sedov_soluce_arrays.hpp

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// -------------------------------------------------------//
//
// SHAMROCK code for hydrodynamics
// Copyright (c) 2021-2026 Timothée David--Cléris <tim.shamrock@proton.me>
// SPDX-License-Identifier: CeCILL Free Software License Agreement v2.1
// Shamrock is licensed under the CeCILL 2.1 License, see LICENSE for more information
//
// -------------------------------------------------------//
 
#pragma once
 
inline double r_theo[] = {
    9.99999999999999955e-07, 1.67721899999999998e-04, 3.34443800000000025e-04,
    5.01165700000000052e-04, 6.67887600000000026e-04, 8.34609499999999999e-04,
    1.00133100000000005e-03, 1.16805300000000006e-03, 1.33477500000000007e-03,
    1.50149700000000007e-03, 1.66821900000000008e-03, 1.83494100000000009e-03,
    2.00166299999999988e-03, 2.16838500000000010e-03, 2.33510699999999989e-03,
    2.50182900000000012e-03, 2.66855099999999991e-03, 2.83527199999999979e-03,
    3.00199400000000002e-03, 3.16871599999999981e-03, 3.33543800000000003e-03,
    3.50215999999999982e-03, 3.66888200000000005e-03, 3.83560399999999984e-03,
    4.00232599999999963e-03, 4.16904799999999985e-03, 4.33577000000000008e-03,
    4.50249099999999996e-03, 4.66921300000000018e-03, 4.83593500000000041e-03,
    5.00265699999999976e-03, 5.16937899999999999e-03, 5.33610100000000021e-03,
    5.50282299999999957e-03, 5.66954499999999979e-03, 5.83626700000000002e-03,
    6.00298900000000024e-03, 6.16971099999999960e-03, 6.33643200000000035e-03,
    6.50315399999999971e-03, 6.66987599999999993e-03, 6.83659800000000015e-03,
    7.00332000000000038e-03, 7.17004199999999974e-03, 7.33676399999999996e-03,
    7.50348600000000018e-03, 7.67020800000000041e-03, 7.83693000000000063e-03,
    8.00365199999999999e-03, 8.17037299999999987e-03, 8.33709499999999923e-03,
    8.50381700000000032e-03, 8.67053899999999968e-03, 8.83726100000000077e-03,
    9.00398300000000013e-03, 9.17070499999999948e-03, 9.33742700000000057e-03,
    9.50414899999999993e-03, 9.67087099999999929e-03, 9.83759300000000038e-03,
    1.00043100000000006e-02, 1.01710399999999992e-02, 1.03377599999999997e-02,
    1.05044800000000001e-02, 1.06712000000000005e-02, 1.08379199999999992e-02,
    1.10046499999999995e-02, 1.11713699999999999e-02, 1.13380900000000003e-02,
    1.15048100000000007e-02, 1.16715299999999994e-02, 1.18382599999999998e-02,
    1.20049800000000002e-02, 1.21717000000000006e-02, 1.23384199999999992e-02,
    1.25051399999999997e-02, 1.26718600000000001e-02, 1.28385900000000004e-02,
    1.30053100000000008e-02, 1.31720299999999995e-02, 1.33387499999999999e-02,
    1.35054700000000003e-02, 1.36722000000000007e-02, 1.38389199999999993e-02,
    1.40056399999999998e-02, 1.41723600000000002e-02, 1.43390800000000006e-02,
    1.45058099999999992e-02, 1.46725299999999996e-02, 1.48392500000000000e-02,
    1.50059700000000004e-02, 1.51726900000000008e-02, 1.53394199999999994e-02,
    1.55061399999999999e-02, 1.56728600000000003e-02, 1.58395799999999989e-02,
    1.60063000000000011e-02, 1.61730300000000014e-02, 1.63397500000000001e-02,
    1.65064699999999988e-02, 1.66731900000000009e-02, 1.68399099999999996e-02,
    1.70066299999999983e-02, 1.71733599999999986e-02, 1.73400800000000008e-02,
    1.75067999999999994e-02, 1.76735200000000016e-02, 1.78402400000000003e-02,
    1.80069700000000006e-02, 1.81736899999999993e-02, 1.83404100000000014e-02,
    1.85071300000000001e-02, 1.86738499999999988e-02, 1.88405799999999991e-02,
    1.90073000000000013e-02, 1.91740200000000000e-02, 1.93407399999999986e-02,
    1.95074600000000008e-02, 1.96741900000000011e-02, 1.98409099999999998e-02,
    2.00076299999999985e-02, 2.01743500000000006e-02, 2.03410699999999993e-02,
    2.05077900000000014e-02, 2.06745199999999983e-02, 2.08412400000000005e-02,
    2.10079599999999991e-02, 2.11746800000000013e-02, 2.13414000000000000e-02,
    2.15081300000000003e-02, 2.16748499999999990e-02, 2.18415700000000011e-02,
    2.20082899999999998e-02, 2.21750099999999985e-02, 2.23417399999999988e-02,
    2.25084600000000010e-02, 2.26751799999999996e-02, 2.28418999999999983e-02,
    2.30086200000000005e-02, 2.31753500000000008e-02, 2.33420699999999995e-02,
    2.35087900000000016e-02, 2.36755100000000003e-02, 2.38422299999999990e-02,
    2.40089500000000011e-02, 2.41756800000000015e-02, 2.43424000000000001e-02,
    2.45091199999999988e-02, 2.46758400000000010e-02, 2.48425599999999996e-02,
    2.50092900000000000e-02, 2.51760099999999987e-02, 2.53427300000000008e-02,
    2.55094499999999995e-02, 2.56761700000000016e-02, 2.58428999999999985e-02,
    2.60096200000000007e-02, 2.61763399999999993e-02, 2.63430600000000015e-02,
    2.65097800000000001e-02, 2.66765100000000005e-02, 2.68432299999999992e-02,
    2.70099500000000013e-02, 2.71766700000000000e-02, 2.73433899999999987e-02,
    2.75101100000000008e-02, 2.76768400000000012e-02, 2.78435599999999998e-02,
    2.80102799999999985e-02, 2.81770000000000007e-02, 2.83437199999999993e-02,
    2.85104499999999997e-02, 2.86771699999999984e-02, 2.88438900000000005e-02,
    2.90106099999999992e-02, 2.91773300000000013e-02, 2.93440600000000017e-02,
    2.95107800000000003e-02, 2.96774999999999990e-02, 2.98442200000000012e-02,
    3.00109399999999998e-02, 3.01776700000000002e-02, 3.03443899999999989e-02,
    3.05111100000000010e-02, 3.06778299999999997e-02, 3.08445499999999984e-02,
    3.10112700000000005e-02, 3.11780000000000009e-02, 3.13447199999999995e-02,
    3.15114400000000017e-02, 3.16781599999999969e-02, 3.18448799999999990e-02,
    3.20116100000000028e-02, 3.21783299999999980e-02, 3.23450500000000002e-02,
    3.25117700000000023e-02, 3.26784899999999975e-02, 3.28452200000000014e-02,
    3.30119399999999966e-02, 3.31786599999999987e-02, 3.33453800000000009e-02,
    3.35121000000000030e-02, 3.36788299999999999e-02, 3.38455500000000020e-02,
    3.40122699999999972e-02, 3.41789899999999994e-02, 3.43457100000000015e-02,
    3.45124299999999967e-02, 3.46791600000000005e-02, 3.48458800000000027e-02,
    3.50125999999999979e-02, 3.51793200000000000e-02, 3.53460400000000022e-02,
    3.55127699999999991e-02, 3.56794900000000012e-02, 3.58462100000000033e-02,
    3.60129299999999986e-02, 3.61796500000000007e-02, 3.63463799999999976e-02,
    3.65130999999999997e-02, 3.66798200000000019e-02, 3.68465399999999971e-02,
    3.70132599999999992e-02, 3.71799900000000030e-02, 3.73467099999999982e-02,
    3.75134300000000004e-02, 3.76801500000000025e-02, 3.78468699999999977e-02,
    3.80135899999999999e-02, 3.81803199999999968e-02, 3.83470399999999989e-02,
    3.85137600000000010e-02, 3.86804800000000032e-02, 3.88471999999999984e-02,
    3.90139300000000022e-02, 3.91806499999999974e-02, 3.93473699999999996e-02,
    3.95140900000000017e-02, 3.96808099999999969e-02, 3.98475400000000007e-02,
    4.00142600000000029e-02, 4.01809799999999981e-02, 4.03477000000000002e-02,
    4.05144200000000024e-02, 4.06811499999999993e-02, 4.08478700000000014e-02,
    4.10145899999999966e-02, 4.11813099999999987e-02, 4.13480300000000009e-02,
    4.15147500000000030e-02, 4.16814799999999999e-02, 4.18482000000000021e-02,
    4.20149199999999973e-02, 4.21816399999999994e-02, 4.23483600000000016e-02,
    4.25150899999999984e-02, 4.26818100000000006e-02, 4.28485300000000027e-02,
    4.30152499999999979e-02, 4.31819700000000001e-02, 4.33486999999999970e-02,
    4.35154199999999991e-02, 4.36821400000000012e-02, 4.38488600000000034e-02,
    4.40155799999999986e-02, 4.41823100000000024e-02, 4.43490299999999976e-02,
    4.45157499999999998e-02, 4.46824700000000019e-02, 4.48491899999999971e-02,
    4.50159099999999993e-02, 4.51826400000000031e-02, 4.53493599999999983e-02,
    4.55160800000000004e-02, 4.56828000000000026e-02, 4.58495199999999978e-02,
    4.60162500000000016e-02, 4.61829699999999968e-02, 4.63496899999999989e-02,
    4.65164100000000011e-02, 4.66831300000000032e-02, 4.68498600000000001e-02,
    4.70165800000000023e-02, 4.71832999999999975e-02, 4.73500199999999996e-02,
    4.75167400000000018e-02, 4.76834699999999986e-02, 4.78501900000000008e-02,
    4.80169100000000029e-02, 4.81836299999999981e-02, 4.83503500000000003e-02,
    4.85170799999999972e-02, 4.86837999999999993e-02, 4.88505200000000014e-02,
    4.90172399999999966e-02, 4.91839599999999988e-02, 4.93506800000000009e-02,
    4.95174099999999978e-02, 4.96841300000000000e-02, 4.98508500000000021e-02,
    5.00175699999999973e-02, 5.01842899999999995e-02, 5.03510200000000033e-02,
    5.05177399999999985e-02, 5.06844600000000006e-02, 5.08511800000000028e-02,
    5.10178999999999980e-02, 5.11846300000000018e-02, 5.13513499999999970e-02,
    5.15180699999999991e-02, 5.16847900000000013e-02, 5.18515100000000034e-02,
    5.20182400000000003e-02, 5.21849600000000025e-02, 5.23516799999999977e-02,
    5.25183999999999998e-02, 5.26851200000000019e-02, 5.28518399999999972e-02,
    5.30185700000000010e-02, 5.31852900000000031e-02, 5.33520099999999983e-02,
    5.35187300000000005e-02, 5.36854500000000026e-02, 5.38521799999999995e-02,
    5.40189000000000016e-02, 5.41856199999999968e-02, 5.43523399999999990e-02,
    5.45190600000000011e-02, 5.46857899999999980e-02, 5.48525100000000002e-02,
    5.50192300000000023e-02, 5.51859499999999975e-02, 5.53526699999999997e-02,
    5.55193999999999965e-02, 5.56861199999999987e-02, 5.58528400000000008e-02,
    5.60195600000000030e-02, 5.61862799999999982e-02, 5.63530000000000003e-02,
    5.65197299999999972e-02, 5.66864499999999993e-02, 5.68531700000000015e-02,
    5.70198899999999967e-02, 5.71866099999999988e-02, 5.73533400000000027e-02,
    5.75200599999999979e-02, 5.76867800000000000e-02, 5.78535000000000021e-02,
    5.80202199999999974e-02, 5.81869500000000012e-02, 5.83536700000000033e-02,
    5.85203899999999985e-02, 5.86871100000000007e-02, 5.88538300000000028e-02,
    5.90205599999999997e-02, 5.91872800000000018e-02, 5.93539999999999970e-02,
    5.95207199999999992e-02, 5.96874400000000013e-02, 5.98541599999999965e-02,
    6.00208900000000004e-02, 6.01876100000000025e-02, 6.03543299999999977e-02,
    6.05210499999999998e-02, 6.06877700000000020e-02, 6.08544999999999989e-02,
    6.10212200000000010e-02, 6.11879400000000032e-02, 6.13546599999999984e-02,
    6.15213800000000005e-02, 6.16881099999999974e-02, 6.18548299999999995e-02,
    6.20215500000000017e-02, 6.21882699999999969e-02, 6.23549899999999990e-02,
    6.25217200000000028e-02, 6.26884399999999981e-02, 6.28551599999999933e-02,
    6.30218800000000023e-02, 6.31885999999999975e-02, 6.33553200000000066e-02,
    6.35220499999999966e-02, 6.36887700000000057e-02, 6.38554900000000009e-02,
    6.40222099999999961e-02, 6.41889300000000051e-02, 6.43556599999999951e-02,
    6.45223800000000042e-02, 6.46890999999999994e-02, 6.48558199999999946e-02,
    6.50225400000000037e-02, 6.51892699999999936e-02, 6.53559900000000027e-02,
    6.55227099999999979e-02, 6.56894299999999931e-02, 6.58561500000000022e-02,
    6.60228800000000060e-02, 6.61896000000000012e-02, 6.63563199999999964e-02,
    6.65230400000000055e-02, 6.66897600000000007e-02, 6.68564799999999959e-02,
    6.70232099999999997e-02, 6.71899299999999949e-02, 6.73566500000000040e-02,
    6.75233699999999992e-02, 6.76900899999999944e-02, 6.78568199999999982e-02,
    6.80235399999999935e-02, 6.81902600000000025e-02, 6.83569799999999977e-02,
    6.85237000000000068e-02, 6.86904299999999968e-02, 6.88571500000000059e-02,
    6.90238700000000011e-02, 6.91905899999999963e-02, 6.93573100000000053e-02,
    6.95240399999999953e-02, 6.96907600000000044e-02, 6.98574799999999996e-02,
    7.00241999999999948e-02, 7.01909200000000039e-02, 7.03576399999999991e-02,
    7.05243700000000029e-02, 7.06910899999999981e-02, 7.08578099999999933e-02,
    7.10245300000000024e-02, 7.11912499999999976e-02, 7.13579800000000014e-02,
    7.15246999999999966e-02, 7.16914200000000057e-02, 7.18581400000000009e-02,
    7.20248599999999961e-02, 7.21915899999999999e-02, 7.23583099999999951e-02,
    7.25250300000000042e-02, 7.26917499999999994e-02, 7.28584699999999946e-02,
    7.30251999999999984e-02, 7.31919199999999937e-02, 7.33586400000000027e-02,
    7.35253599999999979e-02, 7.36920799999999931e-02, 7.38588000000000022e-02,
    7.40255300000000060e-02, 7.41922500000000013e-02, 7.43589699999999965e-02,
    7.45256900000000055e-02, 7.46924100000000007e-02, 7.48591400000000046e-02,
    7.50258599999999998e-02, 7.51925799999999950e-02, 7.53593000000000041e-02,
    7.55260199999999993e-02, 7.56927500000000031e-02, 7.58594699999999983e-02,
    7.60261899999999935e-02, 7.61929100000000026e-02, 7.63596299999999978e-02,
    7.65263600000000016e-02, 7.66930799999999968e-02, 7.68598000000000059e-02,
    7.70265200000000011e-02, 7.71932399999999963e-02, 7.73599600000000054e-02,
    7.75266899999999953e-02, 7.76934100000000044e-02, 7.78601299999999996e-02,
    7.80268499999999948e-02, 7.81935700000000039e-02, 7.83602999999999938e-02,
    7.85270200000000029e-02, 7.86937399999999981e-02, 7.88604599999999933e-02,
    7.90271800000000024e-02, 7.91939100000000062e-02, 7.93606300000000014e-02,
    7.95273499999999967e-02, 7.96940700000000057e-02, 7.98607900000000009e-02,
    8.00275200000000048e-02, 8.01942400000000000e-02, 8.03609599999999952e-02,
    8.05276800000000043e-02, 8.06943999999999995e-02, 8.08611300000000033e-02,
    8.10278499999999985e-02, 8.11945699999999937e-02, 8.13612900000000028e-02,
    8.15280099999999980e-02, 8.16947299999999932e-02, 8.18614599999999970e-02,
    8.20281800000000061e-02, 8.21949000000000013e-02, 8.23616199999999965e-02,
    8.25283400000000056e-02, 8.26950699999999955e-02, 8.28617900000000046e-02,
    8.30285099999999998e-02, 8.31952299999999950e-02, 8.33619500000000041e-02,
    8.35286799999999940e-02, 8.36954000000000031e-02, 8.38621199999999983e-02,
    8.40288399999999935e-02, 8.41955600000000026e-02, 8.43622900000000064e-02,
    8.45290100000000016e-02, 8.46957299999999969e-02, 8.48624500000000059e-02,
    8.50291700000000011e-02, 8.51958899999999963e-02, 8.53626200000000002e-02,
    8.55293399999999954e-02, 8.56960600000000045e-02, 8.58627799999999997e-02,
    8.60294999999999949e-02, 8.61962299999999987e-02, 8.63629499999999939e-02,
    8.65296700000000030e-02, 8.66963899999999982e-02, 8.68631099999999934e-02,
    8.70298399999999972e-02, 8.71965600000000063e-02, 8.73632800000000015e-02,
    8.75299999999999967e-02, 8.76967200000000058e-02, 8.78634499999999957e-02,
    8.80301700000000048e-02, 8.81968900000000000e-02, 8.83636099999999952e-02,
    8.85303300000000043e-02, 8.86970499999999995e-02, 8.88637800000000033e-02,
    8.90304999999999985e-02, 8.91972199999999937e-02, 8.93639400000000028e-02,
    8.95306599999999980e-02, 8.96973900000000018e-02, 8.98641099999999970e-02,
    9.00308300000000061e-02, 9.01975500000000013e-02, 9.03642699999999965e-02,
    9.05310000000000004e-02, 9.06977199999999956e-02, 9.08644400000000046e-02,
    9.10311599999999999e-02, 9.11978799999999951e-02, 9.13646099999999989e-02,
    9.15313299999999941e-02, 9.16980500000000032e-02, 9.18647699999999984e-02,
    9.20314899999999936e-02, 9.21982100000000027e-02, 9.23649400000000065e-02,
    9.25316600000000017e-02, 9.26983799999999969e-02, 9.28651000000000060e-02,
    9.30318200000000012e-02, 9.31985500000000050e-02, 9.33652700000000002e-02,
    9.35319899999999954e-02, 9.36987100000000045e-02, 9.38654299999999997e-02,
    9.40321600000000035e-02, 9.41988799999999987e-02, 9.43655999999999939e-02,
    9.45323200000000030e-02, 9.46990399999999982e-02, 9.48657700000000020e-02,
    9.50324899999999972e-02, 9.51992100000000063e-02, 9.53659300000000015e-02,
    9.55326499999999967e-02, 9.56993700000000058e-02, 9.58660999999999958e-02,
    9.60328200000000048e-02, 9.61995400000000001e-02, 9.63662599999999953e-02,
    9.65329800000000043e-02, 9.66997099999999943e-02, 9.68664300000000034e-02,
    9.70331499999999986e-02, 9.71998699999999938e-02, 9.73665900000000029e-02,
    9.75333200000000067e-02, 9.77000400000000019e-02, 9.78667599999999971e-02,
    9.80334800000000062e-02, 9.82002000000000014e-02, 9.83669300000000052e-02,
    9.85336500000000004e-02, 9.87003699999999956e-02, 9.88670900000000047e-02,
    9.90338099999999999e-02, 9.92005299999999951e-02, 9.93672599999999989e-02,
    9.95339799999999941e-02, 9.97007000000000032e-02, 9.98674199999999984e-02,
    1.00034100000000001e-01, 1.00200899999999996e-01, 1.00367600000000001e-01,
    1.00534299999999993e-01, 1.00700999999999999e-01, 1.00867799999999994e-01,
    1.01034499999999999e-01, 1.01201200000000005e-01, 1.01367899999999997e-01,
    1.01534600000000003e-01, 1.01701399999999997e-01, 1.01868100000000003e-01,
    1.02034799999999995e-01, 1.02201500000000001e-01, 1.02368299999999995e-01,
    1.02535000000000001e-01, 1.02701700000000007e-01, 1.02868399999999999e-01,
    1.03035100000000004e-01, 1.03201899999999999e-01, 1.03368600000000005e-01,
    1.03535299999999997e-01, 1.03702000000000003e-01, 1.03868699999999994e-01,
    1.04035500000000003e-01, 1.04202199999999995e-01, 1.04368900000000001e-01,
    1.04535600000000006e-01, 1.04702400000000001e-01, 1.04869100000000007e-01,
    1.05035799999999999e-01, 1.05202500000000004e-01, 1.05369199999999996e-01,
    1.05536000000000005e-01, 1.05702699999999997e-01, 1.05869400000000002e-01,
    1.06036099999999994e-01, 1.06202900000000003e-01, 1.06369599999999995e-01,
    1.06536300000000000e-01, 1.06703000000000006e-01, 1.06869699999999998e-01,
    1.07036500000000007e-01, 1.07203199999999998e-01, 1.07369900000000004e-01,
    1.07536599999999996e-01, 1.07703400000000005e-01, 1.07870099999999997e-01,
    1.08036800000000002e-01, 1.08203499999999994e-01, 1.08370200000000000e-01,
    1.08536999999999995e-01, 1.08703700000000000e-01, 1.08870400000000006e-01,
    1.09037099999999998e-01, 1.09203800000000004e-01, 1.09370599999999998e-01,
    1.09537300000000004e-01, 1.09703999999999996e-01, 1.09870700000000002e-01,
    1.10037499999999996e-01, 1.10204200000000002e-01, 1.10370899999999994e-01,
    1.10537600000000000e-01, 1.10704300000000005e-01, 1.10871100000000000e-01,
    1.11037800000000006e-01, 1.11204499999999998e-01, 1.11371200000000004e-01,
    1.11537999999999998e-01, 1.11704700000000004e-01, 1.11871399999999996e-01,
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    4.53151099999999973e-01, 4.53317899999999996e-01, 4.53484600000000015e-01,
    4.53651299999999980e-01, 4.53817999999999999e-01, 4.53984800000000022e-01,
    4.54151499999999986e-01, 4.54318200000000005e-01, 4.54484900000000025e-01,
    4.54651599999999989e-01, 4.54818400000000012e-01, 4.54985099999999976e-01,
    4.55151799999999995e-01, 4.55318500000000015e-01, 4.55485299999999982e-01,
    4.55652000000000001e-01, 4.55818700000000021e-01, 4.55985399999999985e-01,
    4.56152100000000005e-01, 4.56318900000000027e-01, 4.56485599999999991e-01,
    4.56652300000000011e-01, 4.56818999999999975e-01, 4.56985699999999995e-01,
    4.57152500000000017e-01, 4.57319199999999981e-01, 4.57485900000000001e-01,
    4.57652600000000020e-01, 4.57819399999999987e-01, 4.57986100000000007e-01,
    4.58152800000000027e-01, 4.58319499999999991e-01, 4.58486200000000010e-01,
    4.58652999999999977e-01, 4.58819699999999997e-01, 4.58986400000000017e-01,
    4.59153099999999981e-01, 4.59319900000000003e-01, 4.59486600000000023e-01,
    4.59653299999999987e-01, 4.59820000000000007e-01, 4.59986700000000026e-01,
    4.60153499999999993e-01, 4.60320200000000013e-01, 4.60486899999999977e-01,
    4.60653599999999996e-01, 4.60820400000000019e-01, 4.60987099999999983e-01,
    4.61153800000000003e-01, 4.61320500000000022e-01, 4.61487199999999986e-01,
    4.61654000000000009e-01, 4.61820699999999973e-01, 4.61987399999999993e-01,
    4.62154100000000012e-01, 4.62320799999999976e-01, 4.62487599999999999e-01,
    4.62654300000000018e-01, 4.62820999999999982e-01, 4.62987700000000002e-01,
    4.63154500000000025e-01, 4.63321199999999989e-01, 4.63487900000000008e-01,
    4.63654599999999972e-01, 4.63821299999999992e-01, 4.63988100000000014e-01,
    4.64154799999999979e-01, 4.64321499999999998e-01, 4.64488200000000018e-01,
    4.64654999999999985e-01, 4.64821700000000004e-01, 4.64988400000000024e-01,
    4.65155099999999988e-01, 4.65321800000000008e-01, 4.65488599999999975e-01,
    4.65655299999999994e-01, 4.65822000000000014e-01, 4.65988699999999978e-01,
    4.66155500000000000e-01, 4.66322200000000020e-01, 4.66488899999999984e-01,
    4.66655600000000004e-01, 4.66822300000000023e-01, 4.66989099999999990e-01,
    4.67155800000000010e-01, 4.67322499999999974e-01, 4.67489199999999994e-01,
    4.67655900000000013e-01, 4.67822699999999980e-01, 4.67989400000000000e-01,
    4.68156100000000019e-01, 4.68322799999999984e-01, 4.68489600000000006e-01,
    4.68656300000000026e-01, 4.68822999999999990e-01, 4.68989700000000009e-01,
    4.69156399999999973e-01, 4.69323199999999996e-01, 4.69489900000000016e-01,
    4.69656599999999980e-01, 4.69823299999999999e-01, 4.69990100000000022e-01,
    4.70156799999999986e-01, 4.70323500000000005e-01, 4.70490200000000025e-01,
    4.70656899999999989e-01, 4.70823700000000012e-01, 4.70990399999999976e-01,
    4.71157099999999995e-01, 4.71323800000000015e-01, 4.71490599999999982e-01,
    4.71657300000000002e-01, 4.71824000000000021e-01, 4.71990699999999985e-01,
    4.72157400000000005e-01, 4.72324200000000027e-01, 4.72490899999999991e-01,
    4.72657600000000011e-01, 4.72824299999999975e-01, 4.72991099999999998e-01,
    4.73157800000000017e-01, 4.73324499999999981e-01, 4.73491200000000001e-01,
    4.73657900000000021e-01, 4.73824699999999988e-01, 4.73991400000000007e-01,
    4.74158100000000027e-01, 4.74324799999999991e-01, 4.74491500000000010e-01,
    4.74658299999999977e-01, 4.74824999999999997e-01, 4.74991700000000017e-01,
    4.75158399999999981e-01, 4.75325200000000003e-01, 4.75491900000000023e-01,
    4.75658599999999987e-01, 4.75825300000000007e-01, 4.75992000000000026e-01,
    4.76158799999999993e-01, 4.76325500000000013e-01, 4.76492199999999977e-01,
    4.76658899999999996e-01, 4.76825700000000019e-01, 4.76992399999999983e-01,
    4.77159100000000003e-01, 4.77325800000000022e-01, 4.77492499999999986e-01,
    4.77659300000000009e-01, 4.77825999999999973e-01, 4.77992699999999993e-01,
    4.78159400000000012e-01, 4.78326199999999979e-01, 4.78492899999999999e-01,
    4.78659600000000018e-01, 4.78826299999999982e-01, 4.78993000000000002e-01,
    4.79159800000000025e-01, 4.79326499999999989e-01, 4.79493200000000008e-01,
    4.79659899999999972e-01, 4.79826599999999992e-01, 4.79993400000000014e-01,
    4.80160099999999979e-01, 4.80326799999999998e-01, 4.80493500000000018e-01,
    4.80660299999999985e-01, 4.80827000000000004e-01, 4.80993700000000024e-01,
    4.81160399999999988e-01, 4.81327100000000008e-01, 4.81493899999999975e-01,
    4.81660599999999994e-01, 4.81827300000000014e-01, 4.81993999999999978e-01,
    4.82160800000000000e-01, 4.82327500000000020e-01, 4.82494199999999984e-01,
    4.82660900000000004e-01, 4.82827600000000023e-01, 4.82994399999999990e-01,
    4.83161100000000010e-01, 4.83327799999999974e-01, 4.83494499999999994e-01,
    4.83661300000000016e-01, 4.83827999999999980e-01, 4.83994700000000000e-01,
    4.84161400000000020e-01, 4.84328099999999984e-01, 4.84494900000000006e-01,
    4.84661600000000026e-01, 4.84828299999999990e-01, 4.84995000000000009e-01,
    4.85161799999999976e-01, 4.85328499999999996e-01, 4.85495200000000016e-01,
    4.85661899999999980e-01, 4.85828599999999999e-01, 4.85995400000000022e-01,
    4.86162099999999986e-01, 4.86328800000000006e-01, 4.86495500000000025e-01,
    4.86662199999999989e-01, 4.86829000000000012e-01, 4.86995699999999976e-01,
    4.87162399999999995e-01, 4.87329100000000015e-01, 4.87495899999999982e-01,
    4.87662600000000002e-01, 4.87829300000000021e-01, 4.87995999999999985e-01,
    4.88162700000000005e-01, 4.88329500000000027e-01, 4.88496199999999992e-01,
    4.88662900000000011e-01, 4.88829599999999975e-01, 4.88996399999999998e-01,
    4.89163100000000017e-01, 4.89329799999999981e-01, 4.89496500000000001e-01,
    4.89663200000000021e-01, 4.89829999999999988e-01, 4.89996700000000007e-01,
    4.90163400000000027e-01, 4.90330099999999991e-01, 4.90496900000000013e-01,
    4.90663599999999978e-01, 4.90830299999999997e-01, 4.90997000000000017e-01,
    4.91163699999999981e-01, 4.91330500000000003e-01, 4.91497200000000023e-01,
    4.91663899999999987e-01, 4.91830600000000007e-01, 4.91997300000000026e-01,
    4.92164099999999993e-01, 4.92330800000000013e-01, 4.92497499999999977e-01,
    4.92664199999999997e-01, 4.92831000000000019e-01, 4.92997699999999983e-01,
    4.93164400000000003e-01, 4.93331100000000022e-01, 4.93497799999999986e-01,
    4.93664600000000009e-01, 4.93831299999999973e-01, 4.93997999999999993e-01,
    4.94164700000000012e-01, 4.94331499999999979e-01, 4.94498199999999999e-01,
    4.94664900000000018e-01, 4.94831599999999983e-01, 4.94998300000000002e-01,
    4.95165100000000025e-01, 4.95331799999999989e-01, 4.95498500000000008e-01,
    4.95665199999999972e-01, 4.95831999999999995e-01, 4.95998700000000015e-01,
    4.96165399999999979e-01, 4.96332099999999998e-01, 4.96498800000000018e-01,
    4.96665599999999985e-01, 4.96832300000000004e-01, 4.96999000000000024e-01,
    4.97165699999999988e-01, 4.97332400000000008e-01, 4.97499199999999975e-01,
    4.97665899999999994e-01, 4.97832600000000014e-01, 4.97999299999999978e-01,
    4.98166100000000001e-01, 4.98332800000000020e-01, 4.98499499999999984e-01,
    4.98666200000000004e-01, 4.98832900000000024e-01, 4.98999699999999990e-01,
    4.99166400000000010e-01, 4.99333099999999974e-01, 4.99499799999999994e-01,
    4.99666600000000016e-01, 4.99833299999999980e-01, 5.00000000000000000e-01,
};
inline double vr_theo[] = {
    2.39999999999999989e-06, 4.02532599999999975e-04, 8.02665200000000001e-04,
    1.20279799999999993e-03, 1.60293000000000002e-03, 2.00306299999999981e-03,
    2.40319499999999990e-03, 2.80332799999999990e-03, 3.20346099999999990e-03,
    3.60359299999999999e-03, 4.00372599999999999e-03, 4.40385800000000008e-03,
    4.80399099999999964e-03, 5.20412400000000008e-03, 5.60425600000000017e-03,
    6.00438899999999973e-03, 6.40452099999999983e-03, 6.80465400000000026e-03,
    7.20478600000000035e-03, 7.60491899999999992e-03, 8.00505200000000035e-03,
    8.40518399999999957e-03, 8.80531700000000001e-03, 9.20544899999999923e-03,
    9.60558199999999966e-03, 1.00057099999999993e-02, 1.04058499999999995e-02,
    1.08059799999999998e-02, 1.12061100000000000e-02, 1.16062400000000003e-02,
    1.20063800000000005e-02, 1.24065100000000008e-02, 1.28066399999999993e-02,
    1.32067799999999996e-02, 1.36069099999999998e-02, 1.40070400000000001e-02,
    1.44071700000000004e-02, 1.48073100000000006e-02, 1.52074399999999992e-02,
    1.56075699999999994e-02, 1.60076999999999997e-02, 1.64078399999999999e-02,
    1.68079699999999985e-02, 1.72081000000000005e-02, 1.76082299999999990e-02,
    1.80083699999999992e-02, 1.84085000000000013e-02, 1.88086299999999998e-02,
    1.92087599999999983e-02, 1.96088999999999986e-02, 2.00090300000000006e-02,
    2.04091599999999991e-02, 2.08092900000000011e-02, 2.12094300000000013e-02,
    2.16095599999999999e-02, 2.20096899999999984e-02, 2.24098200000000004e-02,
    2.28099600000000007e-02, 2.32100899999999992e-02, 2.36102200000000012e-02,
    2.40103499999999997e-02, 2.44104900000000000e-02, 2.48106199999999985e-02,
    2.52107500000000005e-02, 2.56108799999999991e-02, 2.60110199999999993e-02,
    2.64111500000000013e-02, 2.68112799999999998e-02, 2.72114200000000001e-02,
    2.76115499999999986e-02, 2.80116800000000006e-02, 2.84118099999999991e-02,
    2.88119499999999994e-02, 2.92120800000000014e-02, 2.96122099999999999e-02,
    3.00123399999999985e-02, 3.04124799999999987e-02, 3.08126100000000007e-02,
    3.12127399999999992e-02, 3.16128700000000012e-02, 3.20130100000000015e-02,
    3.24131400000000000e-02, 3.28132699999999985e-02, 3.32133999999999971e-02,
    3.36135399999999973e-02, 3.40136700000000028e-02, 3.44138000000000013e-02,
    3.48139299999999999e-02, 3.52140700000000001e-02, 3.56141999999999986e-02,
    3.60143299999999972e-02, 3.64144600000000027e-02, 3.68146000000000029e-02,
    3.72147300000000014e-02, 3.76148600000000000e-02, 3.80149899999999985e-02,
    3.84151299999999987e-02, 3.88152599999999973e-02, 3.92153900000000027e-02,
    3.96155300000000030e-02, 4.00156600000000015e-02, 4.04157900000000000e-02,
    4.08159199999999986e-02, 4.12160599999999988e-02, 4.16161899999999974e-02,
    4.20163200000000028e-02, 4.24164500000000014e-02, 4.28165900000000016e-02,
    4.32167200000000001e-02, 4.36168499999999987e-02, 4.40169799999999972e-02,
    4.44171199999999974e-02, 4.48172500000000029e-02, 4.52173800000000015e-02,
    4.56175100000000000e-02, 4.60176500000000002e-02, 4.64177799999999988e-02,
    4.68179099999999973e-02, 4.72180400000000028e-02, 4.76181800000000030e-02,
    4.80183100000000015e-02, 4.84184400000000001e-02, 4.88185699999999986e-02,
    4.92187099999999988e-02, 4.96188399999999974e-02, 5.00189700000000029e-02,
    5.04191000000000014e-02, 5.08192400000000016e-02, 5.12193700000000002e-02,
    5.16194999999999987e-02, 5.20196399999999989e-02, 5.24197699999999975e-02,
    5.28199000000000030e-02, 5.32200300000000015e-02, 5.36201700000000017e-02,
    5.40203000000000003e-02, 5.44204299999999988e-02, 5.48205599999999973e-02,
    5.52206999999999976e-02, 5.56208300000000030e-02, 5.60209600000000016e-02,
    5.64210900000000001e-02, 5.68212300000000003e-02, 5.72213599999999989e-02,
    5.76214899999999974e-02, 5.80216200000000029e-02, 5.84217600000000031e-02,
    5.88218900000000017e-02, 5.92220200000000002e-02, 5.96221499999999988e-02,
    6.00222899999999990e-02, 6.04224199999999975e-02, 6.08225500000000030e-02,
    6.12226800000000015e-02, 6.16228200000000018e-02, 6.20229500000000003e-02,
    6.24230799999999988e-02, 6.28232100000000043e-02, 6.32233499999999976e-02,
    6.36234799999999961e-02, 6.40236099999999947e-02, 6.44237500000000018e-02,
    6.48238800000000004e-02, 6.52240099999999989e-02, 6.56241399999999975e-02,
    6.60242800000000046e-02, 6.64244100000000032e-02, 6.68245400000000017e-02,
    6.72246700000000003e-02, 6.76248099999999935e-02, 6.80249400000000060e-02,
    6.84250700000000045e-02, 6.88252000000000030e-02, 6.92253399999999963e-02,
    6.96254699999999949e-02, 7.00255999999999934e-02, 7.04257300000000058e-02,
    7.08258699999999991e-02, 7.12259999999999976e-02, 7.16261299999999962e-02,
    7.20262599999999947e-02, 7.24264000000000019e-02, 7.28265300000000004e-02,
    7.32266599999999990e-02, 7.36267899999999975e-02, 7.40269300000000047e-02,
    7.44270600000000032e-02, 7.48271900000000018e-02, 7.52273299999999950e-02,
    7.56274599999999936e-02, 7.60275900000000060e-02, 7.64277200000000045e-02,
    7.68278599999999978e-02, 7.72279899999999964e-02, 7.76281199999999949e-02,
    7.80282499999999934e-02, 7.84283900000000006e-02, 7.88285199999999991e-02,
    7.92286499999999977e-02, 7.96287799999999962e-02, 8.00289200000000034e-02,
    8.04290500000000019e-02, 8.08291800000000005e-02, 8.12293099999999990e-02,
    8.16294500000000062e-02, 8.20295800000000047e-02, 8.24297100000000033e-02,
    8.28298400000000018e-02, 8.32299799999999951e-02, 8.36301099999999936e-02,
    8.40302400000000060e-02, 8.44303799999999993e-02, 8.48305099999999979e-02,
    8.52306399999999964e-02, 8.56307699999999949e-02, 8.60309100000000021e-02,
    8.64310400000000006e-02, 8.68311699999999992e-02, 8.72312999999999977e-02,
    8.76314400000000049e-02, 8.80315700000000034e-02, 8.84317000000000020e-02,
    8.88318300000000005e-02, 8.92319699999999938e-02, 8.96321000000000062e-02,
    9.00322300000000048e-02, 9.04323600000000033e-02, 9.08324999999999966e-02,
    9.12326299999999951e-02, 9.16327599999999937e-02, 9.20329000000000008e-02,
    9.24330299999999994e-02, 9.28331599999999979e-02, 9.32332899999999964e-02,
    9.36334300000000036e-02, 9.40335600000000021e-02, 9.44336900000000007e-02,
    9.48338199999999992e-02, 9.52339600000000064e-02, 9.56340900000000049e-02,
    9.60342200000000035e-02, 9.64343500000000020e-02, 9.68344899999999953e-02,
    9.72346199999999938e-02, 9.76347500000000063e-02, 9.80348899999999995e-02,
    9.84350199999999981e-02, 9.88351499999999966e-02, 9.92352799999999952e-02,
    9.96354200000000023e-02, 1.00035499999999999e-01, 1.00435700000000003e-01,
    1.00835800000000003e-01, 1.01235900000000004e-01, 1.01636099999999993e-01,
    1.02036199999999994e-01, 1.02436299999999994e-01, 1.02836499999999997e-01,
    1.03236599999999998e-01, 1.03636699999999998e-01, 1.04036900000000002e-01,
    1.04437000000000002e-01, 1.04837100000000003e-01, 1.05237300000000006e-01,
    1.05637400000000006e-01, 1.06037500000000007e-01, 1.06437699999999996e-01,
    1.06837799999999997e-01, 1.07237899999999997e-01, 1.07638100000000000e-01,
    1.08038200000000001e-01, 1.08438300000000001e-01, 1.08838500000000005e-01,
    1.09238600000000005e-01, 1.09638700000000006e-01, 1.10038899999999995e-01,
    1.10438999999999996e-01, 1.10839099999999996e-01, 1.11239299999999999e-01,
    1.11639400000000000e-01, 1.12039500000000000e-01, 1.12439700000000004e-01,
    1.12839800000000004e-01, 1.13239900000000004e-01, 1.13640099999999994e-01,
    1.14040199999999994e-01, 1.14440299999999995e-01, 1.14840499999999998e-01,
    1.15240599999999999e-01, 1.15640699999999999e-01, 1.16040900000000002e-01,
    1.16441000000000003e-01, 1.16841100000000003e-01, 1.17241300000000007e-01,
    1.17641399999999993e-01, 1.18041499999999994e-01, 1.18441699999999997e-01,
    1.18841799999999997e-01, 1.19241899999999998e-01, 1.19642100000000001e-01,
    1.20042200000000002e-01, 1.20442300000000002e-01, 1.20842500000000005e-01,
    1.21242600000000006e-01, 1.21642700000000006e-01, 1.22042899999999996e-01,
    1.22442999999999996e-01, 1.22843099999999997e-01, 1.23243300000000000e-01,
    1.23643400000000001e-01, 1.24043500000000001e-01, 1.24443700000000004e-01,
    1.24843800000000005e-01, 1.25243899999999991e-01, 1.25644100000000009e-01,
    1.26044199999999995e-01, 1.26444300000000009e-01, 1.26844499999999999e-01,
    1.27244600000000013e-01, 1.27644700000000000e-01, 1.28044899999999989e-01,
    1.28445000000000004e-01, 1.28845099999999990e-01, 1.29245300000000007e-01,
    1.29645399999999994e-01, 1.30045500000000008e-01, 1.30445699999999998e-01,
    1.30845800000000012e-01, 1.31245899999999999e-01, 1.31646099999999988e-01,
    1.32046200000000002e-01, 1.32446299999999989e-01, 1.32846500000000006e-01,
    1.33246599999999993e-01, 1.33646700000000007e-01, 1.34046899999999997e-01,
    1.34447000000000011e-01, 1.34847099999999998e-01, 1.35247299999999987e-01,
    1.35647400000000001e-01, 1.36047499999999988e-01, 1.36447700000000005e-01,
    1.36847799999999992e-01, 1.37247900000000006e-01, 1.37648099999999995e-01,
    1.38048200000000010e-01, 1.38448299999999996e-01, 1.38848500000000014e-01,
    1.39248600000000000e-01, 1.39648699999999987e-01, 1.40048900000000004e-01,
    1.40448999999999991e-01, 1.40849100000000005e-01, 1.41249299999999994e-01,
    1.41649400000000009e-01, 1.42049499999999995e-01, 1.42449700000000012e-01,
    1.42849799999999999e-01, 1.43249900000000013e-01, 1.43650100000000003e-01,
    1.44050199999999989e-01, 1.44450300000000004e-01, 1.44850499999999993e-01,
    1.45250600000000007e-01, 1.45650699999999994e-01, 1.46050900000000011e-01,
    1.46450999999999998e-01, 1.46851100000000012e-01, 1.47251300000000002e-01,
    1.47651399999999988e-01, 1.48051500000000003e-01, 1.48451699999999992e-01,
    1.48851800000000006e-01, 1.49251899999999993e-01, 1.49652100000000010e-01,
    1.50052199999999997e-01, 1.50452399999999986e-01, 1.50852500000000000e-01,
    1.51252599999999987e-01, 1.51652800000000004e-01, 1.52052899999999991e-01,
    1.52453000000000005e-01, 1.52853199999999995e-01, 1.53253300000000009e-01,
    1.53653399999999996e-01, 1.54053600000000013e-01, 1.54453699999999999e-01,
    1.54853800000000014e-01, 1.55254000000000003e-01, 1.55654099999999990e-01,
    1.56054200000000004e-01, 1.56454399999999993e-01, 1.56854500000000008e-01,
    1.57254599999999994e-01, 1.57654800000000012e-01, 1.58054899999999998e-01,
    1.58455099999999988e-01, 1.58855200000000002e-01, 1.59255299999999989e-01,
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    1.08231699999999997e+00, 1.08305899999999999e+00, 1.08380300000000007e+00,
    1.08454699999999993e+00, 1.08529199999999992e+00, 1.08603699999999992e+00,
    1.08678399999999997e+00, 1.08753100000000003e+00, 1.08827900000000000e+00,
    1.08902800000000011e+00, 1.08977700000000000e+00, 1.09052700000000002e+00,
    1.09127799999999997e+00, 1.09203000000000006e+00, 1.09278300000000006e+00,
    1.09353600000000006e+00, 1.09429099999999990e+00, 1.09504599999999996e+00,
    1.09580100000000003e+00, 1.09655799999999992e+00, 1.09731500000000004e+00,
    1.09807300000000008e+00, 1.09883200000000003e+00, 1.09959199999999990e+00,
    1.10035200000000000e+00, 1.10111399999999993e+00, 1.10187600000000008e+00,
    1.10263899999999992e+00, 1.10340199999999999e+00, 1.10416699999999990e+00,
    1.10493200000000003e+00, 1.10569800000000007e+00, 1.10646500000000003e+00,
    1.10723199999999999e+00, 1.10800100000000001e+00, 1.10877000000000003e+00,
    1.10953999999999997e+00, 1.11031100000000005e+00, 1.11108199999999990e+00,
    1.11185500000000004e+00, 1.11262799999999995e+00, 1.11340200000000000e+00,
    1.11417699999999997e+00, 1.11495199999999994e+00, 1.11572899999999997e+00,
    1.11650600000000000e+00, 1.11728399999999994e+00, 1.11806199999999989e+00,
    1.11884199999999989e+00, 1.11962199999999990e+00, 1.12040399999999996e+00,
    1.12118500000000010e+00, 1.12196800000000008e+00, 1.12275199999999997e+00,
    1.12353600000000009e+00, 1.12432099999999990e+00, 1.12510700000000008e+00,
    1.12589399999999995e+00, 1.12668199999999996e+00, 1.12746999999999997e+00,
    1.12825899999999990e+00, 1.12904899999999997e+00, 1.12983999999999996e+00,
    1.13063200000000008e+00, 1.13142399999999999e+00, 1.13221700000000003e+00,
    1.13301099999999999e+00, 1.13380600000000009e+00, 1.13460200000000011e+00,
    1.13539799999999991e+00, 1.13619599999999998e+00, 1.13699400000000006e+00,
    1.13779300000000005e+00, 1.13859200000000005e+00, 1.13939300000000010e+00,
    1.14019399999999993e+00, 1.14099599999999990e+00, 1.14179900000000001e+00,
    1.14260300000000004e+00, 1.14340700000000006e+00, 1.14421299999999992e+00,
    1.14501900000000001e+00, 1.14582600000000001e+00, 1.14663399999999993e+00,
    1.14744200000000007e+00, 1.14825200000000005e+00, 1.14906200000000003e+00,
    1.14987299999999992e+00, 1.15068499999999996e+00, 1.15149799999999991e+00,
    1.15231100000000009e+00, 1.15312600000000010e+00, 1.15394100000000011e+00,
    1.15475700000000003e+00, 1.15557299999999996e+00, 1.15639099999999995e+00,
    1.15720899999999993e+00, 1.15802899999999998e+00, 1.15884900000000002e+00,
    1.15966900000000006e+00, 1.16049099999999994e+00, 1.16131300000000004e+00,
    1.16213699999999998e+00, 1.16296099999999991e+00, 1.16378599999999999e+00,
    1.16461100000000006e+00, 1.16543799999999997e+00, 1.16626500000000011e+00,
    1.16709400000000008e+00, 1.16792300000000004e+00, 1.16875200000000001e+00,
    1.16958300000000004e+00, 1.17041400000000007e+00, 1.17124699999999993e+00,
    1.17208000000000001e+00, 1.17291400000000001e+00, 1.17374800000000001e+00,
    1.17458400000000007e+00, 1.17541999999999991e+00, 1.17625700000000011e+00,
    1.17709500000000000e+00, 1.17793400000000004e+00, 1.17877399999999999e+00,
    1.17961399999999994e+00, 1.18045500000000003e+00, 1.18129700000000004e+00,
    1.18213999999999997e+00, 1.18298400000000004e+00, 1.18382800000000010e+00,
    1.18467400000000000e+00, 1.18551999999999991e+00, 1.18636699999999995e+00,
    1.18721399999999999e+00, 1.18806300000000009e+00, 1.18891199999999997e+00,
    1.18976299999999990e+00, 1.19061400000000006e+00, 1.19146500000000000e+00,
    1.19231799999999999e+00, 1.19317199999999990e+00, 1.19402600000000003e+00,
    1.19488100000000008e+00, 1.19573700000000005e+00, 1.19659399999999994e+00,
    1.19745100000000004e+00, 1.19830900000000007e+00, 1.19916899999999993e+00,
    1.20002800000000009e+00, 1.20088900000000010e+00, 1.20175100000000001e+00,
    1.20261299999999993e+00, 1.20347599999999999e+00, 1.20433999999999997e+00,
    1.20520500000000008e+00, 1.20607099999999989e+00, 1.20693699999999993e+00,
    1.20780500000000002e+00, 1.20867300000000011e+00, 1.20954199999999990e+00,
    1.21041099999999990e+00, 1.21128199999999997e+00, 1.21215300000000004e+00,
    1.21302500000000002e+00, 1.21389799999999992e+00, 1.21477199999999996e+00,
    1.21564600000000000e+00, 1.21652200000000010e+00, 1.21739799999999998e+00,
    1.21827500000000000e+00, 1.21915299999999993e+00, 1.22003100000000009e+00,
    1.22090999999999994e+00, 1.22179100000000007e+00, 1.22267199999999998e+00,
    1.22355299999999989e+00, 1.22443600000000008e+00, 1.22531900000000005e+00,
    1.22620400000000007e+00, 1.22708900000000010e+00, 1.22797399999999990e+00,
    1.22886099999999998e+00, 1.22974800000000006e+00, 1.23063600000000006e+00,
    1.23152499999999998e+00, 1.23241500000000004e+00, 1.23330600000000001e+00,
    1.23419699999999999e+00, 1.23508900000000010e+00, 1.23598199999999991e+00,
    1.23687600000000009e+00, 1.23777099999999995e+00, 1.23866600000000004e+00,
    1.23956200000000005e+00, 1.24045899999999998e+00, 1.24135700000000004e+00,
    1.24225500000000011e+00, 1.24315500000000001e+00, 1.24405499999999991e+00,
    1.24495599999999995e+00, 1.24585699999999999e+00, 1.24676000000000009e+00,
    1.24766299999999997e+00, 1.24856699999999998e+00, 1.24947199999999992e+00,
    1.25037799999999999e+00, 1.25128400000000006e+00, 1.25219100000000005e+00,
    1.25309899999999996e+00, 1.25400800000000001e+00, 1.25491700000000006e+00,
    1.25582799999999994e+00, 1.25673900000000005e+00, 1.25765100000000007e+00,
    1.25856300000000010e+00, 1.25947699999999996e+00, 1.26039100000000004e+00,
    1.26130600000000004e+00, 1.26222199999999996e+00, 1.26313800000000009e+00,
    1.26405600000000007e+00, 1.26497400000000004e+00, 1.26589299999999993e+00,
    1.26681200000000005e+00, 1.26773300000000000e+00, 1.26865399999999995e+00,
    1.26957600000000004e+00, 1.27049900000000004e+00, 1.27142200000000005e+00,
    1.27234599999999998e+00, 1.27327100000000004e+00, 1.27419700000000002e+00,
    1.27512399999999992e+00, 1.27605100000000005e+00, 1.27697900000000009e+00,
    1.27790800000000004e+00, 1.27883799999999992e+00, 1.27976800000000002e+00,
    1.28069900000000003e+00, 1.28163099999999996e+00, 1.28256400000000004e+00,
    1.28349700000000011e+00, 1.28443100000000010e+00, 1.28536600000000001e+00,
    1.28630200000000006e+00, 1.28723800000000010e+00, 1.28817500000000007e+00,
    1.28911299999999995e+00, 1.29005199999999998e+00, 1.29099199999999992e+00,
    1.29193200000000008e+00, 1.29287299999999994e+00, 1.29381400000000002e+00,
    1.29475699999999994e+00, 1.29570000000000007e+00, 1.29664399999999991e+00,
    1.29758799999999996e+00, 1.29853400000000008e+00, 1.29947999999999997e+00,
    1.30042700000000000e+00, 1.30137400000000003e+00, 1.30232299999999990e+00,
    1.30327199999999999e+00, 1.30422100000000007e+00, 1.30517200000000000e+00,
    1.30612299999999992e+00, 1.30707499999999999e+00, 1.30802799999999997e+00,
    1.30898099999999995e+00, 1.30993599999999999e+00, 1.31089100000000003e+00,
    1.31184600000000007e+00, 1.31280299999999994e+00, 1.31376000000000004e+00,
    1.31471699999999991e+00, 1.31567600000000007e+00, 1.31663500000000000e+00,
    1.31759500000000007e+00, 1.31855600000000006e+00, 1.31951700000000005e+00,
    1.32047899999999996e+00, 1.32144200000000001e+00, 1.32240599999999997e+00,
    1.32336999999999994e+00, 1.32433500000000004e+00, 1.32529999999999992e+00,
    1.32626700000000008e+00, 1.32723400000000002e+00, 1.32820200000000010e+00,
    1.32916999999999996e+00, 1.33013899999999996e+00, 1.33110900000000010e+00,
    1.33207999999999993e+00, 1.33305099999999999e+00, 1.33402299999999996e+00,
    1.33499600000000007e+00, 1.33596899999999996e+00, 1.33694299999999999e+00,
    1.33791799999999994e+00, 1.33889300000000011e+00, 1.33986899999999998e+00,
    1.34084599999999998e+00, 1.34182399999999991e+00, 1.34280200000000005e+00,
    1.34378099999999989e+00, 1.34475999999999996e+00, 1.34574100000000008e+00,
    1.34672199999999997e+00, 1.34770300000000010e+00, 1.34868499999999991e+00,
    1.34966800000000009e+00, 1.35065199999999996e+00, 1.35163600000000006e+00,
    1.35262100000000007e+00, 1.35360700000000000e+00, 1.35459299999999994e+00,
    1.35558000000000001e+00, 1.35656800000000000e+00, 1.35755599999999998e+00,
    1.35854499999999989e+00, 1.35953499999999994e+00, 1.36052499999999998e+00,
    1.36151599999999995e+00, 1.36250699999999991e+00, 1.36349999999999993e+00,
    1.36449299999999996e+00, 1.36548599999999998e+00, 1.36647999999999992e+00,
    1.36747500000000000e+00, 1.36847099999999999e+00, 1.36946699999999999e+00,
    1.37046399999999990e+00, 1.37146100000000004e+00, 1.37245900000000010e+00,
    1.37345800000000007e+00, 1.37445700000000004e+00, 1.37545699999999993e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
    0.00000000000000000e+00, 0.00000000000000000e+00, 0.00000000000000000e+00,
};
inline double rho_theo[] = {
    1.17298699999999997e-09, 1.34121199999999998e-09, 1.36341600000000000e-09,
    1.37078100000000000e-09, 1.38545899999999998e-09, 1.39277300000000007e-09,
    1.40006900000000000e-09, 1.40006900000000000e-09, 1.40006900000000000e-09,
    1.40734800000000009e-09, 1.41461100000000005e-09, 1.41461100000000005e-09,
    1.42185699999999996e-09, 1.42185699999999996e-09, 1.42185699999999996e-09,
    1.42908699999999995e-09, 1.42908699999999995e-09, 1.42908699999999995e-09,
    1.43630100000000000e-09, 1.43630100000000000e-09, 1.43630100000000000e-09,
    1.43630100000000000e-09, 1.43630100000000000e-09, 1.43630100000000000e-09,
    1.43630100000000000e-09, 1.43630100000000000e-09, 1.44349800000000001e-09,
    1.44349800000000001e-09, 1.44349800000000001e-09, 1.73962400000000007e-09,
    2.00856300000000007e-09, 2.26820900000000006e-09, 2.75191299999999999e-09,
    3.19523999999999981e-09, 3.61268599999999982e-09, 4.00966900000000037e-09,
    4.58100100000000011e-09, 5.28889400000000037e-09, 5.96068199999999995e-09,
    6.59665500000000032e-09, 7.36051199999999966e-09, 8.23042100000000011e-09,
    9.19737600000000031e-09, 1.02477499999999999e-08, 1.13760399999999999e-08,
    1.25721999999999992e-08, 1.39461599999999993e-08, 1.52648499999999999e-08,
    1.68423299999999989e-08, 1.84540400000000005e-08, 2.01971899999999998e-08,
    2.21499800000000001e-08, 2.41175000000000007e-08, 2.62680600000000000e-08,
    2.85894599999999998e-08, 3.10655000000000011e-08, 3.36839599999999996e-08,
    3.64325700000000013e-08, 3.94462799999999979e-08, 4.25655900000000005e-08,
    4.59175000000000007e-08, 4.94811800000000026e-08, 5.32441299999999986e-08,
    5.71925499999999969e-08, 6.14270099999999947e-08, 6.58174200000000012e-08,
    7.05184900000000006e-08, 7.54549400000000037e-08, 8.06623099999999975e-08,
    8.61218600000000035e-08, 9.19179099999999941e-08, 9.79786600000000042e-08,
    1.04336599999999995e-07, 1.11015599999999998e-07, 1.17999199999999994e-07,
    1.25351999999999996e-07, 1.33051599999999997e-07, 1.41118400000000002e-07,
    1.49571499999999997e-07, 1.58388099999999994e-07, 1.67622100000000009e-07,
    1.77250200000000013e-07, 1.87286900000000009e-07, 1.97813699999999997e-07,
    2.08737500000000012e-07, 2.20167699999999987e-07, 2.32078900000000004e-07,
    2.44445399999999985e-07, 2.57367700000000002e-07, 2.70786799999999991e-07,
    2.84737499999999978e-07, 2.99250900000000018e-07, 3.14355900000000020e-07,
    3.30022400000000010e-07, 3.46279399999999995e-07, 3.63176799999999986e-07,
    3.80684500000000010e-07, 3.98876200000000015e-07, 4.17695299999999986e-07,
    4.37234700000000008e-07, 4.57461199999999980e-07, 4.78415200000000024e-07,
    5.00086700000000020e-07, 5.22534800000000003e-07, 5.45747299999999973e-07,
    5.69777500000000047e-07, 5.94590900000000015e-07, 6.20258500000000035e-07,
    6.46764600000000013e-07, 6.74155299999999994e-07, 7.02433399999999969e-07,
    7.31639799999999968e-07, 7.61756099999999948e-07, 7.92857999999999965e-07,
    8.24906199999999973e-07, 8.57971799999999964e-07, 8.92067999999999965e-07,
    9.27189700000000003e-07, 9.63383800000000061e-07, 1.00067599999999998e-06,
    1.03907400000000006e-06, 1.07861900000000003e-06, 1.11930000000000002e-06,
    1.16118600000000003e-06, 1.20427800000000008e-06, 1.24859500000000007e-06,
    1.29418099999999993e-06, 1.34105199999999990e-06, 1.38921900000000007e-06,
    1.43872200000000006e-06, 1.48960099999999992e-06, 1.54186300000000005e-06,
    1.59552799999999994e-06, 1.65064400000000007e-06, 1.70723999999999998e-06,
    1.76531999999999998e-06, 1.82492300000000009e-06, 1.88608899999999994e-06,
    1.94884099999999995e-06, 2.01318800000000015e-06, 2.07919000000000008e-06,
    2.14686300000000018e-06, 2.21622599999999993e-06, 2.28733000000000009e-06,
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    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
    1.00000000000000000e+00, 1.00000000000000000e+00, 1.00000000000000000e+00,
};
inline double p_theo[] = {
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72116400000000036e-01, 7.72116400000000036e-01, 7.72116400000000036e-01,
    7.72810600000000014e-01, 7.71155400000000046e-01, 7.73357799999999984e-01,
    7.72116400000000036e-01, 7.72592799999999968e-01, 7.72812900000000025e-01,
    7.71717300000000050e-01, 7.72496300000000025e-01, 7.72596199999999955e-01,
    7.72397400000000012e-01, 7.72226500000000038e-01, 7.72278200000000026e-01,
    7.72689599999999976e-01, 7.72270200000000018e-01, 7.72548400000000024e-01,
    7.72488100000000011e-01, 7.72360500000000005e-01, 7.72315900000000055e-01,
    7.72473300000000029e-01, 7.72279300000000002e-01, 7.72529000000000021e-01,
    7.72428400000000015e-01, 7.72429699999999997e-01, 7.72404300000000044e-01,
    7.72472000000000047e-01, 7.72338500000000039e-01, 7.72328800000000038e-01,
    7.72349399999999964e-01, 7.72355000000000014e-01, 7.72428200000000009e-01,
    7.72411500000000029e-01, 7.72407199999999960e-01, 7.72392500000000037e-01,
    7.72353100000000015e-01, 7.72369500000000042e-01, 7.72347699999999970e-01,
    7.72363800000000045e-01, 7.72409200000000018e-01, 7.72360500000000005e-01,
    7.72407500000000025e-01, 7.72386600000000034e-01, 7.72366299999999950e-01,
    7.72402499999999992e-01, 7.72372199999999953e-01, 7.72378600000000026e-01,
    7.72392500000000037e-01, 7.72394699999999990e-01, 7.72372100000000006e-01,
    7.72375999999999951e-01, 7.72389800000000015e-01, 7.72380399999999967e-01,
    7.72392999999999996e-01, 7.72375699999999998e-01, 7.72392999999999996e-01,
    7.72380900000000037e-01, 7.72381600000000001e-01, 7.72376999999999980e-01,
    7.72387399999999946e-01, 7.72383999999999959e-01, 7.72387999999999963e-01,
    7.72377800000000003e-01, 7.72386099999999964e-01, 7.72382200000000019e-01,
    7.72386499999999976e-01, 7.72384599999999977e-01, 7.72385899999999959e-01,
    7.72380500000000025e-01, 7.72386899999999987e-01, 7.72380199999999961e-01,
    7.72387200000000052e-01, 7.72386499999999976e-01, 7.72382400000000024e-01,
    7.72385499999999947e-01, 7.72386299999999970e-01, 7.72384300000000024e-01,
    7.72384500000000029e-01, 7.72381399999999996e-01, 7.72386099999999964e-01,
    7.72384399999999971e-01, 7.72383400000000053e-01, 7.72384999999999988e-01,
    7.72383500000000001e-01, 7.72382000000000013e-01, 7.72383799999999954e-01,
    7.72385199999999994e-01, 7.72383299999999995e-01, 7.72382800000000036e-01,
    7.72384700000000035e-01, 7.72384799999999982e-01, 7.72382699999999978e-01,
    7.72383500000000001e-01, 7.72384500000000029e-01, 7.72383900000000012e-01,
    7.72382800000000036e-01, 7.72384399999999971e-01, 7.72383799999999954e-01,
    7.72383000000000042e-01, 7.72383999999999959e-01, 7.72383299999999995e-01,
    7.72383799999999954e-01, 7.72384399999999971e-01, 7.72383400000000053e-01,
    7.72383799999999954e-01, 7.72384399999999971e-01, 7.72384199999999965e-01,
    7.72383999999999959e-01, 7.72383599999999948e-01, 7.72384199999999965e-01,
    7.72383599999999948e-01, 7.72383400000000053e-01, 7.72383299999999995e-01,
    7.72383999999999959e-01, 7.72383599999999948e-01, 7.72383400000000053e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383400000000053e-01,
    7.72383500000000001e-01, 7.72383799999999954e-01, 7.72383400000000053e-01,
    7.72383599999999948e-01, 7.72383999999999959e-01, 7.72383500000000001e-01,
    7.72383400000000053e-01, 7.72383700000000006e-01, 7.72383900000000012e-01,
    7.72383799999999954e-01, 7.72383900000000012e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383599999999948e-01, 7.72383500000000001e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383700000000006e-01, 7.72383599999999948e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383599999999948e-01,
    7.72383599999999948e-01, 7.72383599999999948e-01, 7.72383700000000006e-01,
    7.72383799999999954e-01, 7.72383700000000006e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383599999999948e-01, 7.72383700000000006e-01,
    7.72383700000000006e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383700000000006e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383700000000006e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383700000000006e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383799999999954e-01, 7.72383700000000006e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383700000000006e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383799999999954e-01,
    7.72383700000000006e-01, 7.72383700000000006e-01, 7.72383700000000006e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383799999999954e-01, 7.72383799999999954e-01,
    7.72383799999999954e-01, 7.72383900000000012e-01, 7.72383799999999954e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383799999999954e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383900000000012e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383900000000012e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383900000000012e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383900000000012e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383900000000012e-01,
    7.72383900000000012e-01, 7.72383900000000012e-01, 7.72383999999999959e-01,
    7.72383999999999959e-01, 7.72383999999999959e-01, 7.72383999999999959e-01,
    7.72383999999999959e-01, 7.72383999999999959e-01, 7.72383999999999959e-01,
    7.72383999999999959e-01, 7.72383999999999959e-01, 7.72383999999999959e-01,
    7.72383999999999959e-01, 7.72383999999999959e-01, 7.72383999999999959e-01,
    7.72383999999999959e-01, 7.72383999999999959e-01, 7.72384100000000018e-01,
    7.72384100000000018e-01, 7.72384100000000018e-01, 7.72384100000000018e-01,
    7.72384100000000018e-01, 7.72384100000000018e-01, 7.72384100000000018e-01,
    7.72384100000000018e-01, 7.72384100000000018e-01, 7.72384100000000018e-01,
    7.72384100000000018e-01, 7.72384199999999965e-01, 7.72384199999999965e-01,
    7.72384199999999965e-01, 7.72384199999999965e-01, 7.72384199999999965e-01,
    7.72384199999999965e-01, 7.72384199999999965e-01, 7.72384199999999965e-01,
    7.72384199999999965e-01, 7.72384199999999965e-01, 7.72384300000000024e-01,
    7.72384300000000024e-01, 7.72384300000000024e-01, 7.72384300000000024e-01,
    7.72384300000000024e-01, 7.72384300000000024e-01, 7.72384300000000024e-01,
    7.72384300000000024e-01, 7.72384399999999971e-01, 7.72384399999999971e-01,
    7.72384399999999971e-01, 7.72384399999999971e-01, 7.72384399999999971e-01,
    7.72384399999999971e-01, 7.72384500000000029e-01, 7.72384500000000029e-01,
    7.72384500000000029e-01, 7.72384500000000029e-01, 7.72384500000000029e-01,
    7.72384500000000029e-01, 7.72384500000000029e-01, 7.72384599999999977e-01,
    7.72384599999999977e-01, 7.72384599999999977e-01, 7.72384599999999977e-01,
    7.72384599999999977e-01, 7.72384700000000035e-01, 7.72384700000000035e-01,
    7.72384700000000035e-01, 7.72384700000000035e-01, 7.72384700000000035e-01,
    7.72384700000000035e-01, 7.72384799999999982e-01, 7.72384799999999982e-01,
    7.72384799999999982e-01, 7.72384799999999982e-01, 7.72384900000000041e-01,
    7.72384900000000041e-01, 7.72384900000000041e-01, 7.72384900000000041e-01,
    7.72384900000000041e-01, 7.72384999999999988e-01, 7.72384999999999988e-01,
    7.72384999999999988e-01, 7.72384999999999988e-01, 7.72385100000000047e-01,
    7.72385100000000047e-01, 7.72385100000000047e-01, 7.72385100000000047e-01,
    7.72385199999999994e-01, 7.72385199999999994e-01, 7.72385199999999994e-01,
    7.72385199999999994e-01, 7.72385300000000052e-01, 7.72385300000000052e-01,
    7.72385300000000052e-01, 7.72385400000000000e-01, 7.72385400000000000e-01,
    7.72385400000000000e-01, 7.72385499999999947e-01, 7.72385499999999947e-01,
    7.72385499999999947e-01, 7.72385499999999947e-01, 7.72385600000000005e-01,
    7.72385600000000005e-01, 7.72385600000000005e-01, 7.72385699999999953e-01,
    7.72385699999999953e-01, 7.72385800000000011e-01, 7.72385800000000011e-01,
    7.72385800000000011e-01, 7.72385899999999959e-01, 7.72385899999999959e-01,
    7.72385899999999959e-01, 7.72386000000000017e-01, 7.72386000000000017e-01,
    7.72386000000000017e-01, 7.72386099999999964e-01, 7.72386099999999964e-01,
    7.72386200000000023e-01, 7.72386200000000023e-01, 7.72386299999999970e-01,
    7.72386299999999970e-01, 7.72386299999999970e-01, 7.72386400000000028e-01,
    7.72386400000000028e-01, 7.72386499999999976e-01, 7.72386499999999976e-01,
    7.72386600000000034e-01, 7.72386600000000034e-01, 7.72386699999999982e-01,
    7.72386699999999982e-01, 7.72386800000000040e-01, 7.72386800000000040e-01,
    7.72386899999999987e-01, 7.72386899999999987e-01, 7.72387000000000046e-01,
    7.72387000000000046e-01, 7.72387099999999993e-01, 7.72387099999999993e-01,
    7.72387200000000052e-01, 7.72387200000000052e-01, 7.72387299999999999e-01,
    7.72387299999999999e-01, 7.72387399999999946e-01, 7.72387500000000005e-01,
    7.72387500000000005e-01, 7.72387599999999952e-01, 7.72387599999999952e-01,
    7.72387700000000010e-01, 7.72387799999999958e-01, 7.72387799999999958e-01,
    7.72387900000000016e-01, 7.72387999999999963e-01, 7.72387999999999963e-01,
    7.72388100000000022e-01, 7.72388199999999969e-01, 7.72388199999999969e-01,
    7.72388300000000028e-01, 7.72388399999999975e-01, 7.72388399999999975e-01,
    7.72388500000000033e-01, 7.72388599999999981e-01, 7.72388700000000039e-01,
    7.72388700000000039e-01, 7.72388799999999986e-01, 7.72388900000000045e-01,
    7.72388999999999992e-01, 7.72388999999999992e-01, 7.72389100000000051e-01,
    7.72389199999999998e-01, 7.72389299999999945e-01, 7.72389400000000004e-01,
    7.72389499999999951e-01, 7.72389499999999951e-01, 7.72389600000000009e-01,
    7.72389699999999957e-01, 7.72389800000000015e-01, 7.72389899999999963e-01,
    7.72390000000000021e-01, 7.72390099999999968e-01, 7.72390200000000027e-01,
    7.72390299999999974e-01, 7.72390299999999974e-01, 7.72390400000000032e-01,
    7.72390499999999980e-01, 7.72390600000000038e-01, 7.72390699999999986e-01,
    7.72390800000000044e-01, 7.72390899999999991e-01, 7.72391000000000050e-01,
    7.72391099999999997e-01, 7.72391300000000003e-01, 7.72391399999999950e-01,
    7.72391500000000009e-01, 7.72391599999999956e-01, 7.72391700000000014e-01,
    7.72391799999999962e-01, 7.72391900000000020e-01, 7.72391999999999967e-01,
    7.72392100000000026e-01, 7.72392300000000032e-01, 7.72392399999999979e-01,
    7.72392500000000037e-01, 7.72392599999999985e-01, 7.72392700000000043e-01,
    7.72392900000000049e-01, 7.72392999999999996e-01, 7.72393100000000055e-01,
    7.72393299999999949e-01, 7.72393400000000008e-01, 7.72393499999999955e-01,
    7.72393600000000013e-01, 7.72393800000000019e-01, 7.72393899999999967e-01,
    7.72394099999999972e-01, 7.72394200000000031e-01, 7.72394299999999978e-01,
    7.72394499999999984e-01, 7.72394600000000042e-01, 7.72394800000000048e-01,
    7.72394899999999995e-01, 7.72395100000000001e-01, 7.72395199999999948e-01,
    7.72395399999999954e-01, 7.72395500000000013e-01, 7.72395700000000018e-01,
    7.72395799999999966e-01, 7.72395999999999971e-01, 7.72396199999999977e-01,
    7.72396300000000036e-01, 7.72396500000000041e-01, 7.72396700000000047e-01,
    7.72396799999999994e-01, 7.72397000000000000e-01, 7.72397200000000006e-01,
    7.72397299999999953e-01, 7.72397499999999959e-01, 7.72397699999999965e-01,
    7.72397899999999971e-01, 7.72398099999999976e-01, 7.72398200000000035e-01,
    7.72398400000000040e-01, 7.72398600000000046e-01, 7.72398800000000052e-01,
    7.72398999999999947e-01, 7.72399199999999952e-01, 7.72399399999999958e-01,
    7.72399599999999964e-01, 7.72399799999999970e-01, 7.72399999999999975e-01,
    7.72400199999999981e-01, 7.72400399999999987e-01, 7.72400599999999993e-01,
    7.72400799999999998e-01, 7.72401000000000004e-01, 7.72401200000000010e-01,
    7.72401499999999963e-01, 7.72401699999999969e-01, 7.72401899999999975e-01,
    7.72402099999999980e-01, 7.72402299999999986e-01, 7.72402600000000050e-01,
    7.72402799999999945e-01, 7.72402999999999951e-01, 7.72403300000000015e-01,
    7.72403500000000021e-01, 7.72403799999999974e-01, 7.72403999999999979e-01,
    7.72404199999999985e-01, 7.72404500000000049e-01, 7.72404700000000055e-01,
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