194,0.894266,0.889178,0.88393,0.878523,0.872957,0.867235,0.861359,0.855332,0.849159,0.842843,0.836389,0.829805,0.823097,0.816271,0.809337,0.802303,0.79518,0.787976,0.780704,0.773375,0.766002,0.758595,0.75117,0.743738,0.736314,0.728911,0.721543,0.714223,0.706966,0.699785,0.692692,0.6857,0.678821,0.672067,0.665448,0.658974,0.652654,0.646497,0.640509,0.634696,0.629065,0.623618,0.618359,0.61329,0.608412,0.603725,0.599227,0.594917,0.590792,0.586847,0.583079,0.579481,0.576048,0.572772,0.569647,0.566663,0.563814,0.561088,0.558478,0.555972,0.55356,0.551232,0.548976,0.54678,0.544633,0.542521,0.540431,0.53835,0.536264,0.534157,0.532015,0.52982,0.527556,0.525204,0.522744,0.520158,0.517421,0.514513,0.511406,0.508076,0.504493,0.500628,0.496448,0.491919,0.487003,0.481662,0.475854,0.469537,0.462665,0.45519,0.447064,0.43824,0.428667,0.418299,0.407093,0.39501,0.38202,0.368104,0.353262,0.337513,0.320909,0.30354,0.285551,0.26715},
{1.00564,1.00573,1.00582,1.00591,1.00599,1.00607,1.00615,1.00622,1.00629,1.00635,1.00641,1.00647,1.00651,1.00656,1.0066,1.00663,1.00665,1.00667,1.00668,1.00668,1.00667,1.00666,1.00663,1.0066,1.00655,1.0065,1.00643,1.00635,1.00626,1.00616,1.00605,1.00592,1.00577,1.00561,1.00544,1.00525,1.00504,1.00482,1.00457,1.00431,1.00403,1.00372,1.00339,1.00304,1.00267,1.00227,1.00184,1.00139,1.0009,1.00038,0.999837,0.999255,0.998638,0.997984,0.997291,0.996558,0.995782,0.994961,0.994093,0.993177,0.99221,0.991189,0.990111,0.988976,0.987779,0.986518,0.98519,0.983793,0.982322,0.980776,0.979151,0.977443,0.975649,0.973766,0.97179,0.969718,0.967546,0.96527,0.962886,0.960392,0.957782,0.955054,0.952203,0.949226,0.946119,0.942878,0.939501,0.935984,0.932323,0.928516,0.924559,0.920451,0.916189,0.911771,0.907195,0.90246,0.897566,0.892512,0.887297,0.881924,0.876392,0.870705,0.864863,0.858871,0.852732,0.846451,0.840033,0.833483,0.826809,0.820019,0.813119,0.80612,0.79903,0.791861,0.784623,0.777328,0.769987,0.762613,0.75522,0.747821,0.740428,0.733056,0.725719,0.718429,0.711202,0.704049,0.696984,0.69002,0.683169,0.676441,0.669849,0.6634,0.657105,0.650973,0.645009,0.63922,0.633611,0.628187,0.622951,0.617904,0.613047,0.608381,0.603905,0.599616,0.595512,0.591589,0.587842,0.584267,0.580856,0.577604,0.574502,0.571543,0.568719,0.566021,0.563439,0.560963,0.558583,0.556289,0.55407,0.551913,0.549807,0.547741,0.5457,0.543673,0.541645,0.539601,0.537528,0.535408,0.533226,0.530964,0.528603,0.526124,0.523505,0.520725,0.517759,0.514583,0.511168,0.507487,0.503507,0.499196,0.494518,0.489435,0.483908,0.477894,0.471349,0.464226,0.456477,0.448055,0.438908,0.428989,0.418252,0.406653,0.394157,0.380735,0.366375,0.351081,0.334883,0.317844,0.300071,0.281727},
{1.00638,1.0065,1.00661,1.00673,1.00684,1.00695,1.00706,1.00716,1.00727,1.00736,1.00745,1.00754,1.00762,1.0077,1.00777,1.00784,1.0079,1.00795,1.00799,1.00803,1.00805,1.00807,1.00808,1.00808,1.00807,1.00805,1.00802,1.00797,1.00791,1.00784,1.00776,1.00766,1.00755,1.00742,1.00728,1.00712,1.00694,1.00674,1.00653,1.00629,1.00604,1.00576,1.00546,1.00513,1.00478,1.00441,1.004,1.00357,1.00311,1.00262,1.0021,1.00154,1.00095,1.00031,0.999644,0.998933,0.998179,0.997381,0.996536,0.995642,0.994697,0.993698,0.992643,0.99153,0.990355,0.989117,0.987812,0.986437,0.98499,0.983467,0.981865,0.98018,0.978411,0.976552,0.974601,0.972553,0.970406,0.968155,0.965798,0.963329,0.960746,0.958044,0.955221,0.952271,0.949192,0.94598,0.942632,0.939143,0.935512,0.931734,0.927808,0.92373,0.919499,0.915112,0.910567,0.905864,0.901002,0.89598,0.890798,0.885457,0.879958,0.874303,0.868494,0.862535,0.856429,0.850181,0.843796,0.837279,0.830638,0.82388,0.817014,0.810047,0.802989,0.795852,0.788645,0.781381,0.774071,0.766728,0.759365,0.751995,0.744631,0.737287,0.729977,0.722715,0.715514,0.708387,0.701348,0.694408,0.68758,0.680876,0.674305,0.667878,0.661604,0.65549,0.649545,0.643775,0.638184,0.632776,0.627556,0.622524,0.617682,0.61303,0.608566,0.60429,0.600197,0.596285,0.592548,0.588982,0.58558,0.582336,0.579242,0.576291,0.573473,0.570781,0.568205,0.565734,0.563359,0.561069,0.558853,0.5567,0.554598,0.552534,0.550496,0.548471,0.546445,0.544403,0.542331,0.540212,0.538031,0.535769,0.533409,0.53093,0.528311,0.525531,0.522566,0.519389,0.515975,0.512293,0.508313,0.504002,0.499323,0.49424,0.488712,0.482697,0.476151,0.469027,0.461276,0.45285,0.4437,0.433775,0.42303,0.411419,0.398906,0.385463,0.371073,0.355738,0.339486,0.322374,0.304504,0.286033},
{1.00708,1.00723,1.00737,1.00752,1.00766,1.0078,1.00794,1.00808,1.00821,1.00835,1.00847,1.00859,1.00871,1.00883,1.00893,1.00904,1.00913,1.00922,1.0093,1.00937,1.00944,1.00949,1.00954,1.00958,1.00961,1.00962,1.00963,1.00962,1.0096,1.00956,1.00952,1.00946,1.00938,1.00929,1.00918,1.00905,1.00891,1.00874,1.00856,1.00836,1.00813,1.00789,1.00762,1.00732,1.007,1.00666,1.00628,1.00588,1.00545,1.00498,1.00449,1.00396,1.00339,1.00278,1.00214,1.00145,1.00073,0.999952,0.999131,0.998262,0.997341,0.996367,0.995336,0.994247,0.993097,0.991883,0.990602,0.989252,0.987829,0.98633,0.984753,0.983093,0.981349,0.979515,0.977589,0.975567,0.973446,0.971221,0.96889,0.966448,0.963892,0.961217,0.958421,0.9555,0.952449,0.949265,0.945946,0.942487,0.938885,0.935137,0.931241,0.927194,0.922993,0.918637,0.914124,0.909452,0.904622,0.899631,0.894482,0.889173,0.883707,0.878085,0.872309,0.866383,0.86031,0.854094,0.847742,0.841258,0.83465,0.827925,0.82109,0.814156,0.807131,0.800025,0.79285,0.785617,0.778338,0.771026,0.763693,0.756352,0.749018,0.741703,0.734421,0.727187,0.720013,0.712913,0.705899,0.698985,0.692182,0.685501,0.678954,0.67255,0.666298,0.660207,0.654283,0.648534,0.642963,0.637575,0.632374,0.627361,0.622537,0.617903,0.613458,0.609199,0.605124,0.601229,0.59751,0.593961,0.590577,0.58735,0.584275,0.581342,0.578544,0.575872,0.573316,0.570867,0.568515,0.56625,0.56406,0.561934,0.559861,0.557829,0.555826,0.553838,0.551851,0.549853,0.547829,0.545762,0.543637,0.541437,0.539144,0.536739,0.534202,0.53151,0.528641,0.525571,0.522272,0.518717,0.514875,0.510715,0.506201,0.501297,0.495963,0.490159,0.48384,0.476962,0.469475,0.461332,0.452482,0.442875,0.432463,0.421199,0.409043,0.39596,0.381926,0.366935,0.350998,0.334156,0.316488,0.298119},
{1.00774,1.00792,1.00809,1.00827,1.00844,1.00862,1.00879,1.00896,1.00913,1.00929,1.00946,1.00962,1.00977,1.00992,1.01007,1.01021,1.01034,1.01047,1.01059,1.0107,1.01081,1.01091,1.01099,1.01107,1.01114,1.0112,1.01124,1.01128,1.0113,1.01131,1.0113,1.01128,1.01124,1.01119,1.01112,1.01103,1.01092,1.0108,1.01065,1.01049,1.0103,1.01009,1.00985,1.00959,1.00931,1.009,1.00866,1.00829,1.00789,1.00745,1.00699,1.00649,1.00595,1.00537,1.00476,1.0041,1.0034,1.00265,1.00186,1.00102,1.00012,0.999176,0.998172,0.997109,0.995985,0.994797,0.993542,0.992217,0.99082,0.989347,0.987795,0.986161,0.984442,0.982634,0.980734,0.978739,0.976644,0.974445,0.972141,0.969726,0.967196,0.964549,0.96178,0.958886,0.955864,0.952708,0.949417,0.945987,0.942414,0.938695,0.934829,0.930811,0.92664,0.922314,0.917832,0.913191,0.908391,0.903432,0.898313,0.893036,0.887601,0.882011,0.876266,0.870372,0.86433,0.858147,0.851826,0.845373,0.838797,0.832102,0.825299,0.818395,0.8114,0.804325,0.79718,0.789976,0.782727,0.775443,0.768138,0.760825,0.753518,0.746229,0.738974,0.731765,0.724616,0.71754,0.71055,0.703658,0.696877,0.690218,0.683692,0.677308,0.671075,0.665002,0.659096,0.653363,0.647809,0.642437,0.63725,0.632251,0.627441,0.62282,0.618386,0.614139,0.610075,0.60619,0.60248,0.598941,0.595565,0.592346,0.589278,0.586352,0.583561,0.580894,0.578344,0.5759,0.573553,0.571292,0.569106,0.566984,0.564915,0.562886,0.560886,0.5589,0.556917,0.554921,0.552899,0.550835,0.548712,0.546514,0.544224,0.541821,0.539286,0.536597,0.53373,0.530663,0.527367,0.523816,0.519978,0.515821,0.511312,0.506413,0.501085,0.495287,0.488976,0.482104,0.474625,0.466489,0.457646,0.448046,0.437639,0.426379,0.414223,0.401136,0.387092,0.372082,0.356114,0.339226,0.321489,0.303022},
{1.00837,1.00857,1.00877,1.00898,1.00919,1.00939,1.0096,1.0098,1.01,1.01021,1.01041,1.0106,1.0108,1.01098,1.01117,1.01135,1.01153,1.0117,1.01186,1.01202,1.01216,1.0123,1.01244,1.01256,1.01267,1.01277,1.01286,1.01294,1.01301,1.01306,1.0131,1.01312,1.01313,1.01312,1.01309,1.01305,1.01298,1.0129,1.0128,1.01267,1.01253,1.01236,1.01216,1.01194,1.01169,1.01142,1.01112,1.01078,1.01042,1.01002,1.00959,1.00913,1.00862,1.00808,1.0075,1.00687,1.0062,1.00549,1.00473,1.00391,1.00305,1.00213,1.00116,1.00012,0.999028,0.997868,0.996641,0.995344,0.993974,0.992529,0.991005,0.989398,0.987707,0.985926,0.984053,0.982085,0.980017,0.977847,0.97557,0.973182,0.970681,0.968062,0.965321,0.962455,0.959461,0.956335,0.953072,0.949671,0.946127,0.942438,0.938601,0.934614,0.930473,0.926178,0.921726,0.917115,0.912347,0.907418,0.902331,0.897085,0.891681,0.886122,0.880409,0.874546,0.868536,0.862384,0.856094,0.849673,0.843128,0.836464,0.829692,0.822819,0.815854,0.808809,0.801694,0.79452,0.787299,0.780044,0.772767,0.765482,0.758202,0.750941,0.743712,0.736529,0.729405,0.722353,0.715388,0.70852,0.701762,0.695125,0.688621,0.682258,0.676046,0.669993,0.664107,0.658393,0.652857,0.647503,0.642334,0.637353,0.632559,0.627955,0.623537,0.619306,0.615258,0.611389,0.607695,0.604171,0.600811,0.597608,0.594556,0.591647,0.588873,0.586224,0.583692,0.581268,0.578941,0.576701,0.574538,0.572441,0.570397,0.568397,0.566426,0.564474,0.562526,0.560569,0.558588,0.556569,0.554497,0.552353,0.550122,0.547785,0.545321,0.54271,0.539929,0.536955,0.533762,0.530322,0.526607,0.522585,0.518221,0.513482,0.508327,0.502717,0.496609,0.489958,0.482716,0.474834,0.466263,0.456952,0.44685,0.435909,0.424083,0.411333,0.397628,0.382949,0.367296,0.35069,0.333185,0.314875},
{1.00895,1.00919,1.00942,1.00965,1.00989,1.01013,1.01037,1.0106,1.01084,1.01108,1.01132,1.01155,1.01178,1.01201,1.01224,1.01246,1.01268,1.01289,1.0131,1.0133,1.01349,1.01368,1.01385,1.01402,1.01418,1.01433,1.01447,1.01459,1.01471,1.01481,1.01489,1.01496,1.01502,1.01506,1.01508,1.01508,1.01507,1.01503,1.01498,1.0149,1.0148,1.01467,1.01452,1.01434,1.01414,1.01391,1.01365,1.01336,1.01303,1.01268,1.01228,1.01186,1.01139,1.01089,1.01034,1.00975,1.00912,1.00844,1.00771,1.00693,1.0061,1.00521,1.00427,1.00327,1.0022,1.00108,0.999879,0.998612,0.997272,0.995856,0.994361,0.992784,0.991121,0.989369,0.987525,0.985585,0.983546,0.981404,0.979155,0.976796,0.974323,0.971732,0.96902,0.966183,0.963217,0.960119,0.956886,0.953513,0.949999,0.946339,0.942531,0.938573,0.934462,0.930196,0.925774,0.921194,0.916455,0.911557,0.9065,0.901284,0.895911,0.890382,0.884699,0.878866,0.872886,0.866764,0.860505,0.854114,0.847597,0.840964,0.83422,0.827376,0.820441,0.813424,0.806336,0.79919,0.791996,0.784768,0.777518,0.770259,0.763004,0.755767,0.748562,0.741403,0.734302,0.727273,0.720328,0.713481,0.706744,0.700127,0.693641,0.687296,0.681102,0.675066,0.669195,0.663496,0.657975,0.652634,0.647479,0.642509,0.637727,0.633133,0.628726,0.624504,0.620465,0.616604,0.612917,0.6094,0.606046,0.602849,0.599802,0.596897,0.594126,0.59148,0.58895,0.586528,0.584202,0.581963,0.579799,0.577701,0.575656,0.573653,0.57168,0.569724,0.567771,0.565809,0.563823,0.561797,0.559717,0.557565,0.555324,0.552976,0.5505,0.547876,0.545081,0.542092,0.538882,0.535424,0.531688,0.527644,0.523257,0.518492,0.51331,0.50767,0.501529,0.494843,0.487563,0.479641,0.471026,0.461667,0.451513,0.440515,0.428628,0.415811,0.402032,0.387272,0.371529,0.354821,0.337201,0.318761},
{1.00951,1.00977,1.01003,1.01029,1.01056,1.01083,1.0111,1.01137,1.01164,1.01192,1.01219,1.01246,1.01273,1.013,1.01327,1.01353,1.01379,1.01405,1.0143,1.01455,1.01479,1.01502,1.01525,1.01546,1.01567,1.01587,1.01606,1.01623,1.0164,1.01655,1.01669,1.01681,1.01692,1.01701,1.01708,1.01713,1.01717,1.01719,1.01718,1.01715,1.0171,1.01702,1.01692,1.0168,1.01664,1.01646,1.01624,1.016,1.01572,1.01541,1.01506,1.01468,1.01425,1.01379,1.01328,1.01274,1.01214,1.0115,1.01081,1.01007,1.00928,1.00843,1.00752,1.00655,1.00552,1.00443,1.00327,1.00203,1.00072,0.999341,0.997877,0.996331,0.9947,0.992979,0.991165,0.989255,0.987246,0.985134,0.982915,0.980586,0.978143,0.975581,0.972899,0.970092,0.967156,0.964087,0.960884,0.957541,0.954056,0.950426,0.946649,0.94272,0.938639,0.934404,0.930012,0.925462,0.920753,0.915885,0.910858,0.905673,0.90033,0.894831,0.889179,0.883376,0.877427,0.871335,0.865105,0.858744,0.852257,0.845653,0.838939,0.832124,0.825217,0.818228,0.811169,0.80405,0.796884,0.789683,0.782459,0.775225,0.767996,0.760785,0.753604,0.746468,0.739391,0.732385,0.725463,0.718637,0.711921,0.705324,0.698859,0.692533,0.686358,0.68034,0.674487,0.668806,0.663301,0.657977,0.652836,0.647882,0.643116,0.638536,0.634143,0.629935,0.625909,0.622062,0.618389,0.614885,0.611545,0.608361,0.605328,0.602437,0.59968,0.597049,0.594535,0.592128,0.589819,0.587597,0.585452,0.583373,0.58135,0.579369,0.57742,0.57549,0.573566,0.571634,0.569681,0.567692,0.565651,0.563543,0.56135,0.559053,0.556634,0.554073,0.551346,0.548431,0.545303,0.541935,0.538297,0.534361,0.530091,0.525454,0.520411,0.514923,0.508947,0.502439,0.495352,0.487636,0.479243,0.470119,0.460215,0.44948,0.437866,0.42533,0.411835,0.397357,0.381884,0.365425,0.348018,0.329734},
{1.01003,1.01031,1.0106,1.01089,1.01119,1.01149,1.01179,1.0121,1.0124,1.01271,1.01302,1.01333,1.01364,1.01395,1.01426,1.01457,1.01487,1.01517,1.01547,1.01576,1.01605,1.01633,1.01661,1.01687,1.01713,1.01738,1.01762,1.01785,1.01807,1.01827,1.01846,1.01864,1.0188,1.01895,1.01908,1.01919,1.01928,1.01935,1.0194,1.01942,1.01943,1.0194,1.01936,1.01928,1.01918,1.01905,1.01889,1.01869,1.01846,1.0182,1.0179,1.01756,1.01719,1.01677,1.01631,1.01581,1.01526,1.01466,1.01402,1.01332,1.01256,1.01175,1.01089,1.00996,1.00896,1.00791,1.00678,1.00558,1.00431,1.00296,1.00153,1.00002,0.99842,0.996732,0.994951,0.993074,0.991096,0.989015,0.986828,0.984529,0.982117,0.979586,0.976934,0.974157,0.971251,0.968213,0.965039,0.961726,0.958272,0.954672,0.950924,0.947025,0.942974,0.938768,0.934406,0.929885,0.925207,0.920368,0.915371,0.910215,0.904902,0.899432,0.893809,0.888036,0.882115,0.876052,0.869851,0.863518,0.85706,0.850484,0.843797,0.837009,0.830129,0.823168,0.816135,0.809042,0.801901,0.794724,0.787525,0.780315,0.773109,0.765921,0.758762,0.751648,0.744591,0.737605,0.730703,0.723897,0.717198,0.710619,0.70417,0.697861,0.691701,0.685697,0.679858,0.67419,0.668697,0.663385,0.658255,0.653311,0.648554,0.643983,0.639598,0.635397,0.631377,0.627535,0.623867,0.620367,0.617029,0.613848,0.610816,0.607926,0.605169,0.602536,0.60002,0.59761,0.595297,0.59307,0.590919,0.588833,0.586801,0.584811,0.582851,0.580908,0.57897,0.577023,0.575052,0.573043,0.570981,0.568849,0.566629,0.564304,0.561854,0.559257,0.556493,0.553536,0.550363,0.546945,0.543254,0.539259,0.534925,0.530219,0.525101,0.519531,0.513468,0.506864,0.499674,0.491849,0.483336,0.474086,0.464046,0.453165,0.441397,0.428697,0.41503,0.40037,0.384707,0.368051,0.350441,0.331949},
{1.01052,1.01083,1.01114,1.01146,1.01179,1.01211,1.01245,1.01279,1.01313,1.01347,1.01381,1.01416,1.01451,1.01486,1.01521,1.01556,1.01591,1.01625,1.0166,1.01694,1.01727,1.0176,1.01793,1.01825,1.01856,1.01886,1.01916,1.01944,1.01971,1.01997,1.02022,1.02046,1.02067,1.02088,1.02106,1.02123,1.02138,1.02151,1.02162,1.0217,1.02176,1.0218,1.02181,1.02179,1.02175,1.02167,1.02157,1.02143,1.02125,1.02105,1.0208,1.02052,1.02019,1.01983,1.01942,1.01896,1.01846,1.01791,1.01731,1.01666,1.01595,1.01519,1.01436,1.01347,1.01252,1.01151,1.01042,1.00926,1.00803,1.00672,1.00532,1.00385,1.00229,1.00063,0.998886,0.997043,0.9951,0.993052,0.990898,0.988632,0.986252,0.983753,0.981133,0.978387,0.975512,0.972505,0.969362,0.96608,0.962656,0.959086,0.955368,0.9515,0.947479,0.943303,0.93897,0.934479,0.92983,0.925021,0.920053,0.914927,0.909642,0.904202,0.898607,0.892862,0.88697,0.880935,0.874762,0.868457,0.862026,0.855477,0.848817,0.842056,0.835202,0.828265,0.821258,0.814189,0.807073,0.79992,0.792743,0.785557,0.778373,0.771205,0.764068,0.756974,0.749937,0.742969,0.736085,0.729296,0.722614,0.716051,0.709617,0.703322,0.697176,0.691185,0.685358,0.679701,0.674218,0.668915,0.663795,0.658858,0.654108,0.649543,0.645163,0.640966,0.636949,0.633109,0.629442,0.625942,0.622604,0.619421,0.616385,0.613491,0.610728,0.608089,0.605564,0.603144,0.600819,0.598579,0.596413,0.59431,0.592259,0.590247,0.588263,0.586294,0.584326,0.582347,0.58034,0.578292,0.576186,0.574006,0.571734,0.569351,0.566837,0.564172,0.561331,0.558292,0.555028,0.551511,0.547712,0.543599,0.539138,0.534292,0.529023,0.52329,0.517049,0.510254,0.502858,0.49481,0.486059,0.476554,0.466242,0.455074,0.443001,0.429982,0.415982,0.400979,0.384964,0.367955,0.349993,0.331163},
{1.01099,1.01132,1.01165,1.012,1.01235,1.01271,1.01307,1.01344,1.01381,1.01419,1.01457,1.01496,1.01534,1.01573,1.01612,1.01652,1.01691,1.0173,1.01769,1.01808,1.01846,1.01884,1.01922,1.01959,1.01995,1.02031,1.02066,1.021,1.02133,1.02165,1.02196,1.02225,1.02253,1.02279,1.02304,1.02327,1.02348,1.02367,1.02384,1.02399,1.02411,1.02421,1.02428,1.02433,1.02435,1.02433,1.02429,1.02421,1.02409,1.02394,1.02376,1.02353,1.02326,1.02296,1.0226,1.0222,1.02175,1.02126,1.02071,1.02011,1.01945,1.01873,1.01795,1.01712,1.01621,1.01524,1.0142,1.01308,1.01189,1.01062,1.00927,1.00784,1.00631,1.0047,1.00299,1.00118,0.999278,0.997268,0.995149,0.992918,0.990573,0.988109,0.985523,0.982811,0.97997,0.976996,0.973886,0.970636,0.967244,0.963707,0.960021,0.956184,0.952195,0.94805,0.943748,0.939289,0.93467,0.929892,0.924954,0.919858,0.914604,0.909193,0.903629,0.897914,0.892051,0.886045,0.879901,0.873624,0.867222,0.860701,0.854069,0.847335,0.840508,0.833599,0.826617,0.819575,0.812484,0.805357,0.798205,0.791043,0.783883,0.776739,0.769624,0.762553,0.755537,0.748592,0.741729,0.73496,0.728298,0.721755,0.71534,0.709064,0.702935,0.696963,0.691153,0.685513,0.680048,0.674761,0.669657,0.664737,0.660002,0.655454,0.65109,0.646909,0.642909,0.639085,0.635435,0.631953,0.628632,0.625467,0.622451,0.619576,0.616835,0.614218,0.611717,0.609322,0.607024,0.604813,0.602678,0.600608,0.598593,0.596621,0.59468,0.592757,0.59084,0.588916,0.58697,0.584988,0.582954,0.580853,0.578668,0.57638,0.573971,0.57142,0.568705,0.565803,0.56269,0.559338,0.555719,0.551803,0.547557,0.542947,0.537934,0.532479,0.526539,0.520072,0.513029,0.505361,0.497019,0.487949,0.478101,0.467421,0.45586,0.443372,0.429917,0.415461,0.399988,0.383496,0.366008,0.347579},
{1.01142,1.01178,1.01214,1.01251,1.01288,1.01327,1.01366,1.01406,1.01447,1.01488,1.01529,1.01571,1.01614,1.01657,1.017,1.01743,1.01787,1.0183,1.01874,1.01918,1.01961,1.02004,1.02047,1.02089,1.02131,1.02172,1.02213,1.02253,1.02292,1.0233,1.02366,1.02402,1.02436,1.02469,1.025,1.02529,1.02557,1.02582,1.02606,1.02627,1.02646,1.02662,1.02676,1.02687,1.02695,1.02701,1.02702,1.02701,1.02696,1.02688,1.02675,1.02659,1.02638,1.02613,1.02584,1.0255,1.02511,1.02467,1.02418,1.02363,1.02303,1.02237,1.02164,1.02085,1.02,1.01908,1.01808,1.01702,1.01587,1.01465,1.01334,1.01195,1.01047,1.0089,1.00723,1.00547,1.0036,1.00163,0.999547,0.997354,0.995046,0.992618,0.990068,0.987392,0.984585,0.981646,0.978569,0.975353,0.971995,0.96849,0.964837,0.961032,0.957075,0.952961,0.948691,0.944263,0.939675,0.934927,0.93002,0.924954,0.91973,0.914349,0.908814,0.903127,0.897293,0.891316,0.8852,0.878951,0.872576,0.866082,0.859477,0.852769,0.845968,0.839084,0.832128,0.825111,0.818044,0.81094,0.803812,0.796672,0.789534,0.782412,0.775318,0.768267,0.761272,0.754346,0.747501,0.740751,0.734107,0.727581,0.721183,0.714923,0.70881,0.702852,0.697057,0.691431,0.685979,0.680706,0.675614,0.670706,0.665984,0.661446,0.657093,0.652924,0.648934,0.645121,0.641481,0.638009,0.634698,0.631544,0.628538,0.625673,0.622942,0.620336,0.617845,0.615462,0.613176,0.610977,0.608855,0.606799,0.604799,0.602842,0.600918,0.599013,0.597116,0.595213,0.59329,0.591334,0.589328,0.587258,0.585105,0.582854,0.580485,0.577977,0.57531,0.572461,0.569405,0.566117,0.562568,0.558729,0.554566,0.550047,0.545134,0.539788,0.533968,0.527629,0.520726,0.513209,0.505029,0.496133,0.486469,0.475985,0.464629,0.452353,0.439115,0.424878,0.409619,0.39333,0.376024,0.357743},
{1.01184,1.01221,1.01259,1.01299,1.01339,1.0138,1.01422,1.01465,1.01508,1.01553,1.01598,1.01643,1.0169,1.01736,1.01783,1.01831,1.01879,1.01927,1.01975,1.02023,1.02072,1.0212,1.02168,1.02215,1.02263,1.0231,1.02356,1.02402,1.02446,1.0249,1.02533,1.02575,1.02616,1.02655,1.02692,1.02728,1.02763,1.02795,1.02825,1.02853,1.02879,1.02903,1.02923,1.02941,1.02956,1.02969,1.02977,1.02983,1.02985,1.02983,1.02977,1.02968,1.02954,1.02935,1.02913,1.02885,1.02852,1.02815,1.02771,1.02723,1.02668,1.02608,1.02541,1.02468,1.02388,1.02301,1.02207,1.02105,1.01996,1.01879,1.01753,1.01618,1.01475,1.01322,1.0116,1.00988,1.00805,1.00612,1.00408,1.00193,0.99966,0.997271,0.994759,0.992119,0.989349,0.986445,0.983404,0.980223,0.976898,0.973427,0.969807,0.966035,0.96211,0.958028,0.95379,0.949392,0.944835,0.940118,0.935241,0.930204,0.925009,0.919657,0.91415,0.908492,0.902685,0.896735,0.890646,0.884424,0.878075,0.871607,0.865027,0.858344,0.851567,0.844707,0.837774,0.830779,0.823735,0.816652,0.809545,0.802425,0.795307,0.788204,0.781129,0.774096,0.767118,0.760208,0.753379,0.746644,0.740014,0.733501,0.727116,0.720867,0.714766,0.708819,0.703033,0.697416,0.691972,0.686706,0.68162,0.676718,0.672,0.667467,0.663117,0.658949,0.65496,0.651147,0.647506,0.644032,0.640718,0.637559,0.634548,0.631676,0.628937,0.626321,0.62382,0.621423,0.619123,0.616908,0.614767,0.612691,0.610668,0.608686,0.606733,0.604797,0.602866,0.600925,0.59896,0.596958,0.594901,0.592776,0.590563,0.588245,0.585802,0.583215,0.580461,0.577516,0.574357,0.570955,0.567282,0.563307,0.558998,0.554318,0.549232,0.543698,0.537673,0.531114,0.523973,0.5162,0.507745,0.498554,0.488576,0.477758,0.466048,0.4534,0.439772,0.425131,0.409457,0.392745,0.375017,0.356323},
{1.01223,1.01262,1.01302,1.01344,1.01387,1.0143,1.01475,1.01521,1.01567,1.01615,1.01663,1.01712,1.01762,1.01812,1.01863,1.01915,1.01967,1.02019,1.02072,1.02125,1.02178,1.02232,1.02285,1.02338,1.02391,1.02443,1.02495,1.02547,1.02598,1.02648,1.02697,1.02745,1.02792,1.02838,1.02882,1.02925,1.02966,1.03006,1.03043,1.03078,1.03111,1.03142,1.0317,1.03195,1.03218,1.03237,1.03253,1.03266,1.03275,1.03281,1.03282,1.0328,1.03273,1.03262,1.03246,1.03225,1.03199,1.03168,1.03132,1.03089,1.03041,1.02987,1.02927,1.0286,1.02786,1.02705,1.02616,1.0252,1.02416,1.02304,1.02184,1.02054,1.01916,1.01768,1.01611,1.01443,1.01266,1.01077,1.00877,1.00666,1.00444,1.00209,0.999617,0.997017,0.994286,0.991421,0.988417,0.985273,0.981984,0.978549,0.974963,0.971226,0.967334,0.963286,0.95908,0.954715,0.95019,0.945504,0.940658,0.935651,0.930486,0.925164,0.919686,0.914056,0.908278,0.902356,0.896294,0.890099,0.883776,0.877334,0.870779,0.864121,0.857369,0.850533,0.843623,0.836651,0.829629,0.822568,0.815482,0.808383,0.801285,0.794201,0.787145,0.78013,0.773169,0.766276,0.759464,0.752744,0.746129,0.739631,0.733259,0.727024,0.720934,0.714999,0.709225,0.703618,0.698184,0.692927,0.68785,0.682956,0.678245,0.673719,0.669375,0.665213,0.66123,0.657421,0.653784,0.650314,0.647003,0.643846,0.640837,0.637967,0.635228,0.632612,0.63011,0.627713,0.625411,0.623194,0.62105,0.618971,0.616943,0.614956,0.612998,0.611056,0.609117,0.607168,0.605194,0.603182,0.601115,0.598977,0.596751,0.594418,0.59196,0.589355,0.586583,0.583618,0.580436,0.57701,0.573312,0.569309,0.56497,0.560259,0.555138,0.549567,0.543503,0.536902,0.529715,0.521894,0.513387,0.504141,0.494103,0.483221,0.471444,0.458722,0.445015,0.430289,0.414522,0.397709,0.379868,0.361048},
{1.0126,1.01301,1.01343,1.01387,1.01432,1.01478,1.01525,1.01574,1.01623,1.01673,1.01725,1.01777,1.01831,1.01885,1.0194,1.01995,1.02051,1.02108,1.02165,1.02223,1.02281,1.02339,1.02398,1.02456,1.02514,1.02573,1.0263,1.02688,1.02745,1.02801,1.02857,1.02912,1.02965,1.03018,1.03069,1.03119,1.03167,1.03214,1.03259,1.03301,1.03342,1.0338,1.03415,1.03448,1.03478,1.03505,1.03529,1.03549,1.03566,1.03579,1.03589,1.03594,1.03594,1.03591,1.03582,1.03569,1.0355,1.03527,1.03497,1.03462,1.03421,1.03374,1.0332,1.03259,1.03192,1.03117,1.03035,1.02945,1.02847,1.02741,1.02626,1.02502,1.02369,1.02227,1.02075,1.01912,1.01739,1.01556,1.01361,1.01155,1.00936,1.00706,1.00463,1.00208,0.999386,0.99656,0.993597,0.990491,0.987241,0.983842,0.980294,0.976592,0.972736,0.968722,0.96455,0.960219,0.955726,0.951072,0.946258,0.941282,0.936147,0.930855,0.925407,0.919806,0.914056,0.908162,0.902127,0.895959,0.889663,0.883246,0.876716,0.870083,0.863355,0.856542,0.849655,0.842706,0.835705,0.828666,0.8216,0.814521,0.807442,0.800377,0.793339,0.786341,0.779397,0.77252,0.765723,0.759018,0.752417,0.745932,0.739573,0.73335,0.727273,0.721348,0.715584,0.709987,0.704563,0.699314,0.694245,0.689358,0.684655,0.680134,0.675796,0.671639,0.66766,0.663855,0.660222,0.656753,0.653445,0.65029,0.647281,0.644411,0.641672,0.639056,0.636553,0.634153,0.631848,0.629627,0.62748,0.625395,0.623362,0.621369,0.619403,0.617452,0.615504,0.613544,0.611559,0.609534,0.607453,0.605299,0.603056,0.600706,0.598227,0.595601,0.592805,0.589814,0.586605,0.583149,0.579418,0.57538,0.571003,0.566251,0.561086,0.555468,0.549354,0.542698,0.535453,0.527569,0.518995,0.509678,0.499564,0.488601,0.476736,0.463922,0.450116,0.435284,0.419402,0.402467,0.384494,0.36553},
{1.01295,1.01338,1.01382,1.01428,1.01475,1.01523,1.01573,1.01624,1.01676,1.01729,1.01784,1.0184,1.01896,1.01954,1.02012,1.02072,1.02132,1.02193,1.02255,1.02317,1.0238,1.02443,1.02507,1.0257,1.02634,1.02698,1.02762,1.02825,1.02888,1.02951,1.03013,1.03074,1.03135,1.03194,1.03253,1.0331,1.03365,1.03419,1.03471,1.03522,1.0357,1.03616,1.03659,1.037,1.03738,1.03773,1.03805,1.03833,1.03858,1.03879,1.03896,1.03909,1.03918,1.03922,1.03922,1.03916,1.03906,1.03889,1.03868,1.0384,1.03806,1.03766,1.0372,1.03666,1.03606,1.03538,1.03463,1.03379,1.03288,1.03188,1.03079,1.02962,1.02835,1.02698,1.02552,1.02395,1.02227,1.02049,1.01859,1.01658,1.01445,1.01219,1.00981,1.0073,1.00465,1.00187,0.998949,0.995885,0.992675,0.989317,0.985807,0.982144,0.978324,0.974347,0.970211,0.965914,0.961456,0.956835,0.952053,0.94711,0.942007,0.936745,0.931328,0.925757,0.920036,0.91417,0.908163,0.902022,0.895753,0.889362,0.882858,0.87625,0.869546,0.862757,0.855893,0.848966,0.841987,0.834969,0.827924,0.820865,0.813806,0.806759,0.799739,0.792759,0.785832,0.778972,0.772191,0.765501,0.758915,0.752444,0.746099,0.739889,0.733824,0.727912,0.722159,0.716573,0.711159,0.705921,0.700862,0.695984,0.691289,0.686778,0.682448,0.678299,0.674328,0.670531,0.666905,0.663444,0.660142,0.656994,0.653993,0.65113,0.648398,0.645789,0.643293,0.640901,0.638604,0.636391,0.634253,0.632177,0.630154,0.628171,0.626216,0.624277,0.622342,0.620397,0.618427,0.616419,0.614356,0.612223,0.610002,0.607676,0.605225,0.602628,0.599864,0.59691,0.59374,0.590328,0.586645,0.58266,0.578341,0.573653,0.568558,0.563016,0.556985,0.55042,0.543274,0.535498,0.527039,0.517845,0.507863,0.497039,0.48532,0.472658,0.459007,0.444329,0.428599,0.411805,0.393957,0.375091},
{1.01328,1.01373,1.01419,1.01466,1.01515,1.01566,1.01618,1.01671,1.01726,1.01782,1.0184,1.01899,1.01959,1.0202,1.02082,1.02145,1.0221,1.02275,1.02341,1.02408,1.02475,1.02543,1.02612,1.02681,1.0275,1.02819,1.02889,1.02958,1.03028,1.03097,1.03165,1.03233,1.03301,1.03367,1.03432,1.03497,1.0356,1.03621,1.03681,1.03739,1.03795,1.03849,1.039,1.03949,1.03995,1.04039,1.04079,1.04116,1.04149,1.04179,1.04204,1.04226,1.04243,1.04255,1.04263,1.04266,1.04264,1.04256,1.04242,1.04222,1.04197,1.04164,1.04126,1.0408,1.04027,1.03966,1.03898,1.03822,1.03737,1.03644,1.03542,1.03431,1.03311,1.0318,1.0304,1.02889,1.02727,1.02555,1.02371,1.02175,1.01967,1.01746,1.01513,1.01267,1.01007,1.00733,1.00446,1.00144,0.99827,0.994953,0.991484,0.987861,0.98408,0.980141,0.976042,0.971781,0.967358,0.962772,0.958024,0.953114,0.948042,0.942812,0.937425,0.931884,0.926192,0.920354,0.914376,0.908262,0.902018,0.895653,0.889175,0.88259,0.87591,0.869144,0.862303,0.855397,0.84844,0.841442,0.834416,0.827376,0.820335,0.813306,0.806303,0.799339,0.792428,0.785583,0.778816,0.77214,0.765567,0.759108,0.752774,0.746575,0.740521,0.734618,0.728875,0.723297,0.717891,0.71266,0.707608,0.702737,0.698048,0.693541,0.689216,0.685071,0.681104,0.67731,0.673686,0.670227,0.666927,0.66378,0.660779,0.657916,0.655183,0.652573,0.650075,0.647681,0.64538,0.643164,0.641021,0.63894,0.63691,0.63492,0.632958,0.631011,0.629067,0.627111,0.62513,0.623108,0.621032,0.618884,0.616646,0.614302,0.611831,0.609214,0.606427,0.603447,0.600251,0.59681,0.593095,0.589077,0.584722,0.579995,0.574858,0.569271,0.563192,0.556576,0.549375,0.541539,0.533018,0.523757,0.513704,0.502804,0.491004,0.478256,0.464512,0.449736,0.4339,0.416991,0.399019,0.380016},
{1.0136,1.01406,1.01454,1.01503,1.01554,1.01607,1.01661,1.01717,1.01774,1.01833,1.01893,1.01955,1.02018,1.02083,1.02148,1.02215,1.02283,1.02353,1.02423,1.02494,1.02566,1.02639,1.02713,1.02787,1.02862,1.02937,1.03012,1.03087,1.03163,1.03238,1.03313,1.03388,1.03462,1.03536,1.03608,1.0368,1.03751,1.0382,1.03887,1.03953,1.04017,1.04079,1.04139,1.04197,1.04251,1.04303,1.04352,1.04397,1.04439,1.04478,1.04512,1.04543,1.04568,1.0459,1.04606,1.04618,1.04624,1.04625,1.0462,1.04609,1.04591,1.04568,1.04537,1.04499,1.04454,1.04402,1.04341,1.04273,1.04196,1.0411,1.04015,1.03911,1.03798,1.03674,1.0354,1.03396,1.0324,1.03074,1.02896,1.02705,1.02503,1.02288,1.0206,1.01819,1.01565,1.01296,1.01013,1.00716,1.00404,1.00077,0.997342,0.993761,0.990021,0.986122,0.982062,0.977839,0.973454,0.968904,0.964191,0.959315,0.954277,0.94908,0.943724,0.938214,0.932553,0.926744,0.920794,0.914708,0.908492,0.902153,0.8957,0.88914,0.882484,0.875742,0.868923,0.862039,0.855103,0.848125,0.84112,0.834099,0.827077,0.820066,0.81308,0.806132,0.799237,0.792407,0.785654,0.778992,0.772433,0.765987,0.759666,0.753479,0.747435,0.741543,0.73581,0.730243,0.724846,0.719624,0.71458,0.709717,0.705036,0.700537,0.696219,0.692081,0.68812,0.684333,0.680716,0.677263,0.673969,0.670828,0.667833,0.664976,0.66225,0.659645,0.657154,0.654766,0.652472,0.650263,0.648127,0.646054,0.644033,0.642052,0.6401,0.638163,0.63623,0.634286,0.632319,0.630312,0.628252,0.626122,0.623904,0.621582,0.619135,0.616543,0.613786,0.610839,0.607677,0.604275,0.600604,0.596634,0.592331,0.587662,0.582588,0.577071,0.571068,0.564534,0.557423,0.549686,0.54127,0.532123,0.522191,0.51142,0.499756,0.487148,0.473549,0.458919,0.443226,0.426454,0.408604,0.389701},
{1.0139,1.01438,1.01487,1.01538,1.01591,1.01645,1.01702,1.0176,1.0182,1.01881,1.01944,1.02009,1.02075,1.02142,1.02212,1.02282,1.02354,1.02427,1.02502,1.02577,1.02654,1.02732,1.0281,1.02889,1.02969,1.0305,1.03131,1.03212,1.03294,1.03376,1.03457,1.03539,1.0362,1.03701,1.0378,1.0386,1.03938,1.04015,1.0409,1.04164,1.04237,1.04307,1.04375,1.04441,1.04504,1.04565,1.04623,1.04677,1.04728,1.04776,1.04819,1.04859,1.04894,1.04924,1.0495,1.04971,1.04986,1.04996,1.05,1.04998,1.0499,1.04975,1.04953,1.04924,1.04887,1.04843,1.04791,1.0473,1.04661,1.04584,1.04497,1.044,1.04294,1.04177,1.04051,1.03913,1.03764,1.03604,1.03433,1.03249,1.03053,1.02844,1.02622,1.02386,1.02137,1.01874,1.01596,1.01304,1.00996,1.00674,1.00336,0.999824,0.996128,0.992271,0.988252,0.984069,0.979722,0.97521,0.970533,0.965692,0.960689,0.955525,0.950202,0.944723,0.939092,0.933313,0.927392,0.921333,0.915144,0.908832,0.902404,0.895869,0.889236,0.882517,0.87572,0.868857,0.861941,0.854983,0.847997,0.840994,0.833989,0.826994,0.820024,0.813092,0.806211,0.799394,0.792655,0.786006,0.779458,0.773023,0.766712,0.760534,0.7545,0.748617,0.742892,0.737331,0.731941,0.726725,0.721687,0.716829,0.712152,0.707657,0.703343,0.699207,0.695249,0.691463,0.687847,0.684395,0.681101,0.677959,0.674963,0.672104,0.669376,0.666768,0.664273,0.661881,0.659583,0.657367,0.655225,0.653144,0.651115,0.649125,0.647162,0.645214,0.643268,0.641311,0.639328,0.637305,0.635227,0.633077,0.630838,0.628492,0.62602,0.623401,0.620613,0.617634,0.614437,0.610997,0.607285,0.603271,0.598921,0.5942,0.589071,0.583495,0.577428,0.570827,0.563643,0.555827,0.547328,0.538093,0.528066,0.517194,0.505424,0.492703,0.478984,0.464226,0.448399,0.431484,0.413482,0.394417},
{1.01419,1.01468,1.01519,1.01571,1.01626,1.01682,1.01741,1.01801,1.01863,1.01927,1.01992,1.0206,1.02129,1.022,1.02272,1.02346,1.02422,1.02499,1.02577,1.02657,1.02738,1.0282,1.02904,1.02988,1.03073,1.0316,1.03246,1.03334,1.03421,1.03509,1.03597,1.03686,1.03774,1.03861,1.03948,1.04035,1.04121,1.04206,1.04289,1.04372,1.04452,1.04531,1.04608,1.04683,1.04755,1.04825,1.04892,1.04955,1.05016,1.05073,1.05126,1.05175,1.05219,1.05259,1.05295,1.05325,1.0535,1.05369,1.05383,1.0539,1.05391,1.05385,1.05373,1.05353,1.05326,1.0529,1.05247,1.05195,1.05135,1.05065,1.04987,1.04898,1.048,1.04691,1.04572,1.04442,1.04301,1.04148,1.03983,1.03806,1.03616,1.03414,1.03198,1.02968,1.02725,1.02467,1.02195,1.01908,1.01606,1.01289,1.00956,1.00607,1.00242,0.998611,0.994635,0.990495,0.986188,0.981716,0.977078,0.972275,0.967309,0.96218,0.956891,0.951445,0.945846,0.940099,0.934207,0.928178,0.922017,0.915731,0.90933,0.90282,0.896212,0.889516,0.882742,0.875902,0.869007,0.862069,0.855102,0.848118,0.841131,0.834154,0.827201,0.820285,0.813419,0.806617,0.799892,0.793256,0.786721,0.780298,0.773999,0.767833,0.761809,0.755936,0.750221,0.74467,0.739289,0.734082,0.729052,0.724203,0.719534,0.715046,0.71074,0.706612,0.702661,0.698883,0.695274,0.691829,0.688543,0.685409,0.68242,0.67957,0.67685,0.674251,0.671765,0.669383,0.667095,0.664891,0.66276,0.660693,0.658678,0.656703,0.654756,0.652826,0.6509,0.648964,0.647005,0.645008,0.642958,0.640839,0.638635,0.636327,0.633896,0.631323,0.628585,0.625661,0.622526,0.619153,0.615515,0.611581,0.60732,0.602696,0.597674,0.592214,0.586274,0.579811,0.572778,0.565125,0.556801,0.547754,0.53793,0.527273,0.51573,0.503247,0.489776,0.475271,0.459699,0.443034,0.42527,0.406421},
{1.01447,1.01497,1.01549,1.01603,1.01659,1.01717,1.01778,1.0184,1.01904,1.0197,1.02038,1.02108,1.0218,1.02254,1.0233,1.02407,1.02486,1.02567,1.02649,1.02733,1.02819,1.02906,1.02994,1.03083,1.03174,1.03265,1.03357,1.0345,1.03544,1.03638,1.03733,1.03828,1.03923,1.04018,1.04112,1.04206,1.043,1.04393,1.04484,1.04575,1.04664,1.04752,1.04837,1.04921,1.05002,1.05081,1.05157,1.05231,1.05301,1.05367,1.0543,1.05489,1.05543,1.05593,1.05639,1.05679,1.05714,1.05743,1.05766,1.05784,1.05795,1.05799,1.05796,1.05785,1.05768,1.05742,1.05708,1.05665,1.05614,1.05553,1.05483,1.05404,1.05314,1.05213,1.05102,1.0498,1.04846,1.04701,1.04544,1.04374,1.04191,1.03995,1.03786,1.03563,1.03326,1.03074,1.02808,1.02527,1.02231,1.01919,1.01591,1.01247,1.00887,1.0051,1.00117,0.997078,0.992815,0.988384,0.983786,0.979021,0.974092,0.968999,0.963745,0.958332,0.952766,0.947049,0.941188,0.935187,0.929054,0.922796,0.916419,0.909935,0.90335,0.896677,0.889925,0.883105,0.87623,0.869311,0.862362,0.855395,0.848424,0.841462,0.834523,0.827621,0.820768,0.813978,0.807264,0.800638,0.794113,0.7877,0.781408,0.77525,0.769233,0.763366,0.757656,0.75211,0.746733,0.741529,0.736502,0.731654,0.726987,0.7225,0.718193,0.714064,0.710111,0.70633,0.702718,0.699269,0.695978,0.692838,0.689842,0.686984,0.684254,0.681645,0.679148,0.676753,0.67445,0.67223,0.670082,0.667995,0.665959,0.66396,0.661988,0.66003,0.658072,0.656102,0.654106,0.652068,0.649974,0.647806,0.645548,0.643182,0.640688,0.638046,0.635234,0.632228,0.629004,0.625535,0.621791,0.617744,0.613359,0.608601,0.603434,0.597818,0.591709,0.585063,0.577833,0.569969,0.56142,0.552131,0.542049,0.531118,0.519284,0.506494,0.4927,0.477859,0.461937,0.444912,0.426781,0.407563},
{1.01473,1.01524,1.01578,1.01633,1.01691,1.01751,1.01813,1.01877,1.01943,1.02011,1.02082,1.02155,1.02229,1.02306,1.02385,1.02465,1.02548,1.02632,1.02719,1.02807,1.02896,1.02987,1.0308,1.03174,1.0327,1.03367,1.03465,1.03563,1.03663,1.03764,1.03865,1.03966,1.04068,1.0417,1.04272,1.04374,1.04475,1.04576,1.04675,1.04774,1.04872,1.04968,1.05063,1.05156,1.05246,1.05335,1.05421,1.05503,1.05583,1.0566,1.05732,1.05801,1.05866,1.05926,1.05982,1.06033,1.06078,1.06118,1.06151,1.06179,1.062,1.06215,1.06222,1.06222,1.06214,1.06198,1.06174,1.06141,1.06099,1.06048,1.05988,1.05917,1.05836,1.05745,1.05642,1.05528,1.05403,1.05266,1.05116,1.04954,1.04779,1.0459,1.04388,1.04172,1.03942,1.03697,1.03437,1.03162,1.02872,1.02565,1.02243,1.01905,1.0155,1.01179,1.0079,1.00385,0.999637,0.995251,0.990695,0.985972,0.981082,0.976027,0.97081,0.965433,0.9599,0.954217,0.948387,0.942417,0.936313,0.930082,0.923733,0.917274,0.910714,0.904065,0.897335,0.890537,0.883682,0.876783,0.869853,0.862904,0.85595,0.849005,0.842081,0.835193,0.828354,0.821577,0.814875,0.80826,0.801746,0.795343,0.789061,0.782911,0.776903,0.771043,0.765341,0.759801,0.75443,0.749232,0.74421,0.739367,0.734704,0.730221,0.725917,0.721791,0.717841,0.714063,0.710453,0.707006,0.703716,0.700577,0.697582,0.694724,0.691995,0.689386,0.686888,0.684493,0.682189,0.679968,0.677819,0.67573,0.673691,0.671691,0.669716,0.667755,0.665795,0.663821,0.661822,0.65978,0.657682,0.65551,0.653248,0.650877,0.648379,0.645732,0.642914,0.639904,0.636674,0.6332,0.629451,0.625399,0.621009,0.616247,0.611076,0.605456,0.599344,0.592696,0.585464,0.577599,0.569049,0.559761,0.549679,0.538749,0.526916,0.514126,0.500331,0.485486,0.469556,0.452516,0.43436,0.415104},
{1.01499,1.01551,1.01606,1.01662,1.01721,1.01783,1.01846,1.01912,1.0198,1.02051,1.02124,1.02199,1.02276,1.02355,1.02437,1.02521,1.02607,1.02695,1.02785,1.02877,1.0297,1.03066,1.03163,1.03262,1.03363,1.03465,1.03568,1.03673,1.03778,1.03885,1.03992,1.041,1.04209,1.04318,1.04427,1.04537,1.04646,1.04754,1.04862,1.0497,1.05076,1.05181,1.05285,1.05387,1.05487,1.05585,1.0568,1.05773,1.05863,1.0595,1.06033,1.06112,1.06187,1.06258,1.06324,1.06386,1.06442,1.06492,1.06537,1.06575,1.06607,1.06632,1.0665,1.0666,1.06663,1.06658,1.06644,1.06621,1.0659,1.06549,1.06498,1.06437,1.06366,1.06284,1.0619,1.06086,1.05969,1.0584,1.05699,1.05545,1.05378,1.05197,1.05003,1.04794,1.04571,1.04333,1.0408,1.03812,1.03527,1.03227,1.02911,1.02578,1.02229,1.01863,1.0148,1.0108,1.00663,1.00229,0.99778,0.9931,0.988251,0.983236,0.978057,0.972717,0.96722,0.96157,0.955773,0.949834,0.94376,0.937557,0.931235,0.924802,0.918267,0.911641,0.904934,0.898157,0.891323,0.884443,0.877531,0.870599,0.863661,0.856731,0.849821,0.842946,0.83612,0.829354,0.822663,0.816059,0.809554,0.803159,0.796885,0.790742,0.78474,0.778886,0.773188,0.767653,0.762285,0.75709,0.752071,0.747229,0.742567,0.738084,0.73378,0.729654,0.725702,0.721921,0.718308,0.714857,0.711563,0.708419,0.705418,0.702553,0.699816,0.697198,0.694691,0.692284,0.689968,0.687734,0.685569,0.683464,0.681408,0.679387,0.677391,0.675406,0.67342,0.671419,0.669388,0.667313,0.665178,0.662966,0.660661,0.658243,0.655693,0.65299,0.650111,0.647035,0.643734,0.640181,0.636349,0.632205,0.627716,0.622848,0.617561,0.611817,0.605571,0.598779,0.591392,0.583362,0.574634,0.565156,0.554873,0.543729,0.531669,0.51864,0.504594,0.489486,0.473281,0.455958,0.437511,0.417958},
{1.01523,1.01577,1.01632,1.0169,1.0175,1.01813,1.01878,1.01946,1.02016,1.02089,1.02163,1.02241,1.0232,1.02403,1.02487,1.02574,1.02663,1.02754,1.02848,1.02944,1.03041,1.03141,1.03243,1.03347,1.03452,1.03559,1.03668,1.03778,1.03889,1.04002,1.04116,1.04231,1.04346,1.04462,1.04579,1.04695,1.04812,1.04929,1.05045,1.05161,1.05276,1.0539,1.05503,1.05614,1.05724,1.05832,1.05937,1.0604,1.0614,1.06237,1.0633,1.0642,1.06506,1.06588,1.06665,1.06738,1.06805,1.06866,1.06922,1.06972,1.07015,1.07051,1.0708,1.07102,1.07115,1.07121,1.07118,1.07106,1.07085,1.07055,1.07014,1.06964,1.06902,1.0683,1.06747,1.06652,1.06545,1.06425,1.06293,1.06148,1.05989,1.05817,1.0563,1.0543,1.05214,1.04984,1.04738,1.04476,1.04199,1.03905,1.03595,1.03269,1.02925,1.02565,1.02188,1.01793,1.01381,1.00952,1.00506,1.00042,0.99562,0.990647,0.985508,0.980207,0.974747,0.969133,0.96337,0.957463,0.95142,0.945248,0.938954,0.932548,0.926039,0.919437,0.912753,0.905999,0.899185,0.892325,0.885431,0.878517,0.871596,0.864681,0.857786,0.850925,0.844111,0.837358,0.830678,0.824084,0.817588,0.811202,0.804936,0.798801,0.792805,0.786957,0.781265,0.775735,0.770371,0.76518,0.760164,0.755325,0.750665,0.746184,0.741881,0.737755,0.733803,0.730023,0.726409,0.722956,0.71966,0.716514,0.71351,0.710642,0.707901,0.705279,0.702766,0.700354,0.698031,0.69579,0.693617,0.691504,0.689437,0.687406,0.685399,0.683401,0.681402,0.679385,0.677338,0.675246,0.673092,0.670859,0.668531,0.666089,0.663513,0.660782,0.657873,0.654763,0.651427,0.647837,0.643963,0.639775,0.63524,0.630321,0.624981,0.619178,0.612871,0.606013,0.598557,0.590452,0.581645,0.572083,0.561711,0.550473,0.538313,0.525179,0.51102,0.495794,0.479464,0.462007,0.443418,0.423713},
{1.01547,1.01601,1.01658,1.01717,1.01778,1.01842,1.01909,1.01978,1.0205,1.02124,1.02201,1.02281,1.02363,1.02448,1.02535,1.02625,1.02717,1.02811,1.02908,1.03008,1.03109,1.03213,1.0332,1.03428,1.03538,1.0365,1.03764,1.0388,1.03997,1.04116,1.04236,1.04357,1.04479,1.04602,1.04726,1.0485,1.04975,1.05099,1.05224,1.05348,1.05472,1.05595,1.05717,1.05838,1.05957,1.06074,1.0619,1.06303,1.06413,1.06521,1.06625,1.06726,1.06823,1.06916,1.07004,1.07088,1.07167,1.0724,1.07307,1.07368,1.07423,1.07471,1.07511,1.07545,1.0757,1.07587,1.07595,1.07595,1.07585,1.07566,1.07536,1.07496,1.07446,1.07384,1.07311,1.07226,1.07129,1.07019,1.06897,1.06761,1.06611,1.06448,1.0627,1.06078,1.0587,1.05648,1.0541,1.05156,1.04886,1.04599,1.04296,1.03976,1.03639,1.03285,1.02913,1.02524,1.02118,1.01694,1.01253,1.00794,1.00318,0.998255,0.99316,0.9879,0.982479,0.976902,0.971175,0.965303,0.959292,0.953151,0.946887,0.940509,0.934026,0.92745,0.92079,0.914058,0.907266,0.900426,0.893551,0.886655,0.879751,0.872852,0.865972,0.859124,0.852323,0.845582,0.838913,0.83233,0.825843,0.819466,0.813208,0.80708,0.801091,0.795249,0.789563,0.784037,0.778678,0.773491,0.768478,0.763642,0.758984,0.754505,0.750203,0.746079,0.742128,0.738347,0.734733,0.73128,0.727983,0.724836,0.72183,0.71896,0.716216,0.713591,0.711075,0.708659,0.706332,0.704086,0.701908,0.699789,0.697716,0.695678,0.693662,0.691657,0.689648,0.687622,0.685564,0.68346,0.681294,0.679049,0.676706,0.674249,0.671656,0.668908,0.665981,0.662851,0.659494,0.655881,0.651984,0.647771,0.643208,0.638261,0.632891,0.627057,0.620717,0.613824,0.606331,0.598187,0.58934,0.579736,0.569319,0.558034,0.545824,0.532637,0.518422,0.503134,0.486738,0.469207,0.450536,0.430736},
{1.0157,1.01625,1.01682,1.01742,1.01805,1.0187,1.01938,1.02009,1.02082,1.02159,1.02238,1.02319,1.02404,1.02491,1.0258,1.02673,1.02768,1.02866,1.02966,1.03069,1.03175,1.03283,1.03393,1.03506,1.0362,1.03737,1.03857,1.03978,1.04101,1.04225,1.04351,1.04479,1.04608,1.04738,1.04869,1.05,1.05133,1.05265,1.05398,1.05531,1.05664,1.05796,1.05927,1.06057,1.06186,1.06313,1.06439,1.06562,1.06683,1.06802,1.06917,1.07029,1.07137,1.07242,1.07341,1.07437,1.07527,1.07612,1.07691,1.07764,1.07831,1.07891,1.07943,1.07989,1.08026,1.08055,1.08075,1.08087,1.08089,1.08081,1.08063,1.08034,1.07995,1.07944,1.07882,1.07808,1.07721,1.07622,1.07509,1.07383,1.07243,1.07089,1.06921,1.06737,1.06539,1.06325,1.06095,1.05849,1.05586,1.05307,1.05011,1.04698,1.04368,1.0402,1.03655,1.03272,1.02872,1.02453,1.02018,1.01564,1.01093,1.00605,1.001,0.995783,0.990403,0.984866,0.979176,0.973339,0.967363,0.961253,0.95502,0.948671,0.942216,0.935665,0.929029,0.92232,0.91555,0.90873,0.901875,0.894996,0.888108,0.881225,0.874359,0.867525,0.860736,0.854006,0.847347,0.840773,0.834295,0.827926,0.821675,0.815553,0.809569,0.803732,0.798049,0.792527,0.78717,0.781985,0.776973,0.772138,0.76748,0.763,0.758698,0.754572,0.750618,0.746835,0.743217,0.73976,0.736458,0.733305,0.730293,0.727416,0.724664,0.72203,0.719504,0.717077,0.714738,0.712478,0.710286,0.708151,0.706061,0.704004,0.701968,0.699941,0.697908,0.695855,0.693769,0.691634,0.689433,0.687151,0.684769,0.682268,0.679628,0.676828,0.673846,0.670656,0.667234,0.663551,0.659578,0.655283,0.650632,0.64559,0.640117,0.634173,0.627714,0.620694,0.613065,0.604776,0.595774,0.586005,0.575412,0.563941,0.551534,0.53814,0.523706,0.50819,0.491556,0.473778,0.45485,0.434788},
{1.01592,1.01648,1.01706,1.01767,1.0183,1.01897,1.01966,1.02038,1.02114,1.02191,1.02272,1.02356,1.02442,1.02532,1.02624,1.02719,1.02817,1.02918,1.03022,1.03128,1.03237,1.03349,1.03463,1.0358,1.037,1.03822,1.03946,1.04072,1.04201,1.04331,1.04463,1.04597,1.04733,1.04869,1.05008,1.05147,1.05287,1.05427,1.05568,1.0571,1.05851,1.05992,1.06133,1.06272,1.06411,1.06548,1.06684,1.06818,1.0695,1.07079,1.07206,1.07329,1.07449,1.07564,1.07676,1.07783,1.07886,1.07983,1.08074,1.0816,1.08239,1.08311,1.08376,1.08434,1.08484,1.08525,1.08558,1.08581,1.08596,1.086,1.08594,1.08578,1.0855,1.08511,1.0846,1.08397,1.08322,1.08233,1.08131,1.08016,1.07886,1.07742,1.07584,1.0741,1.0722,1.07015,1.06794,1.06557,1.06303,1.06032,1.05743,1.05438,1.05115,1.04774,1.04416,1.04039,1.03645,1.03232,1.02802,1.02354,1.01889,1.01406,1.00905,1.00388,0.998546,0.993051,0.987401,0.981602,0.975661,0.969586,0.963385,0.957067,0.950641,0.944118,0.937508,0.930824,0.924076,0.917278,0.910443,0.903583,0.896713,0.889846,0.882996,0.876176,0.869401,0.862683,0.856036,0.849472,0.843004,0.836643,0.8304,0.824286,0.818309,0.812478,0.806801,0.801283,0.795932,0.79075,0.785742,0.78091,0.776255,0.771778,0.767478,0.763354,0.759402,0.75562,0.752004,0.748548,0.745247,0.742094,0.739083,0.736205,0.733454,0.73082,0.728294,0.725867,0.723528,0.721268,0.719076,0.71694,0.71485,0.712793,0.710757,0.708729,0.706696,0.704644,0.702558,0.700423,0.698224,0.695943,0.693563,0.691064,0.688427,0.685631,0.682653,0.679469,0.676053,0.672378,0.668414,0.66413,0.659491,0.654464,0.649008,0.643083,0.636645,0.62965,0.622049,0.61379,0.604822,0.595091,0.584539,0.573111,0.560751,0.547405,0.533022,0.517555,0.500967,0.48323,0.464335,0.44429},
{1.01613,1.0167,1.01729,1.0179,1.01855,1.01923,1.01993,1.02067,1.02143,1.02223,1.02305,1.02391,1.02479,1.02571,1.02665,1.02763,1.02864,1.02968,1.03074,1.03184,1.03297,1.03412,1.03531,1.03652,1.03776,1.03902,1.04032,1.04163,1.04297,1.04433,1.04571,1.04711,1.04853,1.04997,1.05142,1.05289,1.05436,1.05585,1.05734,1.05884,1.06034,1.06184,1.06334,1.06483,1.06632,1.06779,1.06925,1.0707,1.07213,1.07353,1.0749,1.07625,1.07757,1.07884,1.08008,1.08127,1.08242,1.08352,1.08456,1.08554,1.08645,1.0873,1.08808,1.08879,1.08942,1.08996,1.09042,1.09078,1.09105,1.09122,1.09129,1.09125,1.09109,1.09083,1.09044,1.08993,1.08929,1.08852,1.08761,1.08657,1.08538,1.08405,1.08256,1.08093,1.07913,1.07718,1.07506,1.07277,1.07032,1.06769,1.06489,1.06192,1.05876,1.05543,1.05192,1.04822,1.04434,1.04028,1.03604,1.03162,1.02702,1.02224,1.01729,1.01217,1.00688,1.00143,0.995818,0.990059,0.984156,0.978116,0.971949,0.965662,0.959266,0.952771,0.946188,0.939528,0.932803,0.926027,0.919212,0.912371,0.905518,0.898667,0.891832,0.885025,0.878262,0.871556,0.864919,0.858364,0.851905,0.845551,0.839315,0.833206,0.827234,0.821407,0.815733,0.810219,0.804869,0.799689,0.794682,0.78985,0.785194,0.780716,0.776414,0.772287,0.768333,0.764547,0.760927,0.757466,0.754159,0.751,0.747982,0.745097,0.742337,0.739694,0.737157,0.734719,0.732368,0.730095,0.727888,0.725736,0.723629,0.721553,0.719496,0.717446,0.715388,0.713309,0.711195,0.709029,0.706796,0.704478,0.702058,0.699516,0.696833,0.693986,0.690954,0.68771,0.684231,0.680487,0.676448,0.672084,0.667359,0.662238,0.656683,0.65065,0.644098,0.63698,0.629247,0.620848,0.61173,0.601839,0.591118,0.579511,0.566962,0.553416,0.538823,0.523136,0.506318,0.488344,0.469201,0.448902},
{1.01634,1.01691,1.01751,1.01813,1.01879,1.01947,1.02019,1.02094,1.02172,1.02253,1.02337,1.02424,1.02515,1.02608,1.02705,1.02805,1.02909,1.03015,1.03125,1.03238,1.03354,1.03473,1.03596,1.03721,1.03849,1.0398,1.04114,1.04251,1.0439,1.04532,1.04676,1.04822,1.0497,1.05121,1.05273,1.05427,1.05582,1.05738,1.05896,1.06054,1.06213,1.06372,1.06531,1.0669,1.06848,1.07006,1.07163,1.07318,1.07471,1.07623,1.07772,1.07918,1.08061,1.08201,1.08337,1.08469,1.08596,1.08718,1.08835,1.08946,1.09051,1.09149,1.09241,1.09324,1.094,1.09468,1.09527,1.09577,1.09617,1.09647,1.09667,1.09676,1.09674,1.0966,1.09634,1.09595,1.09543,1.09478,1.094,1.09307,1.092,1.09078,1.0894,1.08787,1.08618,1.08433,1.08231,1.08012,1.07776,1.07522,1.07251,1.06962,1.06655,1.06329,1.05985,1.05623,1.05242,1.04843,1.04426,1.0399,1.03535,1.03063,1.02574,1.02067,1.01542,1.01002,1.00446,0.998739,0.992876,0.986874,0.980743,0.97449,0.968126,0.96166,0.955105,0.948472,0.941772,0.935018,0.928225,0.921404,0.91457,0.907736,0.900916,0.894124,0.887375,0.88068,0.874054,0.86751,0.86106,0.854714,0.848486,0.842383,0.836417,0.830596,0.824926,0.819416,0.81407,0.808892,0.803887,0.799057,0.794403,0.789926,0.785624,0.781498,0.777543,0.773757,0.770135,0.766673,0.763365,0.760204,0.757184,0.754296,0.751533,0.748887,0.746347,0.743904,0.741549,0.739271,0.737059,0.734902,0.732788,0.730706,0.728643,0.726585,0.72452,0.722433,0.720309,0.718134,0.715891,0.713562,0.711131,0.708577,0.705881,0.703022,0.699975,0.696717,0.693222,0.689462,0.685407,0.681026,0.676284,0.671144,0.66557,0.659518,0.652946,0.645807,0.638054,0.629634,0.620495,0.610581,0.599838,0.588208,0.575635,0.562064,0.547443,0.531726,0.514873,0.496857,0.477664,0.457302},
{1.01654,1.01712,1.01772,1.01835,1.01902,1.01971,1.02044,1.0212,1.02199,1.02281,1.02367,1.02456,1.02548,1.02644,1.02743,1.02846,1.02951,1.03061,1.03173,1.03289,1.03409,1.03532,1.03658,1.03787,1.03919,1.04055,1.04193,1.04335,1.04479,1.04627,1.04776,1.04929,1.05084,1.05241,1.054,1.05561,1.05723,1.05887,1.06053,1.0622,1.06387,1.06555,1.06724,1.06892,1.0706,1.07228,1.07395,1.07561,1.07726,1.07888,1.08049,1.08207,1.08362,1.08514,1.08663,1.08807,1.08947,1.09083,1.09213,1.09337,1.09455,1.09567,1.09672,1.09769,1.09859,1.0994,1.10013,1.10077,1.10131,1.10175,1.10208,1.10231,1.10242,1.10241,1.10228,1.10203,1.10164,1.10112,1.10046,1.09965,1.0987,1.0976,1.09634,1.09492,1.09334,1.09159,1.08968,1.08759,1.08533,1.08289,1.08027,1.07747,1.07449,1.07131,1.06796,1.06441,1.06068,1.05676,1.05265,1.04836,1.04388,1.03922,1.03438,1.02936,1.02417,1.01882,1.0133,1.00763,1.00181,0.995848,0.989753,0.983536,0.977205,0.970771,0.964245,0.957639,0.950965,0.944236,0.937464,0.930664,0.923848,0.917032,0.910228,0.903452,0.896715,0.890033,0.883419,0.876885,0.870443,0.864106,0.857884,0.851788,0.845828,0.840011,0.834346,0.828838,0.823495,0.81832,0.813316,0.808487,0.803834,0.799356,0.795055,0.790927,0.786971,0.783183,0.779559,0.776095,0.772783,0.769619,0.766595,0.763703,0.760935,0.758283,0.755738,0.753289,0.750927,0.748642,0.746422,0.744256,0.742133,0.740041,0.737966,0.735897,0.733819,0.731719,0.729581,0.72739,0.72513,0.722784,0.720333,0.717759,0.715041,0.712158,0.709087,0.705802,0.702279,0.698488,0.694401,0.689986,0.685207,0.68003,0.674415,0.66832,0.661703,0.654517,0.646714,0.638241,0.629047,0.619077,0.608273,0.596579,0.583939,0.570298,0.555602,0.539806,0.522867,0.504759,0.485467,0.464994},
{1.01674,1.01732,1.01792,1.01856,1.01923,1.01994,1.02067,1.02144,1.02225,1.02308,1.02396,1.02486,1.0258,1.02678,1.02779,1.02884,1.02992,1.03104,1.0322,1.03339,1.03461,1.03587,1.03717,1.0385,1.03987,1.04127,1.0427,1.04416,1.04566,1.04718,1.04874,1.05032,1.05193,1.05356,1.05522,1.0569,1.0586,1.06032,1.06206,1.06381,1.06557,1.06734,1.06912,1.0709,1.07268,1.07446,1.07624,1.078,1.07976,1.0815,1.08322,1.08492,1.0866,1.08824,1.08985,1.09143,1.09296,1.09444,1.09588,1.09726,1.09858,1.09983,1.10102,1.10214,1.10317,1.10413,1.105,1.10578,1.10646,1.10704,1.10752,1.10788,1.10814,1.10827,1.10828,1.10816,1.10791,1.10752,1.10699,1.10631,1.10549,1.10451,1.10337,1.10207,1.10061,1.09898,1.09717,1.09519,1.09304,1.0907,1.08818,1.08547,1.08258,1.0795,1.07623,1.07276,1.06911,1.06527,1.06123,1.05701,1.0526,1.048,1.04322,1.03827,1.03313,1.02783,1.02236,1.01674,1.01096,1.00504,0.99899,0.992811,0.986515,0.980115,0.97362,0.967043,0.960396,0.953691,0.946943,0.940165,0.933369,0.926571,0.919785,0.913024,0.906302,0.899632,0.89303,0.886506,0.880074,0.873745,0.867531,0.861442,0.855487,0.849676,0.844015,0.838511,0.833171,0.827998,0.822997,0.818169,0.813517,0.80904,0.804738,0.800611,0.796654,0.792865,0.78924,0.785774,0.782461,0.779295,0.776268,0.773374,0.770603,0.767948,0.765399,0.762946,0.76058,0.75829,0.756065,0.753894,0.751766,0.749667,0.747587,0.745511,0.743426,0.741318,0.739172,0.736973,0.734704,0.732349,0.729888,0.727304,0.724576,0.721681,0.718598,0.715302,0.711767,0.707964,0.703864,0.699435,0.694644,0.689453,0.683824,0.677717,0.671087,0.663888,0.656072,0.647587,0.638381,0.628399,0.617584,0.60588,0.593229,0.579575,0.564867,0.549055,0.532098,0.513966,0.494641,0.474124},
{1.01693,1.01751,1.01812,1.01877,1.01945,1.02016,1.0209,1.02168,1.0225,1.02335,1.02423,1.02515,1.02611,1.02711,1.02814,1.02921,1.03031,1.03146,1.03264,1.03386,1.03511,1.03641,1.03774,1.03911,1.04051,1.04195,1.04343,1.04494,1.04649,1.04806,1.04967,1.05131,1.05299,1.05468,1.05641,1.05816,1.05994,1.06173,1.06355,1.06538,1.06723,1.06909,1.07096,1.07283,1.07471,1.0766,1.07848,1.08035,1.08222,1.08408,1.08591,1.08773,1.08953,1.0913,1.09304,1.09474,1.09641,1.09803,1.0996,1.10112,1.10258,1.10398,1.10531,1.10657,1.10775,1.10885,1.10987,1.11079,1.11162,1.11235,1.11297,1.11349,1.11388,1.11416,1.11431,1.11433,1.11422,1.11397,1.11358,1.11304,1.11235,1.1115,1.11049,1.10932,1.10798,1.10646,1.10478,1.10291,1.10087,1.09864,1.09622,1.09362,1.09082,1.08783,1.08465,1.08128,1.07771,1.07395,1.06999,1.06584,1.0615,1.05698,1.05226,1.04737,1.04229,1.03705,1.03163,1.02606,1.02033,1.01446,1.00844,1.0023,0.996046,0.989681,0.983218,0.976672,0.970053,0.963375,0.956651,0.949895,0.943121,0.936342,0.929572,0.922827,0.916119,0.909463,0.902872,0.896359,0.889936,0.883616,0.877409,0.871326,0.865376,0.859569,0.853912,0.848411,0.843073,0.837902,0.832901,0.828074,0.823421,0.818944,0.814641,0.810511,0.806552,0.802761,0.799133,0.795663,0.792346,0.789175,0.786143,0.783242,0.780466,0.777804,0.775247,0.772786,0.770412,0.768112,0.765877,0.763695,0.761555,0.759444,0.75735,0.755259,0.753158,0.751033,0.748869,0.74665,0.74436,0.741982,0.739497,0.736887,0.73413,0.731206,0.728091,0.72476,0.721188,0.717346,0.713204,0.708731,0.703892,0.69865,0.692968,0.686803,0.680113,0.67285,0.664967,0.656411,0.64713,0.637069,0.626171,0.614379,0.601636,0.587886,0.573076,0.557157,0.540086,0.521833,0.502378,0.481723},
{1.01712,1.0177,1.01832,1.01897,1.01965,1.02037,1.02112,1.02191,1.02274,1.0236,1.0245,1.02543,1.02641,1.02742,1.02847,1.02956,1.03069,1.03185,1.03306,1.03431,1.03559,1.03692,1.03828,1.03969,1.04113,1.04261,1.04413,1.04569,1.04728,1.04891,1.05058,1.05228,1.05401,1.05577,1.05756,1.05938,1.06123,1.0631,1.06499,1.06691,1.06884,1.07079,1.07275,1.07472,1.0767,1.07869,1.08067,1.08266,1.08464,1.08661,1.08856,1.0905,1.09243,1.09432,1.09619,1.09803,1.09982,1.10158,1.10329,1.10495,1.10655,1.1081,1.10957,1.11098,1.11231,1.11357,1.11473,1.11581,1.11679,1.11767,1.11844,1.11911,1.11966,1.12008,1.12038,1.12056,1.12059,1.12049,1.12024,1.11984,1.11928,1.11857,1.1177,1.11666,1.11545,1.11406,1.1125,1.11075,1.10882,1.10671,1.1044,1.10191,1.09921,1.09633,1.09324,1.08996,1.08648,1.08281,1.07893,1.07487,1.0706,1.06615,1.0615,1.05667,1.05166,1.04648,1.04112,1.0356,1.02992,1.02409,1.01813,1.01203,1.00581,0.999482,0.993055,0.986541,0.979952,0.973302,0.966604,0.959872,0.953119,0.94636,0.939609,0.932881,0.926188,0.919546,0.912967,0.906465,0.900052,0.89374,0.887541,0.881464,0.875521,0.869718,0.864065,0.858567,0.853232,0.848062,0.843063,0.838236,0.833584,0.829106,0.824802,0.820671,0.816711,0.812917,0.809286,0.805813,0.802493,0.799318,0.796282,0.793377,0.790595,0.787927,0.785365,0.782898,0.780516,0.778209,0.775966,0.773776,0.771626,0.769505,0.7674,0.765298,0.763185,0.761047,0.758869,0.756635,0.754329,0.751934,0.749431,0.746802,0.744025,0.741079,0.737941,0.734586,0.730988,0.727118,0.722948,0.718444,0.713573,0.708298,0.702581,0.69638,0.689651,0.682348,0.674422,0.665823,0.656497,0.646389,0.635442,0.623598,0.610802,0.596996,0.582126,0.566144,0.549005,0.530677,0.511141,0.490393},
{1.0173,1.01789,1.01851,1.01916,1.01985,1.02057,1.02133,1.02213,1.02297,1.02384,1.02475,1.0257,1.02669,1.02771,1.02878,1.02989,1.03104,1.03223,1.03346,1.03474,1.03605,1.03741,1.0388,1.04024,1.04172,1.04325,1.04481,1.04641,1.04805,1.04973,1.05145,1.0532,1.05499,1.05681,1.05867,1.06056,1.06248,1.06442,1.0664,1.06839,1.07041,1.07245,1.0745,1.07657,1.07864,1.08073,1.08282,1.08491,1.08701,1.08909,1.09117,1.09323,1.09528,1.0973,1.0993,1.10127,1.1032,1.1051,1.10695,1.10875,1.1105,1.11219,1.11382,1.11538,1.11686,1.11827,1.11959,1.12082,1.12196,1.12299,1.12393,1.12475,1.12545,1.12603,1.12649,1.12681,1.127,1.12705,1.12695,1.1267,1.12629,1.12572,1.12499,1.12408,1.12301,1.12176,1.12032,1.1187,1.1169,1.1149,1.11271,1.11033,1.10775,1.10497,1.10199,1.09881,1.09542,1.09184,1.08805,1.08407,1.07988,1.07551,1.07093,1.06618,1.06123,1.05611,1.05081,1.04535,1.03972,1.03395,1.02803,1.02198,1.0158,1.00951,1.00312,0.996638,0.990081,0.983461,0.97679,0.970082,0.963352,0.956614,0.949882,0.943171,0.936494,0.929865,0.923299,0.916808,0.910404,0.904101,0.897909,0.891839,0.8859,0.880102,0.874452,0.868956,0.863622,0.858454,0.853454,0.848627,0.843973,0.839493,0.835187,0.831053,0.827088,0.82329,0.819654,0.816175,0.812848,0.809666,0.806623,0.80371,0.800919,0.798241,0.795668,0.793189,0.790795,0.788475,0.786217,0.784011,0.781844,0.779705,0.777581,0.775457,0.773321,0.771158,0.768953,0.766691,0.764354,0.761925,0.759386,0.756718,0.753899,0.750908,0.747721,0.744314,0.74066,0.736731,0.732496,0.727923,0.722978,0.717624,0.711823,0.705531,0.698706,0.691301,0.683267,0.674552,0.665104,0.654866,0.643782,0.631794,0.618846,0.60488,0.589842,0.573683,0.55636,0.53784,0.518102,0.497143},
{1.01748,1.01807,1.01869,1.01935,1.02004,1.02077,1.02154,1.02234,1.02319,1.02407,1.02499,1.02595,1.02696,1.028,1.02908,1.03021,1.03138,1.03259,1.03385,1.03515,1.03649,1.03787,1.0393,1.04078,1.04229,1.04385,1.04545,1.0471,1.04879,1.05052,1.05228,1.05409,1.05594,1.05782,1.05975,1.0617,1.06369,1.06571,1.06776,1.06983,1.07193,1.07406,1.0762,1.07836,1.08054,1.08273,1.08493,1.08713,1.08933,1.09153,1.09373,1.09591,1.09808,1.10024,1.10237,1.10447,1.10654,1.10858,1.11057,1.11252,1.11442,1.11626,1.11804,1.11975,1.1214,1.12296,1.12444,1.12583,1.12713,1.12832,1.12942,1.1304,1.13126,1.13201,1.13262,1.13311,1.13345,1.13366,1.13371,1.13361,1.13336,1.13294,1.13235,1.1316,1.13066,1.12955,1.12825,1.12677,1.12509,1.12322,1.12116,1.1189,1.11643,1.11376,1.11089,1.10781,1.10453,1.10104,1.09735,1.09346,1.08936,1.08506,1.08057,1.07589,1.07101,1.06596,1.06072,1.05532,1.04975,1.04403,1.03816,1.03216,1.02603,1.01978,1.01343,1.00698,1.00046,0.993871,0.987229,0.980548,0.973843,0.967127,0.960416,0.953723,0.947063,0.940449,0.933896,0.927417,0.921024,0.91473,0.908546,0.902483,0.89655,0.890756,0.88511,0.879618,0.874286,0.869119,0.86412,0.859293,0.854639,0.850158,0.84585,0.841713,0.837746,0.833944,0.830305,0.826822,0.82349,0.820303,0.817254,0.814334,0.811536,0.808852,0.806271,0.803783,0.80138,0.79905,0.796781,0.794564,0.792385,0.790232,0.788094,0.785955,0.783803,0.781622,0.779399,0.777116,0.774758,0.772306,0.769743,0.767048,0.764201,0.76118,0.757962,0.75452,0.75083,0.746862,0.742586,0.73797,0.732979,0.727576,0.721723,0.715377,0.708495,0.701029,0.692931,0.68415,0.674631,0.664319,0.653158,0.641089,0.628056,0.614,0.598869,0.582611,0.565184,0.546552,0.526695,0.505606},
{1.01765,1.01824,1.01887,1.01953,1.02023,1.02096,1.02173,1.02255,1.0234,1.02429,1.02522,1.0262,1.02721,1.02827,1.02937,1.03051,1.0317,1.03294,1.03421,1.03554,1.03691,1.03832,1.03978,1.04128,1.04284,1.04443,1.04607,1.04776,1.04949,1.05127,1.05309,1.05495,1.05686,1.0588,1.06078,1.0628,1.06486,1.06695,1.06908,1.07123,1.07342,1.07563,1.07786,1.08012,1.08239,1.08468,1.08698,1.08929,1.09161,1.09392,1.09624,1.09855,1.10084,1.10313,1.10539,1.10763,1.10984,1.11202,1.11416,1.11626,1.11831,1.1203,1.12224,1.12411,1.12591,1.12763,1.12927,1.13083,1.13229,1.13365,1.13491,1.13606,1.13709,1.138,1.13878,1.13943,1.13994,1.14031,1.14052,1.14059,1.14049,1.14023,1.13979,1.13919,1.1384,1.13744,1.13628,1.13494,1.1334,1.13166,1.12973,1.12759,1.12525,1.1227,1.11994,1.11697,1.1138,1.11041,1.10682,1.10302,1.09902,1.09481,1.0904,1.08579,1.08099,1.07601,1.07085,1.06551,1.06,1.05434,1.04852,1.04257,1.03648,1.03028,1.02397,1.01756,1.01108,1.00452,0.997909,0.991257,0.984577,0.977885,0.971194,0.964521,0.957878,0.95128,0.944741,0.938274,0.931892,0.925607,0.919431,0.913374,0.907447,0.901658,0.896015,0.890525,0.885194,0.880028,0.875029,0.870201,0.865544,0.861061,0.85675,0.852609,0.848637,0.844831,0.841185,0.837696,0.834357,0.831162,0.828104,0.825175,0.822367,0.819671,0.817078,0.814577,0.81216,0.809814,0.80753,0.805294,0.803097,0.800924,0.798762,0.7966,0.794422,0.792214,0.78996,0.787645,0.785252,0.782763,0.780159,0.777421,0.774528,0.771456,0.768184,0.764684,0.760932,0.756897,0.752549,0.747856,0.742783,0.737292,0.731345,0.724899,0.717909,0.71033,0.702111,0.693201,0.683546,0.67309,0.661777,0.649548,0.636346,0.622113,0.606795,0.590342,0.572711,0.553867,0.533787,0.512467},
{1.01782,1.01841,1.01904,1.0197,1.02041,1.02115,1.02192,1.02274,1.0236,1.0245,1.02544,1.02643,1.02746,1.02853,1.02964,1.03081,1.03201,1.03326,1.03456,1.03591,1.0373,1.03874,1.04023,1.04177,1.04336,1.04499,1.04667,1.0484,1.05017,1.052,1.05386,1.05578,1.05774,1.05974,1.06178,1.06387,1.06599,1.06816,1.07036,1.07259,1.07486,1.07715,1.07948,1.08183,1.0842,1.08659,1.08899,1.09141,1.09384,1.09627,1.09871,1.10114,1.10356,1.10598,1.10837,1.11075,1.1131,1.11543,1.11771,1.11996,1.12216,1.12431,1.1264,1.12843,1.13039,1.13228,1.13409,1.13581,1.13744,1.13897,1.1404,1.14172,1.14292,1.14401,1.14496,1.14578,1.14646,1.147,1.14738,1.14761,1.14768,1.14758,1.14731,1.14686,1.14623,1.14542,1.14441,1.14322,1.14182,1.14022,1.13843,1.13642,1.13421,1.13178,1.12915,1.1263,1.12324,1.11996,1.11647,1.11277,1.10886,1.10475,1.10043,1.09591,1.09119,1.08628,1.08119,1.07592,1.07048,1.06488,1.05912,1.05322,1.04719,1.04103,1.03476,1.0284,1.02195,1.01543,1.00885,1.00223,0.995577,0.98891,0.982243,0.97559,0.968967,0.962386,0.955862,0.949408,0.943038,0.936764,0.930597,0.924548,0.918627,0.912843,0.907205,0.901718,0.89639,0.891225,0.886227,0.881399,0.876742,0.872257,0.867944,0.863801,0.859826,0.856016,0.852367,0.848873,0.845528,0.842328,0.839263,0.836327,0.833512,0.830808,0.828206,0.825697,0.823269,0.820913,0.818617,0.816369,0.814158,0.811971,0.809795,0.807616,0.805421,0.803194,0.80092,0.798584,0.796168,0.793655,0.791025,0.788259,0.785335,0.782232,0.778926,0.775391,0.7716,0.767525,0.763134,0.758395,0.753274,0.747732,0.74173,0.735227,0.728178,0.720535,0.71225,0.70327,0.693542,0.68301,0.671617,0.659304,0.646014,0.631689,0.616275,0.599721,0.581982,0.563024,0.542822,0.52137},
{1.01799,1.01858,1.01921,1.01988,1.02058,1.02132,1.02211,1.02293,1.0238,1.02471,1.02566,1.02665,1.02769,1.02878,1.02991,1.03108,1.03231,1.03358,1.0349,1.03627,1.03768,1.03915,1.04067,1.04223,1.04385,1.04552,1.04724,1.04901,1.05082,1.05269,1.05461,1.05657,1.05859,1.06064,1.06275,1.0649,1.06709,1.06932,1.0716,1.07391,1.07626,1.07864,1.08105,1.08349,1.08596,1.08845,1.09096,1.09348,1.09602,1.09857,1.10112,1.10368,1.10623,1.10878,1.11131,1.11382,1.11632,1.11879,1.12122,1.12362,1.12597,1.12828,1.13053,1.13273,1.13485,1.13691,1.13889,1.14078,1.14258,1.14429,1.14589,1.14739,1.14876,1.15002,1.15115,1.15215,1.153,1.15372,1.15427,1.15468,1.15491,1.15498,1.15488,1.1546,1.15413,1.15348,1.15263,1.15159,1.15034,1.14889,1.14724,1.14537,1.1433,1.141,1.1385,1.13577,1.13283,1.12967,1.12629,1.1227,1.11889,1.11487,1.11065,1.10622,1.10158,1.09676,1.09174,1.08654,1.08117,1.07563,1.06994,1.0641,1.05812,1.05201,1.04579,1.03947,1.03306,1.02658,1.02004,1.01345,1.00682,1.00018,0.993541,0.98691,0.980306,0.973742,0.967234,0.960794,0.954437,0.948173,0.942014,0.935973,0.930058,0.924279,0.918644,0.91316,0.907834,0.902669,0.897671,0.892841,0.888182,0.883694,0.879377,0.87523,0.871249,0.867433,0.863776,0.860275,0.856922,0.853712,0.850637,0.84769,0.844863,0.842146,0.83953,0.837005,0.834561,0.832187,0.829872,0.827604,0.82537,0.823159,0.820957,0.81875,0.816525,0.814266,0.811957,0.809583,0.807127,0.804569,0.801892,0.799075,0.796097,0.792936,0.789566,0.785963,0.782099,0.777945,0.77347,0.768641,0.763422,0.757777,0.751665,0.745044,0.737869,0.730092,0.721664,0.712533,0.702645,0.691943,0.68037,0.667868,0.654378,0.639844,0.624211,0.607427,0.589449,0.570241,0.549781,0.528061},
{1.01816,1.01875,1.01938,1.02004,1.02075,1.0215,1.02228,1.02311,1.02399,1.0249,1.02586,1.02686,1.02791,1.02901,1.03015,1.03135,1.03259,1.03388,1.03521,1.0366,1.03805,1.03954,1.04108,1.04268,1.04433,1.04603,1.04778,1.04959,1.05145,1.05336,1.05532,1.05734,1.0594,1.06152,1.06368,1.06589,1.06815,1.07045,1.0728,1.07519,1.07761,1.08008,1.08258,1.08511,1.08767,1.09026,1.09287,1.09551,1.09816,1.10082,1.1035,1.10617,1.10885,1.11153,1.1142,1.11685,1.11949,1.1221,1.12469,1.12724,1.12975,1.13222,1.13463,1.13699,1.13929,1.14151,1.14366,1.14573,1.14771,1.14959,1.15138,1.15305,1.15461,1.15605,1.15736,1.15854,1.15958,1.16047,1.16121,1.16179,1.1622,1.16245,1.16252,1.16241,1.16211,1.16163,1.16094,1.16006,1.15897,1.15768,1.15618,1.15446,1.15252,1.15037,1.148,1.1454,1.14259,1.13955,1.13629,1.13281,1.12911,1.1252,1.12107,1.11673,1.11219,1.10745,1.10252,1.0974,1.0921,1.08663,1.08101,1.07522,1.0693,1.06325,1.05708,1.05081,1.04445,1.038,1.0315,1.02494,1.01835,1.01174,1.00512,0.998515,0.991933,0.985389,0.978899,0.972475,0.966131,0.959879,0.953731,0.947699,0.941792,0.936019,0.93039,0.92491,0.919586,0.914424,0.909427,0.904598,0.899939,0.89545,0.891131,0.886981,0.882998,0.879178,0.875518,0.872011,0.868653,0.865438,0.862357,0.859403,0.856568,0.853844,0.851219,0.848685,0.846231,0.843847,0.84152,0.83924,0.836994,0.834769,0.832552,0.830329,0.828087,0.82581,0.823482,0.821087,0.818609,0.816028,0.813327,0.810483,0.807477,0.804286,0.800884,0.797248,0.793348,0.789157,0.784642,0.779771,0.774509,0.768817,0.762657,0.755984,0.748756,0.740923,0.732437,0.723245,0.713293,0.702524,0.690882,0.678308,0.664744,0.650132,0.634416,0.617546,0.599476,0.58017,0.559603,0.537767},
{1.01832,1.01891,1.01954,1.02021,1.02091,1.02166,1.02245,1.02329,1.02417,1.02509,1.02606,1.02707,1.02813,1.02924,1.03039,1.0316,1.03285,1.03416,1.03552,1.03693,1.03839,1.03991,1.04148,1.0431,1.04478,1.04651,1.0483,1.05015,1.05204,1.054,1.05601,1.05807,1.06019,1.06235,1.06458,1.06685,1.06917,1.07154,1.07396,1.07642,1.07893,1.08147,1.08406,1.08668,1.08934,1.09203,1.09474,1.09748,1.10025,1.10302,1.10582,1.10862,1.11143,1.11423,1.11704,1.11983,1.12261,1.12537,1.12811,1.13082,1.13349,1.13611,1.13869,1.14122,1.14369,1.14608,1.14841,1.15066,1.15281,1.15488,1.15685,1.1587,1.16045,1.16208,1.16357,1.16494,1.16616,1.16724,1.16817,1.16893,1.16953,1.16996,1.17021,1.17028,1.17016,1.16985,1.16933,1.16862,1.1677,1.16656,1.16522,1.16365,1.16187,1.15986,1.15763,1.15517,1.15249,1.14958,1.14644,1.14308,1.1395,1.1357,1.13167,1.12744,1.12299,1.11835,1.1135,1.10846,1.10324,1.09785,1.09229,1.08657,1.08071,1.07472,1.0686,1.06238,1.05606,1.04966,1.0432,1.03668,1.03012,1.02354,1.01695,1.01037,1.00381,0.997282,0.990809,0.984401,0.978071,0.971831,0.965693,0.959669,0.953769,0.948001,0.942376,0.936898,0.931576,0.926414,0.921416,0.916585,0.911922,0.907429,0.903106,0.89895,0.89496,0.891132,0.887463,0.883946,0.880578,0.87735,0.874256,0.871288,0.868438,0.865696,0.863054,0.8605,0.858025,0.855618,0.853267,0.85096,0.848685,0.846429,0.844178,0.84192,0.839638,0.837319,0.834945,0.832502,0.82997,0.827332,0.824569,0.821659,0.818581,0.815312,0.811827,0.808101,0.804105,0.79981,0.795184,0.790193,0.784802,0.778973,0.772665,0.765835,0.758438,0.750426,0.741748,0.732353,0.722184,0.711187,0.699303,0.686473,0.672639,0.657744,0.641732,0.624552,0.606161,0.586521,0.565611,0.543422},
{1.01848,1.01907,1.0197,1.02036,1.02107,1.02183,1.02262,1.02346,1.02434,1.02527,1.02624,1.02726,1.02833,1.02945,1.03062,1.03184,1.03311,1.03443,1.03581,1.03723,1.03872,1.04026,1.04185,1.0435,1.04521,1.04698,1.0488,1.05068,1.05262,1.05461,1.05666,1.05877,1.06094,1.06316,1.06544,1.06777,1.07015,1.07259,1.07508,1.07762,1.0802,1.08283,1.0855,1.08821,1.09096,1.09375,1.09657,1.09941,1.10228,1.10518,1.10809,1.11102,1.11395,1.11689,1.11983,1.12276,1.12569,1.1286,1.13149,1.13435,1.13718,1.13997,1.14272,1.14541,1.14805,1.15063,1.15313,1.15556,1.1579,1.16015,1.1623,1.16435,1.16629,1.1681,1.16979,1.17135,1.17277,1.17404,1.17516,1.17611,1.1769,1.17752,1.17796,1.17821,1.17828,1.17814,1.17781,1.17727,1.17652,1.17556,1.17438,1.17297,1.17134,1.16949,1.16741,1.1651,1.16255,1.15978,1.15677,1.15354,1.15008,1.14639,1.14248,1.13835,1.13401,1.12946,1.12471,1.11976,1.11462,1.1093,1.10382,1.09817,1.09238,1.08645,1.08039,1.07422,1.06795,1.0616,1.05517,1.04869,1.04217,1.03562,1.02907,1.02251,1.01598,1.00947,1.00302,0.996631,0.990317,0.98409,0.977965,0.971951,0.966059,0.960299,0.954679,0.949206,0.943887,0.938727,0.93373,0.928899,0.924235,0.919741,0.915414,0.911255,0.907261,0.903428,0.899752,0.89623,0.892853,0.889618,0.886515,0.883537,0.880676,0.877923,0.875269,0.872702,0.870212,0.86779,0.865422,0.863097,0.860803,0.858526,0.856253,0.853971,0.851664,0.849317,0.846914,0.844439,0.841874,0.839199,0.836397,0.833445,0.830323,0.827006,0.823471,0.81969,0.815635,0.811278,0.806586,0.801525,0.796059,0.79015,0.783757,0.776838,0.769346,0.761233,0.752449,0.742942,0.732655,0.721534,0.709519,0.696552,0.682575,0.667529,0.65136,0.634016,0.615452,0.595631,0.574531,0.552143},
{1.01864,1.01922,1.01985,1.02052,1.02123,1.02198,1.02278,1.02362,1.02451,1.02544,1.02642,1.02745,1.02853,1.02966,1.03083,1.03206,1.03335,1.03469,1.03608,1.03753,1.03903,1.04059,1.04221,1.04389,1.04562,1.04742,1.04927,1.05119,1.05316,1.0552,1.05729,1.05945,1.06166,1.06393,1.06627,1.06866,1.0711,1.0736,1.07616,1.07877,1.08143,1.08414,1.0869,1.0897,1.09254,1.09542,1.09834,1.10129,1.10427,1.10728,1.11031,1.11336,1.11642,1.11949,1.12257,1.12565,1.12871,1.13177,1.13482,1.13783,1.14083,1.14378,1.1467,1.14957,1.15238,1.15513,1.15782,1.16043,1.16296,1.1654,1.16774,1.16998,1.17211,1.17413,1.17601,1.17777,1.17938,1.18085,1.18217,1.18332,1.18431,1.18512,1.18575,1.1862,1.18645,1.18651,1.18636,1.186,1.18543,1.18464,1.18364,1.1824,1.18094,1.17925,1.17732,1.17516,1.17276,1.17013,1.16727,1.16417,1.16083,1.15727,1.15348,1.14946,1.14523,1.14078,1.13612,1.13127,1.12622,1.12099,1.11558,1.11001,1.10428,1.09842,1.09242,1.08631,1.08009,1.07379,1.06741,1.06097,1.05449,1.04797,1.04145,1.03492,1.02841,1.02194,1.0155,1.00913,1.00283,0.996623,0.990509,0.984506,0.978623,0.97287,0.967255,0.961787,0.95647,0.951312,0.946315,0.941482,0.936817,0.932319,0.927988,0.923824,0.919823,0.915983,0.9123,0.908767,0.905381,0.902134,0.899019,0.896028,0.893153,0.890384,0.887712,0.885126,0.882617,0.880173,0.877781,0.875431,0.87311,0.870804,0.8685,0.866183,0.86384,0.861453,0.859008,0.856487,0.853873,0.851145,0.848286,0.845273,0.842084,0.838697,0.835085,0.831222,0.82708,0.822628,0.817835,0.812666,0.807084,0.801052,0.794527,0.787467,0.779825,0.771553,0.762599,0.752912,0.742436,0.731113,0.718886,0.705696,0.691483,0.676191,0.659763,0.642149,0.623305,0.603194,0.581792,0.559092},
{1.01879,1.01938,1.02,1.02067,1.02138,1.02214,1.02293,1.02378,1.02467,1.02561,1.02659,1.02763,1.02871,1.02985,1.03104,1.03228,1.03358,1.03493,1.03634,1.0378,1.03933,1.04091,1.04255,1.04425,1.04601,1.04784,1.04972,1.05167,1.05368,1.05576,1.05789,1.06009,1.06235,1.06468,1.06706,1.06951,1.07202,1.07458,1.07721,1.07989,1.08262,1.08541,1.08825,1.09114,1.09407,1.09705,1.10007,1.10312,1.10622,1.10934,1.11249,1.11566,1.11885,1.12205,1.12526,1.12848,1.13169,1.1349,1.1381,1.14127,1.14443,1.14755,1.15064,1.15368,1.15667,1.1596,1.16247,1.16527,1.16799,1.17062,1.17316,1.1756,1.17793,1.18014,1.18223,1.18419,1.18601,1.18768,1.1892,1.19056,1.19175,1.19276,1.19359,1.19424,1.19469,1.19494,1.19498,1.19482,1.19443,1.19383,1.193,1.19194,1.19065,1.18913,1.18737,1.18537,1.18313,1.18065,1.17792,1.17496,1.17176,1.16833,1.16466,1.16077,1.15665,1.15231,1.14776,1.143,1.13805,1.1329,1.12758,1.12209,1.11644,1.11064,1.10471,1.09866,1.0925,1.08625,1.07992,1.07353,1.06709,1.06061,1.05412,1.04763,1.04115,1.03469,1.02829,1.02193,1.01565,1.00946,1.00336,0.997368,0.991495,0.98575,0.980142,0.974679,0.969366,0.96421,0.959214,0.954382,0.949715,0.945215,0.940882,0.936713,0.932707,0.928861,0.92517,0.92163,0.918235,0.914978,0.911852,0.908849,0.905961,0.903178,0.900491,0.897889,0.895362,0.892898,0.890486,0.888114,0.885769,0.883437,0.881105,0.878759,0.876383,0.873963,0.87148,0.86892,0.866262,0.863489,0.86058,0.857515,0.854269,0.850821,0.847144,0.843212,0.838995,0.834464,0.829585,0.824326,0.818647,0.812512,0.805877,0.7987,0.790935,0.782531,0.773439,0.763605,0.752974,0.741488,0.729089,0.715718,0.701316,0.685825,0.669189,0.651358,0.632287,0.61194,0.590293,0.567338},
{1.01894,1.01953,1.02015,1.02082,1.02153,1.02228,1.02308,1.02393,1.02482,1.02576,1.02676,1.0278,1.02889,1.03004,1.03123,1.03249,1.0338,1.03516,1.03658,1.03807,1.03961,1.04121,1.04287,1.0446,1.04638,1.04824,1.05015,1.05213,1.05418,1.05629,1.05847,1.06071,1.06302,1.06539,1.06783,1.07033,1.07289,1.07552,1.07821,1.08096,1.08377,1.08664,1.08956,1.09253,1.09556,1.09863,1.10175,1.10491,1.10811,1.11134,1.11461,1.1179,1.12122,1.12455,1.1279,1.13126,1.13462,1.13797,1.14132,1.14466,1.14798,1.15127,1.15453,1.15774,1.16092,1.16403,1.16709,1.17008,1.17299,1.17582,1.17856,1.1812,1.18373,1.18615,1.18844,1.19061,1.19263,1.19451,1.19624,1.19781,1.19921,1.20043,1.20147,1.20232,1.20297,1.20343,1.20367,1.2037,1.20351,1.2031,1.20246,1.20159,1.20048,1.19913,1.19754,1.1957,1.19362,1.1913,1.18873,1.18592,1.18286,1.17956,1.17603,1.17226,1.16826,1.16404,1.1596,1.15494,1.15009,1.14504,1.13981,1.1344,1.12883,1.1231,1.11724,1.11126,1.10516,1.09896,1.09268,1.08634,1.07994,1.07351,1.06705,1.06059,1.05414,1.04772,1.04133,1.035,1.02874,1.02256,1.01648,1.0105,1.00463,0.998897,0.993295,0.987836,0.982526,0.97737,0.972374,0.96754,0.96287,0.958365,0.954025,0.949849,0.945835,0.941979,0.938277,0.934724,0.931315,0.928043,0.9249,0.921879,0.91897,0.916166,0.913455,0.910827,0.908272,0.905779,0.903335,0.900927,0.898544,0.896172,0.893796,0.891402,0.888974,0.886498,0.883956,0.88133,0.878603,0.875755,0.872764,0.869611,0.866272,0.862722,0.858935,0.854885,0.850542,0.845874,0.84085,0.835433,0.829587,0.823272,0.816445,0.809062,0.801077,0.792439,0.783098,0.772999,0.762086,0.750302,0.737589,0.723886,0.709135,0.693278,0.67626,0.658031,0.638547,0.617772,0.595687,0.572284},
{1.0191,1.01967,1.0203,1.02096,1.02167,1.02243,1.02323,1.02408,1.02497,1.02592,1.02691,1.02796,1.02906,1.03021,1.03142,1.03268,1.034,1.03538,1.03682,1.03831,1.03987,1.04149,1.04318,1.04492,1.04674,1.04862,1.05056,1.05257,1.05465,1.0568,1.05901,1.0613,1.06365,1.06607,1.06856,1.07111,1.07374,1.07643,1.07918,1.082,1.08488,1.08782,1.09083,1.09388,1.097,1.10016,1.10338,1.10664,1.10995,1.1133,1.11668,1.12009,1.12354,1.127,1.13049,1.13398,1.13749,1.141,1.14451,1.148,1.15148,1.15494,1.15838,1.16177,1.16512,1.16843,1.17167,1.17485,1.17796,1.18099,1.18393,1.18678,1.18952,1.19214,1.19465,1.19703,1.19927,1.20136,1.20331,1.20509,1.2067,1.20814,1.20939,1.21046,1.21133,1.21199,1.21244,1.21268,1.21269,1.21248,1.21203,1.21135,1.21043,1.20927,1.20786,1.2062,1.20429,1.20213,1.19972,1.19707,1.19416,1.19101,1.18761,1.18398,1.18011,1.17601,1.17168,1.16714,1.16239,1.15745,1.15231,1.14699,1.1415,1.13586,1.13008,1.12416,1.11813,1.11199,1.10577,1.09948,1.09313,1.08674,1.08033,1.07391,1.06749,1.0611,1.05474,1.04844,1.0422,1.03604,1.02998,1.02401,1.01816,1.01244,1.00685,1.0014,0.996096,0.990947,0.985956,0.981126,0.976459,0.971956,0.967618,0.963442,0.959427,0.95557,0.951867,0.948312,0.9449,0.941625,0.938478,0.935453,0.93254,0.92973,0.927014,0.92438,0.921819,0.919319,0.916867,0.914452,0.912061,0.90968,0.907295,0.904892,0.902455,0.899969,0.897416,0.89478,0.892041,0.889181,0.88618,0.883014,0.879662,0.8761,0.872301,0.868239,0.863883,0.859204,0.854168,0.84874,0.842884,0.836559,0.829723,0.822333,0.814342,0.8057,0.796356,0.786256,0.775345,0.763565,0.750857,0.737162,0.72242,0.706574,0.689567,0.671348,0.651872,0.631102,0.609012,0.585594},
{1.01924,1.01982,1.02044,1.0211,1.02181,1.02257,1.02337,1.02422,1.02511,1.02606,1.02706,1.02811,1.02922,1.03038,1.03159,1.03287,1.0342,1.03559,1.03704,1.03855,1.04012,1.04176,1.04347,1.04523,1.04707,1.04897,1.05095,1.05299,1.0551,1.05728,1.05954,1.06186,1.06425,1.06672,1.06926,1.07187,1.07455,1.0773,1.08011,1.083,1.08595,1.08897,1.09205,1.09519,1.09839,1.10165,1.10497,1.10833,1.11174,1.1152,1.1187,1.12223,1.1258,1.1294,1.13302,1.13666,1.14031,1.14397,1.14763,1.15129,1.15494,1.15857,1.16217,1.16575,1.16928,1.17277,1.17621,1.17959,1.18289,1.18613,1.18927,1.19232,1.19527,1.19811,1.20084,1.20343,1.20589,1.20821,1.21037,1.21237,1.21421,1.21587,1.21734,1.21863,1.21971,1.22059,1.22126,1.2217,1.22193,1.22192,1.22168,1.2212,1.22047,1.2195,1.21828,1.21681,1.21508,1.21309,1.21085,1.20836,1.20561,1.20261,1.19936,1.19587,1.19213,1.18816,1.18396,1.17954,1.1749,1.17006,1.16502,1.1598,1.1544,1.14884,1.14314,1.1373,1.13133,1.12526,1.1191,1.11287,1.10657,1.10023,1.09386,1.08747,1.08109,1.07473,1.06841,1.06213,1.05591,1.04977,1.04372,1.03778,1.03194,1.02623,1.02065,1.0152,1.00991,1.00476,0.999771,0.994941,0.990273,0.985768,0.981425,0.977244,0.973223,0.969358,0.965646,0.962081,0.958657,0.955368,0.952208,0.949166,0.946236,0.943407,0.94067,0.938015,0.935429,0.932903,0.930423,0.927978,0.925554,0.923138,0.920715,0.91827,0.915789,0.913255,0.910651,0.907959,0.905161,0.902238,0.899167,0.895928,0.892496,0.888849,0.884958,0.880798,0.876337,0.871545,0.866388,0.860831,0.854837,0.848365,0.841372,0.833815,0.825646,0.816815,0.807271,0.796959,0.785823,0.773806,0.760848,0.746889,0.731872,0.715736,0.698427,0.679893,0.660089,0.638979,0.616539,0.59276},
{1.01939,1.01996,1.02058,1.02124,1.02195,1.0227,1.0235,1.02435,1.02525,1.0262,1.02721,1.02826,1.02937,1.03054,1.03176,1.03304,1.03438,1.03578,1.03724,1.03877,1.04036,1.04202,1.04374,1.04553,1.04739,1.04931,1.05131,1.05338,1.05553,1.05774,1.06003,1.06239,1.06483,1.06734,1.06993,1.07259,1.07532,1.07813,1.08101,1.08396,1.08698,1.09007,1.09323,1.09646,1.09974,1.10309,1.1065,1.10997,1.11349,1.11705,1.12067,1.12432,1.12802,1.13174,1.1355,1.13928,1.14308,1.14689,1.1507,1.15452,1.15834,1.16214,1.16592,1.16967,1.17339,1.17707,1.18071,1.18428,1.18779,1.19123,1.19458,1.19784,1.20101,1.20407,1.20701,1.20983,1.21251,1.21505,1.21744,1.21967,1.22173,1.22362,1.22532,1.22683,1.22814,1.22925,1.23014,1.2308,1.23125,1.23146,1.23143,1.23115,1.23063,1.22986,1.22884,1.22755,1.22601,1.22421,1.22215,1.21982,1.21724,1.2144,1.21131,1.20796,1.20437,1.20053,1.19646,1.19217,1.18765,1.18292,1.17799,1.17287,1.16757,1.1621,1.15648,1.15072,1.14483,1.13883,1.13273,1.12656,1.12031,1.11402,1.1077,1.10136,1.09502,1.0887,1.0824,1.07615,1.06997,1.06385,1.05782,1.05189,1.04607,1.04037,1.0348,1.02937,1.02408,1.01894,1.01396,1.00913,1.00446,0.99996,0.995617,0.991435,0.987411,0.983542,0.979825,0.976253,0.972823,0.969527,0.966357,0.963306,0.960364,0.957524,0.954774,0.952104,0.949503,0.94696,0.944463,0.941998,0.939554,0.937115,0.934668,0.932199,0.92969,0.927127,0.924492,0.921767,0.918933,0.915971,0.91286,0.909578,0.9061,0.902404,0.898461,0.894245,0.889726,0.884872,0.879649,0.874023,0.867955,0.861405,0.854331,0.846687,0.838428,0.829502,0.819858,0.809441,0.798196,0.786065,0.772988,0.758905,0.743758,0.727486,0.710036,0.691354,0.671395,0.650122,0.627509,0.603547},
{1.01954,1.0201,1.02072,1.02138,1.02208,1.02283,1.02363,1.02448,1.02538,1.02634,1.02734,1.0284,1.02952,1.03069,1.03192,1.03321,1.03456,1.03597,1.03744,1.03898,1.04058,1.04225,1.04399,1.0458,1.04768,1.04964,1.05166,1.05376,1.05593,1.05818,1.0605,1.0629,1.06538,1.06794,1.07057,1.07328,1.07606,1.07893,1.08187,1.08488,1.08797,1.09114,1.09437,1.09768,1.10105,1.10449,1.10799,1.11156,1.11518,1.11885,1.12258,1.12636,1.13017,1.13403,1.13792,1.14184,1.14579,1.14975,1.15372,1.1577,1.16168,1.16565,1.16961,1.17355,1.17745,1.18133,1.18515,1.18893,1.19264,1.19628,1.19985,1.20333,1.20671,1.20999,1.21316,1.2162,1.21911,1.22189,1.22451,1.22697,1.22927,1.23139,1.23332,1.23507,1.23661,1.23794,1.23906,1.23996,1.24062,1.24106,1.24125,1.24119,1.24088,1.24032,1.2395,1.23841,1.23707,1.23546,1.23358,1.23143,1.22903,1.22635,1.22342,1.22023,1.21679,1.2131,1.20917,1.205,1.20061,1.196,1.19118,1.18617,1.18097,1.1756,1.17007,1.16439,1.15858,1.15266,1.14663,1.14051,1.13433,1.1281,1.12182,1.11553,1.10923,1.10294,1.09668,1.09046,1.0843,1.07821,1.07221,1.0663,1.06049,1.05481,1.04925,1.04382,1.03854,1.03341,1.02843,1.0236,1.01894,1.01443,1.01008,1.0059,1.00187,0.997989,0.994263,0.990681,0.987239,0.983929,0.980744,0.977677,0.974718,0.971857,0.969086,0.966392,0.963766,0.961196,0.958669,0.956172,0.953693,0.951217,0.948729,0.946216,0.943661,0.941047,0.938357,0.935574,0.932678,0.929648,0.926464,0.923104,0.919543,0.915757,0.911718,0.907399,0.902769,0.897797,0.892448,0.886687,0.880475,0.873771,0.866534,0.858717,0.850272,0.84115,0.831298,0.820662,0.809184,0.796808,0.783472,0.769118,0.753686,0.737116,0.719354,0.700348,0.680052,0.65843,0.635457,0.611124},
{1.01968,1.02024,1.02085,1.02151,1.02221,1.02296,1.02376,1.02461,1.02551,1.02647,1.02747,1.02854,1.02965,1.03083,1.03207,1.03336,1.03472,1.03614,1.03762,1.03917,1.04079,1.04248,1.04424,1.04606,1.04796,1.04994,1.05199,1.05411,1.05631,1.05859,1.06095,1.06339,1.0659,1.0685,1.07118,1.07393,1.07677,1.07969,1.08269,1.08577,1.08892,1.09216,1.09547,1.09885,1.10231,1.10584,1.10943,1.1131,1.11682,1.1206,1.12445,1.12834,1.13228,1.13627,1.14029,1.14435,1.14844,1.15255,1.15668,1.16082,1.16497,1.16911,1.17325,1.17737,1.18146,1.18553,1.18955,1.19353,1.19745,1.2013,1.20509,1.20878,1.21239,1.21589,1.21929,1.22256,1.22571,1.22872,1.23157,1.23428,1.23681,1.23917,1.24135,1.24333,1.24511,1.24669,1.24804,1.24917,1.25007,1.25074,1.25116,1.25132,1.25124,1.25089,1.25028,1.24941,1.24827,1.24685,1.24517,1.24321,1.24099,1.23849,1.23573,1.23271,1.22942,1.22588,1.2221,1.21807,1.21381,1.20933,1.20463,1.19974,1.19465,1.18938,1.18394,1.17835,1.17263,1.16678,1.16083,1.15479,1.14867,1.14249,1.13627,1.13003,1.12377,1.11753,1.11131,1.10512,1.09899,1.09293,1.08695,1.08106,1.07528,1.06961,1.06406,1.05865,1.05338,1.04825,1.04328,1.03846,1.0338,1.02929,1.02495,1.02076,1.01673,1.01285,1.00912,1.00553,1.00208,0.998763,0.995569,0.992491,0.98952,0.986647,0.983862,0.981154,0.978511,0.975923,0.973376,0.970859,0.968357,0.965857,0.963344,0.960803,0.958219,0.955573,0.95285,0.95003,0.947095,0.944024,0.940797,0.937389,0.933779,0.929939,0.925844,0.921466,0.916772,0.911733,0.906313,0.900477,0.894185,0.887398,0.880073,0.872163,0.863621,0.854397,0.844438,0.833689,0.822095,0.809595,0.796132,0.781645,0.766073,0.749359,0.731445,0.712281,0.691819,0.670023,0.646866,0.622338},
{1.01982,1.02038,1.02099,1.02164,1.02234,1.02309,1.02388,1.02473,1.02563,1.02659,1.0276,1.02866,1.02978,1.03096,1.03221,1.03351,1.03487,1.0363,1.0378,1.03936,1.04099,1.04269,1.04446,1.04631,1.04823,1.05022,1.05229,1.05444,1.05667,1.05898,1.06137,1.06384,1.0664,1.06903,1.07176,1.07456,1.07745,1.08042,1.08348,1.08662,1.08984,1.09314,1.09652,1.09999,1.10353,1.10714,1.11083,1.11459,1.11841,1.1223,1.12626,1.13027,1.13433,1.13844,1.1426,1.1468,1.15104,1.1553,1.15958,1.16389,1.1682,1.17252,1.17683,1.18114,1.18542,1.18968,1.1939,1.19808,1.20221,1.20628,1.21028,1.2142,1.21803,1.22176,1.22539,1.2289,1.23229,1.23553,1.23863,1.24158,1.24436,1.24697,1.24939,1.25162,1.25365,1.25547,1.25707,1.25844,1.25958,1.26049,1.26114,1.26154,1.26169,1.26157,1.26118,1.26052,1.25959,1.25839,1.25691,1.25515,1.25311,1.2508,1.24822,1.24537,1.24225,1.23887,1.23524,1.23136,1.22725,1.2229,1.21833,1.21355,1.20858,1.20342,1.19808,1.19259,1.18696,1.1812,1.17532,1.16935,1.1633,1.15719,1.15103,1.14484,1.13864,1.13244,1.12626,1.12011,1.11401,1.10798,1.10203,1.09616,1.0904,1.08475,1.07922,1.07383,1.06857,1.06345,1.05848,1.05367,1.04901,1.04451,1.04017,1.03598,1.03195,1.02806,1.02433,1.02074,1.01728,1.01396,1.01075,1.00767,1.00468,1.0018,0.999001,0.996279,0.993621,0.991015,0.98845,0.985913,0.98339,0.980867,0.978329,0.975762,0.973148,0.970473,0.967717,0.964863,0.961891,0.958781,0.955511,0.952059,0.948401,0.944511,0.940363,0.935928,0.931175,0.926072,0.920586,0.914679,0.908314,0.901449,0.894041,0.886045,0.877414,0.868095,0.858038,0.847187,0.835485,0.822874,0.809295,0.794687,0.778989,0.762144,0.744093,0.724786,0.704174,0.68222,0.658896,0.634189},
{1.01996,1.02052,1.02112,1.02176,1.02246,1.02321,1.024,1.02485,1.02575,1.02671,1.02772,1.02878,1.02991,1.03109,1.03234,1.03364,1.03502,1.03645,1.03796,1.03953,1.04117,1.04289,1.04467,1.04654,1.04847,1.05049,1.05258,1.05476,1.05701,1.05935,1.06177,1.06427,1.06687,1.06954,1.07231,1.07516,1.07809,1.08112,1.08423,1.08743,1.09071,1.09408,1.09754,1.10108,1.1047,1.1084,1.11217,1.11603,1.11995,1.12395,1.12801,1.13214,1.13633,1.14057,1.14486,1.1492,1.15357,1.15799,1.16243,1.16689,1.17137,1.17586,1.18036,1.18485,1.18932,1.19377,1.1982,1.20258,1.20692,1.21121,1.21543,1.21957,1.22363,1.2276,1.23146,1.23521,1.23884,1.24233,1.24568,1.24888,1.25191,1.25477,1.25744,1.25993,1.26221,1.26428,1.26613,1.26776,1.26915,1.2703,1.2712,1.27184,1.27222,1.27234,1.27218,1.27175,1.27105,1.27006,1.26879,1.26723,1.2654,1.26328,1.26089,1.25822,1.25528,1.25207,1.2486,1.24488,1.24091,1.2367,1.23227,1.22762,1.22277,1.21772,1.2125,1.20711,1.20157,1.1959,1.19011,1.18422,1.17824,1.1722,1.1661,1.15997,1.15382,1.14767,1.14153,1.13543,1.12937,1.12337,1.11745,1.11161,1.10587,1.10024,1.09473,1.08935,1.08411,1.079,1.07405,1.06924,1.06459,1.06009,1.05575,1.05156,1.04753,1.04365,1.03991,1.03631,1.03285,1.02952,1.02631,1.02321,1.02022,1.01733,1.01451,1.01178,1.00911,1.00648,1.0039,1.00135,0.998802,0.996257,0.993696,0.991103,0.988463,0.985759,0.982972,0.980085,0.977079,0.973932,0.970623,0.967129,0.963427,0.959491,0.955293,0.950805,0.945997,0.940836,0.935289,0.929317,0.922884,0.915949,0.908467,0.900394,0.891681,0.882278,0.872133,0.861191,0.849394,0.836685,0.823004,0.808289,0.792482,0.775522,0.757352,0.73792,0.717177,0.695084,0.671612,0.646747},
{1.0201,1.02065,1.02125,1.02189,1.02258,1.02332,1.02412,1.02496,1.02586,1.02682,1.02783,1.0289,1.03002,1.03121,1.03246,1.03377,1.03515,1.03659,1.03811,1.03969,1.04134,1.04307,1.04487,1.04675,1.0487,1.05074,1.05285,1.05505,1.05733,1.05969,1.06214,1.06468,1.06731,1.07002,1.07283,1.07572,1.0787,1.08178,1.08495,1.0882,1.09155,1.09499,1.09851,1.10212,1.10582,1.10961,1.11347,1.11742,1.12144,1.12554,1.12972,1.13396,1.13827,1.14263,1.14706,1.15153,1.15605,1.16061,1.16521,1.16984,1.17449,1.17915,1.18382,1.18849,1.19316,1.19781,1.20244,1.20703,1.21158,1.21608,1.22053,1.2249,1.22919,1.23339,1.2375,1.24149,1.24536,1.24911,1.25271,1.25616,1.25945,1.26256,1.2655,1.26824,1.27078,1.27312,1.27523,1.27711,1.27876,1.28016,1.28132,1.28221,1.28284,1.2832,1.28328,1.28309,1.28261,1.28185,1.2808,1.27946,1.27783,1.27592,1.27372,1.27124,1.26848,1.26545,1.26215,1.25859,1.25478,1.25072,1.24643,1.24192,1.23719,1.23227,1.22716,1.22188,1.21645,1.21087,1.20517,1.19936,1.19347,1.18749,1.18146,1.17539,1.1693,1.1632,1.15711,1.15105,1.14503,1.13907,1.13318,1.12737,1.12165,1.11605,1.11056,1.10519,1.09996,1.09487,1.08992,1.08512,1.08047,1.07598,1.07163,1.06745,1.06341,1.05952,1.05578,1.05217,1.0487,1.04536,1.04214,1.03903,1.03602,1.0331,1.03027,1.02751,1.02482,1.02217,1.01956,1.01697,1.01439,1.01181,1.00921,1.00658,1.00389,1.00114,0.998304,0.995361,0.992295,0.989084,0.985706,0.98214,0.978359,0.974339,0.970051,0.965468,0.960558,0.955289,0.949625,0.943531,0.936967,0.929893,0.922264,0.914035,0.905158,0.895581,0.885252,0.874115,0.862115,0.849191,0.835284,0.820334,0.80428,0.787061,0.768623,0.74891,0.727875,0.705478,0.681692,0.6565},
{1.02024,1.02078,1.02137,1.02201,1.0227,1.02344,1.02423,1.02507,1.02597,1.02692,1.02793,1.029,1.03013,1.03132,1.03257,1.03389,1.03528,1.03673,1.03825,1.03984,1.0415,1.04324,1.04505,1.04694,1.04892,1.05097,1.0531,1.05532,1.05762,1.06002,1.0625,1.06506,1.06772,1.07047,1.07332,1.07625,1.07928,1.08241,1.08563,1.08894,1.09235,1.09585,1.09944,1.10313,1.1069,1.11077,1.11472,1.11876,1.12288,1.12709,1.13137,1.13572,1.14015,1.14464,1.14919,1.15381,1.15847,1.16318,1.16793,1.17272,1.17754,1.18237,1.18723,1.19208,1.19694,1.20179,1.20662,1.21142,1.21619,1.22091,1.22558,1.23018,1.23471,1.23915,1.2435,1.24774,1.25186,1.25586,1.25972,1.26343,1.26698,1.27036,1.27356,1.27657,1.27938,1.28198,1.28436,1.28651,1.28842,1.29009,1.2915,1.29266,1.29354,1.29415,1.29449,1.29453,1.2943,1.29377,1.29295,1.29184,1.29043,1.28873,1.28674,1.28446,1.28189,1.27905,1.27593,1.27254,1.26889,1.26499,1.26085,1.25648,1.2519,1.2471,1.24212,1.23695,1.23163,1.22615,1.22055,1.21483,1.20902,1.20312,1.19717,1.19116,1.18513,1.17909,1.17306,1.16704,1.16107,1.15514,1.14929,1.14351,1.13782,1.13224,1.12677,1.12143,1.11621,1.11113,1.1062,1.10141,1.09677,1.09228,1.08794,1.08376,1.07972,1.07584,1.07209,1.06848,1.06501,1.06166,1.05843,1.05531,1.05229,1.04936,1.04652,1.04375,1.04104,1.03837,1.03574,1.03314,1.03054,1.02793,1.02531,1.02265,1.01993,1.01715,1.01428,1.0113,1.0082,1.00495,1.00153,0.997918,0.994091,0.990021,0.985681,0.981042,0.976073,0.970742,0.965014,0.958852,0.952216,0.945067,0.93736,0.929049,0.920086,0.910421,0.899999,0.888767,0.876666,0.863639,0.849625,0.834564,0.818394,0.801056,0.782492,0.762648,0.741476,0.718935,0.694994,0.669637},
{1.02038,1.02091,1.0215,1.02213,1.02281,1.02355,1.02434,1.02518,1.02607,1.02703,1.02804,1.02911,1.03023,1.03143,1.03268,1.034,1.03539,1.03685,1.03837,1.03997,1.04165,1.04339,1.04522,1.04713,1.04911,1.05118,1.05333,1.05557,1.0579,1.06032,1.06282,1.06542,1.06811,1.0709,1.07378,1.07676,1.07983,1.083,1.08627,1.08964,1.09311,1.09667,1.10033,1.10409,1.10794,1.11189,1.11592,1.12005,1.12427,1.12858,1.13296,1.13743,1.14197,1.14659,1.15127,1.15602,1.16083,1.16568,1.17059,1.17554,1.18052,1.18553,1.19056,1.19561,1.20066,1.2057,1.21074,1.21575,1.22073,1.22568,1.23057,1.23541,1.24017,1.24485,1.24945,1.25394,1.25832,1.26258,1.2667,1.27067,1.27449,1.27814,1.28161,1.2849,1.28798,1.29085,1.29351,1.29593,1.29811,1.30005,1.30173,1.30315,1.3043,1.30517,1.30576,1.30607,1.30608,1.30579,1.30521,1.30433,1.30315,1.30167,1.2999,1.29783,1.29546,1.29281,1.28988,1.28667,1.2832,1.27946,1.27548,1.27126,1.26682,1.26216,1.25731,1.25226,1.24705,1.24169,1.23619,1.23056,1.22484,1.21902,1.21314,1.20721,1.20124,1.19526,1.18928,1.18332,1.17738,1.1715,1.16568,1.15994,1.15428,1.14872,1.14328,1.13795,1.13275,1.12768,1.12276,1.11798,1.11334,1.10886,1.10452,1.10033,1.09629,1.0924,1.08864,1.08502,1.08153,1.07817,1.07492,1.07178,1.06874,1.06579,1.06292,1.06012,1.05737,1.05467,1.05201,1.04936,1.04671,1.04406,1.04138,1.03867,1.03589,1.03304,1.0301,1.02704,1.02386,1.02052,1.01701,1.01329,1.00935,1.00517,1.0007,0.995929,0.990817,0.985332,0.97944,0.973104,0.966282,0.958935,0.951017,0.942483,0.933282,0.923365,0.912677,0.901163,0.888766,0.875426,0.861082,0.845675,0.829142,0.811425,0.792465,0.77221,0.75061,0.727627,0.70323,0.677404},
{1.02051,1.02104,1.02162,1.02225,1.02293,1.02366,1.02444,1.02528,1.02617,1.02712,1.02813,1.0292,1.03033,1.03152,1.03278,1.03411,1.0355,1.03696,1.03849,1.0401,1.04178,1.04354,1.04538,1.04729,1.04929,1.05138,1.05355,1.05581,1.05816,1.0606,1.06313,1.06576,1.06848,1.0713,1.07422,1.07723,1.08035,1.08357,1.08689,1.09031,1.09383,1.09745,1.10118,1.10501,1.10893,1.11296,1.11708,1.1213,1.12561,1.13001,1.1345,1.13908,1.14374,1.14848,1.15329,1.15817,1.16312,1.16813,1.17319,1.17829,1.18344,1.18863,1.19384,1.19907,1.20431,1.20955,1.21479,1.22002,1.22522,1.23039,1.23551,1.24058,1.24559,1.25052,1.25536,1.26011,1.26475,1.26927,1.27365,1.2779,1.28199,1.28592,1.28967,1.29323,1.29659,1.29975,1.30268,1.30539,1.30785,1.31007,1.31203,1.31373,1.31515,1.31629,1.31715,1.31771,1.31798,1.31795,1.31762,1.31698,1.31604,1.31479,1.31324,1.31139,1.30924,1.30679,1.30406,1.30104,1.29775,1.29419,1.29038,1.28632,1.28203,1.27751,1.27279,1.26788,1.26279,1.25754,1.25215,1.24663,1.241,1.23527,1.22948,1.22362,1.21773,1.21181,1.20589,1.19998,1.1941,1.18826,1.18248,1.17678,1.17115,1.16563,1.16021,1.1549,1.14972,1.14467,1.13976,1.13499,1.13037,1.12589,1.12156,1.11738,1.11334,1.10944,1.10568,1.10206,1.09857,1.09519,1.09194,1.08879,1.08573,1.08277,1.07988,1.07706,1.0743,1.07158,1.06889,1.06621,1.06354,1.06086,1.05815,1.05539,1.05258,1.04969,1.04671,1.04361,1.04037,1.03698,1.03341,1.02964,1.02564,1.02138,1.01685,1.012,1.00681,1.00124,0.995255,0.988823,0.981902,0.97445,0.966422,0.957771,0.948449,0.938404,0.927582,0.915929,0.903385,0.889892,0.87539,0.859816,0.843111,0.825214,0.806067,0.785616,0.763812,0.740614,0.715993,0.689931},
{1.02065,1.02117,1.02174,1.02236,1.02304,1.02376,1.02454,1.02538,1.02627,1.02721,1.02822,1.02929,1.03042,1.03161,1.03287,1.0342,1.03559,1.03706,1.0386,1.04021,1.0419,1.04367,1.04552,1.04745,1.04946,1.05156,1.05375,1.05602,1.05839,1.06085,1.06341,1.06607,1.06882,1.07167,1.07462,1.07768,1.08083,1.0841,1.08746,1.09094,1.09451,1.0982,1.10199,1.10588,1.10988,1.11398,1.11818,1.12249,1.12689,1.13139,1.13599,1.14068,1.14545,1.15031,1.15525,1.16026,1.16535,1.1705,1.17571,1.18098,1.1863,1.19165,1.19704,1.20246,1.20789,1.21334,1.21878,1.22422,1.22964,1.23503,1.24039,1.24569,1.25094,1.25612,1.26122,1.26622,1.27112,1.27591,1.28057,1.28509,1.28946,1.29367,1.2977,1.30155,1.3052,1.30864,1.31186,1.31486,1.31761,1.32012,1.32236,1.32434,1.32605,1.32747,1.3286,1.32944,1.32998,1.33021,1.33013,1.32975,1.32906,1.32805,1.32673,1.32511,1.32318,1.32094,1.31842,1.3156,1.3125,1.30912,1.30548,1.30159,1.29746,1.2931,1.28853,1.28375,1.27879,1.27366,1.26838,1.26297,1.25744,1.25181,1.2461,1.24032,1.2345,1.22866,1.2228,1.21695,1.21112,1.20533,1.19959,1.19393,1.18834,1.18284,1.17745,1.17217,1.16701,1.16198,1.15708,1.15232,1.1477,1.14323,1.1389,1.13471,1.13067,1.12677,1.12301,1.11937,1.11587,1.11248,1.10921,1.10604,1.10296,1.09997,1.09706,1.09421,1.09141,1.08865,1.08592,1.0832,1.08049,1.07775,1.07499,1.07218,1.0693,1.06635,1.06329,1.06011,1.05679,1.05331,1.04964,1.04576,1.04165,1.03728,1.03261,1.02763,1.02229,1.01657,1.01042,1.00381,0.996704,0.989053,0.980813,0.971938,0.962379,0.952082,0.940995,0.929061,0.916222,0.902418,0.887589,0.871673,0.854609,0.836336,0.816798,0.79594,0.773714,0.75008,0.725007,0.698481},
{1.02078,1.0213,1.02186,1.02247,1.02314,1.02386,1.02464,1.02547,1.02636,1.0273,1.02831,1.02937,1.0305,1.0317,1.03296,1.03428,1.03568,1.03715,1.0387,1.04031,1.04201,1.04379,1.04564,1.04758,1.04961,1.05172,1.05393,1.05622,1.05861,1.06109,1.06367,1.06635,1.06913,1.07201,1.075,1.07809,1.08129,1.08459,1.08801,1.09153,1.09516,1.0989,1.10275,1.10671,1.11078,1.11496,1.11924,1.12363,1.12813,1.13272,1.13742,1.14221,1.1471,1.15208,1.15714,1.16229,1.16752,1.17281,1.17818,1.1836,1.18908,1.19461,1.20018,1.20578,1.21141,1.21706,1.22271,1.22836,1.234,1.23962,1.2452,1.25075,1.25624,1.26167,1.26703,1.27229,1.27746,1.28252,1.28746,1.29226,1.29691,1.3014,1.30573,1.30986,1.31381,1.31755,1.32107,1.32436,1.32741,1.33021,1.33275,1.33502,1.33702,1.33873,1.34015,1.34127,1.34208,1.34259,1.34278,1.34266,1.34223,1.34147,1.3404,1.33901,1.33731,1.3353,1.33299,1.33038,1.32748,1.3243,1.32085,1.31714,1.31318,1.30898,1.30456,1.29993,1.29511,1.29011,1.28495,1.27965,1.27423,1.2687,1.26308,1.2574,1.25166,1.24589,1.2401,1.23431,1.22854,1.22281,1.21712,1.21149,1.20595,1.20049,1.19512,1.18987,1.18474,1.17973,1.17485,1.1701,1.1655,1.16104,1.15671,1.15254,1.1485,1.1446,1.14083,1.1372,1.13368,1.13029,1.12701,1.12383,1.12074,1.11773,1.1148,1.11193,1.10912,1.10633,1.10358,1.10083,1.09809,1.09532,1.09252,1.08967,1.08676,1.08375,1.08065,1.07742,1.07405,1.07051,1.06678,1.06284,1.05866,1.05422,1.04947,1.04441,1.03898,1.03317,1.02692,1.02021,1.013,1.00523,0.996875,0.987875,0.978184,0.967751,0.95652,0.944436,0.93144,0.917473,0.902473,0.886379,0.869129,0.850664,0.830925,0.809858,0.787413,0.76355,0.738237,0.711459},
{1.02091,1.02142,1.02198,1.02258,1.02325,1.02396,1.02473,1.02556,1.02644,1.02738,1.02839,1.02945,1.03058,1.03177,1.03303,1.03436,1.03576,1.03723,1.03878,1.04041,1.04211,1.04389,1.04576,1.04771,1.04974,1.05187,1.05409,1.0564,1.0588,1.06131,1.06391,1.06661,1.06942,1.07233,1.07535,1.07848,1.08171,1.08506,1.08852,1.09209,1.09577,1.09957,1.10348,1.1075,1.11164,1.11589,1.12025,1.12472,1.12931,1.134,1.13879,1.14369,1.14869,1.15379,1.15898,1.16425,1.16962,1.17506,1.18057,1.18616,1.1918,1.1975,1.20325,1.20904,1.21486,1.2207,1.22656,1.23242,1.23829,1.24413,1.24995,1.25574,1.26148,1.26716,1.27278,1.27831,1.28375,1.28908,1.2943,1.29938,1.30432,1.30911,1.31373,1.31816,1.32241,1.32645,1.33027,1.33386,1.33722,1.34032,1.34317,1.34574,1.34804,1.35005,1.35176,1.35317,1.35427,1.35506,1.35554,1.35569,1.35552,1.35503,1.35421,1.35307,1.35161,1.34984,1.34776,1.34536,1.34268,1.3397,1.33644,1.33291,1.32913,1.3251,1.32084,1.31637,1.31169,1.30683,1.3018,1.29663,1.29132,1.2859,1.28038,1.27478,1.26913,1.26344,1.25773,1.25201,1.2463,1.24062,1.23499,1.22941,1.2239,1.21848,1.21315,1.20793,1.20282,1.19783,1.19297,1.18824,1.18365,1.1792,1.17488,1.17071,1.16667,1.16277,1.159,1.15536,1.15184,1.14844,1.14514,1.14194,1.13884,1.13581,1.13286,1.12996,1.12712,1.12431,1.12152,1.11874,1.11595,1.11314,1.11029,1.10739,1.10442,1.10136,1.09819,1.0949,1.09145,1.08784,1.08403,1.08,1.07572,1.07118,1.06633,1.06115,1.0556,1.04966,1.04328,1.03642,1.02905,1.02113,1.0126,1.00341,0.993532,0.982897,0.971454,0.959146,0.945916,0.931703,0.916446,0.900083,0.882552,0.863794,0.843749,0.822363,0.799587,0.77538,0.749711,0.722562},
{1.02104,1.02154,1.02209,1.02269,1.02335,1.02406,1.02482,1.02564,1.02652,1.02746,1.02846,1.02952,1.03065,1.03184,1.0331,1.03443,1.03583,1.03731,1.03886,1.04049,1.04219,1.04398,1.04586,1.04782,1.04986,1.052,1.05423,1.05656,1.05898,1.0615,1.06413,1.06685,1.06969,1.07263,1.07568,1.07883,1.08211,1.08549,1.08899,1.09261,1.09634,1.10019,1.10416,1.10825,1.11245,1.11677,1.12121,1.12577,1.13044,1.13522,1.14011,1.14512,1.15022,1.15544,1.16075,1.16615,1.17165,1.17723,1.1829,1.18864,1.19445,1.20032,1.20624,1.21222,1.21823,1.22427,1.23034,1.23642,1.2425,1.24858,1.25464,1.26067,1.26666,1.27259,1.27847,1.28427,1.28998,1.29559,1.30109,1.30647,1.3117,1.31679,1.3217,1.32644,1.331,1.33534,1.33948,1.34338,1.34705,1.35047,1.35362,1.35651,1.35911,1.36143,1.36344,1.36516,1.36656,1.36764,1.3684,1.36884,1.36895,1.36873,1.36818,1.3673,1.36609,1.36456,1.36272,1.36056,1.35809,1.35532,1.35227,1.34894,1.34535,1.3415,1.33741,1.33309,1.32857,1.32386,1.31897,1.31392,1.30874,1.30343,1.29802,1.29252,1.28696,1.28136,1.27572,1.27008,1.26444,1.25882,1.25324,1.24772,1.24226,1.23688,1.23159,1.2264,1.22132,1.21636,1.21152,1.20681,1.20223,1.19779,1.19349,1.18932,1.18529,1.18139,1.17762,1.17397,1.17045,1.16703,1.16373,1.16052,1.1574,1.15436,1.15138,1.14847,1.1456,1.14276,1.13994,1.13712,1.1343,1.13145,1.12857,1.12562,1.1226,1.11949,1.11627,1.11291,1.1094,1.10572,1.10184,1.09773,1.09337,1.08874,1.0838,1.07852,1.07287,1.06681,1.06032,1.05334,1.04584,1.03777,1.0291,1.01977,1.00972,0.998919,0.9873,0.974808,0.961384,0.946969,0.931501,0.914918,0.897158,0.87816,0.857866,0.836221,0.813174,0.788685,0.762721,0.735265},
{1.02117,1.02166,1.0222,1.0228,1.02345,1.02415,1.02491,1.02572,1.0266,1.02753,1.02853,1.02959,1.03071,1.0319,1.03316,1.03449,1.0359,1.03737,1.03892,1.04056,1.04227,1.04406,1.04594,1.04791,1.04997,1.05212,1.05436,1.0567,1.05914,1.06168,1.06432,1.06707,1.06993,1.07289,1.07597,1.07916,1.08247,1.08589,1.08943,1.09309,1.09687,1.10078,1.1048,1.10895,1.11322,1.11761,1.12212,1.12676,1.13151,1.13638,1.14137,1.14648,1.1517,1.15702,1.16245,1.16799,1.17362,1.17934,1.18516,1.19105,1.19702,1.20306,1.20917,1.21532,1.22153,1.22777,1.23405,1.24034,1.24665,1.25295,1.25925,1.26552,1.27176,1.27796,1.2841,1.29017,1.29616,1.30205,1.30784,1.31351,1.31904,1.32443,1.32965,1.3347,1.33957,1.34423,1.34868,1.3529,1.35689,1.36063,1.3641,1.36731,1.37023,1.37286,1.3752,1.37722,1.37893,1.38032,1.38138,1.38211,1.38251,1.38257,1.38229,1.38169,1.38074,1.37947,1.37787,1.37595,1.37371,1.37117,1.36833,1.36521,1.36181,1.35815,1.35424,1.3501,1.34574,1.34118,1.33644,1.33153,1.32647,1.32129,1.31599,1.3106,1.30514,1.29963,1.29408,1.28851,1.28295,1.2774,1.27188,1.26641,1.261,1.25566,1.25041,1.24526,1.24022,1.23528,1.23047,1.22578,1.22122,1.2168,1.2125,1.20834,1.20432,1.20042,1.19665,1.193,1.18947,1.18605,1.18274,1.17952,1.17638,1.17332,1.17033,1.16739,1.1645,1.16163,1.15878,1.15594,1.15308,1.15019,1.14726,1.14427,1.14121,1.13804,1.13476,1.13135,1.12777,1.12402,1.12007,1.11588,1.11144,1.10672,1.10168,1.09631,1.09055,1.08438,1.07777,1.07067,1.06304,1.05483,1.04601,1.03653,1.02632,1.01535,1.00356,0.99088,0.977264,0.962647,0.946969,0.930167,0.912179,0.892943,0.872401,0.850498,0.827182,0.802412,0.776155,0.748392},
{1.0213,1.02178,1.02232,1.0229,1.02354,1.02424,1.02499,1.0258,1.02667,1.0276,1.02859,1.02965,1.03077,1.03196,1.03322,1.03455,1.03595,1.03743,1.03898,1.04062,1.04233,1.04413,1.04602,1.04799,1.05006,1.05222,1.05447,1.05682,1.05928,1.06183,1.06449,1.06726,1.07014,1.07313,1.07624,1.07946,1.0828,1.08626,1.08984,1.09354,1.09737,1.10132,1.1054,1.10961,1.11394,1.1184,1.12298,1.1277,1.13253,1.1375,1.14258,1.14778,1.15311,1.15854,1.1641,1.16975,1.17552,1.18138,1.18734,1.19339,1.19952,1.20573,1.21201,1.21835,1.22475,1.2312,1.23768,1.24419,1.25071,1.25725,1.26378,1.2703,1.2768,1.28325,1.28966,1.296,1.30227,1.30846,1.31454,1.3205,1.32633,1.33203,1.33756,1.34293,1.34811,1.3531,1.35787,1.36242,1.36674,1.3708,1.37461,1.37814,1.38139,1.38435,1.38701,1.38935,1.39138,1.39308,1.39445,1.39549,1.39619,1.39654,1.39656,1.39623,1.39556,1.39455,1.39321,1.39154,1.38955,1.38724,1.38463,1.38172,1.37853,1.37507,1.37135,1.36739,1.36321,1.35881,1.35422,1.34946,1.34454,1.33948,1.33431,1.32903,1.32368,1.31826,1.31281,1.30732,1.30184,1.29636,1.29091,1.2855,1.28014,1.27486,1.26965,1.26454,1.25953,1.25463,1.24984,1.24518,1.24064,1.23623,1.23195,1.22781,1.22379,1.2199,1.21613,1.21248,1.20895,1.20553,1.2022,1.19897,1.19582,1.19275,1.18974,1.18678,1.18387,1.18097,1.1781,1.17522,1.17233,1.16941,1.16644,1.16341,1.16029,1.15708,1.15375,1.15028,1.14665,1.14283,1.1388,1.13455,1.13003,1.12523,1.12011,1.11464,1.10878,1.10252,1.09579,1.08858,1.08083,1.0725,1.06355,1.05393,1.04358,1.03246,1.0205,1.00766,0.993877,0.979083,0.96322,0.946224,0.928035,0.908591,0.887831,0.865701,0.842148,0.817131,0.790613,0.762576},
{1.02143,1.0219,1.02243,1.023,1.02364,1.02433,1.02507,1.02588,1.02674,1.02766,1.02865,1.0297,1.03082,1.03201,1.03327,1.03459,1.03599,1.03747,1.03903,1.04066,1.04238,1.04419,1.04608,1.04806,1.05013,1.0523,1.05456,1.05693,1.05939,1.06197,1.06464,1.06743,1.07033,1.07335,1.07648,1.07973,1.0831,1.0866,1.09021,1.09396,1.09783,1.10183,1.10596,1.11022,1.11462,1.11914,1.1238,1.12858,1.1335,1.13855,1.14373,1.14903,1.15445,1.16,1.16567,1.17145,1.17735,1.18335,1.18945,1.19565,1.20195,1.20832,1.21478,1.2213,1.22789,1.23453,1.24122,1.24795,1.2547,1.26147,1.26824,1.275,1.28175,1.28847,1.29515,1.30177,1.30832,1.31479,1.32116,1.32743,1.33357,1.33958,1.34543,1.35112,1.35663,1.36194,1.36704,1.37193,1.37658,1.38098,1.38512,1.38899,1.39258,1.39587,1.39886,1.40154,1.40389,1.40592,1.40761,1.40896,1.40997,1.41063,1.41094,1.41091,1.41052,1.40979,1.40872,1.40731,1.40557,1.40351,1.40114,1.39846,1.39548,1.39223,1.38871,1.38494,1.38093,1.37671,1.37228,1.36767,1.3629,1.35798,1.35293,1.34778,1.34254,1.33723,1.33187,1.32647,1.32107,1.31567,1.31028,1.30494,1.29964,1.29441,1.28925,1.28418,1.27921,1.27434,1.26958,1.26494,1.26043,1.25603,1.25177,1.24763,1.24362,1.23973,1.23596,1.23231,1.22877,1.22534,1.222,1.21876,1.21559,1.2125,1.20946,1.20647,1.20352,1.2006,1.19768,1.19476,1.19183,1.18885,1.18583,1.18274,1.17956,1.17628,1.17288,1.16933,1.16561,1.16171,1.15759,1.15323,1.1486,1.14368,1.13844,1.13284,1.12684,1.12043,1.11355,1.10617,1.09824,1.08973,1.08058,1.07075,1.06018,1.04883,1.03664,1.02355,1.00949,0.994421,0.978267,0.960967,0.94246,0.922684,0.901579,0.879089,0.855163,0.829757,0.802837,0.774381},
{1.02156,1.02202,1.02253,1.0231,1.02373,1.02441,1.02515,1.02595,1.0268,1.02772,1.02871,1.02975,1.03087,1.03205,1.03331,1.03463,1.03603,1.03751,1.03906,1.0407,1.04242,1.04423,1.04612,1.04811,1.05019,1.05237,1.05464,1.05701,1.05949,1.06208,1.06477,1.06758,1.0705,1.07354,1.07669,1.07997,1.08337,1.0869,1.09055,1.09434,1.09825,1.1023,1.10648,1.1108,1.11525,1.11984,1.12456,1.12942,1.13442,1.13955,1.14481,1.15021,1.15574,1.1614,1.16718,1.17308,1.17911,1.18524,1.19149,1.19784,1.20429,1.21084,1.21747,1.22417,1.23095,1.23779,1.24469,1.25163,1.2586,1.2656,1.27261,1.27963,1.28663,1.29361,1.30056,1.30746,1.3143,1.32106,1.32773,1.3343,1.34076,1.34708,1.35326,1.35927,1.36511,1.37076,1.3762,1.38142,1.38642,1.39116,1.39565,1.39987,1.4038,1.40744,1.41077,1.41378,1.41648,1.41884,1.42086,1.42254,1.42387,1.42485,1.42547,1.42574,1.42565,1.42521,1.42442,1.42329,1.42181,1.42001,1.41788,1.41544,1.41269,1.40966,1.40635,1.40278,1.39897,1.39493,1.39067,1.38623,1.38161,1.37683,1.37192,1.3669,1.36177,1.35658,1.35132,1.34602,1.34071,1.33539,1.33008,1.32481,1.31958,1.3144,1.3093,1.30428,1.29934,1.29451,1.28979,1.28518,1.28069,1.27632,1.27207,1.26795,1.26395,1.26006,1.2563,1.25265,1.24911,1.24568,1.24233,1.23908,1.2359,1.23279,1.22973,1.22673,1.22375,1.2208,1.21786,1.2149,1.21193,1.20892,1.20585,1.20272,1.19949,1.19616,1.1927,1.18908,1.1853,1.18133,1.17713,1.17269,1.16799,1.16298,1.15764,1.15194,1.14584,1.13931,1.13232,1.12481,1.11676,1.10811,1.09882,1.08884,1.07812,1.0666,1.05424,1.04097,1.02673,1.01146,0.995106,0.977597,0.958872,0.938869,0.917527,0.894791,0.870607,0.844932,0.817729,0.788977},
{1.02168,1.02213,1.02264,1.0232,1.02382,1.02449,1.02522,1.02601,1.02686,1.02778,1.02875,1.0298,1.03091,1.03209,1.03334,1.03466,1.03606,1.03754,1.03909,1.04073,1.04245,1.04426,1.04616,1.04815,1.05023,1.05242,1.0547,1.05708,1.05957,1.06217,1.06488,1.0677,1.07064,1.0737,1.07688,1.08018,1.08361,1.08717,1.09086,1.09468,1.09864,1.10273,1.10696,1.11133,1.11583,1.12048,1.12527,1.13021,1.13528,1.14049,1.14584,1.15134,1.15696,1.16273,1.16862,1.17464,1.18079,1.18707,1.19345,1.19995,1.20656,1.21327,1.22007,1.22696,1.23393,1.24097,1.24807,1.25522,1.26242,1.26965,1.2769,1.28416,1.29142,1.29867,1.30589,1.31307,1.32019,1.32725,1.33423,1.34111,1.34788,1.35452,1.36102,1.36737,1.37355,1.37953,1.38532,1.39089,1.39624,1.40134,1.40618,1.41075,1.41503,1.41902,1.42271,1.42608,1.42912,1.43183,1.43419,1.43621,1.43787,1.43917,1.44012,1.4407,1.44092,1.44078,1.44029,1.43944,1.43824,1.4367,1.43483,1.43264,1.43014,1.42733,1.42424,1.42089,1.41727,1.41342,1.40935,1.40508,1.40062,1.396,1.39123,1.38634,1.38135,1.37627,1.37112,1.36593,1.36071,1.35548,1.35025,1.34505,1.33989,1.33477,1.32973,1.32475,1.31987,1.31508,1.31039,1.30581,1.30135,1.297,1.29277,1.28866,1.28467,1.28079,1.27703,1.27339,1.26984,1.2664,1.26304,1.25977,1.25658,1.25345,1.25037,1.24734,1.24434,1.24135,1.23837,1.23537,1.23236,1.2293,1.22618,1.22299,1.2197,1.2163,1.21277,1.20908,1.20521,1.20115,1.19686,1.19233,1.18751,1.18239,1.17693,1.17111,1.16488,1.15821,1.15106,1.1434,1.13518,1.12635,1.11687,1.1067,1.09577,1.08404,1.07146,1.05795,1.04346,1.02794,1.01131,0.993521,0.974503,0.954193,0.932532,0.909463,0.884934,0.858898,0.83132,0.802177},
{1.02181,1.02225,1.02274,1.02329,1.0239,1.02457,1.02529,1.02607,1.02692,1.02783,1.0288,1.02984,1.03094,1.03212,1.03336,1.03468,1.03608,1.03755,1.03911,1.04075,1.04247,1.04428,1.04618,1.04817,1.05026,1.05245,1.05474,1.05713,1.05963,1.06224,1.06497,1.06781,1.07076,1.07384,1.07704,1.08037,1.08382,1.08741,1.09113,1.09499,1.09898,1.10312,1.10739,1.11181,1.11637,1.12108,1.12594,1.13094,1.13608,1.14138,1.14681,1.1524,1.15812,1.16399,1.16999,1.17613,1.18241,1.18881,1.19534,1.20199,1.20875,1.21562,1.22259,1.22966,1.23682,1.24405,1.25136,1.25873,1.26615,1.27361,1.2811,1.28861,1.29613,1.30364,1.31114,1.3186,1.32601,1.33337,1.34065,1.34785,1.35493,1.3619,1.36874,1.37542,1.38194,1.38827,1.39441,1.40034,1.40604,1.4115,1.4167,1.42163,1.42628,1.43064,1.43469,1.43842,1.44182,1.44488,1.4476,1.44996,1.45197,1.45362,1.45489,1.4558,1.45635,1.45652,1.45633,1.45578,1.45487,1.45361,1.45201,1.45008,1.44782,1.44526,1.44241,1.43927,1.43587,1.43222,1.42834,1.42425,1.41996,1.41551,1.41089,1.40615,1.40129,1.39634,1.39131,1.38623,1.38111,1.37597,1.37083,1.36571,1.36062,1.35558,1.35059,1.34568,1.34084,1.33609,1.33145,1.3269,1.32247,1.31814,1.31394,1.30984,1.30587,1.302,1.29825,1.29461,1.29106,1.28762,1.28426,1.28098,1.27777,1.27462,1.27153,1.26847,1.26544,1.26242,1.25941,1.25638,1.25332,1.25022,1.24705,1.24381,1.24047,1.23701,1.23341,1.22966,1.22572,1.22158,1.21721,1.21258,1.20767,1.20245,1.19689,1.19095,1.1846,1.17781,1.17053,1.16273,1.15436,1.14539,1.13575,1.12541,1.11431,1.10239,1.08961,1.07591,1.06121,1.04547,1.02862,1.01059,0.991324,0.970758,0.94883,0.925483,0.900662,0.874323,0.846428,0.816951},
{1.02193,1.02236,1.02285,1.02339,1.02399,1.02464,1.02536,1.02613,1.02697,1.02787,1.02884,1.02987,1.03097,1.03214,1.03338,1.0347,1.03609,1.03756,1.03912,1.04075,1.04248,1.04429,1.04619,1.04819,1.05028,1.05247,1.05477,1.05717,1.05968,1.0623,1.06503,1.06788,1.07085,1.07395,1.07717,1.08052,1.084,1.08762,1.09137,1.09526,1.09929,1.10346,1.10778,1.11225,1.11687,1.12163,1.12655,1.13162,1.13683,1.1422,1.14772,1.1534,1.15922,1.16518,1.1713,1.17755,1.18395,1.19048,1.19715,1.20394,1.21085,1.21789,1.22503,1.23227,1.23962,1.24705,1.25456,1.26214,1.26978,1.27748,1.28521,1.29297,1.30075,1.30853,1.31629,1.32404,1.33175,1.33941,1.347,1.3545,1.36192,1.36922,1.37639,1.38341,1.39028,1.39697,1.40346,1.40975,1.41582,1.42164,1.42721,1.43252,1.43754,1.44227,1.44669,1.45079,1.45456,1.45799,1.46107,1.4638,1.46616,1.46816,1.46978,1.47103,1.4719,1.4724,1.47253,1.47229,1.47168,1.47071,1.46939,1.46773,1.46575,1.46344,1.46082,1.45792,1.45474,1.45131,1.44763,1.44373,1.43963,1.43534,1.43089,1.4263,1.42158,1.41676,1.41186,1.4069,1.40189,1.39685,1.39181,1.38677,1.38176,1.37679,1.37187,1.36701,1.36223,1.35753,1.35293,1.34842,1.34402,1.33973,1.33554,1.33147,1.32751,1.32366,1.31991,1.31627,1.31273,1.30928,1.30591,1.30262,1.2994,1.29624,1.29312,1.29004,1.28698,1.28393,1.28089,1.27782,1.27472,1.27157,1.26835,1.26505,1.26165,1.25813,1.25446,1.25063,1.24662,1.24239,1.23793,1.23321,1.2282,1.22288,1.2172,1.21114,1.20467,1.19774,1.19032,1.18237,1.17385,1.16471,1.1549,1.14438,1.13309,1.12098,1.10799,1.09406,1.07914,1.06317,1.04607,1.02778,1.00825,0.987408,0.96519,0.941541,0.916406,0.889738,0.861499,0.831662},
{1.02205,1.02247,1.02295,1.02348,1.02407,1.02471,1.02542,1.02619,1.02702,1.02791,1.02887,1.0299,1.03099,1.03215,1.03339,1.03471,1.03609,1.03756,1.03911,1.04075,1.04247,1.04428,1.04619,1.04818,1.05028,1.05248,1.05478,1.05718,1.0597,1.06233,1.06507,1.06794,1.07092,1.07404,1.07727,1.08064,1.08415,1.08779,1.09157,1.09549,1.09956,1.10377,1.10814,1.11265,1.11731,1.12213,1.12711,1.13224,1.13753,1.14297,1.14857,1.15433,1.16024,1.16631,1.17253,1.1789,1.18541,1.19207,1.19887,1.20581,1.21287,1.22007,1.22738,1.2348,1.24233,1.24995,1.25767,1.26546,1.27333,1.28125,1.28922,1.29723,1.30527,1.31331,1.32136,1.32939,1.33739,1.34535,1.35326,1.36108,1.36882,1.37645,1.38396,1.39134,1.39856,1.4056,1.41246,1.41912,1.42556,1.43176,1.43771,1.4434,1.4488,1.45391,1.45871,1.46319,1.46734,1.47115,1.47461,1.47771,1.48044,1.4828,1.48478,1.48638,1.4876,1.48844,1.48889,1.48897,1.48867,1.48801,1.48699,1.48562,1.4839,1.48186,1.4795,1.47684,1.4739,1.47069,1.46722,1.46353,1.45962,1.45551,1.45123,1.4468,1.44224,1.43757,1.4328,1.42796,1.42307,1.41814,1.4132,1.40825,1.40333,1.39843,1.39358,1.38879,1.38407,1.37943,1.37487,1.3704,1.36604,1.36178,1.35762,1.35357,1.34963,1.34579,1.34206,1.33842,1.33488,1.33143,1.32806,1.32476,1.32153,1.31835,1.31521,1.31211,1.30903,1.30595,1.30287,1.29977,1.29663,1.29343,1.29017,1.28682,1.28336,1.27977,1.27604,1.27215,1.26806,1.26375,1.25921,1.2544,1.24929,1.24386,1.23808,1.23191,1.22531,1.21826,1.21071,1.20262,1.19395,1.18466,1.17469,1.164,1.15254,1.14024,1.12706,1.11294,1.09781,1.08162,1.0643,1.04578,1.02601,1.00491,0.982427,0.958502,0.93308,0.906111,0.877555,0.847387},
{1.02217,1.02258,1.02304,1.02357,1.02415,1.02478,1.02548,1.02624,1.02706,1.02795,1.0289,1.02992,1.03101,1.03216,1.0334,1.0347,1.03609,1.03755,1.0391,1.04073,1.04245,1.04426,1.04617,1.04817,1.05026,1.05246,1.05477,1.05718,1.0597,1.06234,1.0651,1.06797,1.07097,1.0741,1.07735,1.08074,1.08427,1.08793,1.09174,1.09569,1.09979,1.10404,1.10844,1.113,1.11771,1.12259,1.12762,1.13281,1.13817,1.14368,1.14936,1.1552,1.1612,1.16737,1.17369,1.18017,1.1868,1.19358,1.20052,1.20759,1.21481,1.22216,1.22963,1.23723,1.24494,1.25276,1.26068,1.26868,1.27677,1.28492,1.29313,1.30139,1.30968,1.318,1.32632,1.33464,1.34294,1.35121,1.35942,1.36757,1.37564,1.38361,1.39146,1.39919,1.40676,1.41418,1.42141,1.42844,1.43525,1.44184,1.44818,1.45425,1.46004,1.46554,1.47074,1.47561,1.48015,1.48435,1.48819,1.49167,1.49478,1.49752,1.49987,1.50183,1.50341,1.50459,1.50539,1.50581,1.50584,1.50549,1.50477,1.5037,1.50227,1.50051,1.49842,1.49601,1.49331,1.49034,1.4871,1.48361,1.4799,1.47599,1.4719,1.46764,1.46324,1.45871,1.45409,1.44938,1.44461,1.4398,1.43496,1.43012,1.42528,1.42047,1.41569,1.41097,1.40631,1.40172,1.39721,1.39279,1.38847,1.38424,1.38011,1.37608,1.37216,1.36834,1.36461,1.36098,1.35744,1.35399,1.35061,1.3473,1.34405,1.34085,1.3377,1.33457,1.33145,1.32834,1.32522,1.32207,1.31888,1.31563,1.31231,1.30889,1.30537,1.30171,1.2979,1.29391,1.28973,1.28533,1.28068,1.27576,1.27054,1.26499,1.25907,1.25276,1.24602,1.23881,1.2311,1.22283,1.21398,1.2045,1.19433,1.18342,1.17174,1.15921,1.14579,1.13141,1.11601,1.09954,1.08193,1.06311,1.04301,1.02159,0.998762,0.974478,0.948681,0.921322,0.892359,0.861765},
{1.02229,1.02269,1.02314,1.02365,1.02422,1.02485,1.02554,1.02629,1.0271,1.02798,1.02892,1.02993,1.03101,1.03217,1.03339,1.0347,1.03608,1.03754,1.03908,1.04071,1.04243,1.04424,1.04614,1.04814,1.05024,1.05244,1.05474,1.05716,1.05969,1.06233,1.06509,1.06798,1.07099,1.07413,1.0774,1.08081,1.08435,1.08804,1.09187,1.09585,1.09998,1.10427,1.10871,1.11331,1.11807,1.12299,1.12808,1.13333,1.13875,1.14433,1.15009,1.15601,1.1621,1.16835,1.17478,1.18136,1.18811,1.19502,1.20208,1.20929,1.21665,1.22416,1.2318,1.23957,1.24746,1.25547,1.26359,1.2718,1.28011,1.28849,1.29694,1.30545,1.314,1.32259,1.33119,1.33979,1.34839,1.35696,1.36549,1.37397,1.38237,1.39068,1.39888,1.40696,1.4149,1.42269,1.43029,1.43771,1.44491,1.45188,1.45861,1.46508,1.47128,1.47718,1.48277,1.48805,1.49299,1.49759,1.50183,1.50571,1.50921,1.51233,1.51506,1.5174,1.51935,1.5209,1.52205,1.52281,1.52318,1.52317,1.52277,1.52201,1.52088,1.51941,1.5176,1.51546,1.51302,1.51029,1.50729,1.50403,1.50054,1.49683,1.49292,1.48885,1.48462,1.48025,1.47578,1.47121,1.46658,1.46189,1.45717,1.45243,1.44769,1.44297,1.43828,1.43363,1.42904,1.42451,1.42006,1.41569,1.41141,1.40722,1.40313,1.39913,1.39523,1.39143,1.38772,1.3841,1.38057,1.37712,1.37374,1.37042,1.36717,1.36395,1.36078,1.35763,1.35449,1.35135,1.3482,1.34501,1.34179,1.3385,1.33513,1.33166,1.32808,1.32436,1.32049,1.31644,1.31218,1.3077,1.30297,1.29796,1.29265,1.287,1.28098,1.27456,1.2677,1.26037,1.25253,1.24414,1.23515,1.22552,1.2152,1.20414,1.19228,1.17959,1.16598,1.15142,1.13583,1.11916,1.10134,1.0823,1.06199,1.04033,1.01726,0.992719,0.966656,0.939017,0.909759,0.878853},
{1.02241,1.02279,1.02324,1.02374,1.02429,1.02491,1.02559,1.02633,1.02714,1.028,1.02894,1.02994,1.03102,1.03216,1.03338,1.03468,1.03605,1.03751,1.03905,1.04067,1.04239,1.04419,1.04609,1.04809,1.05019,1.05239,1.0547,1.05712,1.05965,1.0623,1.06507,1.06797,1.07099,1.07414,1.07742,1.08084,1.08441,1.08812,1.09197,1.09598,1.10014,1.10445,1.10893,1.11357,1.11837,1.12334,1.12848,1.13379,1.13927,1.14492,1.15075,1.15675,1.16292,1.16927,1.17579,1.18248,1.18934,1.19637,1.20356,1.2109,1.21841,1.22606,1.23387,1.24181,1.24988,1.25808,1.26639,1.27482,1.28334,1.29195,1.30064,1.3094,1.31821,1.32706,1.33594,1.34484,1.35373,1.36261,1.37146,1.38026,1.389,1.39765,1.40621,1.41465,1.42296,1.43112,1.43911,1.44691,1.4545,1.46187,1.46901,1.47588,1.48248,1.4888,1.4948,1.50049,1.50584,1.51085,1.5155,1.51978,1.52369,1.52721,1.53034,1.53307,1.53539,1.53732,1.53885,1.53997,1.54069,1.54102,1.54096,1.54052,1.5397,1.53853,1.53701,1.53516,1.53299,1.53052,1.52776,1.52474,1.52147,1.51798,1.51428,1.51039,1.50634,1.50215,1.49784,1.49342,1.48892,1.48437,1.47976,1.47514,1.47051,1.46588,1.46128,1.45671,1.4522,1.44774,1.44335,1.43903,1.4348,1.43065,1.42659,1.42262,1.41875,1.41497,1.41128,1.40767,1.40414,1.40069,1.39731,1.39399,1.39073,1.3875,1.38431,1.38114,1.37797,1.3748,1.37161,1.36839,1.36512,1.36178,1.35836,1.35484,1.35119,1.34741,1.34346,1.33934,1.335,1.33043,1.32561,1.3205,1.31509,1.30932,1.30319,1.29665,1.28966,1.28219,1.27421,1.26567,1.25652,1.24672,1.23623,1.22499,1.21295,1.20005,1.18625,1.17147,1.15566,1.13876,1.1207,1.10141,1.08083,1.0589,1.03555,1.01071,0.984337,0.956373,0.926774,0.895508},
{1.02253,1.0229,1.02333,1.02382,1.02437,1.02497,1.02564,1.02637,1.02717,1.02803,1.02895,1.02995,1.03101,1.03215,1.03336,1.03465,1.03602,1.03747,1.03901,1.04063,1.04234,1.04414,1.04604,1.04803,1.05013,1.05233,1.05464,1.05706,1.0596,1.06225,1.06503,1.06793,1.07096,1.07412,1.07742,1.08085,1.08443,1.08816,1.09204,1.09607,1.10025,1.1046,1.10911,1.11379,1.11863,1.12364,1.12883,1.13419,1.13973,1.14545,1.15135,1.15742,1.16368,1.17011,1.17673,1.18352,1.19049,1.19763,1.20495,1.21243,1.22007,1.22788,1.23584,1.24395,1.2522,1.26058,1.26909,1.27772,1.28646,1.2953,1.30423,1.31323,1.3223,1.33143,1.34059,1.34977,1.35896,1.36815,1.37732,1.38645,1.39553,1.40453,1.41344,1.42225,1.43093,1.43947,1.44785,1.45604,1.46403,1.47181,1.47935,1.48664,1.49366,1.50039,1.50682,1.51293,1.5187,1.52413,1.52921,1.53391,1.53823,1.54216,1.54569,1.54883,1.55155,1.55387,1.55577,1.55727,1.55836,1.55904,1.55933,1.55923,1.55875,1.55789,1.55668,1.55512,1.55323,1.55103,1.54854,1.54577,1.54273,1.53947,1.53598,1.5323,1.52844,1.52443,1.52028,1.51603,1.51168,1.50726,1.50279,1.49829,1.49377,1.48925,1.48474,1.48026,1.47582,1.47144,1.46711,1.46286,1.45868,1.45458,1.45056,1.44663,1.44279,1.43903,1.43536,1.43177,1.42825,1.42481,1.42143,1.41811,1.41484,1.4116,1.4084,1.40521,1.40202,1.39882,1.39561,1.39235,1.38904,1.38566,1.38219,1.37862,1.37492,1.37108,1.36707,1.36287,1.35846,1.35382,1.34891,1.34372,1.33821,1.33235,1.32611,1.31946,1.31236,1.30478,1.29667,1.288,1.27871,1.26877,1.25813,1.24674,1.23454,1.22148,1.2075,1.19255,1.17655,1.15946,1.1412,1.1217,1.10091,1.07875,1.05517,1.03009,1.00346,0.975222,0.945337,0.913767},
{1.02264,1.023,1.02342,1.0239,1.02443,1.02503,1.02569,1.02641,1.02719,1.02804,1.02896,1.02995,1.031,1.03213,1.03334,1.03462,1.03598,1.03743,1.03896,1.04057,1.04228,1.04407,1.04597,1.04796,1.05006,1.05226,1.05457,1.05699,1.05953,1.06218,1.06496,1.06787,1.0709,1.07407,1.07738,1.08083,1.08443,1.08817,1.09207,1.09612,1.10033,1.1047,1.10924,1.11396,1.11884,1.12389,1.12913,1.13454,1.14014,1.14592,1.15188,1.15803,1.16436,1.17088,1.17759,1.18448,1.19156,1.19881,1.20625,1.21386,1.22164,1.22959,1.23771,1.24598,1.25441,1.26298,1.27168,1.28052,1.28947,1.29854,1.3077,1.31695,1.32628,1.33567,1.34511,1.35458,1.36408,1.37358,1.38306,1.39252,1.40194,1.41129,1.42057,1.42974,1.4388,1.44772,1.45649,1.46509,1.47349,1.48167,1.48963,1.49734,1.50479,1.51195,1.5188,1.52534,1.53155,1.53742,1.54292,1.54805,1.5528,1.55715,1.56111,1.56465,1.56779,1.57051,1.57281,1.57469,1.57616,1.57722,1.57787,1.57812,1.57797,1.57745,1.57656,1.57531,1.57372,1.5718,1.56958,1.56707,1.56428,1.56125,1.55799,1.55452,1.55086,1.54704,1.54308,1.53899,1.5348,1.53053,1.5262,1.52182,1.51742,1.51301,1.5086,1.50422,1.49987,1.49556,1.4913,1.48711,1.48298,1.47893,1.47496,1.47107,1.46725,1.46352,1.45987,1.45629,1.45279,1.44935,1.44597,1.44265,1.43937,1.43612,1.43289,1.42968,1.42646,1.42323,1.41998,1.41668,1.41332,1.40989,1.40636,1.40273,1.39897,1.39505,1.39096,1.38668,1.38219,1.37745,1.37244,1.36714,1.36152,1.35554,1.34917,1.34239,1.33515,1.32741,1.31915,1.31031,1.30085,1.29074,1.27991,1.26832,1.25591,1.24264,1.22844,1.21325,1.19701,1.17966,1.16114,1.14137,1.12029,1.09783,1.07393,1.04853,1.02156,0.992964,0.962702,0.930735},
{1.02276,1.0231,1.02351,1.02397,1.0245,1.02508,1.02573,1.02644,1.02721,1.02806,1.02896,1.02994,1.03099,1.03211,1.03331,1.03458,1.03594,1.03737,1.03889,1.0405,1.0422,1.044,1.04589,1.04788,1.04997,1.05217,1.05447,1.0569,1.05943,1.06209,1.06487,1.06778,1.07082,1.074,1.07732,1.08078,1.08439,1.08815,1.09206,1.09613,1.10037,1.10477,1.10934,1.11408,1.119,1.12409,1.12937,1.13484,1.14048,1.14632,1.15235,1.15857,1.16498,1.17158,1.17837,1.18536,1.19254,1.1999,1.20746,1.21519,1.22311,1.23121,1.23948,1.24791,1.25651,1.26526,1.27416,1.2832,1.29237,1.30165,1.31105,1.32055,1.33013,1.33979,1.3495,1.35927,1.36906,1.37887,1.38868,1.39848,1.40824,1.41794,1.42758,1.43713,1.44657,1.45588,1.46504,1.47404,1.48285,1.49146,1.49984,1.50798,1.51586,1.52345,1.53075,1.53774,1.54439,1.55069,1.55664,1.56221,1.5674,1.57219,1.57658,1.58055,1.58411,1.58725,1.58996,1.59224,1.59411,1.59555,1.59657,1.59719,1.5974,1.59722,1.59666,1.59573,1.59445,1.59283,1.59089,1.58866,1.58613,1.58335,1.58033,1.57708,1.57364,1.57002,1.56624,1.56234,1.55831,1.5542,1.55001,1.54577,1.5415,1.5372,1.53291,1.52862,1.52436,1.52013,1.51595,1.51182,1.50776,1.50376,1.49984,1.49598,1.49221,1.4885,1.48487,1.48132,1.47782,1.47439,1.47102,1.46769,1.46439,1.46113,1.45789,1.45465,1.45141,1.44815,1.44485,1.44151,1.43811,1.43462,1.43104,1.42735,1.42351,1.41952,1.41536,1.41099,1.40641,1.40157,1.39646,1.39105,1.38531,1.37921,1.37272,1.3658,1.35841,1.35053,1.34211,1.3331,1.32348,1.31318,1.30216,1.29037,1.27776,1.26427,1.24984,1.23442,1.21794,1.20034,1.18155,1.1615,1.14013,1.11738,1.09317,1.06743,1.04012,1.01117,0.980524,0.948156},
{1.02287,1.0232,1.0236,1.02405,1.02456,1.02513,1.02577,1.02647,1.02723,1.02806,1.02896,1.02993,1.03097,1.03208,1.03327,1.03453,1.03588,1.03731,1.03882,1.04043,1.04212,1.04391,1.04579,1.04778,1.04986,1.05206,1.05436,1.05678,1.05932,1.06198,1.06476,1.06768,1.07072,1.0739,1.07723,1.0807,1.08432,1.08809,1.09202,1.09611,1.10036,1.10479,1.10938,1.11415,1.11911,1.12424,1.12956,1.13507,1.14077,1.14666,1.15275,1.15903,1.16552,1.1722,1.17908,1.18616,1.19343,1.20091,1.20857,1.21643,1.22449,1.23272,1.24114,1.24974,1.2585,1.26743,1.27652,1.28576,1.29514,1.30465,1.31428,1.32402,1.33385,1.34378,1.35377,1.36383,1.37392,1.38404,1.39418,1.40431,1.41441,1.42447,1.43447,1.4444,1.45422,1.46393,1.47349,1.4829,1.49213,1.50117,1.50998,1.51855,1.52687,1.53491,1.54266,1.5501,1.5572,1.56396,1.57036,1.57639,1.58203,1.58727,1.5921,1.59652,1.60051,1.60408,1.60721,1.60992,1.61219,1.61403,1.61544,1.61644,1.61702,1.6172,1.61699,1.6164,1.61544,1.61414,1.6125,1.61055,1.6083,1.60578,1.603,1.6,1.59678,1.59337,1.5898,1.58608,1.58223,1.57829,1.57426,1.57016,1.56602,1.56185,1.55767,1.55349,1.54933,1.54519,1.5411,1.53704,1.53305,1.52911,1.52523,1.52143,1.51769,1.51402,1.51042,1.50689,1.50341,1.49999,1.49662,1.49329,1.49,1.48673,1.48347,1.48021,1.47695,1.47366,1.47034,1.46696,1.46351,1.45998,1.45635,1.4526,1.4487,1.44465,1.44041,1.43597,1.43131,1.42639,1.42119,1.41568,1.40984,1.40363,1.39702,1.38998,1.38247,1.37446,1.3659,1.35675,1.34698,1.33652,1.32534,1.31338,1.3006,1.28693,1.27231,1.25669,1.24001,1.22219,1.20318,1.18291,1.16131,1.1383,1.11383,1.08783,1.06023,1.03097,1.00001,0.9673},
{1.02298,1.0233,1.02368,1.02412,1.02462,1.02518,1.02581,1.02649,1.02725,1.02806,1.02895,1.02991,1.03094,1.03204,1.03322,1.03448,1.03581,1.03723,1.03874,1.04034,1.04202,1.0438,1.04568,1.04766,1.04974,1.05193,1.05424,1.05665,1.05919,1.06185,1.06463,1.06754,1.07059,1.07378,1.07711,1.08059,1.08421,1.088,1.09194,1.09604,1.10032,1.10476,1.10938,1.11418,1.11917,1.12433,1.12969,1.13525,1.14099,1.14694,1.15308,1.15943,1.16598,1.17274,1.1797,1.18687,1.19424,1.20182,1.2096,1.21758,1.22576,1.23413,1.2427,1.25145,1.26038,1.26949,1.27876,1.2882,1.29778,1.30751,1.31737,1.32736,1.33745,1.34764,1.35791,1.36825,1.37865,1.38908,1.39954,1.41,1.42045,1.43087,1.44124,1.45154,1.46176,1.47186,1.48183,1.49166,1.50131,1.51078,1.52003,1.52905,1.53782,1.54632,1.55452,1.56242,1.56999,1.57721,1.58408,1.59057,1.59667,1.60238,1.60767,1.61254,1.61699,1.621,1.62457,1.62771,1.6304,1.63266,1.63448,1.63587,1.63684,1.63739,1.63754,1.6373,1.63668,1.63571,1.63438,1.63273,1.63077,1.62853,1.62602,1.62326,1.62028,1.6171,1.61374,1.61022,1.60657,1.6028,1.59893,1.595,1.591,1.58697,1.58291,1.57885,1.57479,1.57075,1.56674,1.56277,1.55885,1.55498,1.55116,1.54741,1.54372,1.54009,1.53652,1.53301,1.52956,1.52616,1.5228,1.51948,1.51619,1.51291,1.50965,1.50638,1.5031,1.49979,1.49644,1.49303,1.48955,1.48598,1.4823,1.4785,1.47456,1.47045,1.46615,1.46165,1.45691,1.45192,1.44664,1.44105,1.43512,1.42882,1.42211,1.41497,1.40736,1.39924,1.39056,1.3813,1.3714,1.36081,1.3495,1.33741,1.32448,1.31066,1.2959,1.28012,1.26328,1.2453,1.22612,1.20567,1.18388,1.16068,1.13601,1.10979,1.08197,1.05247,1.02125,0.98827},
{1.02309,1.0234,1.02377,1.02419,1.02468,1.02523,1.02584,1.02651,1.02725,1.02806,1.02894,1.02988,1.0309,1.032,1.03316,1.03441,1.03574,1.03715,1.03865,1.04024,1.04191,1.04369,1.04556,1.04753,1.04961,1.05179,1.05409,1.0565,1.05904,1.06169,1.06447,1.06739,1.07044,1.07363,1.07696,1.08044,1.08408,1.08787,1.09182,1.09594,1.10023,1.1047,1.10934,1.11416,1.11917,1.12438,1.12977,1.13536,1.14115,1.14715,1.15335,1.15976,1.16637,1.1732,1.18024,1.1875,1.19496,1.20264,1.21053,1.21862,1.22693,1.23543,1.24414,1.25305,1.26214,1.27142,1.28088,1.29051,1.3003,1.31025,1.32034,1.33056,1.3409,1.35136,1.36191,1.37253,1.38323,1.39398,1.40476,1.41556,1.42636,1.43714,1.44788,1.45856,1.46917,1.47967,1.49006,1.5003,1.51039,1.52029,1.52999,1.53946,1.54869,1.55765,1.56632,1.57469,1.58274,1.59044,1.59778,1.60475,1.61133,1.61751,1.62328,1.62862,1.63353,1.638,1.64203,1.64561,1.64874,1.65143,1.65367,1.65548,1.65684,1.65779,1.65832,1.65845,1.65818,1.65755,1.65655,1.65522,1.65357,1.65161,1.64938,1.64689,1.64416,1.64121,1.63808,1.63478,1.63132,1.62774,1.62406,1.62029,1.61645,1.61256,1.60864,1.6047,1.60076,1.59683,1.59292,1.58904,1.58519,1.5814,1.57765,1.57396,1.57032,1.56674,1.56321,1.55974,1.55632,1.55294,1.5496,1.54629,1.54301,1.53974,1.53648,1.53321,1.52992,1.5266,1.52323,1.5198,1.5163,1.5127,1.509,1.50516,1.50118,1.49703,1.49269,1.48814,1.48335,1.4783,1.47297,1.46732,1.46132,1.45496,1.44819,1.44098,1.43329,1.42509,1.41634,1.40699,1.39701,1.38635,1.37495,1.36277,1.34976,1.33585,1.321,1.30513,1.2882,1.27013,1.25085,1.23031,1.20842,1.18512,1.16034,1.13401,1.10606,1.07643,1.04507,1.01192},
{1.0232,1.02349,1.02385,1.02426,1.02473,1.02527,1.02587,1.02653,1.02726,1.02805,1.02892,1.02985,1.03086,1.03194,1.0331,1.03434,1.03566,1.03706,1.03855,1.04013,1.04179,1.04356,1.04542,1.04739,1.04946,1.05164,1.05393,1.05634,1.05886,1.06151,1.06429,1.06721,1.07026,1.07345,1.07678,1.08027,1.08391,1.08771,1.09167,1.0958,1.10011,1.10459,1.10925,1.11409,1.11913,1.12436,1.12979,1.13542,1.14125,1.14729,1.15354,1.16001,1.16669,1.17359,1.1807,1.18804,1.19559,1.20336,1.21135,1.21956,1.22799,1.23663,1.24547,1.25453,1.26378,1.27323,1.28287,1.29269,1.30269,1.31285,1.32316,1.33362,1.34421,1.35493,1.36575,1.37667,1.38766,1.39872,1.40983,1.42096,1.43211,1.44325,1.45436,1.46543,1.47643,1.48734,1.49815,1.50882,1.51934,1.52968,1.53983,1.54977,1.55946,1.56889,1.57804,1.58689,1.59542,1.60361,1.61144,1.6189,1.62597,1.63264,1.63889,1.64471,1.6501,1.65505,1.65954,1.66359,1.66718,1.67031,1.67299,1.67522,1.677,1.67835,1.67928,1.67979,1.67989,1.67961,1.67897,1.67796,1.67663,1.67498,1.67303,1.67082,1.66836,1.66566,1.66277,1.65969,1.65645,1.65307,1.64957,1.64597,1.6423,1.63856,1.63479,1.63098,1.62716,1.62335,1.61954,1.61576,1.612,1.60828,1.60461,1.60098,1.5974,1.59387,1.59039,1.58695,1.58356,1.58021,1.57689,1.5736,1.57032,1.56706,1.5638,1.56052,1.55722,1.55389,1.5505,1.54705,1.54352,1.5399,1.53615,1.53228,1.52826,1.52406,1.51967,1.51506,1.51021,1.5051,1.4997,1.49399,1.48792,1.48148,1.47463,1.46734,1.45957,1.45128,1.44244,1.433,1.42292,1.41216,1.40066,1.38838,1.37526,1.36124,1.34628,1.3303,1.31325,1.29506,1.27566,1.25499,1.23298,1.20954,1.18462,1.15814,1.13004,1.10024,1.06868,1.03532},
{1.02331,1.02359,1.02393,1.02432,1.02478,1.02531,1.02589,1.02654,1.02726,1.02804,1.0289,1.02982,1.03081,1.03188,1.03303,1.03426,1.03557,1.03696,1.03844,1.04,1.04166,1.04342,1.04527,1.04723,1.04929,1.05146,1.05375,1.05615,1.05867,1.06132,1.06409,1.067,1.07005,1.07324,1.07658,1.08006,1.08371,1.08751,1.09148,1.09562,1.09994,1.10443,1.10911,1.11398,1.11904,1.12429,1.12975,1.13541,1.14128,1.14737,1.15367,1.16018,1.16692,1.17388,1.18107,1.18848,1.19612,1.20399,1.21208,1.22039,1.22894,1.2377,1.24668,1.25588,1.26529,1.2749,1.28472,1.29472,1.30492,1.31529,1.32582,1.33652,1.34736,1.35833,1.36942,1.38062,1.39192,1.40329,1.41471,1.42618,1.43768,1.44918,1.46066,1.47211,1.48351,1.49483,1.50605,1.51715,1.5281,1.5389,1.5495,1.5599,1.57006,1.57997,1.5896,1.59894,1.60796,1.61664,1.62497,1.63293,1.6405,1.64766,1.65441,1.66073,1.66661,1.67204,1.67701,1.68153,1.68558,1.68917,1.6923,1.69497,1.69718,1.69895,1.70028,1.70118,1.70167,1.70176,1.70146,1.7008,1.69979,1.69846,1.69681,1.69488,1.69269,1.69026,1.6876,1.68475,1.68173,1.67855,1.67525,1.67183,1.66832,1.66474,1.6611,1.65743,1.65373,1.65002,1.64631,1.64262,1.63894,1.63529,1.63168,1.6281,1.62456,1.62106,1.61761,1.61419,1.61081,1.60746,1.60413,1.60083,1.59753,1.59424,1.59094,1.58762,1.58427,1.58087,1.57742,1.57389,1.57028,1.56656,1.56271,1.55873,1.55459,1.55026,1.54573,1.54097,1.53597,1.53069,1.52511,1.5192,1.51293,1.50627,1.49919,1.49165,1.48362,1.47506,1.46594,1.4562,1.4458,1.4347,1.42285,1.41019,1.39668,1.38226,1.36686,1.35044,1.33291,1.31422,1.2943,1.27309,1.25049,1.22646,1.2009,1.17376,1.14496,1.11443,1.08212,1.04796},
{1.02341,1.02368,1.024,1.02439,1.02483,1.02534,1.02591,1.02655,1.02725,1.02803,1.02887,1.02978,1.03076,1.03182,1.03295,1.03417,1.03546,1.03685,1.03831,1.03987,1.04152,1.04327,1.04511,1.04706,1.04911,1.05127,1.05355,1.05594,1.05846,1.0611,1.06387,1.06677,1.06982,1.073,1.07634,1.07983,1.08347,1.08728,1.09126,1.0954,1.09973,1.10423,1.10892,1.11381,1.11889,1.12417,1.12965,1.13535,1.14125,1.14738,1.15372,1.16029,1.16708,1.1741,1.18136,1.18884,1.19656,1.20451,1.2127,1.22112,1.22978,1.23866,1.24778,1.25711,1.26667,1.27645,1.28644,1.29663,1.30702,1.31759,1.32835,1.33928,1.35036,1.36159,1.37295,1.38444,1.39603,1.40771,1.41946,1.43126,1.44311,1.45497,1.46683,1.47867,1.49046,1.50219,1.51383,1.52537,1.53677,1.54802,1.55909,1.56995,1.5806,1.591,1.60112,1.61096,1.62048,1.62968,1.63852,1.64699,1.65507,1.66275,1.67001,1.67683,1.68322,1.68915,1.69463,1.69963,1.70417,1.70824,1.71183,1.71496,1.71762,1.71983,1.72158,1.7229,1.72379,1.72427,1.72435,1.72405,1.72339,1.72239,1.72107,1.71944,1.71754,1.71539,1.713,1.7104,1.70761,1.70466,1.70156,1.69834,1.69502,1.69161,1.68814,1.68461,1.68105,1.67747,1.67389,1.6703,1.66673,1.66317,1.65964,1.65614,1.65267,1.64923,1.64583,1.64245,1.63911,1.6358,1.6325,1.62921,1.62594,1.62265,1.61936,1.61604,1.61269,1.60928,1.60582,1.60227,1.59864,1.59489,1.59102,1.587,1.58282,1.57845,1.57388,1.56907,1.56402,1.55868,1.55304,1.54707,1.54074,1.53402,1.52687,1.51926,1.51116,1.50252,1.49332,1.4835,1.47302,1.46184,1.44991,1.43717,1.42358,1.40907,1.39359,1.37708,1.35946,1.34069,1.32068,1.29937,1.27668,1.25255,1.22689,1.19963,1.17071,1.14004,1.10757,1.07324},
{1.02352,1.02377,1.02408,1.02445,1.02488,1.02537,1.02593,1.02655,1.02724,1.028,1.02883,1.02973,1.0307,1.03175,1.03287,1.03407,1.03536,1.03672,1.03818,1.03973,1.04136,1.0431,1.04493,1.04687,1.04891,1.05107,1.05333,1.05572,1.05822,1.06086,1.06362,1.06652,1.06956,1.07274,1.07607,1.07956,1.0832,1.08701,1.09099,1.09514,1.09947,1.10399,1.10869,1.11359,1.11869,1.12399,1.12949,1.13522,1.14115,1.14731,1.1537,1.16031,1.16716,1.17423,1.18155,1.18911,1.1969,1.20494,1.21322,1.22174,1.2305,1.23951,1.24875,1.25822,1.26793,1.27786,1.28802,1.29839,1.30897,1.31975,1.33072,1.34187,1.3532,1.36468,1.37631,1.38808,1.39996,1.41195,1.42402,1.43616,1.44835,1.46058,1.47281,1.48504,1.49723,1.50938,1.52145,1.53342,1.54527,1.55697,1.56851,1.57986,1.59099,1.60188,1.61251,1.62286,1.63289,1.6426,1.65197,1.66096,1.66957,1.67777,1.68555,1.69291,1.69981,1.70626,1.71225,1.71776,1.7228,1.72736,1.73144,1.73504,1.73817,1.74083,1.74302,1.74477,1.74608,1.74696,1.74743,1.74751,1.74721,1.74656,1.74557,1.74427,1.74267,1.74081,1.7387,1.73636,1.73382,1.7311,1.72823,1.72521,1.72209,1.71886,1.71556,1.71219,1.70878,1.70534,1.70188,1.69841,1.69494,1.69148,1.68803,1.68461,1.68121,1.67784,1.67449,1.67117,1.66786,1.66458,1.66131,1.65805,1.65478,1.65151,1.64822,1.6449,1.64153,1.63811,1.63463,1.63106,1.6274,1.62362,1.61971,1.61565,1.61142,1.607,1.60237,1.5975,1.59238,1.58698,1.58126,1.57521,1.5688,1.56199,1.55475,1.54705,1.53886,1.53012,1.52081,1.51089,1.5003,1.48901,1.47696,1.4641,1.45039,1.43576,1.42015,1.4035,1.38575,1.36684,1.34668,1.32522,1.30238,1.27808,1.25225,1.22481,1.19569,1.1648,1.1321,1.09751},
{1.02362,1.02385,1.02415,1.0245,1.02492,1.0254,1.02594,1.02655,1.02723,1.02797,1.02879,1.02967,1.03063,1.03166,1.03277,1.03396,1.03524,1.03659,1.03804,1.03957,1.0412,1.04292,1.04474,1.04667,1.0487,1.05084,1.0531,1.05547,1.05797,1.06059,1.06335,1.06624,1.06927,1.07245,1.07578,1.07926,1.0829,1.08671,1.09069,1.09484,1.09918,1.1037,1.10841,1.11332,1.11843,1.12375,1.12928,1.13502,1.14099,1.14718,1.1536,1.16026,1.16715,1.17428,1.18166,1.18928,1.19714,1.20526,1.21363,1.22224,1.23111,1.24023,1.24959,1.2592,1.26905,1.27913,1.28945,1.3,1.31076,1.32174,1.33293,1.34431,1.35587,1.3676,1.3795,1.39154,1.40372,1.41601,1.4284,1.44088,1.45342,1.466,1.47861,1.49123,1.50383,1.51639,1.52889,1.5413,1.5536,1.56577,1.57779,1.58962,1.60124,1.61264,1.62378,1.63464,1.6452,1.65544,1.66533,1.67486,1.68401,1.69275,1.70107,1.70896,1.7164,1.72339,1.7299,1.73594,1.74149,1.74656,1.75114,1.75524,1.75884,1.76198,1.76463,1.76683,1.76857,1.76988,1.77076,1.77123,1.77132,1.77103,1.77039,1.76942,1.76815,1.76659,1.76477,1.76271,1.76044,1.75797,1.75533,1.75254,1.74962,1.74659,1.74347,1.74028,1.73703,1.73373,1.73041,1.72707,1.72371,1.72036,1.71702,1.71368,1.71036,1.70706,1.70378,1.70051,1.69726,1.69402,1.69079,1.68756,1.68432,1.68106,1.67779,1.67447,1.67111,1.6677,1.6642,1.66063,1.65695,1.65315,1.64922,1.64513,1.64087,1.63642,1.63176,1.62686,1.62169,1.61625,1.61049,1.60439,1.59793,1.59107,1.58377,1.57602,1.56777,1.55898,1.54961,1.53963,1.52899,1.51764,1.50554,1.49263,1.47886,1.46417,1.44851,1.43181,1.41402,1.39505,1.37485,1.35334,1.33045,1.3061,1.28021,1.25271,1.22351,1.19255,1.15974,1.12503},
{1.02372,1.02394,1.02422,1.02456,1.02496,1.02543,1.02595,1.02655,1.02721,1.02794,1.02874,1.02961,1.03056,1.03158,1.03267,1.03385,1.03511,1.03645,1.03788,1.0394,1.04102,1.04273,1.04454,1.04645,1.04847,1.0506,1.05284,1.05521,1.05769,1.06031,1.06305,1.06594,1.06896,1.07213,1.07545,1.07893,1.08256,1.08637,1.09034,1.0945,1.09884,1.10336,1.10808,1.113,1.11812,1.12345,1.129,1.13476,1.14075,1.14697,1.15343,1.16012,1.16706,1.17424,1.18167,1.18935,1.19728,1.20548,1.21393,1.22263,1.2316,1.24082,1.2503,1.26003,1.27002,1.28025,1.29073,1.30145,1.3124,1.32357,1.33496,1.34656,1.35836,1.37034,1.38249,1.39481,1.40728,1.41987,1.43258,1.44539,1.45827,1.47122,1.48421,1.49721,1.51021,1.52319,1.53612,1.54897,1.56173,1.57437,1.58686,1.59918,1.61131,1.62321,1.63487,1.64625,1.65735,1.66812,1.67856,1.68863,1.69833,1.70762,1.71649,1.72493,1.73292,1.74045,1.74751,1.75408,1.76017,1.76576,1.77086,1.77546,1.77957,1.78318,1.78632,1.78898,1.79117,1.79291,1.79422,1.7951,1.79558,1.79568,1.7954,1.79479,1.79385,1.79261,1.7911,1.78933,1.78733,1.78512,1.78273,1.78017,1.77747,1.77464,1.77171,1.7687,1.76561,1.76247,1.75929,1.75607,1.75284,1.7496,1.74635,1.74311,1.73987,1.73664,1.73342,1.73021,1.72701,1.72381,1.7206,1.7174,1.71418,1.71093,1.70766,1.70435,1.70098,1.69755,1.69404,1.69044,1.68673,1.68289,1.67892,1.67479,1.67048,1.66597,1.66124,1.65628,1.65104,1.64552,1.63968,1.6335,1.62695,1.61999,1.61261,1.60475,1.59639,1.58749,1.57801,1.56792,1.55715,1.54568,1.53344,1.5204,1.5065,1.49167,1.47586,1.45902,1.44107,1.42195,1.40158,1.3799,1.35682,1.33228,1.30619,1.27847,1.24904,1.21782,1.18473,1.14971},
{1.02382,1.02402,1.02429,1.02461,1.025,1.02545,1.02596,1.02654,1.02719,1.0279,1.02869,1.02955,1.03048,1.03148,1.03256,1.03373,1.03497,1.0363,1.03772,1.03922,1.04082,1.04252,1.04431,1.04621,1.04822,1.05034,1.05257,1.05492,1.0574,1.06,1.06273,1.06561,1.06862,1.07178,1.07509,1.07856,1.08219,1.08599,1.08996,1.09411,1.09845,1.10298,1.1077,1.11262,1.11775,1.12309,1.12865,1.13444,1.14045,1.14669,1.15318,1.15991,1.16688,1.17411,1.18159,1.18932,1.19732,1.20558,1.21411,1.2229,1.23196,1.24129,1.25088,1.26074,1.27085,1.28123,1.29186,1.30275,1.31387,1.32524,1.33683,1.34864,1.36067,1.3729,1.38531,1.3979,1.41065,1.42354,1.43657,1.44971,1.46294,1.47625,1.48961,1.50301,1.51641,1.52981,1.54317,1.55647,1.56969,1.5828,1.59578,1.60859,1.62123,1.63365,1.64583,1.65775,1.66939,1.68071,1.6917,1.70233,1.71259,1.72245,1.73189,1.74089,1.74945,1.75754,1.76515,1.77228,1.77892,1.78505,1.79069,1.79582,1.80044,1.80457,1.8082,1.81134,1.81401,1.81621,1.81796,1.81927,1.82017,1.82066,1.82078,1.82053,1.81995,1.81905,1.81786,1.8164,1.8147,1.81277,1.81064,1.80833,1.80587,1.80327,1.80055,1.79773,1.79482,1.79185,1.78883,1.78577,1.78267,1.77956,1.77643,1.7733,1.77016,1.76702,1.76388,1.76075,1.75761,1.75447,1.75133,1.74817,1.74499,1.74178,1.73854,1.73526,1.73191,1.7285,1.72501,1.72141,1.71771,1.71389,1.70991,1.70578,1.70147,1.69696,1.69223,1.68725,1.68201,1.67648,1.67064,1.66445,1.65789,1.65093,1.64354,1.63568,1.62732,1.61843,1.60896,1.59887,1.58812,1.57667,1.56446,1.55145,1.53758,1.5228,1.50705,1.49026,1.47238,1.45333,1.43304,1.41145,1.38847,1.36402,1.33803,1.31041,1.28108,1.24995,1.21695,1.18199},
{1.02392,1.0241,1.02435,1.02466,1.02503,1.02546,1.02596,1.02653,1.02716,1.02786,1.02863,1.02947,1.03039,1.03138,1.03245,1.03359,1.03482,1.03614,1.03754,1.03903,1.04062,1.0423,1.04408,1.04597,1.04796,1.05006,1.05228,1.05462,1.05708,1.05967,1.06239,1.06525,1.06825,1.0714,1.0747,1.07816,1.08178,1.08557,1.08954,1.09369,1.09802,1.10254,1.10727,1.11219,1.11733,1.12268,1.12825,1.13404,1.14007,1.14634,1.15285,1.15961,1.16661,1.17388,1.18141,1.18919,1.19725,1.20558,1.21418,1.22305,1.2322,1.24162,1.25132,1.26129,1.27154,1.28205,1.29283,1.30387,1.31517,1.32672,1.33851,1.35053,1.36278,1.37524,1.38791,1.40077,1.4138,1.42699,1.44033,1.45379,1.46737,1.48103,1.49477,1.50855,1.52236,1.53617,1.54997,1.56372,1.5774,1.59098,1.60444,1.61776,1.6309,1.64384,1.65655,1.66902,1.6812,1.69308,1.70463,1.71583,1.72666,1.73709,1.7471,1.75669,1.76582,1.77448,1.78267,1.79037,1.79757,1.80426,1.81044,1.81611,1.82127,1.82592,1.83006,1.8337,1.83685,1.83953,1.84174,1.8435,1.84482,1.84573,1.84625,1.84639,1.84617,1.84562,1.84477,1.84363,1.84223,1.84059,1.83873,1.83668,1.83446,1.83208,1.82958,1.82696,1.82424,1.82145,1.81858,1.81567,1.81271,1.80972,1.80671,1.80368,1.80063,1.79758,1.79451,1.79144,1.78836,1.78527,1.78217,1.77904,1.77589,1.7727,1.76947,1.76618,1.76284,1.75941,1.7559,1.75229,1.74856,1.7447,1.74069,1.73651,1.73215,1.72758,1.72279,1.71775,1.71244,1.70684,1.70091,1.69464,1.68799,1.68094,1.67345,1.6655,1.65703,1.64803,1.63845,1.62824,1.61738,1.6058,1.59347,1.58033,1.56632,1.5514,1.53551,1.51858,1.50054,1.48133,1.46088,1.43911,1.41595,1.39131,1.36511,1.33726,1.30769,1.2763,1.243,1.20772},
{1.02402,1.02418,1.02441,1.0247,1.02506,1.02548,1.02596,1.02651,1.02713,1.02781,1.02857,1.02939,1.03029,1.03127,1.03232,1.03345,1.03467,1.03596,1.03735,1.03883,1.0404,1.04206,1.04383,1.0457,1.04768,1.04977,1.05197,1.05429,1.05674,1.05931,1.06202,1.06487,1.06785,1.07099,1.07428,1.07773,1.08134,1.08512,1.08908,1.09322,1.09754,1.10206,1.10678,1.11171,1.11684,1.1222,1.12778,1.13358,1.13963,1.14591,1.15244,1.15922,1.16626,1.17356,1.18113,1.18896,1.19707,1.20546,1.21413,1.22307,1.2323,1.24182,1.25162,1.2617,1.27207,1.28271,1.29364,1.30483,1.3163,1.32802,1.34001,1.35224,1.3647,1.3774,1.39032,1.40344,1.41675,1.43023,1.44388,1.45767,1.47159,1.48561,1.49971,1.51389,1.5281,1.54234,1.55656,1.57076,1.58491,1.59897,1.61292,1.62674,1.6404,1.65387,1.66713,1.68014,1.69288,1.70533,1.71745,1.72923,1.74065,1.75167,1.76227,1.77245,1.78217,1.79143,1.80021,1.80849,1.81628,1.82355,1.8303,1.83653,1.84224,1.84743,1.85211,1.85627,1.85994,1.86311,1.8658,1.86803,1.86981,1.87115,1.87209,1.87263,1.87281,1.87264,1.87214,1.87134,1.87027,1.86894,1.86738,1.86561,1.86365,1.86152,1.85925,1.85685,1.85435,1.85175,1.84907,1.84632,1.84352,1.84068,1.8378,1.8349,1.83197,1.82903,1.82606,1.82308,1.82009,1.81707,1.81404,1.81097,1.80788,1.80474,1.80156,1.79832,1.79501,1.79162,1.78814,1.78455,1.78084,1.777,1.77301,1.76885,1.7645,1.75995,1.75517,1.75015,1.74485,1.73926,1.73335,1.7271,1.72047,1.71344,1.70598,1.69805,1.68962,1.68066,1.67112,1.66097,1.65016,1.63865,1.6264,1.61334,1.59943,1.58461,1.56883,1.55202,1.53412,1.51506,1.49477,1.47317,1.45018,1.42572,1.39972,1.37207,1.34269,1.31149,1.27838,1.24327},
{1.02411,1.02426,1.02447,1.02475,1.02509,1.02549,1.02595,1.02649,1.02709,1.02776,1.02849,1.02931,1.03019,1.03115,1.03219,1.0333,1.0345,1.03578,1.03715,1.03861,1.04017,1.04182,1.04357,1.04542,1.04738,1.04945,1.05164,1.05395,1.05638,1.05894,1.06163,1.06446,1.06743,1.07055,1.07383,1.07726,1.08086,1.08463,1.08857,1.0927,1.09702,1.10153,1.10625,1.11117,1.1163,1.12166,1.12724,1.13305,1.13911,1.1454,1.15195,1.15875,1.16582,1.17315,1.18075,1.18863,1.19678,1.20522,1.21395,1.22297,1.23228,1.24188,1.25177,1.26196,1.27244,1.28321,1.29427,1.30561,1.31723,1.32913,1.3413,1.35373,1.36641,1.37934,1.39249,1.40587,1.41945,1.43322,1.44718,1.46129,1.47554,1.48991,1.50439,1.51895,1.53356,1.54821,1.56288,1.57752,1.59213,1.60667,1.62112,1.63545,1.64963,1.66363,1.67743,1.69099,1.7043,1.71732,1.73002,1.74239,1.7544,1.76601,1.77722,1.788,1.79833,1.80819,1.81757,1.82646,1.83484,1.8427,1.85003,1.85684,1.86312,1.86887,1.8741,1.8788,1.88299,1.88667,1.88986,1.89257,1.89481,1.89661,1.89799,1.89895,1.89953,1.89975,1.89962,1.89918,1.89844,1.89743,1.89617,1.89469,1.893,1.89113,1.88911,1.88693,1.88464,1.88224,1.87974,1.87717,1.87453,1.87183,1.86909,1.86631,1.8635,1.86065,1.85778,1.85489,1.85197,1.84902,1.84604,1.84302,1.83997,1.83686,1.83371,1.83048,1.82719,1.82381,1.82033,1.81673,1.81302,1.80916,1.80515,1.80097,1.7966,1.79201,1.7872,1.78213,1.77679,1.77116,1.7652,1.75889,1.75221,1.74513,1.73761,1.72962,1.72113,1.71211,1.70251,1.69229,1.68142,1.66985,1.65753,1.64441,1.63043,1.61555,1.59971,1.58284,1.56487,1.54574,1.52538,1.50371,1.48064,1.4561,1.43,1.40225,1.37275,1.34141,1.30813,1.27282},
{1.0242,1.02434,1.02453,1.02479,1.02511,1.02549,1.02594,1.02646,1.02704,1.0277,1.02842,1.02921,1.03008,1.03102,1.03204,1.03314,1.03432,1.03559,1.03694,1.03839,1.03992,1.04156,1.04329,1.04512,1.04707,1.04912,1.05129,1.05358,1.05599,1.05853,1.06121,1.06402,1.06698,1.07008,1.07334,1.07676,1.08034,1.0841,1.08803,1.09214,1.09645,1.10095,1.10566,1.11057,1.1157,1.12105,1.12664,1.13245,1.13851,1.14481,1.15137,1.15819,1.16528,1.17263,1.18027,1.18818,1.19638,1.20487,1.21365,1.22273,1.23211,1.24179,1.25177,1.26206,1.27265,1.28354,1.29473,1.30621,1.31799,1.33005,1.3424,1.35502,1.36791,1.38106,1.39445,1.40808,1.42193,1.43599,1.45024,1.46467,1.47926,1.49398,1.50883,1.52377,1.53879,1.55386,1.56895,1.58405,1.59913,1.61415,1.6291,1.64394,1.65864,1.67318,1.68753,1.70166,1.71554,1.72915,1.74245,1.75541,1.76803,1.78026,1.79208,1.80348,1.81443,1.82492,1.83492,1.84442,1.85342,1.86189,1.86983,1.87724,1.88411,1.89044,1.89624,1.9015,1.90624,1.91045,1.91417,1.91738,1.92012,1.9224,1.92423,1.92564,1.92665,1.92728,1.92754,1.92748,1.9271,1.92644,1.92551,1.92433,1.92294,1.92136,1.91959,1.91767,1.91561,1.91343,1.91115,1.90877,1.90631,1.90379,1.90121,1.89858,1.8959,1.89319,1.89044,1.88765,1.88483,1.88198,1.87909,1.87616,1.87318,1.87014,1.86705,1.86389,1.86065,1.85732,1.85389,1.85035,1.84667,1.84286,1.83889,1.83475,1.83041,1.82587,1.82109,1.81607,1.81078,1.80519,1.79928,1.79303,1.7864,1.77938,1.77193,1.76402,1.75561,1.74668,1.73718,1.72707,1.71632,1.70488,1.6927,1.67973,1.66593,1.65123,1.63559,1.61893,1.60119,1.58231,1.56221,1.54081,1.51804,1.49381,1.46803,1.44061,1.41144,1.38044,1.3475,1.31252},
{1.0243,1.02441,1.02459,1.02483,1.02513,1.0255,1.02593,1.02643,1.02699,1.02763,1.02834,1.02911,1.02996,1.03089,1.03189,1.03297,1.03414,1.03539,1.03672,1.03815,1.03967,1.04128,1.043,1.04481,1.04674,1.04877,1.05092,1.05319,1.05559,1.05811,1.06076,1.06356,1.06649,1.06958,1.07282,1.07622,1.07979,1.08352,1.08744,1.09154,1.09583,1.10032,1.10502,1.10992,1.11504,1.12039,1.12596,1.13178,1.13784,1.14415,1.15071,1.15754,1.16464,1.17202,1.17968,1.18762,1.19586,1.20439,1.21322,1.22236,1.2318,1.24156,1.25162,1.262,1.27269,1.28369,1.295,1.30662,1.31854,1.33077,1.34329,1.3561,1.36919,1.38255,1.39617,1.41005,1.42416,1.4385,1.45304,1.46778,1.4827,1.49777,1.51298,1.5283,1.54371,1.5592,1.57473,1.59028,1.60582,1.62132,1.63677,1.65212,1.66735,1.68244,1.69734,1.71204,1.7265,1.74069,1.75459,1.76817,1.7814,1.79425,1.8067,1.81873,1.83032,1.84144,1.85207,1.86221,1.87183,1.88093,1.8895,1.89752,1.905,1.91193,1.91831,1.92415,1.92946,1.93423,1.93848,1.94222,1.94547,1.94824,1.95055,1.95242,1.95387,1.95493,1.95561,1.95593,1.95593,1.95563,1.95504,1.95419,1.95311,1.95181,1.95033,1.94867,1.94685,1.9449,1.94283,1.94066,1.93839,1.93605,1.93363,1.93115,1.92862,1.92604,1.92341,1.92073,1.91802,1.91526,1.91245,1.9096,1.90669,1.90373,1.90069,1.89758,1.89439,1.8911,1.88771,1.8842,1.88056,1.87678,1.87284,1.86872,1.8644,1.85988,1.85513,1.85012,1.84485,1.83928,1.83339,1.82716,1.82057,1.81357,1.80615,1.79828,1.78991,1.78103,1.77158,1.76153,1.75084,1.73948,1.72738,1.71451,1.7008,1.68622,1.67069,1.65416,1.63657,1.61784,1.5979,1.57668,1.55408,1.53004,1.50445,1.47722,1.44824,1.41743,1.38466,1.34983},
{1.02438,1.02448,1.02464,1.02486,1.02514,1.02549,1.02591,1.02639,1.02694,1.02756,1.02825,1.02901,1.02984,1.03075,1.03173,1.0328,1.03394,1.03517,1.03649,1.0379,1.03939,1.04099,1.04269,1.04448,1.04639,1.0484,1.05053,1.05278,1.05516,1.05766,1.06029,1.06306,1.06598,1.06905,1.07227,1.07565,1.07919,1.08291,1.08681,1.09089,1.09517,1.09964,1.10432,1.10921,1.11432,1.11965,1.12522,1.13103,1.13709,1.1434,1.14997,1.1568,1.16391,1.17131,1.17898,1.18695,1.19522,1.20379,1.21266,1.22185,1.23135,1.24117,1.25131,1.26177,1.27256,1.28366,1.29509,1.30684,1.3189,1.33128,1.34396,1.35695,1.37023,1.3838,1.39765,1.41176,1.42613,1.44074,1.45558,1.47063,1.48586,1.50128,1.51685,1.53255,1.54836,1.56426,1.58022,1.59621,1.61222,1.62821,1.64416,1.66002,1.67579,1.69142,1.70689,1.72216,1.73721,1.752,1.76651,1.7807,1.79456,1.80805,1.82114,1.83382,1.84605,1.85782,1.86911,1.8799,1.89017,1.89992,1.90912,1.91778,1.92589,1.93344,1.94044,1.94688,1.95277,1.95811,1.96292,1.96722,1.971,1.97429,1.9771,1.97946,1.98138,1.98288,1.98399,1.98474,1.98513,1.98521,1.98499,1.98449,1.98373,1.98275,1.98156,1.98018,1.97864,1.97694,1.97511,1.97316,1.9711,1.96895,1.96672,1.96442,1.96205,1.95962,1.95713,1.95459,1.952,1.94936,1.94666,1.94391,1.9411,1.93823,1.93528,1.93225,1.92914,1.92592,1.9226,1.91916,1.91559,1.91187,1.908,1.90394,1.8997,1.89524,1.89056,1.88562,1.88043,1.87494,1.86914,1.863,1.8565,1.84961,1.84231,1.83455,1.82632,1.81758,1.80828,1.7984,1.7879,1.77673,1.76484,1.7522,1.73875,1.72443,1.70919,1.69297,1.6757,1.65732,1.63775,1.61692,1.59474,1.57113,1.54599,1.51923,1.49075,1.46042,1.42815,1.39382},
{1.02447,1.02455,1.02469,1.02489,1.02516,1.02549,1.02589,1.02635,1.02688,1.02748,1.02815,1.02889,1.02971,1.0306,1.03156,1.03261,1.03374,1.03495,1.03624,1.03763,1.03911,1.04069,1.04236,1.04414,1.04602,1.04802,1.05013,1.05235,1.0547,1.05718,1.05979,1.06255,1.06544,1.06848,1.07168,1.07504,1.07856,1.08226,1.08613,1.0902,1.09445,1.09891,1.10357,1.10844,1.11353,1.11886,1.12441,1.13021,1.13626,1.14256,1.14913,1.15597,1.16309,1.17049,1.17818,1.18617,1.19446,1.20306,1.21197,1.2212,1.23075,1.24063,1.25084,1.26138,1.27224,1.28345,1.29498,1.30685,1.31904,1.33156,1.34441,1.35756,1.37103,1.3848,1.39887,1.41321,1.42783,1.4427,1.45782,1.47317,1.48872,1.50447,1.5204,1.53647,1.55267,1.56898,1.58537,1.60181,1.61828,1.63476,1.6512,1.66759,1.68388,1.70006,1.71609,1.73194,1.74758,1.76298,1.7781,1.79293,1.80742,1.82155,1.83529,1.84863,1.86152,1.87396,1.88591,1.89736,1.9083,1.91871,1.92857,1.93789,1.94664,1.95483,1.96245,1.96951,1.97601,1.98195,1.98734,1.9922,1.99654,2.00036,2.0037,2.00656,2.00896,2.01094,2.0125,2.01368,2.0145,2.01497,2.01513,2.01499,2.01458,2.01393,2.01305,2.01197,2.0107,2.00927,2.00768,2.00597,2.00413,2.00219,2.00015,1.99803,1.99583,1.99356,1.99123,1.98883,1.98637,1.98385,1.98127,1.97862,1.97591,1.97313,1.97027,1.96732,1.96429,1.96115,1.9579,1.95453,1.95102,1.94737,1.94355,1.93956,1.93538,1.93099,1.92637,1.9215,1.91637,1.91096,1.90524,1.89918,1.89277,1.88598,1.87877,1.87113,1.86302,1.8544,1.84525,1.83552,1.82518,1.81419,1.8025,1.79007,1.77684,1.76276,1.74778,1.73184,1.71487,1.6968,1.67757,1.65709,1.63528,1.61206,1.58733,1.56098,1.53292,1.50303,1.47119,1.43728},
{1.02456,1.02461,1.02473,1.02492,1.02517,1.02548,1.02586,1.02631,1.02682,1.0274,1.02805,1.02877,1.02957,1.03044,1.03139,1.03241,1.03352,1.03471,1.03599,1.03735,1.03881,1.04037,1.04202,1.04378,1.04564,1.04761,1.0497,1.0519,1.05423,1.05668,1.05927,1.062,1.06487,1.06788,1.07106,1.07439,1.07789,1.08156,1.08542,1.08945,1.09369,1.09812,1.10276,1.10761,1.11268,1.11799,1.12353,1.12931,1.13535,1.14164,1.1482,1.15504,1.16216,1.16956,1.17726,1.18526,1.19357,1.20219,1.21114,1.2204,1.23,1.23993,1.2502,1.2608,1.27175,1.28304,1.29468,1.30665,1.31897,1.33163,1.34462,1.35794,1.37158,1.38555,1.39982,1.41439,1.42925,1.44438,1.45977,1.47541,1.49128,1.50736,1.52363,1.54007,1.55666,1.57338,1.59019,1.60708,1.62401,1.64097,1.65791,1.67482,1.69165,1.70838,1.72498,1.74141,1.75765,1.77366,1.78941,1.80487,1.82001,1.83479,1.8492,1.8632,1.87677,1.88989,1.90252,1.91466,1.92628,1.93737,1.94791,1.9579,1.96732,1.97617,1.98444,1.99214,1.99927,2.00583,2.01183,2.01728,2.02219,2.02658,2.03046,2.03385,2.03677,2.03924,2.04128,2.04292,2.04417,2.04507,2.04563,2.04588,2.04584,2.04554,2.045,2.04423,2.04326,2.04212,2.04081,2.03935,2.03775,2.03604,2.03422,2.0323,2.0303,2.02821,2.02605,2.02381,2.0215,2.01913,2.01669,2.01417,2.01159,2.00893,2.00618,2.00335,2.00042,1.99739,1.99424,1.99097,1.98757,1.98401,1.9803,1.97641,1.97234,1.96806,1.96355,1.95881,1.9538,1.94852,1.94294,1.93703,1.93078,1.92415,1.91713,1.90968,1.90178,1.89338,1.88447,1.875,1.86494,1.85424,1.84287,1.83078,1.81791,1.80423,1.78967,1.77417,1.75768,1.74012,1.72142,1.70151,1.68031,1.65771,1.63364,1.60798,1.58064,1.55149,1.5204,1.48726},
{1.02464,1.02468,1.02478,1.02495,1.02517,1.02547,1.02583,1.02625,1.02675,1.02731,1.02794,1.02865,1.02942,1.03027,1.0312,1.03221,1.03329,1.03446,1.03572,1.03707,1.0385,1.04004,1.04167,1.0434,1.04524,1.04719,1.04925,1.05143,1.05373,1.05616,1.05872,1.06142,1.06427,1.06726,1.0704,1.07371,1.07718,1.08083,1.08465,1.08867,1.09287,1.09728,1.10189,1.10672,1.11177,1.11705,1.12257,1.12834,1.13436,1.14064,1.14719,1.15401,1.16112,1.16853,1.17623,1.18423,1.19255,1.20119,1.21016,1.21946,1.22909,1.23906,1.24938,1.26005,1.27107,1.28244,1.29416,1.30624,1.31867,1.33145,1.34458,1.35806,1.37187,1.38602,1.40049,1.41527,1.43036,1.44574,1.4614,1.47733,1.4935,1.5099,1.52651,1.54332,1.56029,1.5774,1.59464,1.61196,1.62936,1.64679,1.66423,1.68165,1.69902,1.71631,1.73348,1.7505,1.76733,1.78396,1.80034,1.81644,1.83223,1.84768,1.86276,1.87744,1.8917,1.90551,1.91884,1.93167,1.94399,1.95578,1.96701,1.97769,1.98779,1.99732,2.00627,2.01463,2.02241,2.02961,2.03624,2.0423,2.04781,2.05278,2.05723,2.06117,2.06462,2.0676,2.07014,2.07226,2.07397,2.07531,2.07629,2.07695,2.0773,2.07737,2.07717,2.07674,2.0761,2.07525,2.07423,2.07304,2.0717,2.07023,2.06864,2.06694,2.06514,2.06325,2.06126,2.0592,2.05706,2.05484,2.05255,2.05017,2.04772,2.04519,2.04257,2.03985,2.03704,2.03412,2.03108,2.02792,2.02463,2.02118,2.01758,2.0138,2.00984,2.00567,2.00129,1.99667,1.9918,1.98666,1.98122,1.97547,1.96938,1.96293,1.9561,1.94885,1.94116,1.933,1.92433,1.91513,1.90535,1.89496,1.88392,1.87217,1.85968,1.8464,1.83227,1.81723,1.80122,1.78418,1.76603,1.74669,1.72609,1.70414,1.68073,1.65577,1.62915,1.60074,1.57041,1.53803},
{1.02472,1.02474,1.02482,1.02497,1.02518,1.02545,1.02579,1.0262,1.02667,1.02722,1.02783,1.02851,1.02927,1.0301,1.03101,1.03199,1.03306,1.03421,1.03544,1.03676,1.03818,1.03969,1.0413,1.043,1.04482,1.04674,1.04878,1.05093,1.05321,1.05561,1.05815,1.06082,1.06363,1.0666,1.06971,1.07299,1.07643,1.08005,1.08385,1.08783,1.092,1.09638,1.10097,1.10577,1.11079,1.11605,1.12154,1.12728,1.13328,1.13954,1.14607,1.15289,1.15998,1.16738,1.17507,1.18308,1.19141,1.20006,1.20904,1.21836,1.22802,1.23803,1.24839,1.25911,1.27019,1.28163,1.29343,1.3056,1.31814,1.33104,1.3443,1.35792,1.37189,1.38621,1.40087,1.41586,1.43117,1.44679,1.46271,1.47891,1.49538,1.5121,1.52905,1.54621,1.56355,1.58106,1.59871,1.61648,1.63433,1.65224,1.67018,1.68812,1.70602,1.72386,1.7416,1.75921,1.77666,1.79391,1.81092,1.82767,1.84413,1.86025,1.87602,1.8914,1.90635,1.92087,1.93491,1.94846,1.96149,1.974,1.98595,1.99734,2.00815,2.01838,2.02802,2.03707,2.04552,2.05339,2.06067,2.06737,2.07351,2.07909,2.08413,2.08865,2.09266,2.09618,2.09925,2.10187,2.10407,2.10588,2.10731,2.1084,2.10917,2.10963,2.10982,2.10975,2.10945,2.10893,2.10822,2.10733,2.10628,2.10508,2.10374,2.10229,2.10072,2.09905,2.09728,2.09542,2.09347,2.09144,2.08932,2.08712,2.08484,2.08247,2.08001,2.07745,2.07479,2.07202,2.06914,2.06614,2.063,2.05971,2.05627,2.05266,2.04887,2.04488,2.04069,2.03626,2.0316,2.02667,2.02146,2.01595,2.01012,2.00394,1.9974,1.99046,1.9831,1.97529,1.96701,1.95821,1.94886,1.93893,1.92838,1.91716,1.90523,1.89255,1.87905,1.86469,1.8494,1.83313,1.81579,1.79732,1.77763,1.75664,1.73425,1.71035,1.68484,1.65759,1.62847,1.59734},
{1.0248,1.0248,1.02486,1.02499,1.02518,1.02543,1.02575,1.02614,1.02659,1.02712,1.02771,1.02837,1.02911,1.02992,1.0308,1.03177,1.03281,1.03394,1.03515,1.03645,1.03784,1.03933,1.04091,1.04259,1.04438,1.04628,1.04829,1.05041,1.05266,1.05503,1.05754,1.06018,1.06297,1.0659,1.06899,1.07223,1.07564,1.07923,1.08299,1.08694,1.09109,1.09543,1.09998,1.10475,1.10974,1.11497,1.12044,1.12615,1.13212,1.13836,1.14487,1.15166,1.15874,1.16612,1.1738,1.1818,1.19013,1.19878,1.20777,1.2171,1.22678,1.23681,1.24721,1.25797,1.2691,1.28061,1.29249,1.30474,1.31737,1.33038,1.34376,1.35751,1.37163,1.38611,1.40095,1.41614,1.43166,1.44751,1.46368,1.48015,1.4969,1.51393,1.5312,1.54871,1.56642,1.58432,1.60239,1.62058,1.63889,1.65727,1.6757,1.69416,1.7126,1.73099,1.74931,1.76751,1.78556,1.80344,1.8211,1.83851,1.85563,1.87244,1.8889,1.90498,1.92066,1.93589,1.95066,1.96494,1.97871,1.99195,2.00463,2.01675,2.02829,2.03925,2.0496,2.05936,2.06852,2.07707,2.08503,2.0924,2.09918,2.1054,2.11106,2.11618,2.12078,2.12488,2.12849,2.13164,2.13436,2.13666,2.13858,2.14012,2.14133,2.14221,2.1428,2.14312,2.14319,2.14303,2.14265,2.14208,2.14134,2.14043,2.13938,2.13819,2.13688,2.13545,2.13392,2.13229,2.13056,2.12873,2.12682,2.12482,2.12273,2.12055,2.11828,2.11591,2.11343,2.11085,2.10816,2.10534,2.10239,2.0993,2.09606,2.09265,2.08907,2.08531,2.08134,2.07716,2.07275,2.06809,2.06317,2.05796,2.05245,2.04661,2.04042,2.03387,2.02692,2.01955,2.01172,2.00342,1.9946,1.98523,1.97528,1.9647,1.95345,1.94149,1.92877,1.91523,1.90082,1.88548,1.86913,1.85171,1.83313,1.81331,1.79216,1.76957,1.74543,1.71962,1.69201,1.66245},
{1.02488,1.02486,1.0249,1.025,1.02517,1.02541,1.02571,1.02607,1.02651,1.02701,1.02758,1.02822,1.02894,1.02973,1.03059,1.03153,1.03255,1.03366,1.03485,1.03612,1.03749,1.03895,1.04051,1.04216,1.04392,1.04579,1.04777,1.04987,1.05209,1.05443,1.05691,1.05952,1.06227,1.06517,1.06823,1.07144,1.07481,1.07836,1.08209,1.08601,1.09011,1.09442,1.09894,1.10367,1.10863,1.11382,1.11925,1.12493,1.13087,1.13708,1.14356,1.15032,1.15738,1.16474,1.17241,1.18039,1.18871,1.19735,1.20634,1.21568,1.22537,1.23542,1.24585,1.25664,1.26781,1.27937,1.29131,1.30363,1.31635,1.32945,1.34294,1.35682,1.37107,1.38571,1.40071,1.41608,1.43181,1.44788,1.46429,1.48101,1.49804,1.51536,1.53296,1.5508,1.56887,1.58715,1.60562,1.62424,1.64299,1.66184,1.68077,1.69973,1.7187,1.73765,1.75654,1.77533,1.794,1.8125,1.83081,1.84888,1.86668,1.88419,1.90135,1.91815,1.93455,1.95051,1.96602,1.98105,1.99557,2.00956,2.023,2.03587,2.04816,2.05986,2.07095,2.08144,2.09132,2.10059,2.10925,2.11731,2.12477,2.13165,2.13795,2.14371,2.14892,2.15361,2.1578,2.16152,2.16477,2.1676,2.17001,2.17205,2.17372,2.17505,2.17607,2.1768,2.17726,2.17748,2.17747,2.17724,2.17683,2.17624,2.1755,2.1746,2.17357,2.17241,2.17114,2.16976,2.16827,2.16668,2.165,2.16323,2.16136,2.15939,2.15733,2.15518,2.15292,2.15055,2.14807,2.14547,2.14274,2.13988,2.13688,2.13372,2.13039,2.12689,2.1232,2.11931,2.1152,2.11086,2.10627,2.10142,2.09628,2.09084,2.08508,2.07898,2.07251,2.06564,2.05836,2.05064,2.04243,2.03372,2.02447,2.01463,2.00418,1.99307,1.98124,1.96866,1.95527,1.941,1.9258,1.9096,1.89231,1.87386,1.85415,1.83309,1.81056,1.78645,1.76061,1.73291},
{1.02495,1.02491,1.02493,1.02502,1.02517,1.02538,1.02566,1.026,1.02642,1.0269,1.02745,1.02807,1.02876,1.02953,1.03037,1.03129,1.03229,1.03337,1.03453,1.03578,1.03712,1.03856,1.04009,1.04172,1.04345,1.04529,1.04724,1.04931,1.0515,1.05381,1.05625,1.05883,1.06155,1.06441,1.06743,1.0706,1.07394,1.07745,1.08114,1.08502,1.08909,1.09336,1.09783,1.10253,1.10745,1.1126,1.11799,1.12363,1.12954,1.13571,1.14215,1.14888,1.15591,1.16324,1.17089,1.17885,1.18714,1.19578,1.20476,1.21409,1.22378,1.23385,1.24428,1.2551,1.26631,1.27791,1.2899,1.30228,1.31507,1.32826,1.34184,1.35583,1.37021,1.38499,1.40015,1.41569,1.43161,1.44789,1.46452,1.48149,1.49879,1.5164,1.5343,1.55247,1.5709,1.58955,1.60841,1.62745,1.64664,1.66596,1.68537,1.70484,1.72434,1.74384,1.76331,1.7827,1.80198,1.82112,1.84007,1.85881,1.8773,1.89551,1.91339,1.93091,1.94805,1.96477,1.98103,1.99682,2.01211,2.02687,2.04108,2.05473,2.06779,2.08026,2.09212,2.10337,2.114,2.12401,2.1334,2.14218,2.15035,2.15792,2.1649,2.17132,2.17718,2.1825,2.1873,2.1916,2.19544,2.19882,2.20177,2.20432,2.20649,2.20831,2.20979,2.21097,2.21186,2.21248,2.21287,2.21303,2.21298,2.21275,2.21234,2.21177,2.21106,2.21021,2.20923,2.20814,2.20693,2.20563,2.20422,2.20271,2.20111,2.19941,2.19761,2.19572,2.19372,2.19162,2.18942,2.1871,2.18466,2.18209,2.17939,2.17655,2.17355,2.1704,2.16706,2.16355,2.15984,2.15591,2.15177,2.14738,2.14274,2.13782,2.13262,2.1271,2.12125,2.11506,2.10848,2.1015,2.0941,2.08624,2.07789,2.06902,2.0596,2.04958,2.03892,2.02757,2.01549,2.00263,1.98892,1.9743,1.95869,1.94203,1.92422,1.90517,1.88478,1.86292,1.83948,1.81431},
{1.02503,1.02496,1.02496,1.02503,1.02515,1.02535,1.02561,1.02593,1.02632,1.02678,1.02731,1.02791,1.02858,1.02932,1.03014,1.03103,1.03201,1.03306,1.0342,1.03543,1.03674,1.03815,1.03965,1.04125,1.04296,1.04477,1.04669,1.04872,1.05088,1.05316,1.05556,1.0581,1.06079,1.06361,1.06659,1.06973,1.07303,1.0765,1.08015,1.08398,1.08801,1.09223,1.09667,1.10132,1.10619,1.1113,1.11665,1.12225,1.12811,1.13424,1.14064,1.14734,1.15433,1.16162,1.16923,1.17717,1.18544,1.19405,1.20301,1.21233,1.22202,1.23208,1.24252,1.25336,1.26458,1.27621,1.28824,1.30067,1.31352,1.32678,1.34045,1.35454,1.36903,1.38393,1.39924,1.41494,1.43104,1.44751,1.46436,1.48156,1.49911,1.517,1.53519,1.55368,1.57245,1.59147,1.61071,1.63016,1.64978,1.66956,1.68945,1.70942,1.72945,1.7495,1.76953,1.78952,1.80941,1.82919,1.8488,1.86821,1.8874,1.90631,1.92491,1.94317,1.96106,1.97854,1.99557,2.01214,2.02822,2.04377,2.05877,2.07321,2.08707,2.10033,2.11298,2.12502,2.13642,2.1472,2.15735,2.16688,2.17578,2.18408,2.19177,2.19887,2.20541,2.21139,2.21683,2.22176,2.2262,2.23017,2.23369,2.23679,2.23949,2.24182,2.2438,2.24546,2.24681,2.24788,2.24869,2.24926,2.24962,2.24977,2.24973,2.24953,2.24916,2.24865,2.24801,2.24724,2.24636,2.24536,2.24426,2.24306,2.24176,2.24036,2.23887,2.23728,2.2356,2.23381,2.23193,2.22994,2.22784,2.22562,2.22328,2.22081,2.2182,2.21545,2.21254,2.20947,2.20623,2.2028,2.19917,2.19534,2.19127,2.18698,2.18242,2.1776,2.17249,2.16707,2.16132,2.15522,2.14875,2.14189,2.13459,2.12685,2.11862,2.10986,2.10056,2.09065,2.0801,2.06887,2.05689,2.04411,2.03047,2.01589,2.0003,1.98361,1.96572,1.94654,1.92593,1.90376},
{1.0251,1.02501,1.02499,1.02503,1.02514,1.02531,1.02555,1.02585,1.02622,1.02666,1.02716,1.02774,1.02839,1.02911,1.0299,1.03077,1.03172,1.03275,1.03386,1.03506,1.03635,1.03773,1.0392,1.04077,1.04245,1.04422,1.04611,1.04811,1.05023,1.05248,1.05485,1.05735,1.06,1.06278,1.06572,1.06882,1.07208,1.0755,1.07911,1.0829,1.08688,1.09106,1.09544,1.10004,1.10487,1.10993,1.11523,1.12078,1.1266,1.13268,1.13904,1.14568,1.15263,1.15988,1.16745,1.17535,1.18359,1.19217,1.2011,1.2104,1.22007,1.23012,1.24056,1.25139,1.26263,1.27427,1.28633,1.2988,1.3117,1.32501,1.33876,1.35293,1.36752,1.38253,1.39797,1.41382,1.43007,1.44673,1.46378,1.4812,1.49899,1.51714,1.53561,1.55441,1.5735,1.59287,1.61249,1.63234,1.65238,1.6726,1.69297,1.71344,1.73399,1.75458,1.77518,1.79575,1.81626,1.83667,1.85694,1.87703,1.89691,1.91653,1.93587,1.95488,1.97352,1.99178,2.0096,2.02696,2.04384,2.0602,2.07601,2.09127,2.10595,2.12002,2.13349,2.14633,2.15854,2.17012,2.18106,2.19136,2.20103,2.21008,2.21852,2.22635,2.23359,2.24027,2.24639,2.25198,2.25706,2.26165,2.26578,2.26946,2.27273,2.27561,2.27812,2.28029,2.28214,2.2837,2.28497,2.286,2.28679,2.28736,2.28774,2.28793,2.28796,2.28783,2.28756,2.28716,2.28663,2.286,2.28525,2.2844,2.28345,2.2824,2.28126,2.28004,2.27871,2.2773,2.27579,2.27419,2.27249,2.27068,2.26877,2.26674,2.2646,2.26233,2.25993,2.2574,2.25471,2.25187,2.24886,2.24568,2.24231,2.23874,2.23496,2.23096,2.22671,2.22221,2.21744,2.21238,2.20701,2.20131,2.19526,2.18883,2.182,2.17474,2.16702,2.1588,2.15004,2.14071,2.13076,2.12015,2.1088,2.09668,2.0837,2.06979,2.05487,2.03884,2.0216,2.00303},
{1.02517,1.02506,1.02502,1.02504,1.02512,1.02527,1.02549,1.02577,1.02612,1.02653,1.02701,1.02757,1.02819,1.02888,1.02965,1.0305,1.03142,1.03243,1.03351,1.03468,1.03594,1.03729,1.03873,1.04027,1.04192,1.04366,1.04551,1.04748,1.04957,1.05177,1.0541,1.05657,1.05917,1.06192,1.06481,1.06786,1.07108,1.07446,1.07801,1.08175,1.08568,1.08981,1.09415,1.0987,1.10347,1.10848,1.11373,1.11922,1.12498,1.13101,1.13732,1.14391,1.15081,1.15801,1.16553,1.17339,1.18158,1.19012,1.19901,1.20828,1.21792,1.22795,1.23837,1.2492,1.26043,1.27208,1.28415,1.29665,1.30958,1.32294,1.33674,1.35098,1.36566,1.38078,1.39633,1.41231,1.42871,1.44553,1.46277,1.4804,1.49841,1.51681,1.53555,1.55464,1.57405,1.59376,1.61374,1.63398,1.65444,1.6751,1.69593,1.71689,1.73796,1.75909,1.78026,1.80142,1.82255,1.84359,1.86452,1.8853,1.90588,1.92623,1.9463,1.96607,1.98549,2.00453,2.02316,2.04133,2.05903,2.07622,2.09288,2.10898,2.1245,2.13942,2.15373,2.16741,2.18046,2.19287,2.20464,2.21575,2.22623,2.23607,2.24529,2.25389,2.26189,2.2693,2.27614,2.28243,2.28819,2.29345,2.29823,2.30255,2.30643,2.30991,2.313,2.31573,2.31813,2.32021,2.322,2.32353,2.32481,2.32586,2.3267,2.32735,2.32782,2.32813,2.32829,2.32831,2.32821,2.32799,2.32766,2.32723,2.3267,2.32608,2.32537,2.32458,2.32371,2.32275,2.32171,2.32059,2.31938,2.31809,2.31672,2.31525,2.31369,2.31203,2.31027,2.3084,2.30642,2.30432,2.30209,2.29973,2.29723,2.29457,2.29176,2.28878,2.28562,2.28227,2.27872,2.27495,2.27095,2.26671,2.2622,2.25741,2.25233,2.24692,2.24116,2.23504,2.22851,2.22155,2.21413,2.20621,2.19774,2.18868,2.17897,2.16856,2.15738,2.14536,2.13241,2.11843},
{1.02524,1.02511,1.02504,1.02504,1.0251,1.02523,1.02542,1.02568,1.02601,1.0264,1.02686,1.02738,1.02798,1.02866,1.0294,1.03022,1.03112,1.03209,1.03315,1.03429,1.03552,1.03684,1.03825,1.03976,1.04137,1.04308,1.0449,1.04683,1.04888,1.05104,1.05334,1.05576,1.05832,1.06102,1.06387,1.06687,1.07004,1.07337,1.07688,1.08056,1.08444,1.08852,1.0928,1.09729,1.10201,1.10695,1.11214,1.11758,1.12328,1.12925,1.13549,1.14203,1.14887,1.15601,1.16348,1.17128,1.17942,1.18791,1.19676,1.20598,1.21559,1.22558,1.23598,1.24678,1.258,1.26964,1.28171,1.29422,1.30717,1.32056,1.3344,1.3487,1.36344,1.37864,1.39429,1.41038,1.42692,1.44389,1.46129,1.47911,1.49734,1.51596,1.53496,1.55433,1.57404,1.59407,1.6144,1.63501,1.65588,1.67696,1.69824,1.71968,1.74126,1.76292,1.78465,1.8064,1.82813,1.84982,1.87141,1.89286,1.91415,1.93522,1.95605,1.97658,1.99679,2.01663,2.03607,2.05508,2.07362,2.09166,2.10918,2.12614,2.14253,2.15832,2.17351,2.18806,2.20198,2.21526,2.22788,2.23985,2.25117,2.26185,2.27188,2.28129,2.29008,2.29827,2.30588,2.31292,2.31941,2.32538,2.33086,2.33586,2.3404,2.34452,2.34824,2.35159,2.35458,2.35724,2.3596,2.36168,2.3635,2.36508,2.36644,2.3676,2.36857,2.36938,2.37003,2.37054,2.37092,2.37119,2.37134,2.3714,2.37136,2.37124,2.37103,2.37076,2.37041,2.36999,2.3695,2.36895,2.36834,2.36766,2.36692,2.36612,2.36525,2.36431,2.36331,2.36223,2.36108,2.35986,2.35855,2.35716,2.35568,2.35411,2.35244,2.35067,2.34878,2.34678,2.34465,2.34239,2.33999,2.33744,2.33473,2.33185,2.32878,2.32551,2.32204,2.31833,2.31438,2.31016,2.30565,2.30083,2.29567,2.29014,2.2842,2.27781,2.27094,2.26353,2.25552,2.24686}
};
}
}

3
init.sh.in Normal file
View File

@ -0,0 +1,3 @@
export CATIMAPATH=${PROJECT_BINARY_DIR}
#export PATH=$PATH:$CATIMAPATH/bin
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$CATIMAPATH

41
integrator.cpp Normal file
View File

@ -0,0 +1,41 @@
#include "integrator.h"
#include "gsl/gsl_integration.h"
#include "gsl/gsl_errno.h"
namespace catima{
IntegratorGSL integratorGSL;
double funcwrapper3(double x, void *_c){
std::function<double(double)> *f = (std::function<double(double)> *)_c;
return (*f)(x);
}
IntegratorGSL::IntegratorGSL(){
gsl_set_error_handler_off();
w=gsl_integration_workspace_alloc(500);
};
IntegratorGSL::~IntegratorGSL(){
gsl_integration_workspace_free(w);
};
double IntegratorGSL::Integrate(std::function<double(double)> f, double _min, double _max, double prec, bool adaptive){
gsl_function F;
F.function = funcwrapper3;
F.params = &f;
min = _min;
max = _max;
size_t num;
if(adaptive){
#ifdef USE_THREADS
std::lock_guard<std::mutex> lock(integration_mutex);
#endif
gsl_integration_qag(&F,_min,_max,prec,prec,500,6,w,&result,&error);
}
else
gsl_integration_qng(&F,_min,_max,0,prec,&result,&error,&num);
return result;
};
}

51
integrator.h Normal file
View File

@ -0,0 +1,51 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef INTEGRATOR_H
#define INTEGRATOR_H
#include "gsl/gsl_integration.h"
#include <functional>
#ifdef USE_THREADS
#include <mutex>
#endif
namespace catima{
/// helper class to integrate functions using the GSL library
class IntegratorGSL{
public:
IntegratorGSL();
~IntegratorGSL();
double Integrate(std::function<double(double)> f, double min, double max, double precision, bool adaptive=true);
private:
gsl_integration_workspace *w;
double error;
double precision;
double result;
double min;
double max;
#ifdef USE_THREADS
std::mutex integration_mutex;
#endif
};
extern IntegratorGSL integratorGSL;
}
#endif

36
material_database.cpp Normal file
View File

@ -0,0 +1,36 @@
#include "catima/material_database.h"
#include "catima/nucdata.h"
namespace catima{
Material get_material(int id){
if(id>0 && id<ELEMENT_DENSITY_MAXZ){
return Material(0,id,element_density(id),0.0);
}
switch(id){
case material::PLASTIC : return Material({{0,1,10},{0,6,9}},1.032);
case material::AIR : return Material({{0,7,4}, {0,8,1}},0.0012);
case material::CH2 : return Material({{0,6,1}, {0,1,2}},0.94);
case material::LH2 : return Material({{0,1,1}},0.0708);
case material::LD2 : return Material({{2.014,1,1}},0.162);
case material::WATER : return Material({{0,1,2},{0,8,1}},1.0);
case material::DIAMOND: return Material(0,6,3.52,0.0);
case material::GLASS : return Material({{0,14,1},{0,8,2}},2.4 );
case material::ALMG3: return Material(0,13,2.67,0.0);
case material::ARCO2_30: return Material({{0,18,7},{0,8,6},{0,6,3}}, 0.00171);
case material::CF4 : return Material({{0,6,1},{0,9,4}}, 0.00372 );
case material::ISOBUTANE:return Material({{0,6,4}, {0,1,10}},0.00251);
case material::KAPTON : return Material({{0,1,10}, {0,6,22},{0,7,2},{0,8,5}},1.42);
case material::MYLAR : return Material({{0,6,5}, {0,1,4},{0,8,2}},1.38);
case material::NAF : return Material({{0,11,1}, {0,9,1}},2.56);
case material::P10: return Material({{0,18,9},{0,6,1},{0,1,4}}, 0.00166);
case material::POLYOLEFIN: return Material({{0,1,16},{0,6,10}}, 0.9);
case material::CMO2: return Material({{0,96,1},{0,8,2}}, 12.0);
case material::SUPRASIL : return Material({{0,14,1},{0,8,2}},2.2 );
case material::HAVAR : return Material({{0,27,42},{0,24,40},{0,28,13},{0,26,19},{0,74,1}},8.3);
default:break;
}
return Material();
}
}

35
material_database.h Normal file
View File

@ -0,0 +1,35 @@
#ifndef MATERIAL_DATABASE
#define MATERIAL_DATABASE
#include "catima/catima.h"
namespace catima{
//namespace material{
enum material{
PLASTIC = 201,
AIR = 202,
CH2,
LH2,
LD2,
WATER,
DIAMOND,
GLASS,
ALMG3,
ARCO2_30,
CF4,
ISOBUTANE,
KAPTON,
MYLAR,
NAF,
P10,
POLYOLEFIN,
CMO2,
SUPRASIL,
HAVAR
};
//}
Material get_material(int);
}
#endif

218
nucdata.cpp Normal file
View File

@ -0,0 +1,218 @@
#include "nucdata.h"
namespace catima{
double element_atomic_weights[110]={
0.0,
1.00794, //H
4.0026, //He
6.941, //Li
9.01218, //Be
10.811, //B
12.0107, //C
14.0067, //N
15.9994, //O
18.9984, //F
20.1797, //Ne
22.9898, //Na
24.305, //Mg
26.9815, //Al
28.0855, //Si
30.9738, //P
32.065, //S
35.453, //Cl
39.948, //Ar
39.0983, //K
40.078, //Ca
44.9559, //Sc
47.867, //Ti
50.9415, //V
51.9961, //Cr
54.938, //Mn
55.845, //Fe
58.9332, //Co
58.6934, //Ni
63.546, //Cu
65.409, //Zn
69.723, //Ga
72.64, //Ge
74.9216, //As
78.96, //Se
79.904, //Br
83.798, //Kr
85.4678, //Rb
87.62, //Sr
88.9059, //Y
91.224, //Zr
92.9064, //Nb
95.94, //Mo
97.9072, //Tc
101.07, //Ru
102.906, //Rh
106.42, //Pd
107.868, //Ag
112.411, //Cd
114.818, //In
118.71, //Sn
121.76, //Sb
127.6, //Te
126.904, //I
131.293, //Xe
132.905, //Cs
137.327, //Ba
138.905, //La
140.116, //Ce
140.908, //Pr
144.24, //Nd
144.913, //Pm
150.36, //Sm
151.964, //Eu
157.25, //Gd
158.925, //Tb
162.5, //Dy
164.93, //Ho
167.259, //Er
168.934, //Tm
173.04, //Yb
174.967, //Lu
178.49, //Hf
180.948, //Ta
183.84, //W
186.207, //Re
190.23, //Os
192.217, //Ir
195.078, //Pt
196.967, //Au
200.59, //Hg
204.383, //Tl
207.2, //Pb
208.98, //Bi
208.982, //Po
209.987, //At
222.018, //Rn
223.02, //Fr
226.025, //Ra
227.028, //Ac
232.038, //Th
231.036, //Pa
238.029, //U
237.048, //Np
244.064, //Pu
243.061, //Am
247.07, //Cm
247.07, //Bk
251.08, //Cf
252.083, //Es
257.095, //Fm
258.098, //Md
259.101, //No
262.11, //Lr
261.109, //Rf
262.114, //Db
266.122, //Sg
264.125, //Bh
269.134, //Hs
268.139 //Mt
};
double element_densities[99]={
0.0,
8.37480e-5, // 1,
1.66322e-4, // 2,
0.534 , // 3,
1.848 , // 4,
2.37 , // 5,
2.0 ,// 6,
1.16520e-3, // 7,
1.33151e-3, // 8,
1.58029e-3, // 9,
8.38505e-4, // 10,
0.971 , // 11,
1.74 , // 12,
2.699 , //13,
2.33 , // 14,
2.2 , //15,
2.0 , //16,
2.99473e-3, //17,
1.66201e-3, //18,
0.862 , //19,
1.55 , //20,
2.989 , //21,
4.54 , //22,
6.11 , //23,
7.18 , //24,
7.44 , //25,
7.874 , //26,
8.9 , //27,
8.902 , //28,
8.96 , //29,
7.133 , //30,
5.904 , //31,
5.323 , //32,
5.73 , //33,
4.5 , //34,
3.1028 , //7.07210e-3, //35,
3.47832e-3, //36,
1.532 , //37,
2.54 , //38,
4.469 , //39,
6.506 , //40,
8.57 , //41,
10.22 , //42,
11.50 , //43,
12.41 , //44,
12.41 , //45,
12.02 , //46,
10.5 , //47,
8.65 , //48,
7.31 , //49,
7.31 , //50,
6.691 , //51,
6.24 , //52,
4.93 , //53,
5.48536e-3, //54,
1.873 , //55,
3.5 , //56,
6.154 , //57,
6.657 , //58,
6.71 , //59,
6.9 , //60,
7.22 , //61,
7.46 , //62,
5.243 , //63,
7.9004 , //64,
8.229 , //65,
8.55 , //66,
8.795 , //67,
9.066 , //68,
9.321 , //69,
6.73 , //70,
9.84 , //71,
13.31 , //72,
16.654 , //73,
19.30 , //74,
21.02 , //75,
22.57 , //76,
22.42 , //77,
21.45 , //78,
19.32 , //79,
13.546 , //80,
11.72 , //81,
11.35 , //82,
9.747 , //83,
9.32 , //84,
9.32 , //85
9.00662e-3, //86
1.00 , //87
5.00 , //88
10.07 , //89
11.72 , //90
15.37 , //91
18.95 , //92
20.25 , //93
19.84 , //94
13.67 , //95
13.51 , //96
14.00 , //97
10.00 //98
};
}

39
nucdata.h Normal file
View File

@ -0,0 +1,39 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef nucdata_h
#define nucdata_h
#define ATOMIC_WEIGHT_MAXZ 110
#define ELEMENT_DENSITY_MAXZ 99
namespace catima{
extern double element_atomic_weights[110];
extern double element_densities[99];
inline double element_atomic_weight(int z){
return (z>0 && z<110)?element_atomic_weights[z]:0.0;
}
inline double element_density(int z){
return (z>0 && z<99)?element_densities[z]:0.0;
}
}
#endif

16
setup.py.in Normal file
View File

@ -0,0 +1,16 @@
from distutils.core import setup
from distutils.extension import Extension
from Cython.Build import cythonize
setup(
ext_modules = cythonize(
[Extension("catima", ["catima.pyx"],
language="c++",
#libraries=[${EXTRA_PYTHON_LIBS}],
include_dirs=["${CMAKE_CURRENT_BINARY_DIR}/include"],
extra_objects=["${CATIMA_LIB}"],
extra_compile_args=["-std=c++14"],
extra_link_args=["-std=c++14"]
),
])
)

104
storage.cpp Normal file
View File

@ -0,0 +1,104 @@
#include <math.h>
#include <iostream>
#include "storage.h"
namespace catima {
Data _storage;
bool operator==(const DataPoint &a, const DataPoint &b){
if( (a.m == b.m) && (a.p == b.p) && (a.config == b.config)){
return true;
}
else{
return false;
}
}
DataPoint::~DataPoint(){
}
Data::Data(){
//storage.reserve(max_storage_data);
storage.resize(max_storage_data);
index = storage.begin();
}
Data::~Data(){
}
void Data::Add(const Projectile &p, const Material &t, Config c){
DataPoint dp(p,t,c);
for(auto &e:storage){
if(e==dp)return;
}
if(index==storage.end())index=storage.begin();
#if(0)
*index = dp;
index->range = calculate_range(p,t,c);
index->range_straggling = calculate_range_straggling(p,t,c);
index->angular_variance = calculate_angular_variance(p,t,c);
#else
*index = calculate_DataPoint(p,t,c);
#endif
index++;
}
DataPoint& Data::Get(const Projectile &p, const Material &t, Config c){
for(auto &e:storage){
if( (e.p==p) && (e.m==t) && (e.config==c)){
return e;
}
}
Add(p,t,c);
//return storage.back();
return *std::prev(index);
}
//////////// Interpolator ////////////////////////////////
Interpolator::Interpolator(const double *x, const double *y, int num,interpolation_t type){
acc = gsl_interp_accel_alloc ();
if(type==cspline)
spline = gsl_spline_alloc (gsl_interp_cspline, num);
else
spline = gsl_spline_alloc (gsl_interp_linear, num);
gsl_spline_init (spline, x, y, num);
min= x[0];
max= x[num-1];
}
Interpolator::Interpolator(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type){
//Interpolator(x.data(),y.data(),x.size());
acc = gsl_interp_accel_alloc ();
if(type==cspline)
spline = gsl_spline_alloc (gsl_interp_cspline, x.size());
else
spline = gsl_spline_alloc (gsl_interp_linear, x.size());
gsl_spline_init (spline, x.data(), y.data(), x.size());
min= x[0];
max= x[x.size()-1];
}
Interpolator::~Interpolator(){
gsl_interp_accel_free (acc);
gsl_spline_free (spline);
}
double Interpolator::eval(double x){
if(x<min)x=min;
if(x>max)x=max;
return gsl_spline_eval(spline, x, acc);
}
double Interpolator::derivative(double x){
if(x<min)x=min;
if(x>max)x=max;
return gsl_spline_eval_deriv (spline, x, acc);
}
}

143
storage.h Normal file
View File

@ -0,0 +1,143 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef STORAGE
#define STORAGE
#include <vector>
#include <iterator>
//#include <unordered_set>
#include <gsl/gsl_spline.h>
#include "catima/constants.h"
#include "catima/catima.h"
namespace catima{
enum interpolation_t {cspline, linear};
//inline double energy_function( int i ) { return exp(M_LN10*(logEmin + ((double)i)*(logEmax-logEmin)/(max_datapoints - 1.0))); }
enum DataType{TYPE_RANGE,TYPE_LS};
template<int N>
struct EnergyTable{
constexpr EnergyTable(double logmin, double logmax):values(),step(0.0),num(N){
step = (logmax-logmin)/(N - 1.0);
for(auto i=0;i<N;i++){
values[i]=exp(M_LN10*(logmin + ((double)i)*step));
}
}
double operator()(int i)const{return values[i];}
double values[N];
double step;
std::size_t num;
};
template<int N>
int EnergyTable_index(const EnergyTable<N> &table, double val){
val = log(val)/M_LN10;
if(val<table.values[0] || val>table.values[table.num-1])return -1;
int i = (int)val/table.step;
//double x = 1.0 - ((val - table.valuesp[i])/table.step);
return i;
}
template<int N>
double EnergyTable_interpolate(const EnergyTable<N> &table, double xval, double *y){
double r;
double lxval = log(xval)/M_LN10;
if(lxval<table.values[0] || lxval>table.values[table.num-1])return 0.0;
if(lxval==table.values[table.num-1])return y[table.num-1];
int i = (int)(lxval/table.step);
double linstep = table.values[i+1] - table.values[i];
double x = 1.0 - ((xval - table.values[i])/linstep);
r = (x*y[i]) + ((1-x)*y[i+1]);
return r;
}
/*
template<int N>
struct EnergyTableLinear{
constexpr EnergyTableLinear():values(),num(N){
for(auto i=0;i<N;i++){
values[i]=exp(M_LN10*(logEmin + ((double)i)*(logEmax-logEmin)/(N - 1.0)));
}
}
double operator()(int i)const{return values[i];}
double values[N];
std::size_t num;
};
*/
constexpr EnergyTable<max_datapoints> energy_table(logEmin,logEmax);
class DataPoint{
public:
Projectile p;
Material m;
Config config;
std::vector<double> range;
std::vector<double> range_straggling;
std::vector<double> angular_variance;
DataPoint(){};
DataPoint(const Projectile _p, const Material _m,Config _c=default_config):p(_p),m(_m),config(_c){};
~DataPoint();
friend bool operator==(const DataPoint &a, const DataPoint &b);
};
class Data{
public:
Data();
~Data();
void Add(const Projectile &p, const Material &t, Config c=default_config);
int GetN() const {return storage.size();};
void Reset(){storage.clear();storage.resize(max_storage_data);};
DataPoint& Get(const Projectile &p, const Material &t, Config c=default_config);
int get_index() {return std::distance(storage.begin(),index);}
private:
std::vector<DataPoint> storage;
std::vector<DataPoint>::iterator index;
};
/// Interpolation class, to store interpolated values
class Interpolator{
public:
Interpolator(const double *x, const double *y, int num,interpolation_t type=cspline);
Interpolator(const std::vector<double>& x, const std::vector<double>& y,interpolation_t type=cspline);
~Interpolator();
double operator()(double x){return eval(x);};
double eval(double x);
double derivative(double x);
double get_min(){return min;};
double get_max(){return max;};
private:
double min=0;
double max=0;
gsl_interp_accel *acc;
gsl_spline *spline;
};
extern Data _storage;
inline DataPoint& get_data(const Projectile &p, const Material &t, Config c=default_config){
return _storage.Get(p, t, c);
}
bool operator==(const DataPoint &a, const DataPoint &b);
}
#endif

98
structures.cpp Normal file
View File

@ -0,0 +1,98 @@
#include "structures.h"
#include "catima/nucdata.h"
namespace catima{
bool operator==(const Projectile &a, const Projectile&b){
if( (a.A==b.A) && (a.Z==b.Z) && (a.Q==b.Q)){
return true;
}
else
return false;
}
bool operator==(const Material &a, const Material&b){
if(a.molar_mass != b.molar_mass)return false;
if(a.density() != b.density())return false;
if(a.ncomponents() != b.ncomponents())return false;
for(int i=0;i<a.ncomponents();i++){
if(a.stn[i] != b.stn[i])return false;
if(a.atoms[i].A != b.atoms[i].A)return false;
if(a.atoms[i].Z != b.atoms[i].Z)return false;
}
return true;
}
/*
Material::Material(const std::array<double,2> &list){
add_element(list[0],list[1],1.0);
}
*/
Material::Material(std::initializer_list<std::array<double,3>>list,double _density):rho(_density){
std::initializer_list<std::array<double,3>>::iterator it;
for ( it=list.begin(); it!=list.end(); ++it){
add_element( (*it)[0],(*it)[1],(*it)[2]);
}
}
Material::Material(double _a, int _z, double _rho, double _th):rho(_rho),th(_th){
add_element(_a,_z,1.0);
}
void Material::add_element(double _a, int _z, double _stn){
double a = (_a>0)?_a:element_atomic_weight(_z);
stn.push_back(_stn);
atoms.push_back({a,_z});
molar_mass += _stn*a;
}
std::pair<Target,double> Material::get_element(int i) const{
return std::pair<Target,double>(atoms[i],stn[i]);
}
/*
void Material::calculate(){
molar_mass = 0;
for(int i=0;i<ncomponents();i++){
molar_mass += stn[i]*a[i];
}
}
*/
Layers& Layers::operator=(const Layers& other){
materials.clear();
for(auto&e : other.get_materials()){
materials.push_back(e);
}
return *this;
}
void Layers::add(Material m){
materials.push_back(m);
}
Layers operator+(const Layers &a, const Layers&b){
Layers res;
for(auto &e:a.materials){
res.add(e);
}
for(auto &e:b.materials){
res.add(e);
}
return res;
}
Layers operator+(const Layers &a, const Material &m){
Layers res;
for(auto &e:a.materials){
res.add(e);
}
res.add(m);
}
}

207
structures.h Normal file
View File

@ -0,0 +1,207 @@
/*
* Author: Andrej Prochazka
* Copyright(C) 2017
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef STRUCTURES_H
#define STRUCTURES_H
#include <vector>
#include <array>
#include <initializer_list>
namespace catima{
/**
* Projectile class
* Example usage:
* \code{.cpp}
* Projectile p(12,6);
* p.T = 1000; // setting energy to 1000 MeV/u
* p(1000); // setting energy to 1000 MeV/u
* \endcode
*/
struct Projectile{
double A=0;
double Z=0;
double Q=0;
double T=0;
Projectile& operator()(double e){T=e;return *this;}
Projectile(){}
Projectile(double a, double z, double q=0, double t=0):A(a),Z(z),Q(q),T(t){if(q==0)Q=Z;}
};
bool operator==(const Projectile &a, const Projectile&b);
/**
* Target class is used to store constituents of the Material class
* its just to hold A,Z data for individual atoms.
*/
struct Target{
double A=0;
int Z=0;
};
/**
* Material
* class to store Material information
* This class defines the material with which projectile will interact.
* The class store nuclei constituents, density, thickness etc.
*/
class Material{
private:
double rho=0;
double th=0;
double molar_mass=0;
std::vector<Target>atoms;
std::vector<double>stn;
public:
Material(){};
/**
* constructor to add 1 element into the Material, stn number of the element is set to 1.0
* @param _a - mass number of the atom, is 0 the atomic weight of element _z is taken
* @param _z - proton number of the atom
* @param _rho - density of the material in g/cm3, default 0.0
* @param _th - thickness of the material in g/cm2, default 0.0
*/
Material(double _a, int _z, double _rho=0.0, double _th=0.0);
/**
* constructor to add 1 or multiple element into the Material
* \code{.cpp}
* Maetrial water({
{1,1,2},
{16,8,1},
});
* \endcode
*/
Material(std::initializer_list<std::array<double,3>>list,double _density=0.0);
//Material(const std::array<double,2> &list);
void calculate();
/**
* add atom with mass number _a and proton number _z to the Material
* @param _a - mass number of the atom, is 0 the atomic weight of element _z is taken
* @param _z - proton number of the atom
* @param _stn - stoichiomatric number
*/
void add_element(double _a, int _z, double _stn);
/**
* returns i-th element of the Material as a std::pair of Target and corresponding stoichiometric number
* @param i - index of element to return
* @return std::pair of Target and corresponding stoichiometric number
*/
std::pair<Target,double> get_element(int i) const;
/**
* @return number of components in Material
*/
int ncomponents() const {return stn.size();}
/**
* @return returns Molar Mass of the Material
*/
double M() const {return molar_mass;}
/**
* @return returns density in g/cm^3
*/
double density() const {return rho;};
/**
* sets density in g/cm^3
*/
Material& density(double val){rho = val;return *this;};
/**
* @return returns thickness in g/cm^2
*/
double thickness() const {return th;};
/**
* sets thickness in g/cm^2
*/
Material& thickness(double val){th = val;return *this;};
friend bool operator==(const Material &a, const Material&b);
};
bool operator==(const Material &a, const Material&b);
/**
* structure to store results for calculation per Material
*/
struct Result{
double Ein=0.0;
double Eout=0.0;
double Eloss = 0.0;
double range=0.0;
double dEdxi=0.0;
double dEdxo=0.0;
double sigma_E=0.0;
double sigma_a=0.0;
double sigma_r=0.0;
double tof=0.0;
};
/**
* structure to store results for calculation for multiple layers of materials, ie in catima::Layers
*/
struct MultiResult{
std::vector<Result> results;
Result total_result;
};
/**
* Layers
* class to store multiple material layers
*/
class Layers{
private:
std::vector<Material> materials;
public:
Layers(){};
Layers& operator=(const Layers& other);
/**
* @return reference to the std::vector of stored Materials
*/
const std::vector<Material>& get_materials()const{return materials;}
/**
* add Material m to the Layers
* @param m Material
*/
void add(Material m);
/**
* @return number of stored Materials
*/
int num()const{return materials.size();};
Material& operator[](int i){return materials[i];}
friend Layers operator+(const Layers &a, const Layers&b);
friend Layers operator+(const Layers &a, const Material&b);
};
}
#endif

17
tests/CMakeLists.txt Normal file
View File

@ -0,0 +1,17 @@
add_definitions(-Dlest_FEATURE_COLOURISE=1)
include_directories(${CMAKE_CURRENT_SOURCE_DIR}/tests)
set(CATIMA_TESTS test_calculations test_generated test_storage test_structures test_dedx_range)
foreach(entry ${CATIMA_TESTS})
add_executable(${entry} ${entry}.cpp)
target_link_libraries(${entry} catima)
endforeach(entry in ${CATIMA_TESTS})
set(C_TESTS test_c)
MESSAGE( STATUS "CMAKE_C_COMPILER: " ${CMAKE_C_COMPILER} )
foreach(entry ${C_TESTS})
add_executable(${entry} ${entry}.c)
target_link_libraries(${entry} catima)
endforeach(entry in ${C_TESTS})

1300
tests/lest.hpp Normal file
View File

File diff suppressed because it is too large Load Diff

41
tests/test_c.c Normal file
View File

@ -0,0 +1,41 @@
#include <stdio.h>
#include <math.h>
#include "catima/cwrapper.h"
void expect(int r,const char *title){
if(r){
printf("\033[1;32mpassed\033[0m %s\n",title);
}
else
{
printf("\033[1;31mfailed\033[0m %s\n",title);
}
};
int main()
{
CatimaResult r;
double dif;
r = catima_calculate(12,6,500,12,6,1.0,2.0);
dif = r.dEdxi - 87.78;
expect(fabs(dif)<0.5,"dEdx");
dif = r.Eloss - 88.05;
expect(fabs(dif)<0.5,"Eloss");
dif = r.sigma_a - 1.31e-3;
expect(fabs(dif)<0.5,"sigma_a");
dif = r.sigma_E - 0.18;
expect(fabs(dif)<0.01,"sigma_e");
dif = r.range - 43.7;
expect(fabs(dif)<0.5,"range");
r = catima_calculate(12,6,1000,0,206,1.0,1.0);
dif = r.Eloss - 80.75;
expect(fabs(dif)<1,"Eloss");
return 1.0;
}

339
tests/test_calculations.cpp Normal file
View File

@ -0,0 +1,339 @@
#include "lest.hpp"
#include <math.h>
using namespace std;
#include "catima/catima.h"
using lest::approx;
bool rcompare(double a, double b,double eps){
if(fabs((a-b)/fabs(b))<eps){
return true;
}
else{
std::cout<<"\033[1;31m"<<a<<" == "<<b<<"\033[0m"<<std::endl;
return false;
}
}
const lest::test specification[] =
{
CASE("nuclear stopping power"){
catima::Target carbon{12.0107,6};
catima::Projectile p{4.00151,2,2,1};
double dif;
p.T = 0.1/p.A; //0.1MeV
dif = catima::dedx_n(p,carbon) - 14.27;
EXPECT( fabs(dif)< 1);
p.T = 1/p.A; //1MeV
dif = catima::dedx_n(p,carbon) - 2.161;
EXPECT( fabs(dif)< 0.1);
p.T = 10/p.A; //10MeV
dif = catima::dedx_n(p,carbon) - 0.2874;
EXPECT( fabs(dif) < 0.01);
p.T = 100/p.A; //100MeV
dif = catima::dedx_n(p,carbon) - 0.03455;
EXPECT( fabs(dif) < 0.001);
},
CASE("proton stopping power from srim"){
catima::Projectile p{1,1,1,1};
catima::Target he{4.002600,2};
catima::Target carbon{12.0107,6};
double dif,dif2;
dif = catima::sezi_p_se(1,he) - 283;
EXPECT( fabs(dif)< 1);
p.T = 1;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
dif = catima::sezi_p_se(10,he) - 45.6;
EXPECT( fabs(dif)< 1);
p.T = 10;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
dif = catima::sezi_p_se(30,he) - 18.38;
EXPECT( fabs(dif)< 1);
p.T = 30;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
dif = catima::sezi_p_se(1,carbon) - 229.5;
EXPECT( fabs(dif)< 1);
p.T = 1;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
dif = catima::sezi_p_se(10,carbon) - 40.8;
EXPECT( fabs(dif)< 1);
p.T = 10;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
dif = catima::sezi_p_se(30,carbon) - 16.8;
EXPECT( fabs(dif)< 1);
p.T = 30;
dif2 = catima::sezi_p_se(p.T,he) - catima::sezi_dedx_e(p,he);
EXPECT( fabs(dif2)< 0.000001);
},
CASE("dedx, low energy, from sezi"){
catima::Projectile p{4,2,2,1};
catima::Target carbon{12.0107,6};
double dif;
double exp;
// He projectile case
p.T = 1;
EXPECT( rcompare( catima::dedx(p,carbon), 922.06, 0.0001) );
p.T = 3;
EXPECT( rcompare( catima::dedx(p,carbon), 433.09, 0.0001) );
// C projectile case
p.A = 12;
p.Z = 6;
p.T = 1;
EXPECT( rcompare( catima::dedx(p,carbon), 5792.52, 0.0001) );
p.T = 9.9;
EXPECT( rcompare( catima::dedx(p,carbon), 1485.36, 0.0001) );
},
CASE("LS check: deltaL values"){
catima::Projectile p{238,92,92,1};
catima::Target carbon{12.0107,6};
p.T = 93.1494;
EXPECT( rcompare( catima::bethek_lindhard(p), -0.5688, 0.01) );
p.T = 380.9932;
EXPECT( rcompare( catima::bethek_lindhard(p), 0.549199, 0.02) );
p.T = 996.9855;
EXPECT( rcompare( catima::bethek_lindhard(p), 1.0732, 0.03) );
p.T = 2794.4822;
EXPECT( rcompare( catima::bethek_lindhard(p), 1.358964, 0.02) );
},
CASE("LS check: straggling values"){
catima::Projectile p{238,92,92,1};
catima::Target carbon{12.0107,6};
auto f = [&](){return catima::bethek_lindhard_X(p);};
p.T = 93.1494;
EXPECT( rcompare( f(), 1.56898, 0.01) );
p.T = 380.9932;
EXPECT( rcompare( f(), 1.836008, 0.01) );
p.T = 996.9855;
EXPECT( rcompare( f(), 1.836528, 0.03) );
p.T = 2794.4822;
EXPECT( rcompare( f(), 1.768018, 0.02) );
},
CASE("dEdx for compunds"){
catima::Projectile p{1,1,1,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
double dif;
dif = catima::dedx(p,1000, water) - 2.23;
EXPECT( fabs(dif) < 0.002);
dif = catima::dedx(p,500,water) - 2.76;
EXPECT( fabs(dif) < 0.005);
dif = catima::dedx(p,9,water) - 51.17;
EXPECT( fabs(dif) < 0.005);
},
CASE("dEdx from spline vs dEdx"){
catima::Projectile p{238,92,92,1000};
catima::Material graphite({
{12.011,6,1},
});
double dif;
auto res = catima::calculate(p(1000),graphite);
dif = (catima::dedx(p,1000, graphite) - res.dEdxi)/res.dEdxi;
EXPECT(dif == approx(0).epsilon(0.001) );
res = catima::calculate(p,graphite,500);
dif = catima::dedx(p,500,graphite) - res.dEdxi;
EXPECT(dif/res.dEdxi == approx(0).epsilon(0.001) );
res = catima::calculate(p,graphite,9);
dif = catima::dedx(p,9,graphite) - res.dEdxi;
EXPECT(dif/res.dEdxi == approx(0).epsilon(0.001) );
},
// CASE("dOmega2dx Ferisov test"){
//},
CASE("Eout test"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
catima::Material graphite;
graphite.add_element(12,6,1);
graphite.density(2.0);
graphite.thickness(0.5);
double dif;
auto res = catima::calculate(p,graphite);
dif = res.Eout - 997.077;
EXPECT( fabs(dif) < 0.01);
},
CASE("TOF test"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
water.density(1.0);
water.thickness(1.0);
catima::Material graphite;
graphite.add_element(12,6,1);
graphite.density(2.0);
graphite.thickness(0.5);
double dif;
auto res = catima::calculate(p,water);
dif = res.tof - 0.038;
EXPECT( fabs(dif) < 0.01);
},
CASE("result from stopped material"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
water.density(1.0);
water.thickness(1000.0);
auto res = catima::calculate(p,water);
EXPECT(res.Eout == 0.0);
EXPECT(res.Eloss == 1000*12);
EXPECT(res.sigma_E == 0.0);
EXPECT(res.sigma_a == 0.0);
EXPECT(res.sigma_r > 0.0);
EXPECT(res.dEdxo == 0.0);
EXPECT(res.tof == 0.0);
catima::Layers mat;
mat.add(water);
auto res2= catima::calculate(p,mat);
EXPECT(res2.results.size() == 1);
EXPECT(res2.total_result.Eout == res2.results[0].Eout);
EXPECT(res2.total_result.Eout == 0.0);
EXPECT(res2.total_result.Eloss == 1000*12);
EXPECT(res2.total_result.sigma_E == 0.0);
EXPECT(res2.total_result.sigma_a == 0.0);
EXPECT(res2.total_result.tof == 0.0);
},
CASE("constant results from material"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
water.density(1.0);
water.thickness(10.0);
auto res = catima::calculate(p,water);
auto res2 = catima::calculate(p,water);
EXPECT(res.Eout == res2.Eout);
EXPECT(res.Eloss == res2.Eloss);
EXPECT(res.sigma_E == res2.sigma_E);
EXPECT(res.sigma_a == res2.sigma_a);
EXPECT(res.sigma_r == res2.sigma_r);
EXPECT(res.dEdxo == res2.dEdxo);
EXPECT(res.tof == res2.tof);
},
CASE("simplified calculation"){
catima::Projectile p{12,6,6,1000};
catima::Material graphite({
{12.011,6,1},
});
graphite.density(2.0).thickness(1.0);
auto res1 = catima::calculate(p,graphite);
auto res2 = catima::calculate(12,6,1000,12.011,6,1.0,2.0);
EXPECT(res1.Eout == res2.Eout);
EXPECT(res1.Eloss == res2.Eloss);
EXPECT(res1.sigma_E == res2.sigma_E);
EXPECT(res1.sigma_a == res2.sigma_a);
EXPECT(res1.sigma_r == res2.sigma_r);
EXPECT(res1.dEdxo == res2.dEdxo);
EXPECT(res1.tof == res2.tof);
auto ra = catima::angular_straggling_from_E(p,res1.Ein,res1.Eout,graphite);
EXPECT(res1.sigma_a == ra);
auto re = catima::energy_straggling_from_E(p,res1.Ein,res1.Eout,graphite);
EXPECT(res1.sigma_E == re);
auto eo1 = catima::energy_out(p,1000,graphite);
EXPECT(res1.Eout == eo1);
auto de1 = catima::dedx_from_range(p,1000,graphite);
EXPECT(res1.dEdxi == de1);
},
CASE("multilayer basic"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1.00794,1,2},
{15.9994,8,1}
});
water.density(1.0);
water.thickness(10.0);
catima::Material graphite({
{12.011,6,1},
});
graphite.density(2.0).thickness(1.0);
catima::Layers mat;
mat.add(water);
mat.add(graphite);
auto res = catima::calculate(p(1000),mat);
EXPECT(rcompare(res.total_result.Eout,926.3,0.01));
EXPECT(rcompare(res.total_result.sigma_a,0.00269,0.1));
EXPECT(rcompare(res.total_result.tof,0.402,0.01));
EXPECT(rcompare(res.total_result.Eloss,884.218,0.01));
//EXPECT(rcompare(res.total_result.sigma_E,0.7067,0.2));
EXPECT(rcompare(res.results[0].Eout,932.24,0.01));
EXPECT(rcompare(res.results[0].sigma_a,0.00258,0.1));
EXPECT(rcompare(res.results[0].range,107.163,0.01));
EXPECT(rcompare(res.results[1].Eout,926.3,0.01));
EXPECT(rcompare(res.results[1].sigma_a,0.000774,0.1));
EXPECT(rcompare(res.results[1].range,110.715,0.01));
auto res0 = catima::calculate(p(1000),water);
EXPECT(res0.Eout == res.results[0].Eout);
EXPECT(res0.sigma_a == res.results[0].sigma_a);
EXPECT(res0.sigma_E == res.results[0].sigma_E);
EXPECT(res0.sigma_r == res.results[0].sigma_r);
EXPECT(res0.tof == res.results[0].tof);
}
};
int main( int argc, char * argv[] )
{
return lest::run( specification, argc, argv );
}

127
tests/test_dedx_range.cpp Normal file
View File

@ -0,0 +1,127 @@
#include <iostream>
#include <fstream>
#include <string>
#include <cstdlib>
#include <utility>
#include <vector>
#include "catima/catima.h"
using std::cout;
using std::endl;
double logEmax = catima::logEmax;
double logEmin = catima::logEmin;
template<int N>
struct EnergyTable{
constexpr EnergyTable():values(),num(N){
for(auto i=0;i<N;i++){
values[i]=exp(M_LN10*(logEmin + ((double)i)*(logEmax-logEmin)/(N - 1.0)));
}
}
double operator()(int i)const{return values[i];}
double values[N];
std::size_t num;
};
bool expect(bool r,std::string title=""){
if(r){
if(title.size()>0)
cout << "\033[1;32mpassed\033[0m "<<title<<endl;
}
else
{
cout << "\033[1;31m failed\033[0m "<<title<<endl;
}
return r;
}
double rdif(double v1, double v2){
return (v1-v2)/v2;
}
void comp_dedx(catima::Projectile p, catima::Material t, double epsilon = 0.001, bool fout=false, const char* fname=""){
double dif;
//struct atima_results results;
int tz = t.get_element(0).first.Z;
double ta = t.get_element(0).first.A;
bool res;
cout<<"-----------------------------"<<endl;
cout<<"projectile: A = "<<p.A<<", Z = "<<p.Z<<endl;
cout<<"target: A = "<<ta<<", Z = "<<tz<<endl;
EnergyTable<100> etable;
std::ofstream f;
if(fout){
f.open(fname,std::ofstream::out | std::ofstream::trunc);
}
double v1, v2;
for(auto _e : etable.values){
p.T = _e;
v1 = catima::dedx(p,_e,t);
auto ares = catima::calculate(p(_e),t);
v2 = ares.dEdxi;
dif = rdif(v1,v2);
cout<<"T = "<<_e<<endl;
cout<<v1 << " vs "<<v2<<" -> rel. dif = "<<dif<<endl;
if(fout){
f<<_e<<" "<<v1<<" "<<v2<<std::endl;
}
res = expect(fabs(dif)<epsilon,"");
if(!res)exit(0);
}
if(fout){
f.close();
}
}
int main(){
catima::Projectile p{1,1};
catima::Projectile c{12,6};
catima::Projectile u{238,92};
catima::Material c_target(12.011,6);
catima::Material h_target(1.00794,1);
catima::Material pb_target(207.2,82);
catima::Material water(
{{1,1,2},
{16,8,1}
});
c_target.thickness(0.5);
c_target.density(2.0);
h_target.density(0.001);
h_target.thickness(10.0);
pb_target.density(11.0);
pb_target.thickness(0.1);
water.density(1.0);
water.thickness(1.0);
std::vector<std::pair<double,int>> projectiles = {{1,1},{4,2},{12,6},{238,92}};
bool fwrite = false;
double eps = 0.01;
comp_dedx(p,c_target,eps,fwrite,"dedx_p_c.dat");
comp_dedx(p,h_target,eps,fwrite,"dedx_p_h.dat");
comp_dedx(p,water,eps,fwrite,"dedx_p_water.dat");
comp_dedx(p,pb_target,eps,fwrite,"dedx_p_pb.dat");
comp_dedx(c,c_target,eps,fwrite,"dedx_c_c.dat");
comp_dedx(c,h_target,eps,fwrite,"dedx_c_h.dat");
comp_dedx(c,water,eps,fwrite,"dedx_c_water.dat");
comp_dedx(c,pb_target,eps,fwrite,"dedx_c_pb.dat");
comp_dedx(u,c_target,eps,fwrite,"dedx_u_c.dat");
comp_dedx(u,h_target,eps,fwrite,"dedx_u_h.dat");
comp_dedx(u,water,eps,fwrite,"dedx_u_water.dat");
comp_dedx(u,pb_target,eps,fwrite,"dedx_u_pb.dat");
return 0;
}

132
tests/test_generated.cpp Normal file
View File

@ -0,0 +1,132 @@
#include "lest.hpp"
#include <math.h>
#include "catima/catima.h"
//#include "nucdata.h"
using namespace std;
using lest::approx;
bool rcompare(double a, double b,double eps){
if(fabs((a-b)/fabs(b))<eps){
return true;
}
else{
std::cout<<"\033[1;31m"<<a<<" == "<<b<<"\033[0m"<<std::endl;
return false;
}
}
const lest::test specification[] =
{
CASE("LS generated is equal to calculated"){
catima::Projectile p;
double a,b;
p.A = 238;
p.Z = 92;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard(p);
b = catima::precalculated_lindhard(p);
EXPECT(a==approx(b).epsilon(0.001));
}
p.A = 220;
p.Z = 92;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard(p);
b = catima::precalculated_lindhard(p);
EXPECT(a==approx(b).epsilon(0.01));
}
p.A = 250;
p.Z = 92;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard(p);
b = catima::precalculated_lindhard(p);
EXPECT(a==approx(b).epsilon(0.01));
}
p.A = 200;
p.Z = 76;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard(p);
b = catima::precalculated_lindhard(p);
EXPECT(a==approx(b).epsilon(0.01));
}
p.A = 100;
p.Z = 50;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard(p);
b = catima::precalculated_lindhard(p);
EXPECT(a==approx(b).epsilon(0.01));
}
},
CASE("LS X generated is equal to calculated"){
catima::Projectile p;
double a,b;
p.A = 238;
p.Z = 92;
for(double e:{90.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard_X(p);
b = catima::precalculated_lindhard_X(p);
EXPECT(a==approx(b).epsilon(0.001));
}
p.A = 220;
p.Z = 92;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard_X(p);
b = catima::precalculated_lindhard_X(p);
EXPECT(a==approx(b).epsilon(0.02));
}
p.A = 250;
p.Z = 92;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard_X(p);
b = catima::precalculated_lindhard_X(p);
EXPECT(a==approx(b).epsilon(0.03));
}
p.A = 200;
p.Z = 76;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard_X(p);
b = catima::precalculated_lindhard_X(p);
EXPECT(a==approx(b).epsilon(0.03));
}
p.A = 100;
p.Z = 50;
for(double e:{100.0,1000.0,5000.0,30000.0}){
p.T = e;
a = catima::bethek_lindhard_X(p);
b = catima::precalculated_lindhard_X(p);
EXPECT(a==approx(b).epsilon(0.03));
}
}
};
int main( int argc, char * argv[] )
{
return lest::run( specification, argc, argv );
}

88
tests/test_storage.cpp Normal file
View File

@ -0,0 +1,88 @@
#include "lest.hpp"
#include <math.h>
using namespace std;
#include "catima/catima.h"
#include "catima/storage.h"
bool rcompare(double a, double b,double eps){
if(fabs((a-b)/fabs(b))<eps){
return true;
}
else{
std::cout<<"\033[1;31m"<<a<<" == "<<b<<"\033[0m"<<std::endl;
return false;
}
}
const lest::test specification[] =
{
CASE("datapoints equal operator"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1,1,2},
{16,8,1}
});
catima::Material graphite({
{12,6,1}
});
catima::DataPoint a(p,water);
catima::DataPoint b(p,water);
catima::DataPoint c(p,graphite);
catima::DataPoint d;
d = c;
EXPECT(a == b);
EXPECT(!(a==c));
EXPECT(d == c);
EXPECT(!(d==b));
d = a;
EXPECT(!(d==c));
EXPECT(d==b);
},
CASE("storage add"){
catima::Projectile p{12,6,6,1000};
catima::Material water({
{1,1,2},
{16,8,1}
});
catima::Material graphite({
{12,6,1}
});
catima::_storage.Reset();
EXPECT(catima::_storage.get_index()==0);
catima::_storage.Add(p,water);
EXPECT(catima::_storage.get_index()==1);
catima::_storage.Add(p,water);
EXPECT(catima::_storage.get_index()==1);
catima::_storage.Add(p,graphite);
EXPECT(catima::_storage.get_index()==2);
catima::_storage.Add(p,graphite);
EXPECT(catima::_storage.get_index()==2);
},
CASE("energy table"){
double step = (catima::logEmax - catima::logEmin)/(catima::max_datapoints-1);
EXPECT(catima::energy_table.step==step);
EXPECT(catima::energy_table.values[0]==exp(M_LN10*(catima::logEmin)));
EXPECT(catima::energy_table.values[1]==exp(M_LN10*(catima::logEmin+step)));
EXPECT(catima::energy_table.values[catima::max_datapoints-1]==exp(M_LN10*(catima::logEmax)));
}
};
int main( int argc, char * argv[] )
{
return lest::run( specification, argc, argv );
}

192
tests/test_structures.cpp Normal file
View File

@ -0,0 +1,192 @@
#include "lest.hpp"
#include <math.h>
using namespace std;
#include "catima/catima.h"
#include "catima/material_database.h"
bool rcompare(double a, double b,double eps){
if(fabs((a-b)/fabs(b))<eps){
return true;
}
else{
std::cout<<"\033[1;31m"<<a<<" == "<<b<<"\033[0m"<<std::endl;
return false;
}
}
const lest::test specification[] =
{
CASE("atima material basic tests"){
SETUP(""){
catima::Material water({
{1,1,2},
{16,8,1}
});
catima::Material water2;
water2.add_element(1,1,2);
water2.add_element(16,8,1);
catima::Material graphite;
graphite.add_element(12,6,1);
graphite.density(1.8);
SECTION("component number check"){
EXPECT(graphite.ncomponents()==1);
EXPECT(water.ncomponents()==2);
graphite.add_element(18,40,1);
EXPECT(graphite.ncomponents()==2);
EXPECT(water.M()==18);
}
SECTION("Molar mass check"){
EXPECT(graphite.M()==12);
EXPECT(water.ncomponents()==2);
EXPECT(water.M()==18);
EXPECT(water2.ncomponents()==2);
EXPECT(water2.M()==18);
}
SECTION("equal operator check"){
EXPECT(water==water);
EXPECT(!(water==graphite));
}
}
},
CASE("Material automatic atomic weight"){
catima::Material water({{0,1,2},{0,8,1}});
catima::Material graphite(0,6);
EXPECT(water.get_element(0).first.A == 1.00794);
EXPECT(water.get_element(1).first.A == 15.9994);
EXPECT(graphite.get_element(0).first.A == 12.0107);
EXPECT(water.M()>16);
EXPECT(graphite.M()>12);
},
CASE("default materials"){
catima::Material m = catima::get_material(6);
EXPECT(m.get_element(0).first.A == 12.0107);
EXPECT(m.get_element(0).first.Z == 6);
EXPECT(m.density() == 2.0);
EXPECT(m.M() == 12.0107);
m = catima::get_material(catima::material::WATER);
EXPECT(m.get_element(0).first.A == 1.00794);
EXPECT(m.get_element(0).first.Z == 1);
EXPECT(m.get_element(1).first.A == 15.9994);
EXPECT(m.get_element(1).first.Z == 8);
EXPECT(m.density() == 1.0);
EXPECT(m.M() > 16.0);
},
CASE("Layers"){
catima::Material water2;
water2.add_element(1,1,2);
water2.add_element(16,8,1);
water2.density(1.0).thickness(2.0);
catima::Material graphite;
graphite.add_element(12,6,1);
graphite.density(1.8).thickness(1.0);
catima::Layers detector1;
EXPECT(detector1.num() == 0);
detector1.add(graphite);
EXPECT(detector1.num() == 1);
detector1.add(water2);
detector1.add(graphite);
EXPECT(detector1.num() == 3);
// check correct density and thickness
EXPECT(detector1[0].density()==1.8);
EXPECT(detector1[0].thickness()==1.0);
EXPECT(detector1[1].density()==1.0);
EXPECT(detector1[1].thickness()==2.0);
EXPECT(detector1[0].get_element(0).first.Z == 6);
EXPECT(detector1[0].get_element(0).first.A == 12);
EXPECT(detector1[1].get_element(0).first.A == 1);
EXPECT(detector1[1].get_element(0).first.Z == 1);
EXPECT(detector1[2].density() == 1.8);
detector1[1].density(1.2);
EXPECT(detector1[1].density()==1.2);
catima::Layers detector2;
detector2 = detector1;
EXPECT(detector2.num() == 3);
detector2.add(water2);
detector2.add(graphite);
EXPECT(detector2.num() == 5);
catima::Layers focal_material = detector1 + detector2;
EXPECT(focal_material.num() == 8);
},
CASE("basic projectile tests"){
catima::Projectile p{12,6,6,1000};
EXPECT(p.A==12);
EXPECT(p.Z==6);
EXPECT(p.Q==6);
EXPECT(p.T==1000);
catima::Projectile p2(12,6);
EXPECT(p.A==12);
EXPECT(p2.Z==6);
EXPECT(p2.Q==6);
EXPECT(p2.T==0);
p2(1000);
EXPECT(p2.T==1000);
p2(1000)(500);
EXPECT(p2.T==500);
catima::Projectile p3(12,6,5);
EXPECT(p==p2);
EXPECT( !(p==p3));
},
CASE("basic config test"){
catima::Config c1;
catima::Config c2;
catima::Config c3{catima::z_eff_type::none};
EXPECT(c1==c2);
EXPECT( !(c1==c3));
},
CASE("constructors test"){
catima::Material mat2(12,6,2.5,0.1);
catima::Material mat3(12.01,6);
catima::Material mat4({{12.01,6,1.0}});
catima::Material mat5({
{12.01, 6, 1},
{16.00, 8, 2}
});
EXPECT(mat2.ncomponents()==1);
EXPECT(mat3.ncomponents()==1);
EXPECT(mat3.get_element(0).first.A==12.01);
EXPECT(mat4.ncomponents()==1);
EXPECT(mat4.get_element(0).first.A==12.01);
EXPECT(mat5.ncomponents()==2);
EXPECT(mat5.get_element(0).first.A==12.01);
EXPECT(mat5.get_element(0).first.Z==6);
EXPECT(mat5.get_element(1).first.A==16.0);
EXPECT(mat5.get_element(1).second==2);
catima::Material mat6;
mat6 = mat5;
EXPECT(mat5==mat6);
EXPECT(mat5.ncomponents()==mat6.ncomponents());
EXPECT(mat5.get_element(0).first.A==mat6.get_element(0).first.A);
EXPECT(mat5.get_element(1).first.A==mat6.get_element(1).first.A);
mat5.add_element(12,6,1);
EXPECT(mat5.ncomponents()==mat6.ncomponents()+1);
}
};
int main( int argc, char * argv[] )
{
return lest::run( specification, argc, argv );
}

139
utils/generator.cpp Normal file
View File

@ -0,0 +1,139 @@
#include <iostream>
#include "catima/catima.h"
#include "catima/nucdata.h"
#include <functional>
#include <fstream>
#include <sstream>
using namespace catima;
using std::cout;
using std::endl;
//// configuration ////
constexpr double logEmin_forLS = 0.0;
constexpr double logEmax_forLS = catima::logEmax;
constexpr double num_LS_datapoints = 200;
/////////////////////////////////////////
inline double ls_energy_table( int i ) { return exp(M_LN10*(logEmin_forLS + ((double)i)*(logEmax_forLS-logEmin_forLS)/(num_LS_datapoints - 1.0))); }
int main(){
double r;
double r2;
double dx;
double x1,x2;
#define LS_COEFFICENTS
#ifdef LS_COEFFICENTS
std::ofstream file("generated_LS_coeff.h",std::ofstream::out);
catima::Projectile p;
std::vector<double> ve;
std::stringstream sv1;
std::stringstream sv2;
std::stringstream sx1;
std::stringstream sx2;
file<<"//LS precalculated LS coefficients \n ";
file<<"#include \"catima/storage.h\"";
file<<"\n\n";
file<<"#define LS_NUM_ENERGY_POINTS "<<num_LS_datapoints<<"\n";
file<<"#define LS_MAX_Z "<<ATOMIC_WEIGHT_MAXZ<<"\n";
file<<"namespace catima{\n\n";
file<<"namespace ls_coefficients{\n\n";
file<<"// relative difference of mass number for 2nd mass point ls_coefficients_ahi \n\n";
file<<"constexpr double a_rel_increase=0.05;\n";
file<<"constexpr double logEmin = "<<logEmin_forLS<<";\n";
file<<"constexpr double logEmax = "<<logEmax_forLS<<";\n";
file<<"// energy points array in MeV/u \n";
file<<"constexpr EnergyTable<"<<num_LS_datapoints<<"> ls_energy_table("<<logEmin_forLS<<","<<logEmax_forLS<<");\n";
/*
file<<"double ls_energy_points["<<num_LS_datapoints<<"]={";
for(int i=0;i<num_LS_datapoints;i++){
if(i!=0)file<<",";
file<<ls_energy_table(i);
}
file<<"};\n";
*/
sv1<<"{";
sv2<<"{";
sx1<<"{";
sx2<<"{";
double beta2;
for(int z=1;z<ATOMIC_WEIGHT_MAXZ-1;z++){
p.Z = z;
if(z!=1)sv1<<",";
if(z!=1)sv2<<",";
if(z!=1)sx1<<",";
if(z!=1)sx2<<",";
sv1<<"\n\t{";
sv2<<"\n\t{";
sx1<<"\n\t{";
sx2<<"\n\t{";
for(int i=0;i<num_LS_datapoints;i++){
p.T = ls_energy_table(i);
p.A = element_atomic_weight((int)p.Z);
beta2 = catima::beta_from_T(p.T);
beta2 = beta2*beta2;
r = bethek_lindhard(p);
x1 = bethek_lindhard_X(p);
dx = p.A*0.05;
p.A +=dx;
r2 = bethek_lindhard(p);
x2 = bethek_lindhard_X(p);
if(i!=0)sv1<<",";
sv1<<r;
if(i!=0)sv2<<",";
sv2<<r2;
if(i!=0)sx1<<",";
sx1<<x1;
if(i!=0)sx2<<",";
sx2<<x2;
}
sv1<<"}";
sv2<<"}";
sx1<<"}";
sx2<<"}";
}
sv1<<"\n};";
sv2<<"\n};";
sx1<<"\n};";
sx2<<"\n};";
file<<"\n";
file<<"//arrays dimensions are [z][energy], z=1 starts from index=0\n";
file<<"\n//LS coefficient for A=atomic weight\n";
file<<"double ls_coefficients_a[]["<<num_LS_datapoints<<"]=\n";
file<<sv1.str();
file<<"\n";
file<<"\n//LS coefficient for A=atomic weight * 1.05\n";
file<<"double ls_coefficients_ahi[]["<<num_LS_datapoints<<"]=\n";
file<<sv2.str();
file<<"\n";
file<<"\n";
file<<"//arrays dimensions are [z][energy], z=1 starts from index=0\n";
file<<"\n//LS X coefficient (dE straggling) for A=atomic weight\n";
file<<"double ls_X_coefficients_a[]["<<num_LS_datapoints<<"]=\n";
file<<sx1.str();
file<<"\n";
file<<"\n//LS X coefficient for A=atomic weight * 1.05\n";
file<<"double ls_X_coefficients_ahi[]["<<num_LS_datapoints<<"]=\n";
file<<sx2.str();
file<<"\n";
file<<"\n}\n"; // end of ls_coefficient namespace
file<<"\n}\n"; // end of catima namespace
file.close();
#endif
return 0;
}