dftd_parameters.h

/* This file is part of cpp-d4.
 *
 * Copyright (C) 2019 Sebastian Ehlert, Marvin Friede
 *
 * cpp-d4 is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * cpp-d4 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 Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with cpp-d4.  If not, see <https://www.gnu.org/licenses/>.
 */

/**
 * This is the DFT-D4 equivalent of copyc6, since this is an *empirical*
 * dispersion correction we can hardly avoid having this big, scary blob
 * of data lying around somewhere.
 *
 * Files like this are usually computer generated so avoid modifying it,
 * but have the appropriate tool generate this anew.
 */
#pragma once

namespace dftd4 {

constexpr int MAXELEMENT = 104; // 103 + dummy

// clang-format off
/**
 * Effective nuclear charges from the def2-ECPs used for calculating the
 * reference polarizibilities for DFT-D4.
 */
static const double zeff[119]{
    0,                                                     //  dummy
    1,                                                 2,  //  H-He
    3, 4,                               5, 6, 7, 8, 9,10,  //  Li-Ne
   11,12,                              13,14,15,16,17,18,  //  Na-Ar
   19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,  //  K-Kr
    9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,  //  Rb-Xe
    9,10,11,30,31,32,33,34,35,36,37,38,39,40,41,42,43,     //  Cs-Lu
   12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,           //  Hf-Rn
   // just copy & paste from above
    9,10,11,30,31,32,33,34,35,36,37,38,39,40,41,42,43,     //  Fr-Lr
   12,13,14,15,16,17,18,19,20,21,22,23,24,25,26            //  Rf-Og
};
// clang-format on

/**
 * PBE0/def2-QZVP atomic values calculated by S. Grimme in Gaussian (2010)
 * rare gases recalculated by J. Mewes with PBE0/aug-cc-pVQZ in Dirac (2018)
 * He: 3.4698 -> 3.5544, Ne: 3.1036 -> 3.7943, Ar: 5.6004 -> 5.6638,
 * Kr: 6.1971 -> 6.2312, Xe: 7.5152 -> 8.8367
 * not replaced but recalculated (PBE0/cc-pVQZ) were
 *  H: 8.0589 ->10.9359, Li:29.0974 ->39.7226, Be:14.8517 ->17.7460
 * also new super heavies Cn,Nh,Fl,Lv,Og
 * Am-Rg calculated at 4c-PBE/Dyall-AE4Z (Dirac 2022)
 *
 * These values are actually never used in the code. Only r4r2 is used.
 */
static const double r2r4[119]{
  0.0,                                                           //  dummy
  8.0589,  3.4698,                                               //  H,He
  29.0974, 14.8517, 11.8799, 7.8715,  5.5588,  4.7566,  3.8025,
  3.1036,                                                        //  Li-Ne
  26.1552, 17.2304, 17.7210, 12.7442, 9.5361,  8.1652,  6.7463,
  5.6004,                                                        //  Na-Ar
  29.2012, 22.3934,                                              //  K,Ca
  19.0598, 16.8590, 15.4023, 12.5589, 13.4788,                   //  Sc-
  12.2309, 11.2809, 10.5569, 10.1428, 9.4907,                    //  -Zn
  13.4606, 10.8544, 8.9386,  8.1350,  7.1251,  6.1971,           //  Ga-Kr
  30.0162, 24.4103,                                              //  Rb,Sr
  20.3537, 17.4780, 13.5528, 11.8451, 11.0355,                   //  Y-
  10.1997, 9.5414,  9.0061,  8.6417,  8.9975,                    //  -Cd
  14.0834, 11.8333, 10.0179, 9.3844,  8.4110,  7.5152,           //  In-Xe
  32.7622, 27.5708,                                              //  Cs,Ba
  23.1671, 21.6003, 20.9615, 20.4562, 20.1010, 19.7475, 19.4828, //  La-Eu
  15.6013, 19.2362, 17.4717, 17.8321, 17.4237, 17.1954, 17.1631, //  Gd-Yb
  14.5716, 15.8758, 13.8989, 12.4834, 11.4421,                   //  Lu-
  10.2671, 8.3549,  7.8496,  7.3278,  7.4820,                    //  -Hg
  13.5124, 11.6554, 10.0959, 9.7340,  8.8584,  8.0125,           //  Tl-Rn
  29.8135, 26.3157,                                              // Fr,Ra
  19.1885, 15.8542, 16.1305, 15.6161, 15.1226, 16.1576, 14.6510, // Ac-Am
  14.7178, 13.9108, 13.5623, 13.2326, 12.9189, 12.6133, 12.3142, // Cm-No
  14.8326, 12.3771, 10.6378, 9.3638,  8.2297,                    // Lr-
  7.5667,  6.9456,  6.3946,  5.9159,  5.4929,                    // -Cn
  6.7286,  6.5144,  10.9169, 10.3600, 9.4723,  8.6641            // Nh-Og
};

// r4/r2 expectation value
static const double r4r2[119] = {
  0.0000000000000000,  2.0073489980568899,  1.5663713191197939,
  5.0198692795806270,  3.8537903419880015,  3.6444659393318353,
  3.1049282206129809,  2.7117524212163846,  2.5936168242020377,
  2.3882524992135985,  2.2152251517733568,  6.5858554765764312,
  5.4629596588968861,  5.6521665824928302,  4.8828490693715114,
  4.2972756769707336,  4.0410889621486934,  3.7293234964336643,
  3.4467727589836006,  7.9776274615364162,  7.0762394424824118,
  6.6084406720011986,  6.2879137754450483,  6.0772870539213262,
  5.5464309903432181,  5.8049117133682575,  5.5841560583852772,
  5.4137452777772639,  5.2849722814578488,  5.2259281283712582,
  5.0981714744181961,  6.1214969158821679,  5.5408374261338009,
  5.0669689002570761,  4.8700510092075282,  4.5908964300321058,
  4.3117629804988118,  9.5546171211079258,  8.6739608927142857,
  7.9721018483208512,  7.4343990304814112,  6.5871185720723107,
  6.1953620413463710,  6.0151730164200075,  5.8162339941054615,
  5.6571042504778664,  5.5264067015115925,  5.4426331109255246,
  5.5828535967014172,  7.0208190405393589,  6.4681553296959295,
  5.9808910646449416,  5.8168664579362881,  5.5332180636017965,
  5.2547700208901826,  11.0220455922193850, 10.1567951381952657,
  9.3516781741396819,  9.0692608248575635,  8.9724115095649690,
  8.9009281497318113,  8.8598484393188031,  8.8173683855232063,
  8.7931772110434476,  7.8996961966900985,  8.8058844671566234,
  8.4243920194361230,  8.5428926354984327,  8.4758336161745440,
  8.4509088260500551,  8.4733935649794390,  7.8352563466301675,
  8.2070283916024280,  7.7055906216134344,  7.3275598680119947,
  7.0388739414205759,  6.6897870925184497,  6.0545003906277204,
  5.8875202800638853,  5.7066150672357940,  5.7845069984664086,
  7.7978073841304898,  7.2644385859833260,  6.7815199760703697,
  6.6788316204782516,  6.3902430556467609,  6.0952796570444292,
  11.7915608678254173, 11.1099763280929373, 9.5137780863458268,
  8.6719705788109245,  8.7714070389122991,  8.6540270771013734,
  8.5392351237740272,  8.8502470058292761,  8.4498604706171356,
  8.4913014475207813,  8.2766385419814377,  8.1932875019374354,
  8.1136523096128101,  8.0370703617674035,  7.9612215197130434,
  7.8856617893483829,  8.6756685341357649,  7.9442478826940723,
  7.3825812849614127,  6.9428460127736553,  6.5241351433626953,
  6.2703848794866071,  6.0213865881659316,  5.7908173259518607,
  5.5824669294363725,  5.3912609613237406,  5.9802173503797658,
  5.8972348844620717,  7.6508401506764221,  7.4692909571065345,
  7.1574642870129868,  6.8598912693208112
};

/**
 * Element-specific chemical hardnesses for the charge scaling function used
 * to extrapolate the C6 coefficients in DFT-D4.
 */
static const double gam[119]{
  0.0,        // None
  0.47259288, // H
  0.92203391, // He
  0.17452888, // Li (2nd)
  0.25700733, // Be
  0.33949086, // B
  0.42195412, // C
  0.50438193, // N
  0.58691863, // O
  0.66931351, // F
  0.75191607, // Ne
  0.17964105, // Na (3rd)
  0.22157276, // Mg
  0.26348578, // Al
  0.30539645, // Si
  0.34734014, // P
  0.38924725, // S
  0.43115670, // Cl
  0.47308269, // Ar
  0.17105469, // K  (4th)
  0.20276244, // Ca
  0.21007322, // Sc
  0.21739647, // Ti
  0.22471039, // V
  0.23201501, // Cr
  0.23933969, // Mn
  0.24665638, // Fe
  0.25398255, // Co
  0.26128863, // Ni
  0.26859476, // Cu
  0.27592565, // Zn
  0.30762999, // Ga
  0.33931580, // Ge
  0.37235985, // As
  0.40273549, // Se
  0.43445776, // Br
  0.46611708, // Kr
  0.15585079, // Rb (5th)
  0.18649324, // Sr
  0.19356210, // Y
  0.20063311, // Zr
  0.20770522, // Nb
  0.21477254, // Mo
  0.22184614, // Tc
  0.22891872, // Ru
  0.23598621, // Rh
  0.24305612, // Pd
  0.25013018, // Ag
  0.25719937, // Cd
  0.28784780, // In
  0.31848673, // Sn
  0.34912431, // Sb
  0.37976593, // Te
  0.41040808, // I
  0.44105777, // Xe
  0.05019332, // Cs (6th)
  0.06762570, // Ba
  0.08504445, // La
  0.10247736, // Ce
  0.11991105, // Pr
  0.13732772, // Nd
  0.15476297, // Pm
  0.17218265, // Sm
  0.18961288, // Eu
  0.20704760, // Gd
  0.22446752, // Tb
  0.24189645, // Dy
  0.25932503, // Ho
  0.27676094, // Er
  0.29418231, // Tm
  0.31159587, // Yb
  0.32902274, // Lu
  0.34592298, // Hf
  0.36388048, // Ta
  0.38130586, // W
  0.39877476, // Re
  0.41614298, // Os
  0.43364510, // Ir
  0.45104014, // Pt
  0.46848986, // Au
  0.48584550, // Hg
  0.12526730, // Tl
  0.14268677, // Pb
  0.16011615, // Bi
  0.17755889, // Po
  0.19497557, // At
  0.21240778, // Rn
  0.07263525, // Fr (7th)
  0.09422158, // Ra
  0.09920295, // Ac
  0.10418621, // Th
  0.14235633, // Pa
  0.16394294, // U
  0.18551941, // Np
  0.22370139, // Pu
  0.25110000, // Am
  0.25030000, // Cm
  0.28840000, // Bk
  0.31000000, // Cf
  0.33160000, // Es
  0.35320000, // Fm
  0.36820000, // Md
  0.39630000, // No
  0.40140000, // Lr
  0.00000000, // Rf
  0.00000000, // Db
  0.00000000, // Sg
  0.00000000, // Bh
  0.00000000, // Hs
  0.00000000, // Mt
  0.00000000, // Ds
  0.00000000, // Rg
  0.00000000, // Cn
  0.00000000, // Nh
  0.00000000, // Fl
  0.00000000, // Lv
  0.00000000, // Mc
  0.00000000, // Ts
  0.00000000, // Og
};

static const int refn[MAXELEMENT]{
  0, 2, 1, 3, 4, 5, 7, 5, 4, 2, 1, 3, 4, 4, 5, 4, 3, 2, 1, 3, 4, 4, 4, 4, 4, 3,
  3, 4, 4, 2, 2, 3, 5, 4, 3, 2, 1, 3, 4, 3, 4, 4, 4, 3, 3, 4, 3, 2, 2, 4, 5, 4,
  3, 2, 1, 3, 4, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 3, 5,
  3, 2, 2, 4, 5, 4, 3, 2, 1, 2, 3, 7, 5, 6, 6, 7, 7, 6, 7, 5, 6, 7, 7, 5, 7, 7,
};

// 1
static const double refcn1[2]{
  0.00000000000000,
  0.89422436546040,
};
static const double refq1[2]{
  0.00000000000000,
  0.00000000000000,
};
static const double refsq1[2]{
  0.00000000000000,
  0.00000000000000,
};
static const double refalpha1[46]{
  5.0540160, 4.9668210, 4.7244390, 3.9707860, 3.1655030, 2.4886460, 1.9670460,
  1.5750840, 1.2804290, 1.0565330, 0.8839250, 0.7488080, 0.5550060, 0.4262920,
  0.3369390, 0.2726050, 0.2248580, 0.1483870, 0.1049920, 0.0603100, 0.0390250,
  0.0175590, 0.0099250, 5.4415160, 5.3912720, 5.2466780, 4.7462570, 4.1122050,
  3.4827990, 2.9256260, 2.4586020, 2.0763900, 1.7660350, 1.5138980, 1.3080740,
  0.9987770, 0.7833600, 0.6286810, 0.5145050, 0.4281480, 0.2867670, 0.2047270,
  0.1187560, 0.0772270, 0.0349350, 0.0197880,
};
static const double refascale1[2]{
  1.00000000000000,
  0.50000000000000,
};
static const double refscount1[2]{
  0.00000000000000,
  0.00000000000000,
};
static const int refsys1[2]{
  1,
  1,
};
static const int refc1[2]{
  3,
  1,
};

// 2
static const double refcn2[1]{
  0.00000000000000,
};
static const double refq2[1]{
  0.00000000000000,
};
static const double refsq2[1]{
  0.00000000000000,
};
static const double refalpha2[23]{
  1.4546360, 1.4502130, 1.4371400, 1.3875900, 1.3135450, 1.2243600,
  1.1286130, 1.0327800, 0.9410580, 0.8557720, 0.7779290, 0.7077040,
  0.5886400, 0.4940120, 0.4187090, 0.3583530, 0.3095160, 0.2223000,
  0.1665090, 0.1026240, 0.0691900, 0.0327930, 0.0189800,
};
static const double refascale2[1]{
  1.00000000000000,
};
static const double refscount2[1]{
  0.00000000000000,
};
static const int refsys2[1]{
  1,
};
static const int refc2[1]{
  3,
};

// 3
static const double refcn3[3]{
  0.00000000000000,
  0.80196797025252,
  4.55700000000000,
};
static const double refq3[3]{
  0.00000000000000,
  0.37061732228445,
  0.502335497838,
};
static const double refsq3[3]{
  0.00000000000000,
  -0.37061732228445,
  -0.50233549783851,
};
static const double refalpha3[69]{
  149.6846930, 101.0937750, 51.6672830, 18.0181080, 8.9093460,  5.3309030,
  3.5697190,   2.5730730,   1.9537540,  1.5421740,  1.2543870,  1.0449370,
  0.7658330,   0.5922860,   0.4760820,  0.3938140,  0.3330090,  0.2345470,
  0.1766850,   0.1133040,   0.0802740,  0.0424220,  0.0264160,  27.7934790,
  25.9220070,  21.8214140,  14.1717810, 9.4824880,  6.7129090,  4.9857250,
  3.8465020,   3.0589760,   2.4932250,  2.0736610,  1.7541010,  1.3073430,
  1.0165020,   0.8161580,   0.6719100,  0.5643080,  0.3893270,  0.2870170,
  0.1768550,   0.1211260,   0.0602840,  0.0362580,  84.6459010, 83.6841238,
  80.9655079,  72.0284169,  61.4818132, 51.5922762, 43.1612588, 36.2527416,
  30.6710866,  26.1700904,  22.5260442, 19.5557200, 15.0928030, 11.9795535,
  9.7376006,   8.0762262,   6.8136584,  4.7267579,  3.4948520,  2.1681444,
  1.4997611,   0.7718181,   0.4815951,
};
static const double refascale3[3]{
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount3[3]{
  0.00000000000000,
  1.00000000000000,
  4.00000000000000,
};
static const int refsys3[3]{
  1,
  1,
  17,
};
static const int refc3[3]{
  3,
  1,
  1,
};

// 4
static const double refcn4[4]{
  0.00000000000000,
  0.87483634146801,
  1.75692293756846,
  8.44900000000000,
};
static const double refq4[4]{
  0.00000000000000,
  0.17355187691088,
  0.31121011558254,
  0.3470000000,
};
static const double refsq4[4]{
  0.00000000000000,
  -0.17355187691088,
  -0.15560505779127,
  -0.34700000000000,
};
static const double refalpha4[92]{
  42.8790460, 39.9295910, 33.1319060, 19.8584460, 12.0562070, 7.8731240,
  5.5003700,  4.0522140,  3.1097180,  2.4633930,  2.0011630,  1.6591860,
  1.1965720,  0.9061710,  0.7119670,  0.5756820,  0.4763260,  0.3199380,
  0.2321350,  0.1411470,  0.0965570,  0.0488560,  0.0302000,  33.9191750,
  30.6229690, 25.1809150, 17.1197860, 12.0494810, 8.7823960,  6.6233290,
  5.1483500,  4.1059930,  3.3462160,  2.7771820,  2.3408840,  1.7276510,
  1.3276250,  1.0528460,  0.8562260,  0.7107890,  0.4781520,  0.3456310,
  0.2073370,  0.1396630,  0.0681800,  0.0409330,  20.3763510, 19.9881660,
  18.9207290, 15.6997430, 12.3941440, 9.6994520,  7.6613340,  6.1448630,
  5.0098820,  4.1485350,  3.4841730,  2.9633890,  2.2143260,  1.7146750,
  1.3662970,  1.1143890,  0.9266450,  0.6239030,  0.4502460,  0.2684610,
  0.1795900,  0.0862930,  0.0511440,  50.8062040, 50.0592716, 48.0905154,
  42.5028663, 36.7056665, 31.5232793, 27.1066190, 23.4118521, 20.3403941,
  17.7870106, 15.6568911, 13.8703586, 11.0817107, 9.0435022,  7.5156407,
  6.3438199,  5.4266858,  3.8505033,  2.8781608,  1.9058183,  1.2248615,
  0.6029055,  0.3602096,
};
static const double refascale4[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount4[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
};
static const int refsys4[4]{
  1,
  1,
  1,
  9,
};
static const int refc4[4]{
  3,
  1,
  1,
  1,
};

// 5
static const double refcn5[5]{
  0.00000000000000,
  0.93017535174568,
  1.86318070483743,
  2.79150308430417,
  4.41327468359181,
};
static const double refq5[5]{
  0.00000000000000,
  -0.10464538187607,
  -0.20153708141000,
  -0.28222637549158,
  -0.3403882070,
};
static const double refsq5[5]{
  0.00000000000000,
  0.10464538187607,
  0.10076854070500,
  0.09407545849719,
  0.11346273566869,
};
static const double refalpha5[115]{
  22.1068880, 21.3442260, 19.4317910, 14.6694210, 10.6975470, 7.9023200,
  5.9922100,  4.6684490,  3.7269880,  3.0389440,  2.5231990,  2.1277390,
  1.5720620,  1.2095680,  0.9603270,  0.7816570,  0.6491900,  0.4364560,
  0.3146920,  0.1873730,  0.1252700,  0.0602010,  0.0356010,  20.5521070,
  19.9101690, 18.3552210, 14.5802680, 11.3056180, 8.8165140,  6.9794390,
  5.6206180,  4.6022690,  3.8263850,  3.2251530,  2.7516720,  2.0664510,
  1.6059710,  1.2828710,  1.0479810,  0.8721210,  0.5869300,  0.4224710,
  0.2500750,  0.1661340,  0.0788140,  0.0462310,  20.2806350, 19.1635070,
  17.8009360, 14.8840980, 12.0983160, 9.7836060,  7.9569310,  6.5370310,
  5.4328530,  4.5678260,  3.8830910,  3.3348630,  2.5273350,  1.9752950,
  1.5835380,  1.2965230,  1.0804740,  0.7281530,  0.5240250,  0.3095240,
  0.2050450,  0.0966460,  0.0564440,  17.3839000, 17.1992340, 16.6725580,
  14.8986510, 12.7407520, 10.6754850, 8.8969080,  7.4349140,  6.2546920,
  5.3056760,  4.5401840,  3.9186610,  2.9899200,  2.3464510,  1.8858730,
  1.5464990,  1.2900300,  0.8701190,  0.6260260,  0.3691130,  0.2439620,
  0.1143850,  0.0665550,  33.3389310, 33.0011270, 32.0357710, 28.7639060,
  24.7422160, 20.8503600, 17.4641170, 14.6555110, 12.3709610, 10.5223950,
  9.0236300,  7.8016400,  5.9670990,  4.6901690,  3.7733460,  3.0963780,
  2.5840490,  1.7440470,  1.2552220,  0.7404570,  0.4896440,  0.2299100,
  0.1339700,
};
static const double refascale5[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
};
static const double refscount5[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  6.00000000000000,
};
static const int refsys5[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc5[5]{
  3,
  1,
  1,
  1,
  1,
};

// 6
static const double refcn6[7]{
  0.00000000000000,
  0.91894761153698,
  1.90786062124811,
  2.83122393221341,
  3.74870030209262,
  2.91832701804388,
  0.85560990866661,
};
static const double refq6[7]{
  0.00000000000000,
  -0.17123705791311,
  -0.14210003554128,
  -0.22250854670718,
  -0.25653918216622,
  -0.10441353918078,
  0.2103031269,
};
static const double refsq6[7]{
  0.00000000000000,
  0.17123705791311,
  0.14210003554128,
  0.11125427335359,
  0.08551306072207,
  0.10441353918078,
  -0.21030312699251,
};
static const double refalpha6[161]{
  12.3555340, 12.1386640, 11.5492610, 9.7999490,  7.9916820,  6.4691120,
  5.2715550,  4.3463700,  3.6298580,  3.0691570,  2.6246820,  2.2676780,
  1.7384300,  1.3729830,  1.1110210,  0.9172590,  0.7701000,  0.5269110,
  0.3835030,  0.2298730,  0.1535810,  0.0732580,  0.0431920,  14.5482810,
  14.2754640, 13.3786710, 11.3492310, 9.4185310,  7.7719120,  6.4361850,
  5.3728750,  4.5287720,  3.8553340,  3.3134960,  2.8732790,  2.2127670,
  1.7514880,  1.4184590,  1.1710210,  0.9825780,  0.6705550,  0.4865370,
  0.2899040,  0.1927160,  0.0910580,  0.0533330,  23.0116230, 22.7312670,
  21.9447640, 19.4160980, 16.5257670, 13.8835800, 11.6644030, 9.8566400,
  8.3954220,  7.2118160,  6.2469570,  5.4540580,  4.2475560,  3.3914730,
  2.7655050,  2.2955930,  1.9346700,  1.3305920,  0.9701360,  0.5811850,
  0.3874320,  0.1836940,  0.1078100,  27.4537640, 27.0921900, 26.0934140,
  23.0050050, 19.6170750, 16.5717410, 14.0107840, 11.9057630, 10.1859920,
  8.7791490,  7.6227700,  6.6661200,  5.2000230,  4.1529630,  3.3845150,
  2.8065480,  2.3623130,  1.6190990,  1.1765830,  0.7009620,  0.4652560,
  0.2188710,  0.1277540,  28.3352760, 28.0932470, 27.3990360, 25.0151020,
  22.0076950, 18.9989890, 16.2867160, 13.9588710, 12.0051730, 10.3795410,
  9.0286370,  7.9030880,  6.1676970,  4.9231280,  4.0083160,  3.3200870,
  2.7913060,  1.9077980,  1.3830030,  0.8207370,  0.5431290,  0.2541200,
  0.1477570,  68.5832590, 67.5115260, 64.6123080, 56.1286650, 47.4318310,
  39.9459190, 33.7814890, 28.7553020, 24.6561470, 21.2992860, 18.5340330,
  16.2406480, 12.7133690, 10.1832050, 8.3194640,  6.9133790,  5.8298100,
  4.0106600,  2.9230920,  1.7494800,  1.1654830,  0.5523060,  0.3242020,
  7.7402500,  7.6643000,  7.4486700,  6.7286500,  5.8533600,  5.0045500,
  4.2585700,  3.6316200,  3.1142900,  2.6894300,  2.3397600,  2.0503600,
  1.6066900,  1.2894400,  1.0561100,  0.8801010,  0.7443600,  0.5158280,
  0.3784030,  0.2287990,  0.1535500,  0.0736385,  0.0435460,
};
static const double refascale6[7]{
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
  0.50000000000000,
  0.50000000000000,
  0.16666666666667,
  1.00000000000000,
};
static const double refscount6[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
  6.00000000000000,
  6.00000000000000,
  1.00000000000000,
};
static const int refsys6[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  2,
};
static const int refc6[7]{
  3,
  3,
  1,
  3,
  1,
  3,
  3,
};

// 7
static const double refcn7[5]{
  0.00000000000000,
  0.85827791612782,
  1.83985112339643,
  2.58039902538908,
  0.98085535554904,
};
static const double refq7[5]{
  0.00000000000000,
  -0.35298592555229,
  -0.30125788296606,
  -0.82429723124422,
  0.0000000000,
};
static const double refsq7[5]{
  0.00000000000000,
  0.35298592555229,
  0.30125788296606,
  0.27476574374807,
  0.00000000000000,
};
static const double refalpha7[115]{
  7.5385090,  7.4657840,  7.2592230,  6.5708420,  5.7412090,  4.9445040,
  4.2474110,  3.6605820,  3.1734720,  2.7700380,  2.4347170,  2.1542670,
  1.7174610,  1.3984350,  1.1591760,  0.9755810,  0.8318860,  0.5852590,
  0.4337270,  0.2654650,  0.1792040,  0.0860960,  0.0507150,  9.8340890,
  9.6980440,  9.3521500,  8.3811310,  7.3184230,  6.3183850,  5.4407240,
  4.6956550,  4.0720980,  3.5523310,  3.1184230,  2.7545880,  2.1872670,
  1.7734490,  1.4640490,  1.2275070,  1.0430710,  0.7283800,  0.5365400,
  0.3254160,  0.2182610,  0.1038080,  0.0607780,  18.5281530, 18.3270930,
  17.7675350, 15.9940890, 13.9674690, 12.0720960, 10.4237930, 9.0298300,
  7.8623050,  6.8857300,  6.0666250,  5.3763210,  4.2923510,  3.4950320,
  2.8948440,  2.4334700,  2.0721210,  1.4520950,  1.0718490,  0.6513790,
  0.4372510,  0.2081480,  0.1219450,  13.8928580, 13.7335660, 13.2948950,
  11.9342710, 10.4022050, 8.9706190,  7.7218140,  6.6635680,  5.7772340,
  5.0371340,  4.4181730,  3.8984410,  3.0872240,  2.4956330,  2.0539790,
  1.7170460,  1.4549570,  1.0095450,  0.7395630,  0.4445600,  0.2961500,
  0.1392520,  0.0809340,  11.6125430, 11.5410500, 11.3332410, 10.5895270,
  9.5886300,  8.5228410,  7.5106350,  6.6043140,  5.8164280,  5.1406550,
  4.5636850,  4.0709240,  3.2858130,  2.6994530,  2.2527560,  1.9059510,
  1.6320270,  1.1565830,  0.8609730,  0.5294970,  0.3582750,  0.1725840,
  0.1018070,
};
static const double refascale7[5]{
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
  1.00000000000000,
  0.50000000000000,
};
static const double refscount7[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  0.00000000000000,
};
static const int refsys7[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc7[5]{
  3,
  3,
  1,
  1,
  3,
};

// 8
static const double refcn8[4]{
  0.00000000000000,
  0.80416789582615,
  1.61123940672270,
  0.97984400975835,
};
static const double refq8[4]{
  0.00000000000000,
  -0.35471470167212,
  -0.59881526060460,
  0.0000000000,
};
static const double refsq8[4]{
  0.00000000000000,
  0.35471470167212,
  0.29940763030230,
  0.00000000000000,
};
static const double refalpha8[92]{
  5.1967090, 5.1644300, 5.0715690, 4.7484500,  4.3273530,  3.8854260,
  3.4648010, 3.0838640, 2.7478290, 2.4553310,  2.2021600,  1.9832410,
  1.6287590, 1.3587170, 1.1492470, 0.9838790,  0.8512370,  0.6158310,
  0.4654260, 0.2921270, 0.2001820, 0.0978590,  0.0579230,  7.2941570,
  7.2356790, 7.0728280, 6.5406890, 5.8872890,  5.2288430,  4.6198180,
  4.0794700, 3.6098730, 3.2056430, 2.8587920,  2.5610180,  2.0831650,
  1.7231230, 1.4466600, 1.2304460, 1.0585030,  0.7570550,  0.5672680,
  0.3517810, 0.2391180, 0.1155270, 0.0679560,  9.3715840,  9.2917670,
  9.0663960, 8.3227770, 7.4235050, 6.5392070,  5.7386200,  5.0398020,
  4.4396540, 3.9274640, 3.4907530, 3.1176580,  2.5222470,  2.0764190,
  1.7359450, 1.4709930, 1.2612520, 0.8959550,  0.6678320,  0.4109820,
  0.2778660, 0.1331600, 0.0779780, 10.3975870, 10.3144230, 10.0802310,
  9.3150480, 8.4027020, 7.5095120, 6.6939110,  5.9700690,  5.3361820,
  4.7845300, 4.3054570, 3.8891980, 3.2100590,  2.6878840,  2.2798670,
  1.9559530, 1.6950280, 1.2295900, 0.9306730,  0.5848620,  0.4008950,
  0.1959850, 0.1160240,
};
static const double refascale8[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
};
static const double refscount8[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  0.00000000000000,
};
static const int refsys8[4]{
  1,
  1,
  1,
  1,
};
static const int refc8[4]{
  3,
  3,
  1,
  3,
};

// 9
static const double refcn9[2]{
  0.00000000000000,
  0.74076991274917,
};
static const double refq9[2]{
  0.00000000000000,
  -0.2477391549,
};
static const double refsq9[2]{
  0.00000000000000,
  0.24773915491465,
};
static const double refalpha9[46]{
  3.6338390, 3.6196960, 3.5783940, 3.4279380, 3.2173720, 2.9799290, 2.7383490,
  2.5057910, 2.2889990, 2.0908140, 1.9117910, 1.7512000, 1.4795260, 1.2627740,
  1.0886880, 0.9474060, 0.8314380, 0.6189740, 0.4778550, 0.3086410, 0.2153540,
  0.1079130, 0.0645990, 5.4170520, 5.3885820, 5.3062630, 5.0155720, 4.6285580,
  4.2137360, 3.8104020, 3.4368990, 3.0998560, 2.7999440, 2.5350070, 2.3017150,
  1.9155660, 1.6145960, 1.3772910, 1.1876550, 1.0340620, 0.7578460, 0.5783980,
  0.3678490, 0.2541230, 0.1255490, 0.0746120,
};
static const double refascale9[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount9[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys9[2]{
  1,
  1,
};
static const int refc9[2]{
  3,
  1,
};

// 10
static const double refcn10[1]{
  0.00000000000000,
};
static const double refq10[1]{
  0.0000000000,
};
static const double refsq10[1]{
  0.00000000000000,
};
static const double refalpha10[23]{
  2.6227940, 2.6160810, 2.5963010, 2.5221150, 2.4130070, 2.2831850,
  2.1442240, 2.0040890, 1.8677460, 1.7380750, 1.6165850, 1.5039070,
  1.3049180, 1.1383170, 0.9993630, 0.8832020, 0.7855560, 0.6010260,
  0.4739350, 0.3155110, 0.2245720, 0.1157090, 0.0702160,
};
static const double refascale10[1]{
  1.00000000000000,
};
static const double refscount10[1]{
  0.00000000000000,
};
static const int refsys10[1]{
  1,
};
static const int refc10[1]{
  3,
};

// 11
static const double refcn11[3]{
  0.00000000000000,
  0.78077255822701,
  6.00100000000000,
};
static const double refq11[3]{
  0.00000000000000,
  0.37895090683878,
  0.543073552864,
};
static const double refsq11[3]{
  0.00000000000000,
  -0.37895090683878,
  -0.54307355286424,
};
static const double refalpha11[69]{
  170.9285310, 119.1946230, 62.8166710, 22.2250350, 11.0609650, 6.7225680,
  4.6167630,   3.4360280,   2.7038020,  2.2145400,  1.8682650,  1.6117710,
  1.2586520,   1.0272610,   0.8636930,  0.7418060,  0.6474800,  0.4849210,
  0.3823130,   0.2620130,   0.1947130,  0.1108050,  0.0717200,  40.8166710,
  37.3885700,  30.2959980,  18.3845350, 11.8437670, 8.2528940,  6.1199710,
  4.7572100,   3.8333160,   3.1762600,  2.6903860,  2.3193520,  1.7948680,
  1.4454310,   1.1979870,   1.0146980,  0.8742120,  0.6365370,  0.4905090,
  0.3247020,   0.2353690,   0.1290210,  0.0819540,  92.6411774, 91.4243783,
  88.0445743,  77.4364073,  65.6163384, 54.9685877, 46.0979628, 38.9126798,
  33.1338025,  28.4756146,  24.6963717, 21.6046368, 16.9269705, 13.6278912,
  11.2244983,  9.4230737,   8.0391231,  5.7141662,  4.3121698,  2.9652901,
  1.9616546,   1.0496861,   0.6661557,
};
static const double refascale11[3]{
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount11[3]{
  0.00000000000000,
  1.00000000000000,
  4.00000000000000,
};
static const int refsys11[3]{
  1,
  1,
  17,
};
static const int refc11[3]{
  3,
  1,
  1,
};

// 12
static const double refcn12[4]{
  0.00000000000000,
  0.82437946770105,
  1.66972660811953,
  13.95600000000000,
};
static const double refq12[4]{
  0.00000000000000,
  0.32933884303798,
  0.51074920852765,
  0.3430000000,
};
static const double refsq12[4]{
  0.00000000000000,
  -0.32933884303798,
  -0.25537460426383,
  -0.34300000000000,
};
static const double refalpha12[92]{
  75.6666810, 68.6955210, 53.9153050, 29.2692840, 16.8382330, 10.6997010,
  7.3793160,  5.4168470,  4.1702110,  3.3314920,  2.7405460,  2.3081520,
  1.7285400,  1.3653680,  1.1201210,  0.9447260,  0.8135180,  0.5959160,
  0.4626290,  0.3079420,  0.2219990,  0.1188580,  0.0745220,  65.0041490,
  57.3670330, 44.6926220, 26.8427890, 17.2249920, 11.8363720, 8.6109420,
  6.5554130,  5.1738650,  4.2034870,  3.4965440,  2.9655110,  2.2334680,
  1.7623610,  1.4391360,  1.2060360,  1.0311360,  0.7419490,  0.5670970,
  0.3688080,  0.2617440,  0.1369550,  0.0847940,  34.5442750, 33.5344340,
  30.8656630, 23.6561780, 17.3397030, 12.8432530, 9.7723270,  7.6521380,
  6.1504810,  5.0567630,  4.2388110,  3.6123090,  2.7314370,  2.1542960,
  1.7542370,  1.4641950,  1.2461470,  0.8862330,  0.6703080,  0.4289380,
  0.3010120,  0.1548430,  0.0949500,  74.6298821, 72.6677188, 67.9314704,
  56.5001225, 46.4504007, 38.4956042, 32.3037179, 27.4626661, 23.6358080,
  20.5710128, 18.0838250, 16.0395958, 12.9096858, 10.6544671, 8.9710814,
  7.6771288,  6.6579370,  4.8778230,  3.8586312,  2.8394394,  1.7107782,
  0.8784693,  0.5365232,
};
static const double refascale12[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount12[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
};
static const int refsys12[4]{
  1,
  1,
  1,
  9,
};
static const int refc12[4]{
  3,
  1,
  1,
  1,
};

// 13
static const double refcn13[4]{
  0.00000000000000,
  0.86567622356503,
  1.73262223552501,
  2.61541321571983,
};
static const double refq13[4]{
  0.00000000000000,
  0.03709152257935,
  0.05079767549293,
  0.0529139611,
};
static const double refsq13[4]{
  0.00000000000000,
  -0.03709152257935,
  -0.02539883774646,
  -0.01763798704591,
};
static const double refalpha13[92]{
  60.8923430, 56.3100140, 46.7886820, 29.5825800, 18.9999900, 12.8554770,
  9.1653720,  6.8351170,  5.2901970,  4.2211880,  3.4539770,  2.8860210,
  2.1186190,  1.6376640,  1.3157820,  1.0890010,  0.9224950,  0.6556710,
  0.5002950,  0.3292210,  0.2377920,  0.1286420,  0.0807650,  56.2109890,
  52.4017100, 44.3132520, 29.4084250, 19.9025080, 14.0717810, 10.3773750,
  7.9372390,  6.2599590,  5.0653090,  4.1877030,  3.5255730,  2.6117110,
  2.0262590,  1.6284670,  1.3453070,  1.1360060,  0.7989100,  0.6026620,
  0.3886840,  0.2764850,  0.1461420,  0.0906750,  43.0078740, 40.3049500,
  35.7272810, 26.8099970, 19.8081180, 14.8306090, 11.3606550, 8.9171350,
  7.1607780,  5.8687510,  4.8965000,  4.1493490,  3.0979680,  2.4116390,
  1.9395410,  1.6007580,  1.3490360,  0.9419730,  0.7048990,  0.4480100,
  0.3150480,  0.1635630,  0.1005420,  32.2831180, 31.7115930, 30.1255060,
  25.2170820, 20.0120360, 15.6749350, 12.3626340, 9.8945680,  8.0530620,
  6.6626970,  5.5965060,  4.7654850,  3.5787890,  2.7932030,  2.2479080,
  1.8542580,  1.5606340,  1.0843300,  0.8067590,  0.5072070,  0.3535600,
  0.1809750,  0.1104040,
};
static const double refascale13[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount13[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys13[4]{
  1,
  1,
  1,
  1,
};
static const int refc13[4]{
  3,
  1,
  1,
  1,
};

// 14
static const double refcn14[5]{
  0.00000000000000,
  0.89153537011814,
  1.82343155163634,
  2.80029114356397,
  3.66675219599495,
};
static const double refq14[5]{
  0.00000000000000,
  0.01649127941162,
  -0.00640083798505,
  -0.03084420203156,
  -0.0658597573,
};
static const double refsq14[5]{
  0.00000000000000,
  -0.01649127941162,
  0.00320041899253,
  0.01542210101578,
  0.02195325245915,
};
static const double refalpha14[115]{
  38.9490650, 37.5127500, 33.9244170, 25.1761170, 18.0845250, 13.1765080,
  9.8616700,  7.5917060,  5.9982420,  4.8493400,  3.9995310,  3.3561160,
  2.4668840,  1.8982190,  1.5134620,  1.2411020,  1.0410670,  0.7226000,
  0.5405560,  0.3465530,  0.2471760,  0.1332610,  0.0845050,  38.0097750,
  36.6441270, 33.3701090, 25.5897470, 19.0941400, 14.3691430, 11.0297080,
  8.6569570,  6.9417830,  5.6758970,  4.7217950,  3.9882980,  2.9570580,
  2.2858030,  1.8259530,  1.4975500,  1.2548440,  0.8660940,  0.6430810,
  0.4060490,  0.2858610,  0.1507420,  0.0943940,  37.2763200, 36.2054630,
  33.4711240, 26.4376500, 20.2438260, 15.5716430, 12.1648030, 9.6798740,
  7.8448670,  6.4670510,  5.4140820,  4.5954000,  3.4297600,  2.6610590,
  2.1295730,  1.7474840,  1.4637430,  1.0070410,  0.7441640,  0.4650030,
  0.3243180,  0.1681920,  0.1042810,  75.2662880, 72.3612970, 65.6345910,
  50.8100850, 38.9033790, 30.0787730, 23.6268450, 18.8896320, 15.3681050,
  12.7085630, 10.6661350, 9.0717390,  6.7912830,  5.2803260,  4.2321590,
  3.4767820,  2.9147970,  2.0082810,  1.4853250,  0.9289700,  0.6481770,
  0.3362410,  0.2084750,  61.7861480, 60.8116450, 58.0975290, 49.5798710,
  40.2758690, 32.2331470, 25.8672360, 20.9751250, 17.2319240, 14.3488200,
  12.1032080, 10.3316220, 7.7698820,  6.0547620,  4.8568220,  3.9895410,
  3.3422950,  2.2952740,  1.6903860,  1.0479590,  0.7255320,  0.3711770,
  0.2282300,
};
static const double refascale14[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
  0.50000000000000,
};
static const double refscount14[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
  6.00000000000000,
};
static const int refsys14[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc14[5]{
  3,
  1,
  1,
  1,
  1,
};

// 15
static const double refcn15[4]{
  0.00000000000000,
  0.97498969761258,
  1.95559430261502,
  2.92666412421238,
};
static const double refq15[4]{
  0.00000000000000,
  -0.17987135979307,
  -0.12671124139840,
  -0.1746792742,
};
static const double refsq15[4]{
  0.00000000000000,
  0.17987135979307,
  0.12671124139840,
  0.05822642474110,
};
static const double refalpha15[92]{
  25.9470070, 25.4290340, 24.0216260, 19.8723550, 15.6749860, 12.2514680,
  9.6516650,  7.7129690,  6.2628530,  5.1656700,  4.3233980,  3.6669330,
  2.7311570,  2.1144260,  1.6888290,  1.3835900,  1.1574800,  0.7949870,
  0.5875340,  0.3687610,  0.2592740,  0.1378720,  0.0875080,  27.8753970,
  27.3122270, 25.8232190, 21.5634300, 17.2591270, 13.6872210, 10.9190600,
  8.8162050,  7.2183460,  5.9933920,  5.0426620,  4.2948080,  3.2172770,
  2.4989620,  1.9991280,  1.6384630,  1.3701110,  0.9379270,  0.6897680,
  0.4281650,  0.2979330,  0.1553700,  0.0974170,  55.7853670, 54.5314410,
  51.2683850, 42.3425800, 33.7346300, 26.7484370, 21.3755400, 17.2987970,
  14.1966540, 11.8128320, 9.9578290,  8.4949500,  6.3802250,  4.9651180,
  3.9775280,  3.2633040,  2.7309600,  1.8718860,  1.3776140,  0.8557670,
  0.5956760,  0.3107310,  0.1948320,  30.4586930, 29.9832590, 28.6718190,
  24.6351360, 20.2683100, 16.4561420, 13.3810200, 10.9693570, 9.0896850,
  7.6189190,  6.4582620,  5.5327160,  4.1782340,  3.2605350,  2.6145330,
  2.1444890,  1.7926280,  1.2223890,  0.8934200,  0.5466340,  0.3750780,
  0.1903100,  0.1172040,
};
static const double refascale15[4]{
  1.00000000000000,
  1.00000000000000,
  0.50000000000000,
  1.00000000000000,
};
static const double refscount15[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys15[4]{
  1,
  1,
  1,
  1,
};
static const int refc15[4]{
  3,
  1,
  1,
  1,
};

// 16
static const double refcn16[3]{
  0.00000000000000,
  0.92198495968462,
  1.84453813661707,
};
static const double refq16[3]{
  0.00000000000000,
  -0.16267234588041,
  -0.237751714488,
};
static const double refsq16[3]{
  0.00000000000000,
  0.16267234588041,
  0.11887585724439,
};
static const double refalpha16[69]{
  19.6135110, 19.3396950, 18.5777950, 16.1740460, 13.4828010, 11.0662650,
  9.0764420,  7.4918500,  6.2419920,  5.2546810,  4.4695850,  3.8397190,
  2.9119750,  2.2796060,  1.8328050,  1.5069310,  1.2625940,  0.8658660,
  0.6364800,  0.3940160,  0.2736140,  0.1429400,  0.0902880,  22.2041430,
  21.8891090, 21.0218000, 18.3279640, 15.3337320, 12.6407210, 10.4119420,
  8.6265960,  7.2105080,  6.0862970,  5.1884110,  4.4652670,  3.3950220,
  2.6615450,  2.1411100,  1.7603030,  1.4740840,  1.0081850,  0.7383390,
  0.4532570,  0.3121980,  0.1604390,  0.1002160,  24.5118610, 24.1774360,
  23.2503900, 20.3440110, 17.0929990, 14.1530500, 11.7050130, 9.7320240,
  8.1583820,  6.9030290,  5.8962250,  5.0824590,  3.8729230,  3.0400830,
  2.4470470,  2.0119580,  1.6842890,  1.1498080,  0.8397730,  0.5122980,
  0.3506710,  0.1779010,  0.1101270,
};
static const double refascale16[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount16[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys16[3]{
  1,
  1,
  1,
};
static const int refc16[3]{
  3,
  1,
  1,
};

// 17
static const double refcn17[2]{
  0.00000000000000,
  0.84439969796621,
};
static const double refq17[2]{
  0.00000000000000,
  -0.1504505745,
};
static const double refsq17[2]{
  0.00000000000000,
  0.15045057451823,
};
static const double refalpha17[46]{
  14.6510610, 14.5166850, 14.1329320, 12.8305660, 11.2118050, 9.6110460,
  8.1817260,  6.9658720,  5.9541940,  5.1193500,  4.4310730,  3.8619390,
  2.9935150,  2.3788950,  1.9324470,  1.6000440,  1.3469040,  0.9286160,
  0.6827690,  0.4202900,  0.2895830,  0.1489740,  0.0934510,  17.2630540,
  17.0983080, 16.6294740, 15.0531340, 13.1168290, 11.2193720, 9.5356020,
  8.1091300,  6.9254200,  5.9504380,  5.1476860,  4.4845120,  3.4734290,
  2.7582120,  2.2387270,  1.8518950,  1.5572580,  1.0703600,  0.7842990,
  0.4793850,  0.3280880,  0.1664540,  0.1033810,
};
static const double refascale17[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount17[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys17[2]{
  1,
  1,
};
static const int refc17[2]{
  3,
  1,
};

// 18
static const double refcn18[1]{
  0.00000000000000,
};
static const double refq18[1]{
  0.0000000000,
};
static const double refsq18[1]{
  0.00000000000000,
};
static const double refalpha18[23]{
  11.1080370, 11.0394140, 10.8402330, 10.1295640, 9.1733700, 8.1487470,
  7.1654820,  6.2757630,  5.4960060,  4.8240080,  4.2494460, 3.7594860,
  2.9839560,  2.4128240,  1.9852170,  1.6593100,  1.4065440, 0.9797740,
  0.7235180,  0.4456840,  0.3060220,  0.1557480,  0.0970350,
};
static const double refascale18[1]{
  1.00000000000000,
};
static const double refscount18[1]{
  0.00000000000000,
};
static const int refsys18[1]{
  1,
};
static const int refc18[1]{
  3,
};

// 19
static const double refcn19[3]{
  0.00000000000000,
  0.77389074718844,
  11.45000000000000,
};
static const double refq19[3]{
  0.00000000000000,
  0.44376242787490,
  0.304000000000,
};
static const double refsq19[3]{
  0.00000000000000,
  -0.44376242787490,
  -0.30400000000000,
};
static const double refalpha19[69]{
  366.6173270, 195.2407260, 83.8654450, 28.8051330, 15.9216120,  10.9496410,
  8.4035800,   6.8431600,   5.7666680,  4.9640380,  4.3344440,   3.8237620,
  3.0427910,   2.4756550,   2.0494570,  1.7214130,  1.4641050,   1.0222030,
  0.7516860,   0.4544310,   0.3045490,  0.1458010,  0.0862690,   53.4389170,
  47.8463210,  37.7399140,  23.4699070, 16.3225240, 12.3576000,  9.8698810,
  8.1579680,   6.9001080,   5.9321790,  5.1625350,  4.5358880,   3.5804740,
  2.8930340,   2.3815560,   1.9913210,  1.6874660,  1.1703840,   0.8568800,
  0.5151140,   0.3439260,   0.1635940,  0.0963540,  112.8769963, 111.5382559,
  107.8201226, 96.1458563,  83.0747922, 71.1307898, 60.9421945,  52.4432551,
  45.3906629,  39.5298970,  34.6393638, 30.5368708, 24.1382573,  19.4781015,
  16.0067586,  13.3663894,  11.3195232, 7.8610363,  5.7811058,   3.5249696,
  2.3940353,   1.1879380,   0.7245068,
};
static const double refascale19[3]{
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount19[3]{
  0.00000000000000,
  1.00000000000000,
  4.00000000000000,
};
static const int refsys19[3]{
  1,
  1,
  17,
};
static const int refc19[3]{
  3,
  1,
  1,
};

// 20
static const double refcn20[4]{
  0.00000000000000,
  0.80173786145238,
  1.57758711825521,
  15.14000000000000,
};
static const double refq20[4]{
  0.00000000000000,
  0.31814452979636,
  0.50078886624431,
  0.2440000000,
};
static const double refsq20[4]{
  0.00000000000000,
  -0.31814452979636,
  -0.25039443312215,
  -0.24400000000000,
};
static const double refalpha20[92]{
  167.3331200, 138.7350820, 92.3660100, 41.0298690, 22.5025050, 14.5451620,
  10.4632190,  8.0723760,   6.5267080,  5.4500180,  4.6561940,  4.0450480,
  3.1618950,   2.5524970,   2.1073550,  1.7698140,  1.5069710,  1.0569390,
  0.7807210,   0.4750180,   0.3195680,  0.1538130,  0.0914010,  158.1508830,
  111.6461600, 67.9213530,  33.9702430, 21.3038760, 15.0163380, 11.3779670,
  9.0482850,   7.4431400,   6.2742820,  5.3861210,  4.6885960,  3.6641970,
  2.9506000,   2.4285760,   2.0334750,  1.7267590,  1.2044810,  0.8862100,
  0.5363960,   0.3596090,   0.1720510,  0.1017830,  47.8971840, 45.8022250,
  40.7933190,  29.6764790,  21.5460190, 16.2269040, 12.6953380, 10.2550730,
  8.4973390,   7.1832110,   6.1691650,  5.3658830,  4.1801140,  3.3536760,
  2.7508620,   2.2964010,   1.9450020,  1.3500690,  0.9899710,  0.5965960,
  0.3988370,   0.1899030,   0.1119470,  92.8563023, 91.1707612, 86.7243129,
  74.2666422,  62.0928688,  52.1273713, 44.3017181, 38.1421847, 33.2177260,
  29.2098267,  25.8942119,  23.1129142, 18.7302605, 15.4634027, 12.9627169,
  11.0083621,  9.4545882,   6.7335695,  5.0260366,  3.0995061,  2.1015110,
  1.0184280,   0.6045719,
};
static const double refascale20[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount20[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
};
static const int refsys20[4]{
  1,
  1,
  1,
  9,
};
static const int refc20[4]{
  3,
  1,
  1,
  1,
};

// 21
static const double refcn21[4]{
  0.00000000000000,
  1.60644512750973,
  2.50274820582596,
  3.83500003814697,
};
static const double refq21[4]{
  0.00000000000000,
  0.50144727255861,
  0.62485373296540,
  0.7870000000,
};
static const double refsq21[4]{
  0.00000000000000,
  -0.25072363627930,
  -0.20828457765513,
  -0.26200000000000,
};
static const double refalpha21[92]{
  125.6799050, 108.3144390, 77.2929700, 37.1320260, 20.7670580, 13.4119080,
  9.5811350,   7.3353090,   5.8931080,  4.8989950,  4.1745440,  3.6229180,
  2.8357880,   2.2984530,   1.9074130,  1.6106400,  1.3787470,  0.9784770,
  0.7296280,   0.4499330,   0.3052790,  0.1484840,  0.0886520,  43.3830910,
  45.0959100,  39.5276970,  28.9987430, 21.3879050, 16.2717510, 12.7943430,
  10.3540150,  8.5813500,   7.2517530,  6.2258690,  5.4147740,  4.2221260,
  3.3947970,   2.7929060,   2.3393880,  1.9883760,  1.3919190,  1.0282690,
  0.6267560,   0.4221330,   0.2026710,  0.1197200,  45.7861990, 44.3266490,
  40.7084650,  31.7823730,  24.2343690, 18.7383620, 14.8308240, 12.0175160,
  9.9446720,   8.3787230,   7.1672090,  6.2095210,  4.8060710,  3.8394390,
  3.1416970,   2.6197890,   2.2184260,  1.5421450,  1.1337000,  0.6865730,
  0.4605190,   0.2197990,   0.1294090,  25.7885399, 25.5284328, 24.8018055,
  22.4847965,  19.8432083,  17.4046421, 15.3140812, 13.5610819, 12.0932360,
  10.8561134,  9.8039074,   8.9004927,  7.4345994,  6.3020196,  5.4061413,
  4.6844025,   4.0943751,   3.0185883,  2.3095038,  1.4697241,  1.0145692,
  0.5013176,   0.2990179,
};
static const double refascale21[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount21[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  1.50000000000000,
};
static const int refsys21[4]{
  1,
  1,
  1,
  11,
};
static const int refc21[4]{
  3,
  1,
  1,
  1,
};

// 22
static const double refcn22[4]{
  0.00000000000000,
  1.62278979228613,
  3.43281247525220,
  4.43849000000000,
};
static const double refq22[4]{
  0.00000000000000,
  0.32259167829296,
  0.53505953733387,
  0.9040000000,
};
static const double refsq22[4]{
  0.00000000000000,
  -0.16129583914648,
  -0.13376488433347,
  -0.22575000000000,
};
static const double refalpha22[92]{
  114.7243640, 99.7786920, 73.3046090, 37.5872700, 22.0065650, 14.6330060,
  10.6399730,  8.2278720,  6.6441090,  5.5356020,  4.7202080,  4.0964710,
  3.2058500,   2.6004600,  2.1623770,  1.8313070,  1.5731530,  1.1271400,
  0.8480460,   0.5303920,  0.3633330,  0.1787040,  0.1068890,  46.0919720,
  42.4892580,  37.6213730, 28.0117340, 20.8457830, 15.9626110, 12.6095600,
  10.2373540,  8.5034920,  7.1973670,  6.1869270,  5.3870300,  4.2107080,
  3.3956060,   2.8031890,  2.3567820,  2.0108410,  1.4205320,  1.0576160,
  0.6522060,   0.4427770,  0.2149140,  0.1275310,  48.7114030, 47.2968810,
  43.6774280,  34.4392690, 26.5310300, 20.7154850, 16.5179260, 13.4481710,
  11.1565010,  9.4084180,  8.0473770,  6.9676210,  5.3829550,  4.2933920,
  3.5097360,   2.9257120,  2.4779210,  1.7256070,  1.2717960,  0.7740440,
  0.5212220,   0.2500910,  0.1474550,  31.8693190, 31.5954595, 30.8154120,
  28.1936583,  24.9990546, 21.9123454, 19.2042984, 16.9162029, 15.0030479,
  13.4005228,  12.0488331, 10.8986824, 9.0558940,  7.6529726,  6.5554549,
  5.6780283,   4.9642843,  3.6680250,  2.8144887,  1.8007388,  1.2482416,
  0.6204756,   0.3709690,
};
static const double refascale22[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount22[4]{
  0.00000000000000,
  2.00000000000000,
  4.00000000000000,
  4.00000000000000,
};
static const int refsys22[4]{
  1,
  1,
  1,
  11,
};
static const int refc22[4]{
  3,
  1,
  1,
  1,
};

// 23
static const double refcn23[4]{
  0.00000000000000,
  1.72211010302514,
  2.62026342999598,
  3.38800000000000,
};
static const double refq23[4]{
  0.00000000000000,
  0.30538713298844,
  0.39745931358650,
  0.9350000000,
};
static const double refsq23[4]{
  0.00000000000000,
  -0.15269356649422,
  -0.13248643786217,
  -0.18700000000000,
};
static const double refalpha23[92]{
  100.9910610, 88.6597800, 66.6115730, 35.5163660, 21.2160720, 14.2442310,
  10.4067670,  8.0678270,  6.5248700,  5.4425580,  4.6458490,  4.0364450,
  3.1669610,   2.5767360,  2.1500770,  1.8277610,  1.5763140,  1.1406790,
  0.8660900,   0.5494430,  0.3799770,  0.1891620,  0.1136620,  44.7007430,
  42.0873530,  37.1472140, 27.4044260, 20.3770970, 15.6299000, 12.3710770,
  10.0613500,  8.3699050,  7.0937900,  6.1054940,  5.3225590,  4.1705140,
  3.3719800,   2.7915250,  2.3540000,  2.0147100,  1.4344300,  1.0757290,
  0.6710700,   0.4591900,  0.2251960,  0.1341810,  43.8589710, 41.9185700,
  37.9612250,  29.4769420, 22.6653000, 17.7162500, 14.1578990, 11.5615470,
  9.6256600,   8.1492470,  6.9989060,  6.0850100,  4.7397660,  3.8101490,
  3.1377770,   2.6337640,  2.2450370,  1.5855880,  1.1821140,  0.7316980,
  0.4982510,   0.2427270,  0.1441100,  39.4919722, 39.0027923, 37.6740133,
  33.6693555,  29.3313719, 25.4515734, 22.2023666, 19.5294838, 17.3268203,
  15.4949224,  13.9540832, 12.6434247, 10.5397592, 8.9322131,  7.6697405,
  6.6569547,   5.8306559,  4.3239152,  3.3270116,  2.1370028,  1.4850445,
  0.7404650,   0.4431346,
};
static const double refascale23[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount23[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  5.00000000000000,
};
static const int refsys23[4]{
  1,
  1,
  1,
  11,
};
static const int refc23[4]{
  3,
  1,
  1,
  1,
};

// 24
static const double refcn24[4]{
  0.00000000000000,
  1.65041632145300,
  9.59333666980809,
  5.09941611449080,
};
static const double refq24[4]{
  0.00000000000000,
  0.17721817570715,
  0.16754955881404,
  0.6146777616,
};
static const double refsq24[4]{
  0.00000000000000,
  -0.08860908785357,
  -0.01396246323450,
  -0.19615593415441,
};
static const double refalpha24[92]{
  81.4204420, 70.3861320, 51.0334860, 26.6035920,  16.4401450,  11.5586160,
  8.7956620,  7.0404390,  5.8344750,  4.9584520,   4.2948990,   3.7754900,
  3.0150310,  2.4847490,  2.0937350,  1.7938190,   1.5570520,   1.1409650,
  0.8747790,  0.5634010,  0.3939510,  0.1991850,   0.1204340,   45.3318020,
  42.4171170, 37.0714340, 26.9188730, 19.8754030,  15.2233940,  12.0588400,
  9.8211890,  8.1820250,  6.9441660,  5.9847000,   5.2241990,   4.1047330,
  3.3284220,  2.7636460,  2.3373710,  2.0062470,   1.4381260,   1.0851790,
  0.6841550,  0.4719940,  0.2343080,  0.1403490,   56.4761320,  55.4404440,
  52.7176090, 45.1454930, 37.6466880, 31.2740070,  26.0862050,  21.9197000,
  18.5802620, 15.8937900, 13.7180050, 11.9412500,  9.2607000,   7.3778240,
  6.0116860,  4.9917560,  4.2112130,  2.9083100,   2.1307140,   1.2874000,
  0.8631570,  0.4110260,  0.2406390,  119.6067900, 117.3611800, 111.4540000,
  95.2456700, 79.7390500, 66.9517800, 56.7007000,  48.4921200,  41.8757900,
  36.4928900, 32.0685600, 28.3948300, 22.7080700,  18.5713200,  15.4707700,
  13.0875400, 11.2163200, 7.9816700,  5.9708100,   3.7056100,   2.5262500,
  1.2328500,  0.7325600,
};
static const double refascale24[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount24[4]{
  0.00000000000000,
  2.00000000000000,
  12.00000000000000,
  6.00000000000000,
};
static const int refsys24[4]{
  1,
  1,
  1,
  8,
};
static const int refc24[4]{
  3,
  1,
  1,
  1,
};

// 25
static const double refcn25[3]{
  0.00000000000000,
  1.45861721080984,
  8.78012041793345,
};
static const double refq25[3]{
  0.00000000000000,
  0.26888428905691,
  -0.014387948072,
};
static const double refsq25[3]{
  0.00000000000000,
  -0.13444214452845,
  0.00130799527933,
};
static const double refalpha25[69]{
  82.1201120, 73.0648270, 56.5578050, 31.8457630, 19.5848590, 13.3420540,
  9.8197330,  7.6416120,  6.1931620,  5.1733980,  4.4221950,  3.8482630,
  3.0320160,  2.4803430,  2.0824750,  1.7818650,  1.5468520,  1.1371080,
  0.8757490,  0.5688430,  0.4003450,  0.2041230,  0.1236650,  37.5942320,
  36.5102540, 33.7065530, 26.3778710, 20.0194940, 15.4093840, 12.1689910,
  9.8609100,  8.1746400,  6.9089940,  5.9348110,  5.1678620,  4.0486360,
  3.2798880,  2.7243850,  2.3069400,  1.9834830,  1.4290960,  1.0840060,
  0.6895570,  0.4788650,  0.2397600,  0.1439400,  48.8093290, 48.0980790,
  46.1748290, 40.4031130, 34.1760690, 28.6218290, 23.9924040, 20.2296980,
  17.1934700, 14.7402990, 12.7472650, 11.1157910, 8.6475930,  6.9086080,
  5.6437710,  4.6974660,  3.9718750,  2.7571320,  2.0290510,  1.2349290,
  0.8324270,  0.3994510,  0.2345940,
};
static const double refascale25[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount25[3]{
  0.00000000000000,
  2.00000000000000,
  11.00000000000000,
};
static const int refsys25[3]{
  1,
  1,
  1,
};
static const int refc25[3]{
  3,
  1,
  1,
};

// 26
static const double refcn26[3]{
  0.00000000000000,
  1.52985788829933,
  8.47495927159456,
};
static const double refq26[3]{
  0.00000000000000,
  0.16108330144470,
  0.054932425134,
};
static const double refsq26[3]{
  0.00000000000000,
  -0.08054165072235,
  -0.00549324251347,
};
static const double refalpha26[69]{
  65.1578920, 57.4961000, 43.3419800, 23.8760970, 15.1156130, 10.7673250,
  8.2713540,  6.6686050,  5.5550430,  4.7375840,  4.1131870,  3.6217190,
  2.8999580,  2.3973090,  2.0280480,  1.7456620,  1.5229730,  1.1305990,
  0.8773050,  0.5763700,  0.4092270,  0.2118590,  0.1294110,  34.5401790,
  33.5667420, 31.1228640, 24.7676090, 19.0811590, 14.8373870, 11.7962700,
  9.6020150,  7.9844480,  6.7625510,  5.8177240,  5.0715270,  3.9797330,
  3.2288080,  2.6862250,  2.2786720,  1.9629540,  1.4214720,  1.0834860,
  0.6950870,  0.4860810,  0.2464070,  0.1489560,  45.9056800, 45.2093150,
  43.3396340, 37.7811330, 31.8440890, 26.6022340, 22.2699010, 18.7694260,
  15.9553430, 13.6865850, 11.8454300, 10.3389430, 8.0596090,  6.4524730,
  5.2822830,  4.4057560,  3.7328380,  2.6038570,  1.9248540,  1.1805840,
  0.8007680,  0.3884140,  0.2295320,
};
static const double refascale26[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount26[3]{
  0.00000000000000,
  2.00000000000000,
  10.00000000000000,
};
static const int refsys26[3]{
  1,
  1,
  1,
};
static const int refc26[3]{
  3,
  1,
  1,
};

// 27
static const double refcn27[4]{
  0.00000000000000,
  1.60281178943204,
  2.73732238386544,
  7.27710111777824,
};
static const double refq27[4]{
  0.00000000000000,
  0.21568151580380,
  0.20590049778110,
  -0.0157789481,
};
static const double refsq27[4]{
  0.00000000000000,
  -0.10784075790190,
  -0.06863349926037,
  0.00175321646512,
};
static const double refalpha27[92]{
  60.7910330, 56.2385650, 46.3237860, 28.3000530, 18.0784830, 12.5506200,
  9.3329520,  7.3060380,  5.9416390,  4.9729450,  4.2552790,  3.7050500,
  2.9212400,  2.3925770,  2.0131210,  1.7278630,  1.5057010,  1.1191290,
  0.8715490,  0.5771900,  0.4126650,  0.2164470,  0.1333190,  33.6766540,
  32.2795850, 29.8110510, 23.6860370, 18.3057380, 14.2980140, 11.4150610,
  9.3244580,  7.7757940,  6.6008390,  5.6888800,  4.9663640,  3.9055760,
  3.1737960,  2.6443420,  2.2465040,  1.9383190,  1.4096790,  1.0792130,
  0.6978430,  0.4912380,  0.2521090,  0.1535920,  33.0681610, 31.8814040,
  29.3779300, 23.6057900, 18.6463550, 14.9145580, 12.1627890, 10.1071300,
  8.5395170,  7.3190970,  6.3509310,  5.5699740,  4.4005400,  3.5786790,
  2.9775460,  2.5232770,  2.1705940,  1.5662690,  1.1907560,  0.7619390,
  0.5325880,  0.2706440,  0.1640920,  44.7198600, 43.9726200, 41.9679160,
  36.1202890, 30.0864670, 24.9191710, 20.7437800, 17.4226860, 14.7811930,
  12.6668970, 10.9594050, 9.5668070,  7.4655900,  5.9866860,  4.9103160,
  4.1038230,  3.4842290,  2.4429010,  1.8145610,  1.1222760,  0.7664210,
  0.3762730,  0.2239990,
};
static const double refascale27[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount27[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  9.00000000000000,
};
static const int refsys27[4]{
  1,
  1,
  1,
  1,
};
static const int refc27[4]{
  3,
  1,
  1,
  1,
};

// 28
static const double refcn28[4]{
  0.00000000000000,
  1.68368353980441,
  6.15501721386632,
  5.91752241519496,
};
static const double refq28[4]{
  0.00000000000000,
  0.09850839901243,
  0.02948298358915,
  0.0243968931,
};
static const double refsq28[4]{
  0.00000000000000,
  -0.04925419950621,
  -0.00368537294864,
  -0.00304961164871,
};
static const double refalpha28[92]{
  65.1471670, 59.7497700, 48.4286590, 28.5849020, 17.8269450, 12.1955640,
  8.9866060,  6.9942690,  5.6675310,  4.7335770,  4.0463770,  3.5223700,
  2.7801490,  2.2820840,  1.9256220,  1.6580700,  1.4498280,  1.0871500,
  0.8537840,  0.5733100,  0.4140840,  0.2208130,  0.1373770,  33.2010460,
  31.9092910, 29.3670970, 23.1912300, 17.8686070, 13.9453180, 11.1368280,
  9.1041990,  7.5992180,  6.4570670,  5.5699260,  4.8664170,  3.8320980,
  3.1174810,  2.6000250,  2.2111480,  1.9099840,  1.3937010,  1.0709720,
  0.6975870,  0.4941560,  0.2566390,  0.1576070,  43.8557940, 42.9928330,
  40.7502500, 34.4926310, 28.3244810, 23.2253070, 19.2045670, 16.0592920,
  13.5864050, 11.6233040, 10.0473580, 8.7676580,  6.8450210,  5.4965520,
  4.5167510,  3.7830110,  3.2192030,  2.2703070,  1.6957880,  1.0589930,
  0.7288230,  0.3627090,  0.2177520,  46.9971430, 45.7683980, 42.6546550,
  34.8257600, 28.0599290, 22.8623880, 18.8881430, 15.8119240, 13.3988200,
  11.4815020, 9.9393620,  8.6844580,  6.7937410,  5.4634420,  4.4945350,
  3.7676420,  3.2083130,  2.2653470,  1.6933670,  1.0583620,  0.7286770,
  0.3627700,  0.2178100,
};
static const double refascale28[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount28[4]{
  0.00000000000000,
  2.00000000000000,
  8.00000000000000,
  8.00000000000000,
};
static const int refsys28[4]{
  1,
  1,
  1,
  1,
};
static const int refc28[4]{
  3,
  1,
  1,
  1,
};

// 29
static const double refcn29[2]{
  0.00000000000000,
  0.89816244646957,
};
static const double refq29[2]{
  0.00000000000000,
  0.0545062888,
};
static const double refsq29[2]{
  0.00000000000000,
  -0.05450628884215,
};
static const double refalpha29[46]{
  51.7659850, 46.4291690, 36.0204980, 20.5952700, 13.2155350, 9.4590740,
  7.2960120,  5.9145750,  4.9593020,  4.2583130,  3.7208220,  3.2950100,
  2.6629290,  2.2171860,  1.8871890,  1.6338740,  1.4337810,  1.0804860,
  0.8509580,  0.5739100,  0.4162210,  0.2239360,  0.1401690,  32.2640590,
  30.7643190, 27.3346460, 19.9931860, 14.6605450, 11.1745880, 8.8578670,
  7.2504740,  6.0856020,  5.2091410,  4.5290430,  3.9879440,  3.1856560,
  2.6238350,  2.2117070,  1.8983580,  1.6531670,  1.2266060,  0.9549290,
  0.6340400,  0.4552650,  0.2415160,  0.1500870,
};
static const double refascale29[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount29[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys29[2]{
  1,
  1,
};
static const int refc29[2]{
  3,
  1,
};

// 30
static const double refcn30[2]{
  0.00000000000000,
  1.75336283145604,
};
static const double refq30[2]{
  0.00000000000000,
  0.2579691884,
};
static const double refsq30[2]{
  0.00000000000000,
  -0.12898459420177,
};
static const double refalpha30[46]{
  44.8764280, 42.4015380, 36.5011020, 24.0580460, 15.9961690, 11.3275720,
  8.5125980,  6.7050110,  5.4750510,  4.5962800,  3.9426060,  3.4399690,
  2.7216070,  2.2355020,  1.8860970,  1.6235520,  1.4194560,  1.0657210,
  0.8398960,  0.5698780,  0.4161790,  0.2271770,  0.1438000,  29.2304490,
  28.6434220, 27.0389880, 22.2870810, 17.5546960, 13.8059590, 11.0322270,
  8.9976380,  7.4858160,  6.3399040,  5.4528720,  4.7523760,  3.7286630,
  3.0264940,  2.5210460,  2.1430610,  1.8515770,  1.3547510,  1.0459910,
  0.6893360,  0.4939420,  0.2624940,  0.1638640,
};
static const double refascale30[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount30[2]{
  0.00000000000000,
  2.00000000000000,
};
static const int refsys30[2]{
  1,
  1,
};
static const int refc30[2]{
  3,
  1,
};

// 31
static const double refcn31[3]{
  0.00000000000000,
  0.88820287155353,
  1.78721228422408,
};
static const double refq31[3]{
  0.00000000000000,
  0.02870304944818,
  0.045114169232,
};
static const double refsq31[3]{
  0.00000000000000,
  -0.02870304944818,
  -0.02255708461617,

};
static const double refalpha31[69]{
  56.2798430, 51.9167870, 43.2310870, 28.1416200, 18.8462820, 13.2994650,
  9.8600450,  7.6193980,  6.0894620,  5.0007640,  4.1981820,  3.5884760,
  2.7347440,  2.1738840,  1.7818110,  1.4944090,  1.2758120,  0.9086190,
  0.6839730,  0.4300690,  0.2959040,  0.1458990,  0.0867970,  53.3046110,
  49.9067250, 42.6926500, 29.2253470, 20.4243950, 14.8882280, 11.2916180,
  8.8592270,  7.1500550,  5.9073300,  4.9763880,  4.2607350,  3.2471250,
  2.5751450,  2.1036730,  1.7579590,  1.4954520,  1.0567390,  0.7907280,
  0.4933050,  0.3378040,  0.1654770,  0.0980990,  40.6953470, 38.6598060,
  34.9271010, 27.0292080, 20.5104160, 15.7311360, 12.3171900, 9.8626390,
  8.0655210,  6.7210170,  5.6931530,  4.8912630,  3.7391050,  2.9659310,
  2.4200560,  2.0186870,  1.7137410,  1.2049770,  0.8979620,  0.5570650,
  0.3801550,  0.1853670,  0.1096290,
};
static const double refascale31[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount31[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys31[3]{
  1,
  1,
  1,
};
static const int refc31[3]{
  3,
  1,
  1,
};

// 32
static const double refcn32[5]{
  0.00000000000000,
  0.89941149965103,
  1.85525243419195,
  2.78448725734282,
  3.71823460680579,
};
static const double refq32[5]{
  0.00000000000000,
  0.00938786608492,
  -0.00592798448224,
  -0.03161585463110,
  -0.0644555854,
};
static const double refsq32[5]{
  0.00000000000000,
  -0.00938786608492,
  0.00296399224112,
  0.01053861821037,
  0.01611389637169,
};
static const double refalpha32[115]{
  41.6184280, 39.9833160, 35.9872960, 26.6103970, 19.2286830, 14.1743150,
  10.7638470, 8.4179500,  6.7587960,  5.5514820,  4.6493180,  3.9588270,
  2.9887560,  2.3535080,  1.9131390,  1.5937360,  1.3534810,  0.9566170,
  0.7184900,  0.4529630,  0.3132500,  0.1561230,  0.0935260,  40.4520440,
  39.0264160, 35.5809840, 27.3666530, 20.5342330, 15.5791490, 12.0769830,
  9.5821540,  7.7708270,  6.4264770,  5.4066710,  4.6170600,  3.4943900,
  2.7511970,  2.2328710,  1.8558220,  1.5719620,  1.1037790,  0.8243160,
  0.5154070,  0.3545620,  0.1754620,  0.1047250,  40.4418220, 39.2545360,
  36.2478860, 28.6222220, 21.9792320, 16.9925560, 13.3626540, 10.7138950,
  8.7539710,  7.2776830,  6.1448790,  5.2599430,  3.9900180,  3.1421830,
  2.5480020,  2.1146930,  1.7881720,  1.2499950,  0.9298180,  0.5780120,
  0.3961690,  0.1950880,  0.1161420,  37.6716300, 36.8525860, 34.6926590,
  28.6826580, 22.8485090, 18.1179570, 14.4936950, 11.7568160, 9.6831810,
  8.0946770,  6.8606380,  5.8877070,  4.4784020,  3.5295510,  2.8613170,
  2.3726930,  2.0040290,  1.3963730,  1.0356150,  0.6409590,  0.4381220,
  0.2150380,  0.1278320,  34.9443880, 34.4589550, 33.0932300, 28.6849650,
  23.6815050, 19.2193090, 15.6074480, 12.7869910, 10.6029230, 8.9045950,
  7.5710690,  6.5114240,  4.9643950,  3.9154690,  3.1737400,  2.6301480,
  2.2195640,  1.5427250,  1.1415220,  0.7041370,  0.4803530,  0.2352710,
  0.1397600,
};
static const double refascale32[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount32[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys32[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc32[5]{
  3,
  1,
  1,
  1,
  1,
};

// 33
static const double refcn33[4]{
  0.00000000000000,
  0.96810324138508,
  1.93762986034873,
  2.90829444959119,
};
static const double refq33[4]{
  0.00000000000000,
  -0.09954248086481,
  -0.11896736577051,
  -0.1022538471,
};
static const double refsq33[4]{
  0.00000000000000,
  0.09954248086481,
  0.05948368288525,
  0.03408461572369,
};
static const double refalpha33[92]{
  30.9622720, 30.2682480, 28.4117290, 23.1419060, 18.0459760, 14.0238200,
  11.0354630, 8.8374630,  7.2065030,  5.9774600,  5.0352070,  4.3004040,
  3.2496190,  2.5521200,  2.0662400,  1.7139300,  1.4497910,  1.0172000,
  0.7612360,  0.4798100,  0.3329600,  0.1673800,  0.1007870,  32.9857230,
  32.2738720, 30.3903080, 25.0725470, 19.8545550, 15.6403290, 12.4395230,
  10.0416420, 8.2363030,  6.8602630,  5.7958010,  4.9597520,  3.7548970,
  2.9491190,  2.3851990,  1.9752150,  1.6674560,  1.1635310,  0.8662610,
  0.5416150,  0.3738430,  0.1866530,  0.1120540,  34.5403260, 33.8506380,
  32.0374310, 26.8393630, 21.5730010, 17.1996430, 13.8049410, 11.2190870,
  9.2473150,  7.7296440,  6.5466390,  5.6118890,  4.2560500,  3.3436390,
  2.7026150,  2.2355180,  1.8844910,  1.3096800,  0.9712870,  0.6035540,
  0.4148920,  0.2060850,  0.1234480,  35.5626970, 34.9738250, 33.3553240,
  28.4265670, 23.1867600, 18.6947170, 15.1290090, 12.3689250, 10.2393320,
  8.5855950,  7.2877370,  6.2567940,  4.7529590,  3.7354930,  3.0182630,
  2.4945970,  2.1006490,  1.4553950,  1.0760650,  0.6653780,  0.4558740,
  0.2254990,  0.1348450,
};
static const double refascale33[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount33[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys33[4]{
  1,
  1,
  1,
  1,
};
static const int refc33[4]{
  3,
  1,
  1,
  1,
};

// 34
static const double refcn34[3]{
  0.00000000000000,
  0.92195274896170,
  1.84493749809528,
};
static const double refq34[3]{
  0.00000000000000,
  -0.12327157100582,
  -0.175358037223,
};
static const double refsq34[3]{
  0.00000000000000,
  0.12327157100582,
  0.08767901861183,
};
static const double refalpha34[69]{
  25.7234860, 25.2967560, 24.1266960, 20.5754680, 16.8021780, 13.5652820,
  10.9952140, 9.0046390,  7.4667080,  6.2701390,  5.3290860,  4.5800740,
  3.4849480,  2.7424650,  2.2186000,  1.8360660,  1.5483750,  1.0775180,
  0.8008720,  0.5007840,  0.3466260,  0.1746160,  0.1055700,  28.5144970,
  28.0475240, 26.7740720, 22.9293920, 18.8329680, 15.2899050, 12.4503800,
  10.2324530, 8.5069500,  7.1570530,  6.0907950,  5.2391750,  3.9892260,
  3.1385090,  2.5367660,  2.0966900,  1.7654690,  1.2233860,  0.9054680,
  0.5621910,  0.3871530,  0.1936670,  0.1167080,  30.9890680, 30.5032140,
  29.1715810, 25.1156940, 20.7515920, 16.9397500, 13.8556780, 11.4267060,
  9.5242290,  8.0279190,  6.8410310,  5.8898910,  4.4887500,  3.5316780,
  2.8531070,  2.3561140,  1.9817540,  1.3689360,  1.0099510,  0.6236450,
  0.4277790,  0.2128400,  0.1279540,
};
static const double refascale34[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount34[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys34[3]{
  1,
  1,
  1,
};
static const int refc34[3]{
  3,
  1,
  1,
};

// 35
static const double refcn35[2]{
  0.00000000000000,
  0.87141367228098,
};
static const double refq35[2]{
  0.00000000000000,
  -0.1449078212,
};
static const double refsq35[2]{
  0.00000000000000,
  0.14490782122377,
};
static const double refalpha35[46]{
  20.8160780, 20.5760200, 19.8987130, 17.6813900, 15.0736970, 12.6318500,
  10.5528970, 8.8524810,  7.4812900,  6.3774160,  5.4848940,  4.7581530,
  3.6676360,  2.9082370,  2.3624100,  1.9587510,  1.6526030,  1.1479460,
  0.8506710,  0.5297310,  0.3663790,  0.1854320,  0.1127450,  23.7818040,
  23.5043600, 22.7232600, 20.1781530, 17.1975750, 14.4112140, 12.0390110,
  10.0975330, 8.5309690,  7.2693050,  6.2490260,  5.4182350,  4.1716820,
  3.3037540,  2.6800190,  2.2188460,  1.8691920,  1.2933190,  0.9547540,
  0.5906060,  0.4063970,  0.2041110,  0.1236350,
};
static const double refascale35[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount35[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys35[2]{
  1,
  1,
};
static const int refc35[2]{
  3,
  1,
};

// 36
static const double refcn36[1]{
  0.00000000000000,
};
static const double refq36[1]{
  0.0000000000,
};
static const double refsq36[1]{
  0.00000000000000,
};
static const double refalpha36[23]{
  16.8771250, 16.7404080, 16.3473440, 14.9868570, 13.2465280, 11.4802080,
  9.8697990,  8.4773240,  7.3035050,  6.3243740,  5.5096050,  4.8302660,
  3.7825130,  3.0313660,  2.4797800,  2.0653280,  1.7472760,  1.2164410,
  0.9007200,  0.5591630,  0.3861250,  0.1959080,  0.1197080,
};
static const double refascale36[1]{
  1.00000000000000,
};
static const double refscount36[1]{
  0.00000000000000,
};
static const int refsys36[1]{
  1,
};
static const int refc36[1]{
  3,
};

// 37
static const double refcn37[3]{
  0.00000000000000,
  0.77155167960451,
  12.39000000000000,
};
static const double refq37[3]{
  0.00000000000000,
  0.44852683448077,
  0.416000000000,
};
static const double refsq37[3]{
  0.00000000000000,
  -0.44852683448077,
  -0.41600000000000,
};
static const double refalpha37[69]{
  410.1570650, 214.3629420, 92.2189500, 33.0762760, 19.1702550,  13.6453490,
  10.6953320,  8.8115010,   7.4699530,  6.4487380,  5.6381240,   4.9766630,
  3.9619960,   3.2244460,   2.6697510,  2.2421050,  1.9059170,   1.3262900,
  0.9698860,   0.5775830,   0.3804570,  0.1743570,  0.0992380,   62.1046880,
  55.3737420,  43.5682870,  27.4983580, 19.5497690, 15.0663500,  12.1785660,
  10.1413920,  8.6158260,   7.4268580,  6.4740940,  5.6949060,   4.5031460,
  3.6435490,   3.0024770,   2.5119750,  2.1288570,  1.4737190,   1.0743370,
  0.6377080,   0.4194260,   0.1919380,  0.1091900,  126.6310029, 125.1559058,
  121.0742788, 108.3482901, 94.1247762, 81.0337905, 69.7439741,  60.2269348,
  52.2628997,  45.6040488,  40.0235464, 35.3278801, 27.9808202,  22.6114560,
  18.5992009,  15.5379934,  13.1579386, 9.1200087,  6.6812408,   4.0309298,
  2.7053916,   1.3052810,   0.7781749,
};
static const double refascale37[3]{
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount37[3]{
  0.00000000000000,
  1.00000000000000,
  4.00000000000000,
};
static const int refsys37[3]{
  1,
  1,
  17,
};
static const int refc37[3]{
  3,
  1,
  1,
};

// 38
static const double refcn38[4]{
  0.00000000000000,
  0.79294768050705,
  1.54805734413866,
  15.12100028991699,
};
static const double refq38[4]{
  0.00000000000000,
  0.42643340166796,
  0.64902814271780,
  0.5140000000,
};
static const double refsq38[4]{
  0.00000000000000,
  -0.42643340166796,
  -0.32451407135890,
  -0.51400000000000,
};
static const double refalpha38[92]{
  207.0959830, 167.4062640, 107.5395190, 46.8864590,  26.2027860,  17.4151700,
  12.8603380,  10.1317340,  8.3169810,   7.0156000,   6.0305450,   5.2554110,
  4.1095420,   3.3041900,   2.7115560,   2.2617260,   1.9123040,   1.3185610,
  0.9589950,   0.5679990,   0.3733060,   0.1708320,   0.0972390,   203.7569620,
  136.2520380, 79.3342830,  39.0709150,  24.8495540,  17.8598820,  13.7760240,
  11.1115300,  9.2347870,   7.8382880,   6.7567000,   5.8938450,   4.6058940,
  3.6968050,   3.0281860,   2.5217330,   2.1292640,   1.4647060,   1.0638290,
  0.6292740,   0.4133770,   0.1891240,   0.1076560,   56.7366690,  53.8312150,
  47.2695200,  33.9461020,  24.8182410,  18.9521460,  15.0374310,  12.2916810,
  10.2772390,  8.7433090,   7.5399850,   6.5735100,   5.1255840,   4.1035260,
  3.3535750,   2.7871740,   2.3494990,   1.6113550,   1.1681150,   0.6895060,
  0.4524650,   0.2067690,   0.1176430,   116.4505849, 114.1968844, 108.2963555,
  92.1203844,  76.7209726,  64.3033634,  54.5977463,  46.9458079,  40.8022639,
  35.7806868,  31.6136150,  28.1128216,  22.5997820,  18.5077567,  15.3957648,
  12.9813495,  11.0757782,  7.7757352,   5.7345816,   3.4676638,   2.3132969,
  1.0842547,   0.6262415,
};
static const double refascale38[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount38[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
};
static const int refsys38[4]{
  1,
  1,
  1,
  9,
};
static const int refc38[4]{
  3,
  1,
  1,
  1,
};

// 39
static const double refcn39[3]{
  0.00000000000000,
  1.61670701598223,
  2.43996146811665,
};
static const double refq39[3]{
  0.00000000000000,
  0.57618546114280,
  0.723128476321,
};
static const double refsq39[3]{
  0.00000000000000,
  -0.28809273057140,
  -0.24104282544034,
};
static const double refalpha39[69]{
  156.5816530, 133.4096570, 94.6810390, 47.1887390, 27.8621270, 18.8348770,
  13.9092620,  10.8900460,  8.8730220,  7.4352670,  6.3585500,  5.5211390,
  4.3014730,   3.4566600,   2.8399260,  2.3734080,  2.0112610,  1.3945770,
  1.0190510,   0.6075350,   0.4008910,  0.1843540,  0.1051420,  126.8052320,
  88.7747170,  64.1464690,  40.2998810, 28.2499780, 21.0643660, 16.4186290,
  13.2334170,  10.9441490,  9.2339520,  7.9151340,  6.8713270,  5.3330370,
  4.2636390,   3.4855460,   2.9002550,  2.4485960,  1.6861640,  1.2266060,
  0.7275190,   0.4787640,   0.2194880,  0.1250190,  51.9455750, 50.4162010,
  46.5373240,  36.6790590,  28.1986330, 21.9785510, 17.5295770, 14.3039920,
  11.9077650,  10.0810740,  8.6547010,  7.5170970,  5.8310100,  4.6555680,
  3.8004240,   3.1579800,   2.6630160,  1.8296590,  1.3289880,  0.7868860,
  0.5173750,   0.2369610,   0.1349160,
};
static const double refascale39[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount39[3]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys39[3]{
  1,
  1,
  1,
};
static const int refc39[3]{
  3,
  1,
  1,
};

// 40
static const double refcn40[4]{
  0.00000000000000,
  1.66263906536582,
  3.35991209283567,
  6.09300000000000,
};
static const double refq40[4]{
  0.00000000000000,
  0.34661262612707,
  0.56547785565182,
  0.9430000000,
};
static const double refsq40[4]{
  0.00000000000000,
  -0.17330631306353,
  -0.14136946391296,
  -0.23575000000000,
};
static const double refalpha40[92]{
  129.1649250, 112.9115260, 84.2744150, 45.2123570, 27.6899320, 19.0856380,
  14.2390790,  11.2024000,  9.1447760,  7.6666660,  6.5563690,  5.6928180,
  4.4382110,   3.5726300,   2.9422010,  2.4654780,  2.0949780,  1.4616900,
  1.0734540,   0.6444360,   0.4270850,  0.1974770,  0.1128890,  59.5329360,
  59.0731440,  49.3004260,  35.6901590, 26.5930640, 20.4777520, 16.2621680,
  13.2552040,  11.0380980,  9.3543390,  8.0423850,  6.9973630,  5.4495930,
  4.3698600,   3.5825450,   2.9890610,  2.5300090,  1.7518420,  1.2798730,
  0.7635970,   0.5043350,   0.2322730,  0.1325630,  53.7033680, 52.3694770,
  48.8771380,  39.4788990,  30.9424830, 24.4286920, 19.6266710, 16.0687640,
  13.3881100,  11.3281120,  9.7137520,  8.4253900,  6.5198670,  5.1977820,
  4.2403830,   3.5235900,   2.9725540,  2.0460840,  1.4892320,  0.8847240,
  0.5830200,   0.2678100,   0.1526730,  33.6465243, 33.4038388, 32.7056564,
  30.2880677,  27.2060499,  24.0984692, 21.2765610, 18.8296599, 16.7447048,
  14.9743210,  13.4663529,  12.1742122, 10.0904600, 8.4969686,  7.2491379,
  6.2526961,   5.4441107,   3.9836870,  3.0306974,  1.9121250,  1.3109813,
  0.6388831,   0.3766424,
};
static const double refascale40[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount40[4]{
  0.00000000000000,
  2.00000000000000,
  4.00000000000000,
  4.00000000000000,
};
static const int refsys40[4]{
  1,
  1,
  1,
  11,
};
static const int refc40[4]{
  3,
  1,
  1,
  1,
};

// 41
static const double refcn41[4]{
  0.00000000000000,
  1.75136276843804,
  2.61865286219105,
  4.02900000000000,
};
static const double refq41[4]{
  0.00000000000000,
  0.42830519499403,
  0.56050948600940,
  1.2460000000,
};
static const double refsq41[4]{
  0.00000000000000,
  -0.21415259749701,
  -0.18683649533647,
  -0.24920000000000,
};
static const double refalpha41[92]{
  112.5868220, 98.9946210, 75.5219100, 42.5430350, 26.8101620, 18.7904950,
  14.1713590,  11.2319370, 9.2165940,  7.7556700,  6.6508620,  5.7874800,
  4.5279270,   3.6564020,  3.0206270,  2.5390860,  2.1640690,  1.5202440,
  1.1226240,   0.6790940,  0.4521310,  0.2102320,  0.1204560,  55.9986780,
  60.8749560,  50.6953400, 35.6643390, 26.4531740, 20.4359360, 16.2988900,
  13.3351670,  11.1377280, 9.4604950,  8.1484630,  7.1004180,  5.5443520,
  4.4569430,   3.6632070,  3.0641820,  2.6001160,  1.8107380,  1.3291220,
  0.7982160,   0.5293550,  0.2450550,  0.1401740,  51.3329100, 49.0284950,
  44.6433950,  35.3677840, 27.6830280, 21.9413960, 17.7220800, 14.5880150,
  12.2159700,  10.3838810, 8.9410440,  7.7843510,  6.0637690,  4.8619510,
  3.9865780,   3.3277110,  2.8186730,  1.9562960,  1.4327150,  0.8581570,
  0.5683180,   0.2626950,  0.1501750,  39.2699458, 38.9559085, 38.0619736,
  35.0545164,  31.3566941, 27.7212247, 24.4670081, 21.6658391, 19.2870190,
  17.2695766,  15.5513454, 14.0783331, 11.7000325, 9.8776054,  8.4472870,
  7.3024041,   6.3710983,  4.6822974,  3.5742534,  2.2657569,  1.5581961,
  0.7625966,   0.4505494,
};
static const double refascale41[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount41[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  5.00000000000000,
};
static const int refsys41[4]{
  1,
  1,
  1,
  11,
};
static const int refc41[4]{
  3,
  1,
  1,
  1,
};

// 42
static const double refcn42[4]{
  0.00000000000000,
  1.89510707051732,
  10.77850977361032,
  5.59646145748005,
};
static const double refq42[4]{
  0.00000000000000,
  0.46738200215089,
  0.47338670395900,
  0.5942767778,
};
static const double refsq42[4]{
  0.00000000000000,
  -0.23369100107545,
  -0.03944889199658,
  -0.09904612964760,
};
static const double refalpha42[92]{
  80.1166370, 72.0033490, 56.3464510, 33.3622730, 22.2521730, 16.3666450,
  12.8045350, 10.4296810, 8.7352680,  7.4656260,  6.4789340,  5.6904860,
  4.5115160,  3.6758650,  3.0566210,  2.5826100,  2.2106410,  1.5662560,
  1.1641470,  0.7106370,  0.4758290,  0.2228080,  0.1280230,  57.3696220,
  53.6619600, 46.4519190, 33.7721100, 25.3796990, 19.8008640, 15.9255030,
  13.1223040, 11.0249000, 9.4107880,  8.1389620,  7.1166930,  5.5878340,
  4.5113880,  3.7214650,  3.1229210,  2.6576930,  1.8625700,  1.3742440,
  0.8315500,  0.5541640,  0.2581730,  0.1480840,  67.2624950, 66.0303950,
  62.7575620, 53.5269770, 44.3751560, 36.6776440, 30.4829790, 25.5527440,
  21.6261800, 18.4804960, 15.9392930, 13.8670690, 10.7428020, 8.5472490,
  6.9523710,  5.7601520,  4.8468120,  3.3211190,  2.4114970,  1.4303190,
  0.9425060,  0.4333420,  0.2472210,  57.1122440, 54.5507140, 49.8607540,
  40.5094150, 32.7396620, 26.6350470, 21.9139730, 18.2593580, 15.4061580,
  13.1523240, 11.3489830, 9.8875440,  7.6939570,  6.1540760,  5.0326460,
  4.1907210,  3.5424610,  2.4502640,  1.7914150,  1.0718980,  0.7099120,
  0.3284040,  0.1878520,
};
static const double refascale42[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount42[4]{
  0.00000000000000,
  2.00000000000000,
  12.00000000000000,
  6.00000000000000,
};
static const int refsys42[4]{
  1,
  1,
  1,
  1,
};
static const int refc42[4]{
  3,
  1,
  1,
  1,
};

// 43
static const double refcn43[3]{
  0.00000000000000,
  1.56460355314490,
  8.94426823783675,
};
static const double refq43[3]{
  0.00000000000000,
  0.24709379453256,
  0.181981739171,
};
static const double refsq43[3]{
  0.00000000000000,
  -0.12354689726628,
  -0.01654379447015,
};
static const double refalpha43[69]{
  92.9387160, 81.9452450, 63.3698580, 37.3296730, 24.3564850, 17.4779390,
  13.4110250, 10.7755340, 8.9429790,  7.5986600,  6.5712030,  5.7605070,
  4.5631700,  3.7227110,  3.1024520,  2.6281370,  2.2556760,  1.6085080,
  1.2022890,  0.7402780,  0.4986150,  0.2353880,  0.1357590,  75.8730320,
  65.9104100, 51.9040420, 34.7083320, 25.4784390, 19.7433960, 15.8501840,
  13.0603640, 10.9826550, 9.3875760,  8.1320480,  7.1229420,  5.6121410,
  4.5457470,  3.7609510,  3.1646320,  2.6999290,  1.9026050,  1.4102760,
  0.8594030,  0.5755190,  0.2699220,  0.1552940,  58.5751980, 57.7047570,
  55.3283600, 48.1684600, 40.5340630, 33.8274610, 28.3028200, 23.8467240,
  20.2669430, 17.3809560, 15.0378770, 13.1192270, 10.2118960, 8.1570940,
  6.6575030,  5.5321270,  4.6670770,  3.2152040,  2.3443700,  1.3987970,
  0.9253150,  0.4276690,  0.2445830,
};
static const double refascale43[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount43[3]{
  0.00000000000000,
  2.00000000000000,
  11.00000000000000,
};
static const int refsys43[3]{
  1,
  1,
  1,
};
static const int refc43[3]{
  3,
  1,
  1,
};

// 44
static const double refcn44[3]{
  0.00000000000000,
  1.82293327778554,
  8.72336154530085,
};
static const double refq44[3]{
  0.00000000000000,
  0.32415456703039,
  0.363756744985,
};
static const double refsq44[3]{
  0.00000000000000,
  -0.16207728351520,
  -0.03637567449858,
};
static const double refalpha44[69]{
  64.2873650, 58.2984130, 46.6241190, 28.9081460, 19.8860070, 14.9414970,
  11.8820490, 9.8067370,  8.3050910,  7.1669030,  6.2736860,  5.5536060,
  4.4638560,  3.6792510,  3.0894480,  2.6322260,  2.2694820,  1.6317090,
  1.2266730,  0.7613680,  0.5156110,  0.2453210,  0.1420300,  45.7015170,
  44.1640550, 40.0828620, 30.9952860, 23.8618350, 18.8259100, 15.2521470,
  12.6439180, 10.6826650, 9.1676420,  7.9697090,  7.0033880,  5.5501890,
  4.5187320,  3.7556240,  3.1728410,  2.7165260,  1.9281300,  1.4370560,
  0.8825770,  0.5941370,  0.2807420,  0.1621180,  53.6449610, 52.9021650,
  50.8530030, 44.5291150, 37.6245730, 31.4884170, 26.4097500, 22.3040630,
  19.0002040, 16.3321480, 14.1620830, 12.3817320, 9.6763600,  7.7570110,
  6.3512380,  5.2927530,  4.4766230,  3.1006590,  2.2704610,  1.3630470,
  0.9053930,  0.4209110,  0.2414160,
};
static const double refascale44[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount44[3]{
  0.00000000000000,
  2.00000000000000,
  10.00000000000000,
};
static const int refsys44[3]{
  1,
  1,
  1,
};
static const int refc44[3]{
  3,
  1,
  1,
};

// 45
static const double refcn45[4]{
  0.00000000000000,
  1.84241892648043,
  2.88090049147235,
  4.69798180984017,
};
static const double refq45[4]{
  0.00000000000000,
  0.14509956942986,
  0.18388211183689,
  0.2454979880,
};
static const double refsq45[4]{
  0.00000000000000,
  -0.07254978471493,
  -0.06129403727896,
  -0.04909959760867,
};
static const double refalpha45[92]{
  68.1542450, 62.9960050, 52.0807400, 32.9144330, 22.1117060, 16.1257920,
  12.5115460, 10.1406800, 8.4788070,  7.2525150,  6.3108490,  5.5647590,
  4.4563970,  3.6717400,  3.0873140,  2.6361620,  2.2786150,  1.6486870,
  1.2462650,  0.7799260,  0.5311430,  0.2547010,  0.1480120,  43.3417530,
  41.4841810, 37.5198890, 29.0651560, 22.5178410, 17.8848750, 14.5797210,
  12.1532300, 10.3179030, 8.8923860,  7.7596700,  6.8419520,  5.4542350,
  4.4628030,  3.7251260,  3.1588890,  2.7134840,  1.9388590,  1.4524300,
  0.8985520,  0.6078940,  0.2892870,  0.1676290,  37.7442490, 36.6313080,
  34.0210470, 27.9047180, 22.6219420, 18.5364410, 15.4279090, 13.0366770,
  11.1653460, 9.6752930,  8.4697300,  7.4802140,  5.9656450,  4.8738020,
  4.0587720,  3.4331020,  2.9417130,  2.0906290,  1.5597110,  0.9597480,
  0.6472660,  0.3069220,  0.1776240,  50.7362600, 49.4436100, 46.2123700,
  37.7336800, 30.0265600, 24.1196600, 19.7259100, 16.4228700, 13.8898500,
  11.9075300, 10.3272700, 9.0468100,  7.1181400,  5.7535600,  4.7506500,
  3.9906900,  3.4003100,  2.3920200,  1.7726100,  1.0819100,  0.7262700,
  0.3424400,  0.1977000,
};
static const double refascale45[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount45[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  5.00000000000000,
};
static const int refsys45[4]{
  1,
  1,
  1,
  1,
};
static const int refc45[4]{
  3,
  1,
  1,
  1,
};

// 46
static const double refcn46[3]{
  0.00000000000000,
  1.82751376419277,
  5.62156480548985,
};
static const double refq46[3]{
  0.00000000000000,
  0.22956514930613,
  0.554449714293,
};
static const double refsq46[3]{
  0.00000000000000,
  -0.11478257465306,
  -0.06930621428674,
};
static const double refalpha46[69]{
  60.8864630, 56.8478940, 47.8540600, 30.9841900, 21.0472500, 15.4485530,
  12.0425860, 9.7984690,  8.2204320,  7.0529890,  6.1545310,  5.4412960,
  4.3791150,  3.6247120,  3.0609020,  2.6240310,  2.2764150,  1.6598380,
  1.2622490,  0.7967230,  0.5457380,  0.2639640,  0.1541040,  40.2110290,
  38.5072500, 34.8932240, 27.2138020, 21.2371640, 16.9805470, 13.9260910,
  11.6707350, 9.9551980,  8.6156180,  7.5460330,  6.6757400,  5.3527110,
  4.4016410,  3.6902360,  3.1415360,  2.7079930,  1.9489220,  1.4681030,
  0.9154940,  0.6227080,  0.2987130,  0.1738250,  52.9449710, 51.8101820,
  48.8650090, 40.9527250, 33.5198470, 27.5254650, 22.8486080, 19.2026620,
  16.3345560, 14.0509400, 12.2094700, 10.7060500, 8.4272930,  6.8085780,
  5.6176560,  4.7154850,  4.0151810,  2.8211020,  2.0891520,  1.2745700,
  0.8557330,  0.4038840,  0.2333960,
};
static const double refascale46[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount46[3]{
  0.00000000000000,
  2.00000000000000,
  8.00000000000000,
};
static const int refsys46[3]{
  1,
  1,
  1,
};
static const int refc46[3]{
  3,
  1,
  1,
};

// 47
static const double refcn47[2]{
  0.00000000000000,
  0.91215552676727,
};
static const double refq47[2]{
  0.00000000000000,
  0.1067036177,
};
static const double refsq47[2]{
  0.00000000000000,
  -0.10670361771604,
};
static const double refalpha47[46]{
  54.1989880, 49.0489660, 38.9829400, 23.9821320, 16.6050290, 12.6373760,
  10.1995360, 8.5437370,  7.3366070,  6.4116550,  5.6772120,  5.0784690,
  4.1592690,  3.4860530,  2.9720170,  2.5673730,  2.2414010,  1.6540770,
  1.2685970,  0.8095530,  0.5581500,  0.2721620,  0.1594640,  36.6000980,
  35.1208740, 31.6461790, 24.0228290, 18.3425350, 14.4988310, 11.8463360,
  9.9378870,  8.5081750,  7.4002440,  6.5179040,  5.7995690,  4.7030760,
  3.9082530,  3.3079420,  2.8402610,  2.4670520,  1.8034180,  1.3743830,
  0.8703890,  0.5975480,  0.2899250,  0.1695250,
};
static const double refascale47[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount47[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys47[2]{
  1,
  1,
};
static const int refc47[2]{
  3,
  1,
};

// 48
static const double refcn48[2]{
  0.00000000000000,
  1.77531555102521,
};
static const double refq48[2]{
  0.00000000000000,
  0.2189854054,
};
static const double refsq48[2]{
  0.00000000000000,
  -0.10949270272585,
};
static const double refalpha48[46]{
  51.2430300, 48.3502990, 41.5746300, 27.7890000, 19.1321820, 14.1382230,
  11.0784560, 9.0587800,  7.6378310,  6.5859030,  5.7753370,  5.1307120,
  4.1675160,  3.4798590,  2.9630260,  2.5600920,  2.2373290,  1.6578750,
  1.2772960,  0.8215180,  0.5698100,  0.2806600,  0.1654590,  35.9140330,
  35.1566180, 33.1068480, 27.1969530, 21.5145310, 17.1191360, 13.8992970,
  11.5355770, 9.7648350,  8.4054680,  7.3368940,  6.4788070,  5.1930790,
  4.2809850,  3.6036050,  3.0826690,  2.6710330,  1.9469920,  1.4831570,
  0.9406720,  0.6472420,  0.3156970,  0.1853400,
};
static const double refascale48[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount48[2]{
  0.00000000000000,
  2.00000000000000,
};
static const int refsys48[2]{
  1,
  1,
};
static const int refc48[2]{
  3,
  1,
};

// 49
static const double refcn49[4]{
  0.00000000000000,
  0.88719377220275,
  1.78495637384615,
  2.70420959057537,
};
static const double refq49[4]{
  0.00000000000000,
  0.06391398485994,
  0.10806425732282,
  0.1417169899,
};
static const double refsq49[4]{
  0.00000000000000,
  -0.06391398485994,
  -0.05403212866141,
  -0.04723899664934,
};
static const double refalpha49[92]{
  72.9150960, 66.0753600, 53.3578280, 33.5644110, 22.4687340, 16.1472430,
  12.3105260, 9.8245790,  8.1173940,  6.8860560,  5.9610840,  5.2425400,
  4.1995990,  3.4778910,  2.9472540,  2.5398030,  2.2168390,  1.6430710,
  1.2690370,  0.8214960,  0.5729700,  0.2844110,  0.1681820,  68.5448320,
  63.3499550, 52.9158640, 35.1620400, 24.4638730, 18.0151280, 13.9204010,
  11.1780650, 9.2513440,  7.8406570,  6.7710770,  5.9359020,  4.7209280,
  3.8821540,  3.2690480,  2.8016450,  2.4338840,  1.7877840,  1.3722790,
  0.8814810,  0.6120400,  0.3021170,  0.1782190,  50.7622140, 48.0385490,
  43.0567370, 32.8278830, 24.7634540, 19.0651230, 15.0969960, 12.2851460,
  10.2375520, 8.7031490,  7.5220080,  6.5906520,  5.2252970,  4.2790840,
  3.5880180,  3.0628180,  2.6512680,  1.9334490,  1.4763250,  0.9418740,
  0.6513060,  0.3198580,  0.1882630,  41.1871070, 40.4130170, 38.2892500,
  31.9210850, 25.4481130, 20.2225040, 16.3010840, 13.3954500, 11.2196820,
  9.5597380,  8.2670060,  7.2399920,  5.7255130,  4.6728770,  3.9045910,
  3.3221260,  2.8671790,  2.0782430,  1.5798240,  1.0020180,  0.6904450,
  0.3375630,  0.1982910,
};
static const double refascale49[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount49[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys49[4]{
  1,
  1,
  1,
  1,
};
static const int refc49[4]{
  3,
  1,
  1,
  1,
};

// 50
static const double refcn50[5]{
  0.00000000000000,
  0.90042437628478,
  1.84687551160093,
  2.77047146659601,
  3.70466711294240,
};
static const double refq50[5]{
  0.00000000000000,
  0.03599066704066,
  0.04368851386536,
  0.03463534758499,
  0.0141822127,
};
static const double refsq50[5]{
  0.00000000000000,
  -0.03599066704066,
  -0.02184425693268,
  -0.01154511586166,
  -0.00354555319366,
};
static const double refalpha50[115]{
  57.3040270, 54.4476260, 47.7957070, 33.6841460, 23.7376670, 17.3960520,
  13.3024310, 10.5620400, 8.6525610,  7.2708170,  6.2366020,  5.4393040,
  4.2988630,  3.5266460,  2.9701000,  2.5497820,  2.2208960,  1.6446800,
  1.2728700,  0.8288590,  0.5812410,  0.2912600,  0.1732200,  53.7298320,
  51.4329790, 46.0716700, 34.2024090, 25.1302790, 18.9316540, 14.7246270,
  11.8066270, 9.7217990,  8.1863100,  7.0228060,  6.1183050,  4.8155710,
  3.9303330,  3.2929680,  2.8132790,  2.4396930,  1.7907330,  1.3769680,
  0.8891430,  0.6203820,  0.3088870,  0.1831710,  53.3912050, 51.4589370,
  46.7536920, 35.7231120, 26.8682930, 20.5832790, 16.1845180, 13.0610500,
  10.7905050, 9.0973330,  7.8031170,  6.7910320,  5.3263460,  4.3288220,
  3.6113910,  3.0730140,  2.6553170,  1.9347190,  1.4797110,  0.9488200,
  0.6592330,  0.3264620,  0.1931150,  48.1721000, 46.9654470, 43.8406630,
  35.4940690, 27.7965480, 21.8303470, 17.4239690, 14.1866160, 11.7798410,
  9.9575870,  8.5500830,  7.4414740,  5.8269560,  4.7227970,  3.9280720,
  3.3323920,  2.8712630,  2.0794750,  1.5831290,  1.0088640,  0.6982730,
  0.3440760,  0.2030650,  44.3809730, 43.6657010, 41.6751380, 35.4583760,
  28.7575380, 23.0706960, 18.6492860, 15.2988620, 12.7583260, 10.8093490,
  9.2904440,  8.0867420,  6.3242650,  5.1145440,  4.2431700,  3.5905930,
  3.0863030,  2.2237000,  1.6862000,  1.0687380,  0.7372220,  0.3616620,
  0.2130010,
};
static const double refascale50[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount50[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys50[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc50[5]{
  3,
  1,
  1,
  1,
  1,
};

// 51
static const double refcn51[4]{
  0.00000000000000,
  0.93580947053485,
  1.87397783659382,
  2.81393944504634,
};
static const double refq51[4]{
  0.00000000000000,
  -0.01439446368141,
  -0.01543201581300,
  -0.0098535719,
};
static const double refsq51[4]{
  0.00000000000000,
  0.01439446368141,
  0.00771600790650,
  0.00328452399254,
};
static const double refalpha51[92]{
  44.8358450, 43.5130560, 40.0926450, 31.1774780, 23.4511520, 17.8471750,
  13.9239600, 11.1566290, 9.1627500,  7.6898730,  6.5744680,  5.7098380,
  4.4725460,  3.6404470,  3.0472370,  2.6044190,  2.2616350,  1.6693460,
  1.2920700,  0.8442200,  0.5942970,  0.2999110,  0.1791200,  45.9916410,
  44.7450290, 41.5208600, 32.9820310, 25.3160810, 19.5590470, 15.4150740,
  12.4297230, 10.2444980, 8.6111660,  7.3634730,  6.3902070,  4.9895020,
  4.0440290,  3.3698710,  2.8676280,  2.4801170,  1.8150710,  1.3958700,
  0.9043070,  0.6333220,  0.3175040,  0.1890550,  46.6496880, 45.5197710,
  42.5927060, 34.6039430, 27.0775160, 21.2059700, 16.8636310, 13.6742900,
  11.3067400, 9.5188430,  8.1427680,  7.0635060,  5.5024820,  4.4452150,
  3.6909720,  3.1298080,  2.6978790,  1.9604550,  1.4994800,  0.9643160,
  0.6723070,  0.3350840,  0.1989840,  46.7552750, 45.8323020, 43.3346180,
  36.0394380, 28.7272660, 22.7845200, 18.2688140, 14.8903330, 12.3496050,
  10.4129670, 8.9123290,  7.7296420,  6.0113260,  4.8438310,  4.0103740,
  3.3908020,  2.9147740,  2.1053690,  1.6027900,  1.0241710,  0.7112070,
  0.3526470,  0.2089120,
};
static const double refascale51[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount51[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys51[4]{
  1,
  1,
  1,
  1,
};
static const int refc51[4]{
  3,
  1,
  1,
  1,
};

// 52
static const double refcn52[3]{
  0.00000000000000,
  0.94900106848812,
  1.89954395376061,
};
static const double refq52[3]{
  0.00000000000000,
  -0.09115200126999,
  -0.096780033450,
};
static const double refsq52[3]{
  0.00000000000000,
  0.09115200126999,
  0.04839001672511,
};
static const double refalpha52[69]{
  38.7558670, 37.8891050, 35.5765770, 29.0541470, 22.7985480, 17.8842260,
  14.2354170, 11.5477160, 9.5486370,  8.0375580,  6.8745420,  5.9631130,
  4.6477480,  3.7603970,  3.1299390,  2.6624490,  2.3034360,  1.6910060,
  1.3067460,  0.8554460,  0.6045040,  0.3075880,  0.1846460,  41.2800660,
  40.4036870, 38.0648030, 31.4147320, 24.9165410, 19.7095440, 15.7789570,
  12.8463230, 10.6436490, 8.9662810,  7.6680330,  6.6463830,  5.1661270,
  4.1647840,  3.4530650,  2.9259730,  2.5221220,  1.8367870,  1.4105310,
  0.9154730,  0.6434690,  0.3251430,  0.1945560,  43.3767540, 42.5220370,
  40.2233370, 33.5679210, 26.9051580, 21.4529440, 17.2695530, 14.1098870,
  11.7148730, 9.8784450,  8.4497140,  7.3210330,  5.6796140,  4.5661840,
  3.7742540,  3.1881760,  2.7398680,  1.9821020,  1.5140480,  0.9753820,
  0.6823680,  0.3426700,  0.2044490,
};
static const double refascale52[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount52[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys52[3]{
  1,
  1,
  1,
};
static const int refc52[3]{
  3,
  1,
  1,
};

// 53
static const double refcn53[2]{
  0.00000000000000,
  0.91239969640123,
};
static const double refq53[2]{
  0.00000000000000,
  -0.1374076768,
};
static const double refsq53[2]{
  0.00000000000000,
  0.13740767685282,
};
static const double refalpha53[46]{
  32.5364480, 32.0135530, 30.5701660, 26.1371840, 21.4024280, 17.3505230,
  14.1439250, 11.6664030, 9.7557500,  8.2712240,  7.1046010,  6.1759850,
  4.8153900,  3.8867100,  3.2241390,  2.7330620,  2.3571070,  1.7206990,
  1.3260350,  0.8674990,  0.6140980,  0.3141040,  0.1892860,  35.5939760,
  35.0391840, 33.5058920, 28.7725970, 23.6664920, 19.2510560, 15.7268020,
  12.9864250, 10.8631350, 9.2076450,  7.9032670,  6.8629800,  5.3359890,
  4.2925500,  3.5482480,  2.9972560,  2.5762480,  1.8666410,  1.4298640,
  0.9275130,  0.6530570,  0.3316710,  0.1992050,
};
static const double refascale53[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount53[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys53[2]{
  1,
  1,
};
static const int refc53[2]{
  3,
  1,
};

// 54
static const double refcn54[1]{
  0.00000000000000,
};
static const double refq54[1]{
  0.0000000000,
};
static const double refsq54[1]{
  0.00000000000000,
};
static const double refalpha54[23]{
  27.3277050, 27.0110760, 26.1157860, 23.1734500, 19.7140260, 16.4952160,
  13.7782840, 11.5745650, 9.8106950,  8.3998660,  7.2654260,  6.3458240,
  4.9718440,  4.0169210,  3.3286250,  2.8159860,  2.4230090,  1.7595470,
  1.3513270,  0.8819580,  0.6246870,  0.3206970,  0.1938380,
};
static const double refascale54[1]{
  1.00000000000000,
};
static const double refscount54[1]{
  0.00000000000000,
};
static const int refsys54[1]{
  1,
};
static const int refc54[1]{
  3,
};

// 55
static const double refcn55[3]{
  0.00000000000000,
  0.78131762864252,
  13.94000000000000,
};
static const double refq55[3]{
  0.00000000000000,
  0.46524059775602,
  0.492000000000,
};
static const double refsq55[3]{
  0.00000000000000,
  -0.46524059775602,
  -0.49200000000000,
};
static const double refalpha55[69]{
  537.0897540, 251.2031120, 104.6716850, 40.1908390,  24.9381150,  18.3967650,
  14.5779860,  11.9651660,  10.0264350,  8.5234170,   7.3270290,   6.3574360,
  4.8990430,   3.8742590,   3.1301840,   2.5751510,   2.1515440,   1.4501300,
  1.0384390,   0.6036570,   0.3927120,   0.1776630,   0.1006850,   65.7018290,
  59.8918430,  49.3703130,  33.8726930,  25.2509890,  19.8576040,  16.1061580,
  13.3278610,  11.1931740,  9.5136360,   8.1692610,   7.0782580,   5.4392600,
  4.2914390,   3.4609450,   2.8433200,   2.3731020,   1.5968080,   1.1424900,
  0.6636650,   0.4316520,   0.1952610,   0.1106580,   159.0053270, 157.1436212,
  151.9731787, 135.7037659, 117.3153187, 100.2482652, 85.4662885,  73.0126871,
  62.6425221,  54.0415555,  46.9052446,  40.9663710,  31.8279948,  25.2977404,
  20.5185492,  16.9398730,  14.2032476,  9.6642916,   6.9942505,   4.1611863,
  2.7731001,   1.3285730,   0.7903369,
};
static const double refascale55[3]{
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount55[3]{
  0.00000000000000,
  1.00000000000000,
  4.00000000000000,
};
static const int refsys55[3]{
  1,
  1,
  17,
};
static const int refc55[3]{
  3,
  1,
  1,
};

// 56
static const double refcn56[4]{
  0.00000000000000,
  0.78501458609867,
  1.47819220471197,
  14.67700004577637,
};
static const double refq56[4]{
  0.00000000000000,
  0.42198236936188,
  0.63397117832958,
  0.5280000000,
};
static const double refsq56[4]{
  0.00000000000000,
  -0.42198236936188,
  -0.31698558916479,
  -0.52800000000000,
};
static const double refalpha56[92]{
  288.2408830, 220.1240810, 131.4902760, 55.2586600,  31.5893280,  21.6257080,
  16.3339130,  13.0455460,  10.7783530,  9.1050960,   7.8133370,   6.7850620,
  5.2566000,   4.1863800,   3.4065330,   2.8211540,   2.3711900,   1.6174560,
  1.1682080,   0.6862840,   0.4490360,   0.2044320,   0.1161510,   309.5716070,
  175.3545830, 94.6066250,  46.0830780,  30.0147260,  22.0684410,  17.2886740,
  14.0639130,  11.7253160,  9.9472460,   8.5510400,   7.4290820,   5.7511370,
  4.5735640,   3.7161310,   3.0735940,   2.5806020,   1.7570230,   1.2676610,
  0.7440160,   0.4866820,   0.2215860,   0.1259200,   66.9605790,  63.0034800,
  54.8221920,  39.7272000,  29.6372990,  23.0260300,  18.4860590,  15.2106190,
  12.7502140,  10.8439290,  9.3316440,   8.1096160,   6.2753070,   4.9860280,
  4.0475020,   3.3448150,   2.8062400,   1.9080120,   1.3753850,   0.8064740,
  0.5272920,   0.2399460,   0.1363100,   155.5094396, 152.2957198, 143.9110133,
  121.2148688, 100.0521440, 83.2245940,  70.1280996,  60.7626607,  51.5155269,
  44.7636011,  39.1938022,  34.5522205,  27.3444515,  22.1012480,  18.1884416,
  15.2025580,  12.8788334,  8.9266992,   6.5294153,   3.9103194,   2.5946296,
  1.2081345,   0.6957280,
};
static const double refascale56[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  0.25000000000000,
};
static const double refscount56[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  4.00000000000000,
};
static const int refsys56[4]{
  1,
  1,
  1,
  9,
};
static const int refc56[4]{
  3,
  1,
  1,
  1,
};

// 57
static const double refcn57[3]{
  0.00000000000000,
  1.60493415835961,
  2.41715875994685,
};
static const double refq57[3]{
  0.00000000000000,
  0.65599616057853,
  0.830848605303,
};
static const double refsq57[3]{
  0.00000000000000,
  -0.32799808028927,
  -0.27694953510110,
};
static const double refalpha57[69]{
  215.8140220, 176.8449270, 118.3158760, 56.5506640, 33.7025040, 23.2152200,
  17.4335570,  13.8111350,  11.3289880,  9.5173300,  8.1343090,  7.0437020,
  5.4382140,   4.3231050,   3.5139470,   2.9079640,  2.4428210,  1.6648090,
  1.2017740,   0.7056550,   0.4616280,   0.2101180,  0.1193250,  174.1703670,
  109.8104790, 78.4184010,  48.3320410,  33.8987960, 25.4468050, 19.9742230,
  16.1822840,  13.4194490,  11.3279880,  9.6974550,  8.3967050,  6.4683870,
  5.1269150,   4.1557730,   3.4309420,   2.8764740,  1.9535170,  1.4072110,
  0.8245040,   0.5388600,   0.2450480,   0.1391110,  66.6599540, 64.3784460,
  58.7168170,  45.1581050,  34.3061210,  26.6622110, 21.2769290, 17.3778510,
  14.4673110,  12.2338560,  10.4793230,  9.0738430,  6.9849920,  5.5308960,
  4.4789930,   3.6947640,   3.0955470,   2.0997350,  1.5114130,  0.8848790,
  0.5781220,   0.2628230,   0.1491850,
};
static const double refascale57[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount57[3]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys57[3]{
  1,
  1,
  1,
};
static const int refc57[3]{
  3,
  1,
  1,
};

// 58
static const double refcn58[1]{
  2.32446531201143,
};
static const double refq58[1]{
  0.7873339331,
};
static const double refsq58[1]{
  -0.26244464437392,
};
static const double refalpha58[23]{
  63.1803350, 60.8655150, 55.6077000, 42.9730420, 32.8160560, 25.6410650,
  20.5717660, 16.8914020, 14.1378050, 12.0210120, 10.3558470, 9.0204850,
  7.0330480,  5.6466750,  4.6410990,  3.8887730,  3.3113370,  2.3420650,
  1.7576480,  1.1111050,  0.7737220,  0.3918750,  0.2365100,
};
static const double refascale58[1]{
  1.00000000000000,
};
static const double refscount58[1]{
  3.00000000000000,
};
static const int refsys58[1]{
  1,
};
static const int refc58[1]{
  1,
};

// 59
static const double refcn59[2]{
  0.00000000000000,
  2.44976242184767,
};
static const double refq59[2]{
  0.00000000000000,
  0.7825521412,
};
static const double refsq59[2]{
  0.00000000000000,
  -0.26085071373976,
};
static const double refalpha59[46]{
  253.6075830, 185.3478080, 117.3131200, 51.4986990, 29.5194860, 20.1469030,
  15.2121030,  12.1925180,  10.1406100,  8.6417550,  7.4910100,  6.5762820,
  5.2119620,   4.2469660,   3.5345800,   2.9924220,  2.5699090,  1.8461480,
  1.3998220,   0.8963550,   0.6292150,   0.3225380,  0.1960510,  61.2373490,
  58.9335430,  53.9743400,  41.9343430,  32.1281250, 25.1481370, 20.2000000,
  16.6031610,  13.9109010,  11.8406070,  10.2112030, 8.9035100,  6.9541880,
  5.5908190,   4.5991840,   3.8553720,   3.2832050,  2.3202580,  1.7385060,
  1.0952390,   0.7607110,   0.3842190,   0.2318250,
};
static const double refascale59[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount59[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys59[2]{
  1,
  1,
};
static const int refc59[2]{
  3,
  1,
};

// 60
static const double refcn60[2]{
  0.00000000000000,
  2.45621204848065,
};
static const double refq60[2]{
  0.00000000000000,
  0.7860843086,
};
static const double refsq60[2]{
  0.00000000000000,
  -0.26202810288884,
};
static const double refalpha60[46]{
  224.5762180, 179.2684400, 114.5509860, 50.7711900, 29.0959830, 19.8086410,
  14.9251210,  11.9483050,  9.9338740,   8.4673600,  7.3439400,  6.4519280,
  5.1215350,   4.1790220,   3.4814770,   2.9491840,  2.5333290,  1.8187150,
  1.3768350,   0.8783290,   0.6146620,   0.3138300,  0.1905480,  59.8908920,
  57.8663720,  53.0214580,  41.2308960,  31.6026170, 24.7396280, 19.8738380,
  16.3389450,  13.6950980,  11.6632880,  10.0646540, 8.7815920,  6.8677690,
  5.5271730,   4.5502380,   3.8160260,   3.2502340,  2.2958240,  1.7180490,
  1.0790660,   0.7475530,   0.3762800,   0.2268030,
};
static const double refascale60[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount60[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys60[2]{
  1,
  1,
};
static const int refc60[2]{
  3,
  1,
};

// 61
static const double refcn61[2]{
  0.00000000000000,
  2.45653273553474,
};
static const double refq61[2]{
  0.00000000000000,
  0.7912465341,
};
static const double refsq61[2]{
  0.00000000000000,
  -0.26374884470785,
};
static const double refalpha61[46]{
  216.5540280, 174.0685600, 112.0657200, 49.9521540, 28.5964740, 19.4194800,
  14.6027420,  11.6781260,  9.7072940,   8.2773840,  7.1844350,  6.3175570,
  5.0245550,   4.1068450,   3.4257530,   2.9044660,  2.4960780,  1.7917290,
  1.3546830,   0.8610840,   0.6005800,   0.3050960,  0.1848870,  57.9857080,
  56.0520210,  51.4036550,  40.1715870,  30.9043600, 24.2360810, 19.4864830,
  16.0303390,  13.4446280,  11.4577250,  9.8945360,  8.6397290,  6.7667310,
  5.4526280,   4.4930820,   3.7704490,   3.2125050,  2.2688980,  1.6962120,
  1.0622980,   0.7339400,   0.3678790,   0.2213700,
};
static const double refascale61[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount61[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys61[2]{
  1,
  1,
};
static const int refc61[2]{
  3,
  1,
};

// 62
static const double refcn62[2]{
  0.00000000000000,
  2.45472309204146,
};
static const double refq62[2]{
  0.00000000000000,
  0.7897250610,
};
static const double refsq62[2]{
  0.00000000000000,
  -0.26324168703303,
};
static const double refalpha62[46]{
  209.4821630, 169.3264270, 109.7496270, 49.1677750, 28.1221600, 19.0508730,
  14.2954700,  11.4178440,  9.4862320,   8.0895200,  7.0245330,  6.1810260,
  4.9234940,   4.0299890,   3.3654240,   2.8555240,  2.4550980,  1.7622060,
  1.3308620,   0.8430750,   0.5860700,   0.2961160,  0.1790130,  60.4975550,
  56.8914260,  51.7310830,  40.1100700,  30.7211290, 24.0196790, 19.2720050,
  15.8320160,  13.2674100,  11.3021990,  9.7592770,  8.5225050,  6.6783810,
  5.3848030,   4.4395640,   3.7268880,   3.1759310,  2.2423610,  1.6746190,
  1.0457120,   0.7204260,   0.3593990,   0.2157950,
};
static const double refascale62[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount62[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys62[2]{
  1,
  1,
};
static const int refc62[2]{
  3,
  1,
};

// 63
static const double refcn63[2]{
  0.00000000000000,
  1.53272635693059,
};
static const double refq63[2]{
  0.00000000000000,
  0.6532628141,
};
static const double refsq63[2]{
  0.00000000000000,
  -0.32663140707424,
};
static const double refalpha63[46]{
  203.2111900, 165.0774090, 107.6941350, 48.4835280, 27.7173710, 18.7379040,
  14.0329820,  11.1932480,  9.2933470,   7.9237680,  6.8819260,  6.0580060,
  4.8307140,   3.9582910,   3.3084100,   2.8088210,  2.4157350,  1.7336990,
  1.3079430,   0.8259450,   0.5723790,   0.2877150,  0.1735300,  58.3846820,
  55.5074830,  48.9596600,  35.5239180,  26.2422590, 20.2406920, 16.2113610,
  13.3691670,  11.2734740,  9.6705860,   8.4080470,  7.3900200,  5.8559040,
  4.7635490,   3.9543760,   3.3370760,   2.8551160,  2.0281870,  1.5187450,
  0.9491330,   0.6530540,   0.3246600,   0.1946040,
};
static const double refascale63[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount63[2]{
  0.00000000000000,
  2.00000000000000,
};
static const int refsys63[2]{
  1,
  1,
};
static const int refc63[2]{
  3,
  1,
};

// 64
static const double refcn64[2]{
  0.00000000000000,
  2.41754019361739,
};
static const double refq64[2]{
  0.00000000000000,
  0.7899444636,
};
static const double refsq64[2]{
  0.00000000000000,
  -0.26331482122356,
};
static const double refalpha64[46]{
  141.8420640, 116.8571040, 82.4531150, 42.8638860, 26.4230410, 18.5963810,
  14.2465310,  11.5139220,  9.6332520,  8.2500980,  7.1830900,  6.3311290,
  5.0514610,   4.1367300,   3.4541820,  2.9295050,  2.5169890,  1.8023770,
  1.3572570,   0.8545860,   0.5909780,  0.2962180,  0.1784510,  59.9521870,
  57.6299620,  52.3452910,  40.4588930, 30.8901980, 24.0499010, 19.2156040,
  15.7302290,  13.1464310,  11.1770130, 9.6378050,  8.4085080,  6.5823240,
  5.3050770,   4.3727770,   3.6698530,  3.1261280,  2.2035920,  1.6416690,
  1.0191840,   0.6982840,   0.3451090,  0.2062760,
};
static const double refascale64[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount64[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys64[2]{
  1,
  1,
};
static const int refc64[2]{
  3,
  1,
};

// 65
static const double refcn65[2]{
  0.00000000000000,
  2.45190848719608,
};
static const double refq65[2]{
  0.00000000000000,
  0.7946243928,
};
static const double refsq65[2]{
  0.00000000000000,
  -0.26487479761653,
};
static const double refalpha65[46]{
  229.3015960, 148.7572060, 83.8992590, 37.7525280, 23.0411680, 16.4030610,
  12.7361960,  10.4183080,  8.8072510,  7.6095540,  6.6757310,  5.9225500,
  4.7760310,   3.9431820,   3.3133000,  2.8236490,  2.4350780,  1.7540070,
  1.3245690,   0.8351270,   0.5770300,  0.2882710,  0.1732830,  55.7777620,
  53.9540020,  49.4627260,  38.5259830, 29.5462910, 23.1049190, 18.5294200,
  15.2134150,  12.7449150,  10.8576310, 9.3793010,  8.1965330,  6.4356150,
  5.2004630,   4.2962800,   3.6126080,  3.0823350,  2.1790430,  1.6261760,
  1.0110080,   0.6927930,   0.3420770,  0.2042870,
};
static const double refascale65[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount65[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys65[2]{
  1,
  1,
};
static const int refc65[2]{
  3,
  1,
};

// 66
static const double refcn66[2]{
  0.00000000000000,
  2.44535641509585,
};
static const double refq66[2]{
  0.00000000000000,
  0.7951810734,
};
static const double refsq66[2]{
  0.00000000000000,
  -0.26506035780811,
};
static const double refalpha66[46]{
  232.4656730, 135.1836000, 80.1286950, 37.7486970, 23.2434510, 16.5330840,
  12.7969630,  10.4341740,  8.7966470,  7.5842480,  6.6428660,  5.8863450,
  4.7393580,   3.9091410,   3.2824410,  2.7957150,  2.4096230,  1.7330220,
  1.3064720,   0.8207680,   0.5653110,  0.2809900,  0.1685370,  60.4090430,
  55.9872550,  50.3819660,  38.5219880, 29.3573150, 22.8882210, 18.3247830,
  15.0311820,  12.5861420,  10.7203330, 9.2606660,  8.0937380,  6.3571910,
  5.1389330,   4.2464670,   3.5710020,  3.0465710,  2.1519680,  1.6036830,
  0.9935670,   0.6786190,   0.3332680,  0.1985350,
};
static const double refascale66[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount66[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys66[2]{
  1,
  1,
};
static const int refc66[2]{
  3,
  1,
};

// 67
static const double refcn67[2]{
  0.00000000000000,
  2.47312888776754,
};
static const double refq67[2]{
  0.00000000000000,
  0.8093048024,
};
static const double refsq67[2]{
  0.00000000000000,
  -0.26976826747468,
};
static const double refalpha67[46]{
  174.3579710, 145.3475730, 98.3386140, 45.6653390, 26.1535730, 17.5697070,
  13.0686310,  10.3734350,  8.5909150,  7.3206360,  6.3633450,  5.6111750,
  4.4954000,   3.7014620,   3.1066380,  2.6458480,  2.2803750,  1.6387150,
  1.2329370,   0.7701030,   0.5271880,  0.2591200,  0.1545480,  52.4790850,
  50.9455980,  47.0541390,  37.1641820, 28.6862320, 22.4764090, 18.0300540,
  14.8000680,  12.3955370,  10.5586820, 9.1212810,  7.9722170,  6.2625620,
  5.0632080,   4.1843110,   3.5187310,  3.0016100,  2.1184470,  1.5764470,
  0.9730470,   0.6620460,   0.3227820,  0.1915480,
};
static const double refascale67[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount67[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys67[2]{
  1,
  1,
};
static const int refc67[2]{
  3,
  1,
};

// 68
static const double refcn68[2]{
  0.00000000000000,
  2.48043640078965,
};
static const double refq68[2]{
  0.00000000000000,
  0.8130673035,
};
static const double refsq68[2]{
  0.00000000000000,
  -0.27102243451532,
};
static const double refalpha68[46]{
  169.5086700, 141.8311300, 96.4854630, 44.9898390, 25.7372660, 17.2457070,
  12.7960440,  10.1383860,  8.3867110,  7.1428030,  6.2082610,  5.4756830,
  4.3910800,   3.6198210,   3.0414510,  2.5926580,  2.2360160,  1.6079710,
  1.2093860,   0.7535860,   0.5142640,  0.2510880,  0.1491740,  50.9243700,
  49.4869020,  45.8178160,  36.3744420, 28.1606380, 22.0904510, 17.7252050,
  14.5487700,  12.1834110,  10.3771780, 8.9646510,  7.8362150,  6.1584380,
  4.9818960,   4.1194840,   3.4659310,  2.9576820,  2.0882320,  1.5534830,
  0.9571210,   0.6496440,   0.3150810,  0.1863840,
};
static const double refascale68[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount68[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys68[2]{
  1,
  1,
};
static const int refc68[2]{
  3,
  1,
};

// 69
static const double refcn69[2]{
  0.00000000000000,
  2.48120800603580,
};
static const double refq69[2]{
  0.00000000000000,
  0.8140837048,
};
static const double refsq69[2]{
  0.00000000000000,
  -0.27136123496666,
};
static const double refalpha69[46]{
  164.8744790, 138.5034170, 94.7797640, 44.4385580, 25.4312120, 17.0158970,
  12.6028120,  9.9697610,   8.2378580,  7.0109450,  6.0912830,  5.3717500,
  4.3084370,   3.5531670,   2.9867270,  2.5468500,  2.1969270,  1.5796200,
  1.1870370,   0.7375970,   0.5018220,  0.2436440,  0.1443670,  50.9258390,
  49.3627740,  45.6624910,  36.1857370, 27.9704110, 21.9122080, 17.5625150,
  14.4018520,  12.0514680,  10.2590760, 8.8591280,  7.7419770,  6.0830330,
  4.9209200,   4.0693970,   3.4240270,  2.9219510,  2.0623180,  1.5329870,
  0.9422880,   0.6379740,   0.3079830,  0.1817680,
};
static const double refascale69[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount69[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys69[2]{
  1,
  1,
};
static const int refc69[2]{
  3,
  1,
};

// 70
static const double refcn70[2]{
  0.00000000000000,
  2.41884356027485,
};
static const double refq70[2]{
  0.00000000000000,
  0.7841584373,
};
static const double refsq70[2]{
  0.00000000000000,
  -0.26138614578463,
};
static const double refalpha70[46]{
  163.7379070, 137.4016000, 93.8094750, 43.7828040, 24.9508110, 16.6301360,
  12.2781120,  9.6905770,   7.9955170,  6.7996180,  5.9064770,  5.2097330,
  4.1828480,   3.4544290,   2.9077830,  2.4825740,  2.1436170,  1.5435770,
  1.1603320,   0.7200560,   0.4887560,  0.2360610,  0.1394570,  54.1811670,
  52.3584220,  48.1909980,  37.7829980, 28.8680310, 22.3694590, 17.7640250,
  14.4601420,  12.0316690,  10.1983910, 8.7787560,  7.6539450,  5.9967880,
  4.8445850,   4.0040030,   3.3683890,  2.8743980,  2.0286710,  1.5073600,
  0.9248310,   0.6246590,   0.3000110,  0.1765320,
};
static const double refascale70[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount70[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys70[2]{
  1,
  1,
};
static const int refc70[2]{
  3,
  1,
};

// 71
static const double refcn71[2]{
  0.00000000000000,
  2.48673110207243,
};
static const double refq71[2]{
  0.00000000000000,
  0.8226318727,
};
static const double refsq71[2]{
  0.00000000000000,
  -0.27421062424350,
};
static const double refalpha71[46]{
  136.8530670, 104.2975620, 76.5562240, 40.2834860, 24.1515190, 16.4764390,
  12.3100420,  9.7790490,   8.0987470,  6.9030530,  6.0050390,  5.3018750,
  4.2621270,   3.5227910,   2.9673480,  2.5350740,  2.1903720,  1.5797660,
  1.1891950,   0.7393030,   0.5021560,  0.2423920,  0.1430370,  48.9452970,
  47.6317230,  44.2461460,  35.3576300, 27.4507560, 21.5311680, 17.2508500,
  14.1326890,  11.8136070,  10.0470280, 8.6694960,  7.5721550,  5.9462740,
  4.8097520,   3.9777670,   3.3472210,  2.8563980,  2.0147310,  1.4952460,
  0.9145890,   0.6157550,   0.2938290,  0.1722380,
};
static const double refascale71[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount71[2]{
  0.00000000000000,
  3.00000000000000,
};
static const int refsys71[2]{
  1,
  1,
};
static const int refc71[2]{
  3,
  1,
};

// 72
static const double refcn72[4]{
  0.00000000000000,
  1.64596625526870,
  3.32095096313483,
  4.62300000000000,
};
static const double refq72[4]{
  0.00000000000000,
  0.44266476936835,
  0.68407375970491,
  0.9430000000,
};
static const double refsq72[4]{
  0.00000000000000,
  -0.22133238468418,
  -0.17101843992623,
  -0.23575000000000,
};
static const double refalpha72[92]{
  106.2816210, 95.4891650, 75.3034870, 44.1393100, 28.1355730, 19.6843670,
  14.7522820,  11.6120870, 9.4717210,  7.9330520,  6.7792700,  5.8843260,
  4.5893730,   3.6999000,  3.0536720,  2.5653680,  2.1856620,  1.5348190,
  1.1334250,   0.6859220,  0.4568140,  0.2123490,  0.1215650,  82.4536570,
  70.5184470,  56.7403060, 38.8993780, 28.3733700, 21.5865770, 16.9965970,
  13.7660430,  11.4103040, 9.6381650,  8.2684630,  7.1847890,  5.5917520,
  4.4881220,   3.6863220,  3.0827340,  2.6157700,  1.8222580,  1.3383190,
  0.8045950,   0.5339520,  0.2472490,  0.1413400,  50.2657100, 49.2005530,
  46.3604080,  38.3345580, 30.5672240, 24.3724470, 19.6879820, 16.1687550,
  13.4975460,  11.4368740, 9.8188790,  8.5264490,  6.6139230,  5.2863370,
  4.3241350,   3.6027470,  3.0471630,  2.1096360,  1.5428050,  0.9227930,
  0.6106910,   0.2819190,  0.1609740,  32.7095574, 32.4889582, 31.8527540,
  29.6320422,  26.7617762, 23.8245539, 21.1219459, 18.7537050, 16.7198153,
  14.9828615,  13.4971673, 12.2201143, 10.1536814, 8.5678059,  7.3223689,
  6.3253685,   5.5145527,  4.0455469,  3.0833508,  1.9496957,  1.3382618,
  0.6527061,   0.3847355,
};
static const double refascale72[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount72[4]{
  0.00000000000000,
  2.00000000000000,
  4.00000000000000,
  4.00000000000000,
};
static const int refsys72[4]{
  1,
  1,
  1,
  11,
};
static const int refc72[4]{
  3,
  1,
  1,
  1,
};

// 73
static const double refcn73[4]{
  0.00000000000000,
  1.71671961147963,
  2.55699041057149,
  3.96300000000000,
};
static const double refq73[4]{
  0.00000000000000,
  0.23523422154086,
  0.30980440015125,
  1.0930000000,
};
static const double refsq73[4]{
  0.00000000000000,
  -0.11761711077043,
  -0.10326813338375,
  -0.21860000000000,
};
static const double refalpha73[92]{
  88.9256120, 81.9318660, 67.3277280, 41.9543150, 27.7130410, 19.8298060,
  15.0833980, 11.9897820, 9.8427490,  8.2781960,  7.0935190,  6.1684980,
  4.8227300,  3.8952850,  3.2207380,  2.7107210,  2.3138110,  1.6320700,
  1.2099340,  0.7365720,  0.4925290,  0.2302270,  0.1321400,  69.3801270,
  62.6525490, 52.3321990, 37.2824880, 27.8804010, 21.6007000, 17.2276620,
  14.0778720, 11.7401200, 9.9582810,  8.5679630,  7.4606290,  5.8231300,
  4.6837700,  3.8543220,  3.2291230,  2.7448770,  1.9201830,  1.4153120,
  0.8555430,  0.5698730,  0.2652310,  0.1519760,  53.1343510, 50.1385310,
  45.3135370, 36.1734470, 28.5997780, 22.7928480, 18.4525250, 15.2001580,
  12.7291810, 10.8187030, 9.3147510,  8.1103590,  6.3220940,  5.0755740,
  4.1686360,  3.4861320,  2.9585540,  2.0630420,  1.5171890,  0.9145820,
  0.6082630,  0.2826130,  0.1618310,  38.0167314, 37.7505450, 36.9868016,
  34.3581519, 31.0182858, 27.6354658, 24.5337826, 21.8145582, 19.4741943,
  17.4704983, 15.7528316, 14.2738200, 11.8766483, 10.0346794, 8.5871211,
  7.4275650,  6.4837949,  4.7709367,  3.6456491,  2.3144054,  1.5929899,
  0.7800977,  0.4607918,
};
static const double refascale73[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount73[4]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  5.00000000000000,
};
static const int refsys73[4]{
  1,
  1,
  1,
  11,
};
static const int refc73[4]{
  3,
  1,
  1,
  1,
};

// 74
static const double refcn74[3]{
  0.00000000000000,
  1.84852525804219,
  10.44998431099169,
};
static const double refq74[3]{
  0.00000000000000,
  0.31319918056428,
  0.230207052908,
};
static const double refsq74[3]{
  0.00000000000000,
  -0.15659959028214,
  -0.01918392107569,
};
static const double refalpha74[69]{
  72.6835210, 66.5725390, 54.5218660, 35.1042250, 24.3743050, 18.1885020,
  14.2758210, 11.6114380, 9.6940500,  8.2552810,  7.1400870,  6.2531290,
  4.9373670,  4.0140520,  3.3348740,  2.8174560,  2.4125540,  1.7123560,
  1.2753760,  0.7814210,  0.5246740,  0.2466040,  0.1418950,  57.9535230,
  54.3254100, 47.3716060, 35.2077750, 26.9133880, 21.1900880, 17.1120840,
  14.1184440, 11.8610010, 10.1176970, 8.7429580,  7.6387710,  5.9912880,
  4.8355390,  3.9899060,  3.3503580,  2.8537360,  2.0050600,  1.4831160,
  0.9012110,  0.6023820,  0.2816950,  0.1617650,  69.9811980, 68.7138070,
  65.3381200, 55.7596720, 46.2137800, 38.1741940, 31.7064340, 26.5625450,
  22.4690330, 19.1923040, 16.5475190, 14.3927290, 11.1480040, 8.8712130,
  7.2191730,  5.9850930,  5.0399870,  3.4609450,  2.5183910,  1.4990770,
  0.9903650,  0.4569140,  0.2609890,
};
static const double refascale74[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount74[3]{
  0.00000000000000,
  2.00000000000000,
  12.00000000000000,
};
static const int refsys74[3]{
  1,
  1,
  1,
};
static const int refc74[3]{
  3,
  1,
  1,
};

// 75
static const double refcn75[3]{
  0.00000000000000,
  1.69673556648333,
  9.19053013143453,
};
static const double refq75[3]{
  0.00000000000000,
  0.10191716059118,
  -0.034513036233,
};
static const double refsq75[3]{
  0.00000000000000,
  -0.05095858029559,
  0.00313754874849,
};
static const double refalpha75[69]{
  70.9067150, 65.7037140, 55.2189840, 36.8309030, 25.6365300, 19.0080410,
  14.8342930, 12.0225100, 10.0181560, 8.5243540,  7.3716210,  6.4572650,
  5.1034730,  4.1544350,  3.4564620,  2.9246120,  2.5081950,  1.7869670,
  1.3354090,  0.8224190,  0.5541320,  0.2617050,  0.1509270,  63.2047780,
  58.0228720, 48.8925050, 34.6221050, 25.8457800, 20.1387260, 16.1920480,
  13.3396770, 11.2072140, 9.5682700,  8.2790220,  7.2445840,  5.7011200,
  4.6167910,  3.8216470,  3.2187300,  2.7492670,  1.9432630,  1.4442130,
  0.8833880,  0.5929380,  0.2787900,  0.1604910,  61.9391170, 61.0033150,
  58.4522600, 50.8001250, 42.6897350, 35.5953060, 29.7653350, 25.0690300,
  21.2990290, 18.2612110, 15.7959520, 13.7781660, 10.7227960, 8.5655510,
  6.9926320,  5.8130460,  4.9067170,  3.3857530,  2.4728560,  1.4797000,
  0.9808630,  0.4545450,  0.2601570,
};
static const double refascale75[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount75[3]{
  0.00000000000000,
  2.00000000000000,
  11.00000000000000,
};
static const int refsys75[3]{
  1,
  1,
  1,
};
static const int refc75[3]{
  3,
  1,
  1,
};

// 76
static const double refcn76[3]{
  0.00000000000000,
  1.85014246784508,
  8.97974115543403,
};
static const double refq76[3]{
  0.00000000000000,
  0.19864391765550,
  -0.064740208571,
};
static const double refsq76[3]{
  0.00000000000000,
  -0.09932195882775,
  0.00647402085719,
};
static const double refalpha76[69]{
  59.6083520, 56.2806020, 48.8648650, 34.1600550, 24.4374970, 18.4318460,
  14.5524170, 11.8947470, 9.9775490,  8.5355150,  7.4142660,  6.5190680,
  5.1830340,  4.2381040,  3.5384920,  3.0026950,  2.5815390,  1.8484760,
  1.3867840,  0.8588690,  0.5808420,  0.2757360,  0.1594300,  46.6731420,
  44.2599930, 40.9119690, 32.7985670, 25.8416100, 20.6679230, 16.8773970,
  14.0534960, 11.9009790, 10.2230790, 8.8884890,  7.8079950,  6.1792880,
  5.0231940,  4.1694910,  3.5191180,  3.0110530,  2.1356650,  1.5915890,
  0.9776240,  0.6581110,  0.3107410,  0.1792660,  55.8892400, 55.1763930,
  53.1894280, 46.9039320, 39.8479720, 33.4618590, 28.1191240, 23.7725720,
  20.2616430, 17.4199010, 15.1054600, 13.2052620, 10.3167870, 8.2680590,
  6.7685540,  5.6403850,  4.7711490,  3.3068100,  2.4236090,  1.4575360,
  0.9693850,  0.4512540,  0.2588140,
};
static const double refascale76[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount76[3]{
  0.00000000000000,
  2.00000000000000,
  10.00000000000000,
};
static const int refsys76[3]{
  1,
  1,
  1,
};
static const int refc76[3]{
  3,
  1,
  1,
};

// 77
static const double refcn77[5]{
  0.00000000000000,
  1.82924504495576,
  2.88910972828218,
  3.78801363268039,
  4.66121308138933,
};
static const double refq77[5]{
  0.00000000000000,
  -0.01399684403519,
  -0.04786532465344,
  -0.07756443085155,
  -0.1204273319,
};
static const double refsq77[5]{
  0.00000000000000,
  0.00699842201760,
  0.01595510821781,
  0.01939110771289,
  0.02408546639218,
};
static const double refalpha77[115]{
  51.5493740, 49.2234270, 43.7106450, 31.7225470, 23.2089290, 17.7566590,
  14.1614650, 11.6653050, 9.8468960,  8.4684340,  7.3894730,  6.5229570,
  5.2199510,  4.2901010,  3.5965860,  3.0623010,  2.6403160,  1.9013040,
  1.4325800,  0.8926780,  0.6061140,  0.2892620,  0.1676580,  42.7200080,
  41.3931980, 38.3655160, 31.0080660, 24.6653650, 19.9066380, 16.3877970,
  13.7425380, 11.7090270, 10.1115020, 8.8318110,  7.7890930,  6.2044270,
  5.0689240,  4.2241180,  3.5767130,  3.0685910,  2.1879850,  1.6370730,
  1.0112500,  0.6832680,  0.3242250,  0.1874750,  40.1998410, 39.0125180,
  36.3126410, 30.1829760, 24.8286850, 20.5587890, 17.2259500, 14.6163560,
  12.5495230, 10.8901200, 9.5396530,  8.4265790,  6.7165300,  5.4810030,
  4.5587850,  3.8517520,  3.2974500,  2.3400930,  1.7446250,  1.0727640,
  0.7229650,  0.3420560,  0.1975510,  43.2638615, 41.8727089, 38.9775692,
  32.5354682, 26.8687902, 22.3369089, 18.7845502, 15.9853930, 13.7519014,
  11.9455547, 10.4662014, 9.2409010,  7.3500768,  5.9807691,  4.9594258,
  4.1782069,  3.5675888,  2.5185219,  1.8706839,  1.1451485,  0.7699740,
  0.3635000,  0.2098079,  49.3567100, 48.1701200, 45.3609500, 38.0546700,
  31.0840500, 25.4572400, 21.1008600, 17.7296600, 15.0901300, 12.9932400,
  11.3032400, 9.9227200,  7.8265900,  6.3334100,  5.2320700,  4.3961000,
  3.7462100,  2.6360300,  1.9540400,  1.1932200,  0.8010500,  0.3773100,
  0.2175100,
};
static const double refascale77[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount77[5]{
  0.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
};
static const int refsys77[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc77[5]{
  3,
  1,
  1,
  1,
  1,
};

// 78
static const double refcn78[3]{
  0.00000000000000,
  1.86072268763509,
  6.46855936294889,
};
static const double refq78[3]{
  0.00000000000000,
  0.00248540621951,
  0.101118882988,
};
static const double refsq78[3]{
  0.00000000000000,
  -0.00124270310976,
  -0.01263986037358,
};
static const double refalpha78[69]{
  41.1424820, 39.3180510, 35.0148090, 25.8710280, 19.5216660, 15.4256100,
  12.6507620, 10.6590770, 9.1609870,  7.9929620,  7.0565850,  6.2892190,
  5.1074490,  4.2422610,  3.5845540,  3.0705210,  2.6600560,  1.9319420,
  1.4641410,  0.9193200,  0.6271910,  0.3012380,  0.1751400,  40.5572290,
  39.3599010, 36.5944450, 29.7359090, 23.7699580, 19.2758940, 15.9444510,
  13.4329020, 11.4953860, 9.9672740,  8.7381500,  7.7325090,  6.1953270,
  5.0856920,  4.2547590,  3.6144440,  3.1095350,  2.2291660,  1.6746000,
  1.0403320,  0.7055790,  0.3365800,  0.1951260,  54.9491410, 53.9578470,
  51.3088730, 43.7409950, 36.2053630, 29.9365010, 24.9624590, 21.0441630,
  17.9395030, 15.4543750, 13.4423040, 11.7944940, 9.2888530,  7.5040460,
  6.1891800,  5.1927300,  4.4193840,  3.1019380,  2.2955520,  1.3992410,
  0.9386560,  0.4419430,  0.2547950,
};
static const double refascale78[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount78[3]{
  0.00000000000000,
  2.00000000000000,
  8.00000000000000,
};
static const int refsys78[3]{
  1,
  1,
  1,
};
static const int refc78[3]{
  3,
  1,
  1,
};

// 79
static const double refcn79[2]{
  0.00000000000000,
  0.91830179564855,
};
static const double refq79[2]{
  0.00000000000000,
  0.0256095212,
};
static const double refsq79[2]{
  0.00000000000000,
  -0.02560952126341,
};
static const double refalpha79[46]{
  37.7290460, 36.1091840, 32.2722340, 24.0716250, 18.3385860, 14.6143630,
  12.0774260, 10.2474000, 8.8635320,  7.7783310,  6.9031680,  6.1817050,
  5.0613040,  4.2321700,  3.5957550,  3.0941580,  2.6907340,  1.9683670,
  1.4994510,  0.9481020,  0.6497440,  0.3139430,  0.1830170,  36.6153320,
  35.4187520, 32.5691470, 25.9574740, 20.5780280, 16.6720520, 13.8374270,
  11.7244450, 10.1016410, 8.8215770,  7.7887820,  6.9395760,  5.6295900,
  4.6707850,  3.9429090,  3.3749190,  2.9220340,  2.1203720,  1.6065850,
  1.0093190,  0.6892520,  0.3316860,  0.1930410,
};
static const double refascale79[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount79[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys79[2]{
  1,
  1,
};
static const int refc79[2]{
  3,
  1,
};

// 80
static const double refcn80[2]{
  0.00000000000000,
  1.89515764632510,
};
static const double refq80[2]{
  0.00000000000000,
  0.1199114691,
};
static const double refsq80[2]{
  0.00000000000000,
  -0.05995573459960,
};
static const double refalpha80[46]{
  37.1668150, 35.9903170, 32.9876470, 25.5237630, 19.5407590, 15.4358360,
  12.6124980, 10.5949600, 9.0927810,  7.9334090,  7.0116660,  6.2609290,
  5.1108470,  4.2707020,  3.6306640,  3.1280940,  2.7244100,  2.0009140,
  1.5295470,  0.9722000,  0.6686340,  0.3246570,  0.1896630,  35.5596890,
  34.9453750, 33.2600440, 28.2046230, 23.0451020, 18.8299000, 15.6024300,
  13.1484490, 11.2575930, 9.7724990,  8.5831260,  7.6133220,  6.1348920,
  5.0678290,  4.2663670,  3.6457370,  3.1535120,  2.2866750,  1.7331020,
  1.0902810,  0.7455680,  0.3596280,  0.2095320,
};
static const double refascale80[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount80[2]{
  0.00000000000000,
  2.00000000000000,
};
static const int refsys80[2]{
  1,
  1,
};
static const int refc80[2]{
  3,
  1,
};

// 81
static const double refcn81[4]{
  0.00000000000000,
  0.83218042800594,
  1.73451304607259,
  2.64455909521743,
};
static const double refq81[4]{
  0.00000000000000,
  0.05732791283824,
  0.10187349213041,
  0.1401232564,
};
static const double refsq81[4]{
  0.00000000000000,
  -0.05732791283824,
  -0.05093674606521,
  -0.04670775213539,
};
static const double refalpha81[92]{
  75.4787320, 66.9797680, 52.7293310, 33.2800020, 23.1647510, 17.3598020,
  13.7123950, 11.2540670, 9.5015210,  8.1942640,  7.1828260,  6.3767320,
  5.1706100,  4.3089140,  3.6612600,  3.1566110,  2.7528300,  2.0300880,
  1.5579660,  0.9964200,  0.6883510,  0.3365720,  0.1974540,  73.7909520,
  67.2077030, 55.1633950, 36.6818870, 26.1091350, 19.7299200, 15.6034900,
  12.7753400, 10.7414800, 9.2191530,  8.0412980,  7.1046070,  5.7107080,
  4.7240350,  3.9895440,  3.4223730,  2.9722160,  2.1752900,  1.6611010,
  1.0561290,  0.7272340,  0.3542350,  0.2074800,  51.2159910, 49.0618590,
  44.5281440, 34.5954290, 26.6152220, 20.8897950, 16.8343740, 13.9090070,
  11.7406120, 10.0876440, 8.7945760,  7.7596980,  6.2135910,  5.1188320,
  4.3061810,  3.6812160,  3.1873790,  2.3191740,  1.7638260,  1.1158640,
  0.7661990,  0.3719620,  0.2175450,  44.4232940, 43.5695950, 41.2468990,
  34.4223640, 27.6300950, 22.1919640, 18.1026400, 15.0481770, 12.7356250,
  10.9495660, 9.5411710,  8.4086990,  6.7118360,  5.5101390,  4.6201450,
  3.9379650,  3.4008700,  2.4620390,  1.8658870,  1.1752790,  0.8049870,
  0.3896270,  0.2275810,
};
static const double refascale81[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount81[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys81[4]{
  1,
  1,
  1,
  1,
};
static const int refc81[4]{
  3,
  1,
  1,
  1,
};

// 82
static const double refcn82[5]{
  0.00000000000000,
  0.90267202371440,
  1.86326667138745,
  2.79951773292937,
  3.76444392234350,
};
static const double refq82[5]{
  0.00000000000000,
  0.11449566751294,
  0.16758459323190,
  0.18265663815354,
  0.1782566271,
};
static const double refsq82[5]{
  0.00000000000000,
  -0.11449566751294,
  -0.08379229661595,
  -0.06088554605118,
  -0.04456415679904,
};
static const double refalpha82[115]{
  63.2905510, 59.5286430, 51.2607860, 35.4025850, 25.1394190, 18.7947900,
  14.7040930, 11.9322080, 9.9660590,  8.5145470,  7.4056250,  6.5334430,
  5.2518040,  4.3552580,  3.6919830,  3.1808980,  2.7750050,  2.0530120,
  1.5823440,  1.0201520,  0.7090500,  0.3497720,  0.2060120,  57.4725650,
  54.8466790, 48.8575900, 36.1749940, 26.8405620, 20.5425950, 16.2594910,
  13.2605030, 11.0893760, 9.4661890,  8.2168000,  7.2301920,  5.7780700,
  4.7643580,  4.0179560,  3.4461300,  2.9946910,  2.1989640,  1.6860470,
  1.0800310,  0.7479170,  0.3673300,  0.2159550,  53.0414450, 51.0751360,
  46.8366890, 36.7990540, 28.3107680, 22.1045460, 17.6826350, 14.4967630,
  12.1481600, 10.3717920, 8.9944640,  7.9020540,  6.2898170,  5.1644070,
  4.3379580,  3.7072310,  3.2113990,  2.3434100,  1.7888720,  1.1395320,
  0.7865880,  0.3848350,  0.2258800,  53.1115280, 51.7198390, 48.1733620,
  38.8959490, 30.4802980, 24.0395110, 19.3203190, 15.8625500, 13.2876830,
  11.3287250, 9.8050600,  8.5950040,  6.8096590,  5.5666540,  4.6574470,
  3.9666200,  3.4259370,  2.4857500,  1.8900620,  1.1981450,  0.8247670,
  0.4021920,  0.2357430,  50.0879780, 49.2042630, 46.7719060, 39.3982430,
  31.7542100, 25.4539200, 20.6426050, 17.0297710, 14.2980180, 12.1992850,
  10.5566110, 9.2468670,  7.3088260,  5.9581810,  4.9713460,  4.2231630,
  3.6391300,  2.6281690,  1.9916070,  1.2570530,  0.8631290,  0.4196110,
  0.2456340,
};
static const double refascale82[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount82[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys82[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc82[5]{
  3,
  1,
  1,
  1,
  1,
};

// 83
static const double refcn83[4]{
  0.00000000000000,
  0.93840398774753,
  1.87829610127455,
  2.81907131341312,
};
static const double refq83[4]{
  0.00000000000000,
  0.04276095694715,
  0.06545183973370,
  0.0766288646,
};
static const double refsq83[4]{
  0.00000000000000,
  -0.04276095694715,
  -0.03272591986685,
  -0.02554295489333,
};
static const double refalpha83[92]{
  51.1916750, 49.4069930, 44.9458450, 34.1505430, 25.5045870, 19.5073500,
  15.3898030, 12.4998210, 10.4110930, 8.8561170,  7.6660440,  6.7322080,
  5.3700990,  4.4292980,  3.7418080,  3.2175040,  2.8044220,  2.0757420,
  1.6033620,  1.0390450,  0.7253430,  0.3603050,  0.2129720,  51.6147800,
  50.0629560, 46.1204110, 36.1339090, 27.6118910, 21.4077340, 17.0101490,
  13.8592580, 11.5510200, 9.8174290,  8.4832410,  7.4329030,  5.8982610,
  4.8394220,  4.0683880,  3.4831190,  3.0243540,  2.2217570,  1.7070420,
  1.0988490,  0.7641350,  0.3778150,  0.2228850,  51.7479250, 50.4406230,
  47.0464190, 37.9441110, 29.6097990, 23.2406220, 18.5881070, 15.1912320,
  12.6725630, 10.7660510, 9.2914280,  8.1270340,  6.4226970,  5.2472620,
  4.3934730,  3.7477030,  3.2435420,  2.3673900,  1.8104910,  1.1585430,
  0.8028630,  0.3953020,  0.2327880,  51.5178550, 50.4932930, 47.7156380,
  39.5948620, 31.5084490, 25.0123180, 20.1276560, 16.4983230, 13.7774350,
  11.7031450, 10.0914150, 8.8151820,  6.9437270,  5.6530110,  4.7171930,
  4.0113480,  3.4620540,  2.5126730,  1.9137260,  1.2181320,  0.8415320,
  0.4127710,  0.2426840,
};
static const double refascale83[4]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount83[4]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
};
static const int refsys83[4]{
  1,
  1,
  1,
  1,
};
static const int refc83[4]{
  3,
  1,
  1,
  1,
};

// 84
static const double refcn84[3]{
  0.00000000000000,
  0.93512916979697,
  1.87110482058901,
};
static const double refq84[3]{
  0.00000000000000,
  -0.04479748091835,
  -0.022019956697,
};
static const double refsq84[3]{
  0.00000000000000,
  0.04479748091835,
  0.01100997834863,
};
static const double refalpha84[69]{
  45.7354800, 44.5177550, 41.3554830, 32.9793560, 25.5092680, 19.9242900,
  15.8977680, 12.9790260, 10.8242560, 9.1984520,  7.9445240,  6.9570500,
  5.5167450,  4.5271540,  3.8097850,  3.2672340,  2.8429600,  2.1014180,
  1.6245240,  1.0563850,  0.7399150,  0.3695680,  0.2190670,  47.9831520,
  46.8085170, 43.7444240, 35.4613210, 27.8088110, 21.9082420, 17.5604940,
  14.3629380, 11.9797160, 10.1702660, 8.7691240,  7.6631150,  6.0479100,
  4.9390680,  4.1374920,  3.5335950,  3.0634060,  2.2476620,  1.7283170,
  1.1162240,  0.7787240,  0.3870890,  0.2289900,  49.9757880, 48.8536140,
  45.9097740, 37.7785020, 29.9993350, 23.8231110, 19.1794330, 15.7185060,
  13.1162960, 11.1291240, 9.5845740,  8.3625420,  6.5753180,  5.3486700,
  4.4636720,  3.7988870,  3.2830670,  2.3934820,  1.8318420,  1.1759270,
  0.8174500,  0.4045760,  0.2388960,
};
static const double refascale84[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount84[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys84[3]{
  1,
  1,
  1,
};
static const int refc84[3]{
  3,
  1,
  1,
};

// 85
static const double refcn85[2]{
  +0.00000000000000,
  +0.97711087656722,
};
static const double refq85[2]{
  +0.00000000000000,
  -0.07596582020000,
};
static const double refsq85[2]{
  +0.00000000000000,
  +0.07596582020292,
};
static const double refalpha85[46]{
  39.1638670, 38.4250150, 36.4213580, 30.5411780, 24.6134160, 19.7657890,
  16.0524090, 13.2471470, 11.1156700, 9.4745710,  8.1909470,  7.1705270,
  5.6711490,  4.6378720,  3.8904420,  3.3277200,  2.8899970,  2.1310810,
  1.6471780,  1.0734420,  0.7539160,  0.3784910,  0.2250150,  42.3026280,
  41.5366110, 39.4596880, 33.3254640, 27.0380510, 21.8068890, 17.7463530,
  14.6509070, 12.2850030, 10.4566080, 9.0232990,  7.8825660,  6.2059600,
  5.0520660,  4.2196050,  3.5950280,  3.1110670,  2.2775460,  1.7510350,
  1.1332590,  0.7926970,  0.3959980,  0.2349320,
};
static const double refascale85[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount85[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys85[2]{
  1,
  1,
};
static const int refc85[2]{
  3,
  1,
};

// 86
static const double refcn86[1]{
  +0.00000000000000,
};
static const double refq86[1]{
  +0.00000000000000,
};
static const double refsq86[1]{
  +0.00000000000000,
};
static const double refalpha86[23]{
  33.6514050, 33.1852420, 31.8852830, 27.7786920, 23.2154680, 19.1736050,
  15.8877090, 13.2945880, 11.2595530, 9.6544200,  8.3760900,  7.3462510,
  5.8137240,  4.7476360,  3.9742240,  3.3924070,  2.9410550,  2.1630540,
  1.6707900,  1.0904110,  0.7676850,  0.3873300,  0.2309680,
};
static const double refascale86[1]{
  1.00000000000000,
};
static const double refscount86[1]{
  0.00000000000000,
};
static const int refsys86[1]{
  1,
};
static const int refc86[1]{
  3,
};

// 87
static const double refcn87[2]{
  +0.00000000000000,
  +0.76514673233032,
};
static const double refq87[2]{
  +0.00000000000000,
  +0.07920000000000,
};
static const double refsq87[2]{
  +0.00000000000000,
  -0.07920000000000,
};
static const double refalpha87[46]{
  432.7147900, 233.5579300, 107.0182700, 44.0853000, 28.1033000, 20.9345200,
  16.6243700,  13.6315900,  11.3991600,  9.6677100,  8.2919500,  7.1799800,
  5.5146000,   4.3508500,   3.5097800,   2.8846600,  2.4088600,  1.6232600,
  1.1631100,   0.6772800,   0.4412400,   0.1999500,  0.1133100,  71.7862700,
  65.5632800,  54.1920400,  37.3256900,  27.8786200, 21.9222000, 17.7602400,
  14.6759000,  12.3098200,  10.4527500,  8.9700500,  7.7695700,  5.9709800,
  4.7146000,   3.8067300,   3.1317800,   2.6177400,  1.7677400,  1.2686700,
  0.7402500,   0.4828000,   0.2190400,   0.1241800,
};
static const double refascale87[2]{
  1.00000000000000,
  1.00000000000000,
};
static const double refscount87[2]{
  0.00000000000000,
  1.00000000000000,
};
static const int refsys87[2]{
  1,
  1,
};
static const int refc87[2]{
  3,
  1,
};

// 88
static const double refcn88[3]{
  +0.00000000000000,
  +0.77520757913589,
  +1.54451191425323,
};
static const double refq88[3]{
  +0.00000000000000,
  +0.23880000000000,
  +0.30820000000000,
};
static const double refsq88[3]{
  +0.00000000000000,
  -0.23880000000000,
  -0.15410000000000,
};
static const double refalpha88[69]{
  264.1946900, 208.7128200, 131.0867200, 58.5103700, 34.5223400, 24.0579200,
  18.3378700,  14.7007500,  12.1522900,  10.2528100, 8.7789200,  7.6034500,
  5.8576000,   4.6401400,   3.7578800,   3.0994100,  2.5960600,  1.7595800,
  1.2657400,   0.7404100,   0.4834900,   0.2196400,  0.1246000,  265.1396600,
  169.9509800, 98.1252400,  49.9054300,  32.9673500, 24.3765600, 19.1292900,
  15.5551100,  12.9496000,  10.9644700,  9.4055800,  8.1543000,  6.2879300,
  4.9836600,   4.0379200,   3.3319000,   2.7920600,  1.8943900,  1.3638400,
  0.7986700,   0.5218500,   0.2372200,   0.1346000,  71.5606700, 67.8481200,
  59.6614200,  43.5416700,  32.5219600,  25.2514100, 20.2337300, 16.6050300,
  13.8797700,  11.7724500,  10.1056100,  8.7631600,  6.7575400,  5.3557300,
  4.3397400,   3.5815800,   3.0019600,   2.0380900,  1.4681100,  0.8603800,
  0.5624200,   0.2557800,   0.1451500,
};
static const double refascale88[3]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount88[3]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
};
static const int refsys88[3]{
  1,
  1,
  1,
};
static const int refc88[3]{
  3,
  1,
  1,
};

// 89
static const double refcn89[7]{
  +0.00000000000000,
  +0.81221771240234,
  +1.61096704006195,
  +2.40822887420654,
  +3.16141414642334,
  +3.86818122863770,
  +4.60221958160400,
};
static const double refq89[7]{
  +0.00000000000000,
  -0.06810000000000,
  -0.12420000000000,
  -0.17080000000000,
  -0.20670000000000,
  -0.22920000000000,
  -0.24890000000000,
};
static const double refsq89[7]{
  +0.00000000000000,
  +0.06810000000000,
  +0.06210000000000,
  +0.05690000000000,
  +0.05170000000000,
  +0.04580000000000,
  +0.04150000000000,
};
static const double refalpha89[161]{
  204.4018400, 167.2135700, 116.6976800, 58.9801600, 35.5482400,  24.5444200,
  18.4663300,  14.6614600,  12.0557600,  10.1553600, 8.7067400,   7.5671200,
  5.8964700,   4.7423400,   3.9076000,   3.2826400,  2.8016000,   1.9881000,
  1.4911800,   0.9333500,   0.6399800,   0.3122800,  0.1836600,   183.4136300,
  151.7816800, 106.8128600, 57.3476600,  36.6708800, 26.2420200,  20.1262600,
  16.1394300,  13.3398900,  11.2678800,  9.6750900,  8.4158400,   6.5630000,
  5.2798300,   4.3506000,   3.6543400,   3.1181300,  2.2109300,   1.6567900,
  1.0353700,   0.7091700,   0.3455500,   0.2030800,  161.4079900, 115.7143200,
  81.7711600,  50.0677900,  34.9561700,  26.1999400, 20.5872400,  16.7260600,
  13.9261300,  11.8135400,  10.1705400,  8.8622700,  6.9258900,   5.5789300,
  4.6011200,   3.8672800,   3.3014200,   2.3426400,  1.7561200,   1.0977400,
  0.7519600,   0.3664300,   0.2153500,   67.3757700, 65.1171500,  59.4934200,
  45.8749400,  34.8544000,  27.0905200,  21.6503900, 17.7357500,  14.8287300,
  12.6068900,  10.8666700,  9.4754700,   7.4103600,  5.9711300,   4.9253800,
  4.1400800,   3.5342800,   2.5073400,   1.8789300,  1.1737000,   0.8036000,
  0.3913300,   0.2299000,   164.9995400, 91.9493300, 68.8420500,  49.6464500,
  37.6575900,  29.3281700,  23.4479400,  19.1936000, 16.0278600,  13.6085200,
  11.7157200,  10.2048100,  7.9668900,   6.4110900,  5.2827000,   4.4364700,
  3.7843300,   2.6802300,   2.0057200,   1.2503000,  0.8548300,   0.4154600,
  0.2438300,   171.2481300, 134.6702700, 94.9592200, 58.8184700,  42.2048900,
  32.1668700,  25.4549400,  20.7156500,  17.2342600, 14.5947900,  12.5409800,
  10.9080400,  8.4991200,   6.8305600,   5.6230500,  4.7187200,   4.0224300,
  2.8447600,   2.1261800,   1.3226700,   0.9029500,  0.4378600,   0.2566800,
  213.4703400, 168.2418500, 114.2009000, 65.8443700, 46.0049400,  34.7217600,
  27.3472300,  22.1892600,  18.4196600,  15.5715000, 13.3612300,  11.6077400,
  9.0274800,   7.2449200,   5.9573100,   4.9942800,  4.2535700,   3.0024700,
  2.2403700,   1.3900500,   0.9471100,   0.4579200,  0.2680300,
};
static const double refascale89[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount89[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys89[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc89[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 90
static const double refcn90[5]{
  +0.00000000000000,
  +0.84210479259491,
  +1.67266535758972,
  +2.50573635101318,
  +3.33462429046631,
};
static const double refq90[5]{
  +0.00000000000000,
  +0.34490000000000,
  +0.43280000000000,
  +0.47390000000000,
  +0.49620000000000,
};
static const double refsq90[5]{
  +0.00000000000000,
  -0.34490000000000,
  -0.21640000000000,
  -0.15800000000000,
  -0.12405000000000,
};
static const double refalpha90[115]{
  151.3054900, 132.0224300, 100.3446200, 57.1424100, 36.8572000,  26.3120900,
  20.0921500,  16.0586100,  13.2526600,  11.1956600, 9.6267100,   8.3934800,
  6.5881000,   5.3414100,   4.4388100,   3.7617600,  3.2393500,   2.3514000,
  1.8034400,   1.1755900,   0.8333100,   0.4292000,  0.2596900,   142.0153100,
  121.7330500, 91.8672700,  54.6347100,  36.9218200, 27.1645700,  21.1160700,
  17.0503600,  14.1521300,  11.9928500,  10.3287100, 9.0118800,   7.0733400,
  5.7296600,   4.7553200,   4.0241000,   3.4599200,  2.5018100,   1.9119000,
  1.2389500,   0.8744800,   0.4476600,   0.2700600,  117.3109500, 99.2297800,
  76.8788200,  50.3595500,  36.4314400,  27.8344800, 22.0825100,  18.0276800,
  15.0511500,  12.7931800,  11.0336600,  9.6319300,  7.5576900,   6.1154900,
  5.0688400,   4.2834100,   3.6777200,   2.6504100,  2.0194200,   1.3024000,
  0.9161700,   0.4667500,   0.2809400,   94.3173000, 83.8298000,  69.2480800,
  49.5421600,  37.3912000,  29.1786500,  23.3999800, 19.2059800,  16.0744500,
  13.6753400,  11.7953000,  10.2929700,  8.0657000,  6.5163900,   5.3926400,
  4.5501000,   3.9009900,   2.8019000,   2.1285900,  1.3664400,   0.9580200,
  0.4857600,   0.2917000,   63.9384900,  62.4467300, 58.5371300,  47.9250300,
  38.0867400,  30.4192900,  24.6745200,  20.3673800, 17.0925200,  14.5573700,
  12.5588400,  10.9564600,  8.5756600,   6.9183100,  5.7167300,   4.8165800,
  4.1237600,   2.9526000,   2.2370000,   1.4299100,  0.9995000,   0.5045900,
  0.3023800,
};
static const double refascale90[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount90[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys90[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc90[5]{
  3,
  1,
  1,
  1,
  1,
};

// 91
static const double refcn91[6]{
  +0.00000000000000,
  +0.85091900825500,
  +1.68243002891541,
  +2.56143164634705,
  +3.41472434997559,
  +4.33161783218384,
};
static const double refq91[6]{
  +0.00000000000000,
  +0.42640000000000,
  +0.54680000000000,
  +0.61000000000000,
  +0.64360000000000,
  +0.66540000000000,
};
static const double refsq91[6]{
  +0.00000000000000,
  -0.42640000000000,
  -0.27340000000000,
  -0.20330000000000,
  -0.16090000000000,
  -0.13308000000000,
};
static const double refalpha91[138]{
  166.6277700, 141.2842200, 102.4567200, 54.4640100, 34.1796000,  24.3027300,
  18.6668300,  15.0570800,  12.5481800,  10.6993500, 9.2777300,   8.1496500,
  6.4741500,   5.2950000,   4.4269000,   3.7665900,  3.2513500,   2.3641100,
  1.8104700,   1.1736900,   0.8277200,   0.4229700,  0.2549700,   157.0760700,
  129.9417100, 94.0821000,  52.6866900,  34.7765300, 25.4911900,  19.9067900,
  16.1943000,  13.5495700,  11.5701000,  10.0337700, 8.8082300,   6.9822000,
  5.6964600,   4.7512600,   4.0337400,   3.4750100,  2.5159300,   1.9200100,
  1.2381800,   0.8700300,   0.4423200,   0.2659800,  125.3575000, 97.8437100,
  72.3248100,  46.3109800,  33.6240800,  25.9618100, 20.8399900,  17.1993700,
  14.4962900,  12.4214900,  10.7866200,  9.4708600,  7.4982900,   6.1056300,
  5.0822500,   4.3065100,   3.7034900,   2.6713600,  2.0325600,   1.3050400,
  0.9143500,   0.4629900,   0.2778900,   85.9686200, 76.5627700,  64.2651600,
  46.9223500,  35.8900500,  28.3126800,  22.9032600, 18.9260700,  15.9240300,
  13.6038600,  11.7728300,  10.3012100,  8.1047700,  6.5655300,   5.4424900,
  4.5964700,   3.9422400,   2.8298800,   2.1464100,  1.3730200,   0.9600200,
  0.4849700,   0.2907800,   68.2275000,  65.6186000, 60.0315200,  47.6359800,
  37.5304200,  29.9830600,  24.3945000,  20.2072400, 17.0133900,  14.5306100,
  12.5652700,  10.9835700,  8.6224300,   6.9698300,  5.7663500,   4.8615200,
  4.1631000,   2.9787200,   2.2534400,   1.4359100,  1.0013000,   0.5039200,
  0.3015900,   64.6792300,  62.7768600,  58.3981800, 48.0808200,  38.8769800,
  31.5484100,  25.8960300,  21.5514400,  18.1846400, 15.5419400,  13.4379700,
  11.7392400,  9.1986100,   7.4202100,   6.1267800,  5.1560200,   4.4080900,
  3.1434800,   2.3721400,   1.5065200,   1.0484700,  0.5263900,   0.3147100,

};
static const double refascale91[6]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount91[6]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
};
static const int refsys91[6]{
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc91[6]{
  3,
  1,
  1,
  1,
  1,
  1,
};

// 92
static const double refcn92[6]{
  +0.00000000000000,
  +0.84563773870468,
  +2.50075340270996,
  +3.38830232620239,
  +3.57048654556274,
  +5.12557458877563,
};
static const double refq92[6]{
  +0.00000000000000,
  +0.24430000000000,
  +0.37210000000000,
  +0.40480000000000,
  +0.39870000000000,
  +0.43570000000000,
};
static const double refsq92[6]{
  +0.00000000000000,
  -0.24430000000000,
  -0.12406000000000,
  -0.10120000000000,
  -0.07974000000000,
  -0.07260000000000,
};
static const double refalpha92[138]{
  159.6501800, 135.8961000, 98.5086800, 52.3884600, 32.9239600, 23.4920600,
  18.1199800,  14.6740300,  12.2716700, 10.4952600, 9.1247400,  8.0337300,
  6.4060900,   5.2539700,   4.4011800,  3.7493700,  3.2386800,  2.3549100,
  1.8011700,   1.1639600,   0.8188100,  0.4171000,  0.2511700,  152.0261400,
  128.0014000, 92.7351000,  51.5592200, 33.7876600, 24.6849400, 19.2730100,
  15.7026800,  13.1693600,  11.2756900, 9.8051000,  8.6299200,  6.8721500,
  5.6267000,   4.7052700,   4.0017400,  3.4511800,  2.5003900,  1.9065000,
  1.2259300,   0.8593000,   0.4354100,  0.2615100,  61.4627600, 58.1569300,
  52.5979400,  41.1735600,  32.1632900, 25.6872500, 21.0129300, 17.5503200,
  14.9129800,  12.8533700,  11.2101300, 9.8751400,  7.8533600,  6.4113200,
  5.3437800,   4.5300700,   3.8949000,  2.8030200,  2.1254800,  1.3553100,
  0.9444200,   0.4745300,   0.2838200,  57.7404400, 56.8541900, 53.0160000,
  43.4071000,  34.8271900,  28.1717400, 23.1478600, 19.3339400, 16.3930700,
  14.0847800,  12.2416000,  10.7465100, 8.4924500,  6.8966500,  5.7238900,
  4.8357500,   4.1463100,   2.9695700,  2.2450200,  1.4268600,  0.9927100,
  0.4980100,   0.2977000,   79.4643700, 66.1195700, 58.3424900, 45.8165000,
  36.2236200,  29.1719600,  23.9622200, 20.0392100, 17.0204000, 14.6497200,
  12.7534500,  11.2117900,  8.8796900,  7.2209000,  5.9978900,  5.0687300,
  4.3458600,   3.1091800,   2.3465400,  1.4858200,  1.0304100,  0.5142300,
  0.3065600,   70.4499300,  68.4799400, 63.4736400, 50.8489300, 40.1019100,
  32.1246100,  26.2551100,  21.8601000, 18.4967500, 15.8683700, 13.7750900,
  12.0799000,  9.5275500,   7.7224500,  6.3968700,  5.3938000,  4.6158900,
  3.2908100,   2.4778500,   1.5648600,  1.0839000,  0.5404200,  0.3221200,

};
static const double refascale92[6]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount92[6]{
  0.00000000000000,
  1.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys92[6]{
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc92[6]{
  3,
  1,
  1,
  3,
  3,
  1,
};

// 93
static const double refcn93[7]{
  +0.00000000000000,
  +0.84929960966110,
  +1.68312501907349,
  +2.51682710647583,
  +3.39772701263428,
  +4.23597240447998,
  +5.09381914138794,
};
static const double refq93[7]{
  +0.00000000000000,
  +0.33410000000000,
  +0.41750000000000,
  +0.45490000000000,
  +0.48260000000000,
  +0.49400000000000,
  +0.50440000000000,
};
static const double refsq93[7]{
  +0.00000000000000,
  -0.33410000000000,
  -0.20870000000000,
  -0.15163000000000,
  -0.12065000000000,
  -0.09880000000000,
  -0.08410000000000,
};
static const double refalpha93[161]{
  152.1283900, 112.6033100, 75.4650300, 40.7348500, 27.3560900,  20.6809600,
  16.6270800,  13.8529700,  11.8126700, 10.2408900, 8.9906800,   7.9726400,
  6.4187100,   5.2954100,   4.4526000,  3.8023100,  3.2892800,   2.3947900,
  1.8308500,   1.1805100,   0.8288300,  0.4212400,  0.2535000,   134.2373900,
  104.3913800, 73.7094800,  42.8461500, 29.7209900, 22.6356900,  18.1746800,
  15.0874400,  12.8155700,  11.0712300, 9.6898800,  8.5700300,   6.8703800,
  5.6495500,   4.7380100,   4.0373300,  3.4861800,  2.5287800,   1.9276900,
  1.2375000,   0.8661200,   0.4381200,  0.2630300,  114.7257000, 89.7632500,
  66.6972100,  42.9194500,  31.1632400, 24.1344200, 19.4813300,  16.1874400,
  13.7402200,  11.8546900,  10.3605200, 9.1499700,  7.3160300,   6.0025000,
  5.0243200,   4.2741300,   3.6851700,  2.6647300,  2.0260500,   1.2952900,
  0.9037800,   0.4550000,   0.2725000,  60.0193300, 57.7069100,  52.4809600,
  40.8285800,  31.7259300,  25.2753700, 20.6624400, 17.2654300,  14.6871900,
  12.6773600,  11.0746900,  9.7721500,  7.7962000,  6.3820200,   5.3309800,
  4.5267100,   3.8966600,   2.8084000,  2.1298400,  1.3565600,   0.9440800,
  0.4735100,   0.2830500,   57.6363300, 55.7487000, 51.6348100,  42.1036900,
  33.8112200,  27.4066600,  22.5760500, 18.9076000, 16.0757400,  13.8491000,
  12.0671800,  10.6181700,  8.4249600,  6.8637500,  5.7104900,   4.8330900,
  4.1492500,   2.9761400,   2.2502400,  1.4284600,  0.9924900,   0.4969800,
  0.2969000,   79.8320500,  75.1734800, 66.0772100, 49.2762900,  37.7995500,
  29.9549600,  24.3770500,  20.2708100, 17.1576200, 14.7371100,  12.8142200,
  11.2583100,  8.9139600,   7.2512400,  6.0254600,  5.0940400,   4.3687700,
  3.1261200,   2.3585600,   1.4918700,  1.0337700,  0.5155700,   0.3073900,
  90.8035900,  85.6049900,  74.5057100, 54.1947900, 40.9874200,  32.2515300,
  26.1389000,  21.6751400,  18.3064600, 15.6954400, 13.6261600,  11.9551600,
  9.4434900,   7.6670300,   6.3603600,  5.3693600,  4.5989500,   3.2819800,
  2.4708700,   1.5580000,   1.0772700,  0.5356400,  0.3188900,
};
static const double refascale93[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount93[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys93[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc93[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 94
static const double refcn94[7]{
  +0.00000000000000,
  +0.81253784894943,
  +1.65689170360565,
  +2.49969720840454,
  +3.36243820190430,
  +4.19367313385010,
  +5.02024745941162,
};
static const double refq94[7]{
  +0.00000000000000,
  +0.34760000000000,
  +0.46690000000000,
  +0.52750000000000,
  +0.56890000000000,
  +0.58730000000000,
  +0.60200000000000,
};
static const double refsq94[7]{
  +0.00000000000000,
  -0.34760000000000,
  -0.23345000000000,
  -0.17583000000000,
  -0.14222500000000,
  -0.11746000000000,
  -0.10033000000000,
};
static const double refalpha94[161]{
  172.7406800, 145.6047800, 101.7601400, 50.1348300, 29.9893400, 20.8783400,
  15.9825000,  12.9731100,  10.9295300,  9.4374300,  8.2894300,  7.3720700,
  5.9862600,   4.9830600,   4.2229300,   3.6292400,  3.1552100,  2.3146600,
  1.7749500,   1.1443800,   0.8013800,   0.4048900,  0.2429100,  140.6592400,
  109.3082900, 72.9347700,  39.9873900,  27.0421600, 20.3958100, 16.3706000,
  13.6552700,  11.6835500,  10.1759300,  8.9796700,  8.0042800,  6.5061100,
  5.4099300,   4.5766100,   3.9256600,   3.4065100,  2.4886100,  1.9018600,
  1.2200100,   0.8514000,   0.4280500,   0.2561900,  97.7401900, 76.6673600,
  59.4821600,  39.5056600,  28.9200100,  22.5125400, 18.2688400, 15.2650100,
  13.0297600,  11.3019800,  9.9268200,   8.8070400,  7.0972100,  5.8592800,
  4.9281200,   4.2075800,   3.6375400,   2.6400100,  2.0092900,  1.2829500,
  0.8931300,   0.4477700,   0.2676600,   55.3410200, 53.3923900, 49.1137600,
  38.9121200,  30.5323900,  24.4542300,  20.0613900, 16.8098900, 14.3347700,
  12.4010300,  10.8558900,  9.5975700,   7.6828900,  6.3067200,  5.2796300,
  4.4905800,   3.8702400,   2.7935500,   2.1188100,  1.3475800,  0.9361600,
  0.4682200,   0.2795900,   64.4204800,  57.8758900, 51.6984400, 41.3225200,
  33.0419600,  26.7589700,  22.0508700,  18.4869900, 15.7401000, 13.5812100,
  11.8528500,  10.4460800,  8.3125000,   6.7886100,  5.6588800,  4.7963800,
  4.1220200,   2.9602100,   2.2380800,   1.4185000,  0.9837900,  0.4912400,
  0.2931600,   84.8162300,  79.2047800,  68.1430500, 49.2446000, 37.2617800,
  29.3656200,  23.8516500,  19.8304800,  16.7967800, 14.4437200, 12.5760100,
  11.0645900,  8.7844200,   7.1628000,   5.9634200,  5.0490700,  4.3348800,
  3.1059900,   2.3434800,   1.4801600,   1.0238100,  0.5091100,  0.3031800,
  104.8008500, 96.5146400,  80.5042500,  55.4090700, 40.9972200, 31.9652500,
  25.8009100,  21.3575000,  18.0287900,  15.4598100, 13.4288200, 11.7907500,
  9.3295100,   7.5870700,   6.3030100,   5.3269500,  4.5664200,  3.2619200,
  2.4554500,   1.5457800,   1.0668200,   0.5288100,  0.3144200,
};
static const double refascale94[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount94[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys94[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc94[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 95
static const double refcn95[6]{
  +0.00000000000000,
  +0.76201480627060,
  +1.54385828971863,
  +2.39868640899658,
  +3.99497199058533,
  +4.80997991561890,
};
static const double refq95[6]{
  +0.00000000000000,
  +0.29480000000000,
  +0.38370000000000,
  +0.43070000000000,
  +0.47130000000000,
  +0.48330000000000,
};
static const double refsq95[6]{
  +0.00000000000000,
  -0.29480000000000,
  -0.19190000000000,
  -0.14357000000000,
  -0.09426000000000,
  -0.08050000000000,
};
static const double refalpha95[138]{
  165.6020400, 140.4979000, 99.0178200,  49.3590700, 29.6192400, 20.6060600,
  15.7483000,  12.7644400,  10.7432900,  9.2721600,  8.1436800,  7.2441600,
  5.8886700,   4.9088800,   4.1662600,   3.5853900,  3.1206400,  2.2934000,
  1.7596300,   1.1336300,   0.7927300,   0.3995400,  0.2395000,  133.0355100,
  104.9201500, 71.4375700,  39.7059900,  26.7872400, 20.1190900, 16.0990800,
  13.4053800,  11.4612800,  9.9817600,   8.8116500,  7.8596000,  6.3993200,
  5.3309000,   4.5175500,   3.8808200,   3.3717600,  2.4680100,  1.8873900,
  1.2100600,   0.8433800,   0.4230600,   0.2530100,  60.0171500, 56.0454500,
  48.5551000,  35.1426600,  26.4217100,  20.8389700, 17.0639300, 14.3636900,
  12.3396900,  10.7652600,  9.5044800,   8.4716500,  6.8811000,  5.7167700,
  4.8322200,   4.1417200,   3.5912700,   2.6182600,  1.9964200,  1.2747700,
  0.8861000,   0.4428000,   0.2643000,   54.6144300, 51.1618600, 47.1127900,
  37.5251800,  29.5311700,  23.6871500,  19.4572200, 16.3294500, 13.9514500,
  12.0946300,  10.6104900,  9.4005700,   7.5548800,  6.2225400,  5.2235600,
  4.4526600,   3.8440900,   2.7818200,   2.1119300,  1.3427900,  0.9317700,
  0.4650300,   0.2774800,   98.4837900,  88.6034800, 72.3488700, 49.5093900,
  36.7445600,  28.7272700,  23.2551600,  19.3161900, 16.3678900, 14.0916600,
  12.2892600,  10.8318700,  8.6315200,   7.0619800,  5.8964000,  5.0039600,
  4.3039800,   3.0923300,   2.3354600,   1.4743400,  1.0182900,  0.5049000,
  0.3003000,   113.3351500, 102.5160900, 83.0136200, 55.2298300, 40.3635400,
  31.3181900,  25.2331600,  20.8827200,  17.6395700, 15.1435500, 13.1727500,
  11.5836000,  9.1935200,   7.4970200,   6.2426800,  5.2859400,  4.5379900,
  3.2490100,   2.4478600,   1.5405500,   1.0620400,  0.5253100,  0.3120700,

};
static const double refascale95[6]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount95[6]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys95[6]{
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc95[6]{
  3,
  1,
  1,
  1,
  1,
  1,
};

// 96
static const double refcn96[7]{
  +0.00000000000000,
  +0.83212512731552,
  +1.64380240440369,
  +2.46540093421936,
  +3.25204372406006,
  +4.04486131668091,
  +4.84447526931763,
};
static const double refq96[7]{
  +0.00000000000000,
  +0.23790000000000,
  +0.28320000000000,
  +0.30250000000000,
  +0.31270000000000,
  +0.31910000000000,
  +0.32360000000000,
};
static const double refsq96[7]{
  +0.00000000000000,
  -0.23790000000000,
  -0.14160000000000,
  -0.10080000000000,
  -0.07817500000000,
  -0.06382000000000,
  -0.05390000000000,
};
static const double refalpha96[161]{
  134.3978700, 116.1743200, 86.3865200, 47.1493500, 29.7740500, 21.2860100,
  16.4817600,  13.4221500,  11.2973100, 9.7266500,  8.5121400,  7.5414700,
  6.0822400,   5.0364900,   4.2521500,  3.6447100,  3.1627600,  2.3136500,
  1.7709800,   1.1384800,   0.7953700,  0.4005600,  0.2401100,  126.6120300,
  109.3212500, 81.5723600,  47.0010300, 31.2023600, 22.8860500, 17.8996500,
  14.6120400,  12.2877600,  10.5566200, 9.2154200,  8.1444900,  6.5400500,
  5.3965000,   4.5430500,   3.8848100,  3.3643500,  2.4514700,  1.8709800,
  1.1977200,   0.8343200,   0.4183500,  0.2502100,  99.2439600, 79.0151500,
  60.3295100,  40.0819000,  29.3585500, 22.7763000, 18.3964100, 15.3028700,
  13.0129200,  11.2536800,  9.8618400,  8.7345600,  7.0243600,  5.7942800,
  4.8728300,   4.1613700,   3.5989600,  2.6140800,  1.9897500,  1.2686500,
  0.8813000,   0.4401500,   0.2627100,  54.6754500, 52.9826400, 48.7627000,
  38.4660300,  29.9916200,  23.8921900, 19.5266100, 16.3253800, 13.9077500,
  12.0304700,  10.5370300,  9.3243200,  7.4828000,  6.1594600,  5.1700200,
  4.4076700,   3.8062400,   2.7561600,  2.0929600,  1.3299400,  0.9217200,
  0.4587400,   0.2733100,   84.5347300, 75.7999500, 62.7375400, 44.4811000,
  33.5258000,  26.3562200,  21.3871200, 17.7920400, 15.0970200, 13.0153700,
  11.3665700,  10.0328800,  8.0175800,  6.5776600,  5.5060700,  4.6835900,
  4.0367900,   2.9122400,   2.2054600,  1.3961500,  0.9652100,  0.4787100,
  0.2847100,   110.6679000, 96.7153000, 75.9750200, 50.3030900, 36.9564000,
  28.7507400,  23.1990700,  19.2245300, 16.2621200, 13.9830200, 12.1836800,
  10.7323800,  8.5473900,   6.9930100,  5.8404300,  4.9584700,  4.2666900,
  3.0681000,   2.3178500,   1.4623100,  1.0086600,  0.4986500,  0.2960800,
  133.9582500, 116.0314800, 88.6352200, 56.0350700, 40.3477900, 31.1150200,
  24.9872400,  20.6390300,  17.4139100, 14.9408800, 12.9935600, 11.4264900,
  9.0740700,   7.4064100,   6.1734700,  5.2323900,  4.4958300,  3.2234500,
  2.4298500,   1.5281900,   1.0519100,  0.5184700,  0.3073900,
};
static const double refascale96[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount96[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys96[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc96[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 97
static const double refcn97[5]{
  +0.00000000000000,
  +0.82979065179825,
  +1.66842269897461,
  +2.50224256515503,
  +3.36453199386597,
};
static const double refq97[5]{
  +0.00000000000000,
  +0.29820000000000,
  +0.33910000000000,
  +0.35450000000000,
  +0.36420000000000,
};
static const double refsq97[5]{
  +0.00000000000000,
  -0.29820000000000,
  -0.16950000000000,
  -0.11820000000000,
  -0.09110000000000,
};
static const double refalpha97[115]{
  150.0841600, 129.4893000, 93.3386400, 47.5743700, 28.7210300, 19.9726200,
  15.2301700,  12.3184200,  10.3534300, 8.9302400,  7.8439100,  6.9817100,
  5.6882700,   4.7562600,   4.0498600,  3.4960800,  3.0513700,  2.2538700,
  1.7336700,   1.1172700,   0.7795800,  0.3907500,  0.2335900,  125.9274100,
  104.0728300, 75.8864500,  43.2369500, 28.7502800, 21.1786000, 16.6537700,
  13.6738100,  11.5652200,  9.9908500,  8.7667100,  7.7849900,  6.3038300,
  5.2375000,   4.4339000,   3.8085000,  3.3099800,  2.4257000,  1.8562800,
  1.1892700,   0.8272800,   0.4132100,  0.2466400,  94.2400900, 77.5243900,
  58.9429600,  39.0623400,  28.6154000, 22.2014200, 17.9361600, 14.9285100,
  12.7060600,  11.0009500,  9.6528800,  8.5611300,  6.9035300,  5.7087500,
  4.8112700,   4.1162600,   3.5652100,  2.5958700,  1.9780000,  1.2610500,
  0.8749900,   0.4358100,   0.2598000,  52.9670000, 51.2081000, 47.2097200,
  37.3875500,  29.2191000,  23.3037200, 19.0603100, 15.9482500, 13.5995200,
  11.7770200,  10.3277100,  9.1508100,  7.3623200,  6.0746100,  5.1093500,
  4.3635300,   3.7734800,   2.7388300,  2.0819400,  1.3228100,  0.9157300,
  0.4545600,   0.2705000,   64.0310000, 57.6315700, 50.4511300, 39.9025500,
  31.7426200,  25.6004300,  21.0403300, 17.6213600, 15.0076100, 12.9656800,
  11.3372000,  10.0142700,  8.0081100,  6.5712100,  5.5008800,  4.6791300,
  4.0329000,   2.9093900,   2.2032000,  1.3943200,  0.9635500,  0.4775600,
  0.2840300,
};
static const double refascale97[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount97[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys97[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc97[5]{
  3,
  1,
  1,
  1,
  1,
};

// 98
static const double refcn98[6]{
  +0.00000000000000,
  +0.81898736953735,
  +1.63452363014221,
  +2.50784802436829,
  +3.34391856193542,
  +4.98358106613159,
};
static const double refq98[6]{
  +0.00000000000000,
  +0.30920000000000,
  +0.38470000000000,
  +0.42160000000000,
  +0.44080000000000,
  +0.45810000000000,
};
static const double refsq98[6]{
  +0.00000000000000,
  -0.30920000000000,
  -0.19235000000000,
  -0.14053000000000,
  -0.11020000000000,
  -0.07635000000000,
};
static const double refalpha98[138]{
  148.0091900, 127.6682800, 91.8844400,  46.6738900, 28.1153000, 19.5155900,
  14.8547000,  11.9926300,  10.0613000,  8.6633000,  7.5974500,  6.7529100,
  5.4897600,   4.5835000,   3.8992300,   3.3643900,  2.9357800,  2.1685400,
  1.6684900,   1.0758700,   0.7512000,   0.3775400,  0.2264700,  130.7987300,
  103.8691600, 70.9979000,  39.3130600,  26.2475400, 19.4913500, 15.4458200,
  12.7645500,  10.8527200,  9.4145600,   8.2889000,  7.3811000,  6.0026700,
  5.0036700,   4.2470200,   3.6557100,   3.1826600,  2.3393000,  1.7930400,
  1.1501400,   0.8003400,   0.4003300,   0.2395400,  53.3942300, 50.4801000,
  44.7056500,  33.0884500,  24.9852400,  19.6813400, 16.0762000, 13.5014100,
  11.5794600,  10.0917600,  8.9061400,   7.9389900,  6.4567000,  5.3760200,
  4.5560600,   3.9153900,   3.4033800,   2.4929000,  1.9054800,  1.2173400,
  0.8447900,   0.4208400,   0.2512500,   50.4030000, 48.8894600, 45.1750100,
  36.0185500,  28.2961100,  22.6345400,  18.5399200, 15.5218100, 13.2371200,
  11.4612700,  10.0478300,  8.8996800,   7.1551800,  5.9001600,  4.9603600,
  4.2349300,   3.6614600,   2.6567500,   2.0192700,  1.2829000,  0.8883200,
  0.4418100,   0.2636500,   81.5874700,  68.6608200, 56.5880100, 41.3108400,
  31.7640400,  25.2149100,  20.5502500,  17.1270100, 14.5428400, 12.5405500,
  10.9527700,  9.6681900,   7.7278400,   6.3423900,  5.3117300,  4.5206000,
  3.8981800,   2.8146400,   2.1321200,   1.3489800,  0.9318000,  0.4619400,
  0.2752100,   129.7014900, 111.1968900, 84.3720000, 53.9448000, 39.1948300,
  30.3204900,  24.3568100,  20.1026300,  16.9427700, 14.5209100, 12.6163400,
  11.0860700,  8.7940400,   7.1734200,   5.9775200,  5.0658000,  4.3526900,
  3.1210200,   2.3523500,   1.4782600,   1.0166200,  0.5008300,  0.2974000,

};
static const double refascale98[6]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount98[6]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  6.00000000000000,
};
static const int refsys98[6]{
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc98[6]{
  3,
  1,
  1,
  1,
  1,
  1,
};

// 99
static const double refcn99[7]{
  +0.00000000000000,
  +0.79849386215210,
  +1.60774898529053,
  +2.48593425750732,
  +3.30908131599426,
  +4.11455059051514,
  +4.89267015457153,
};
static const double refq99[7]{
  +0.00000000000000,
  +0.25690000000000,
  +0.32810000000000,
  +0.36510000000000,
  +0.38330000000000,
  +0.39420000000000,
  +0.40070000000000,
};
static const double refsq99[7]{
  +0.00000000000000,
  -0.25690000000000,
  -0.16405000000000,
  -0.12170000000000,
  -0.09582500000000,
  -0.07884000000000,
  -0.06680000000000,
};
static const double refalpha99[161]{
  141.2201700, 122.5206800, 89.0107400, 45.7447300, 27.7131900, 19.2896700,
  14.6962900,  11.8616100,  9.9415300,  8.5482600,  7.4847800,  6.6420500,
  5.3832200,   4.4828400,   3.8054200,  3.2777200,  2.8560600,  2.1040800,
  1.6159000,   1.0393900,   0.7247100,  0.3640000,  0.2186500,  127.1190700,
  101.1671600, 69.0944700,  38.4335200, 25.7933500, 19.2100200, 15.2410000,
  12.5963000,  10.7033800,  9.2761300,  8.1577800,  7.2557300,  5.8873100,
  4.8978500,   4.1503900,   3.5677000,  3.1025200,  2.2754300,  1.7412300,
  1.1142700,   0.7742600,   0.3869300,  0.2317800,  51.5499300, 49.1951700,
  43.8725300,  32.7274200,  24.7930800, 19.5486400, 15.9633400, 13.3936100,
  11.4716600,  9.9828300,   8.7965200,  7.8296100,  6.3505900,  5.2757400,
  4.4628300,   3.8294800,   3.3245500,  2.4293800,  1.8537300,  1.1814400,
  0.8186900,   0.4074700,   0.2435100,  48.7142300, 47.1908400, 43.6761400,
  35.1176500,  27.7848700,  22.3133400, 18.3099600, 15.3383400, 13.0793500,
  11.3191000,  9.9161400,   8.7758300,  7.0433800,  5.7983900,  4.8676300,
  4.1504500,   3.5844500,   2.5951700,  1.9692400,  1.2483100,  0.8632400,
  0.4290200,   0.2562900,   85.3606600, 70.4284500, 56.8603800, 40.9584000,
  31.3950300,  24.9036700,  20.2901400, 16.9042800, 14.3470300, 12.3646900,
  10.7923500,  9.5202500,   7.5994900,  6.2293800,  5.2113800,  4.4309500,
  3.8176500,   2.7516900,   2.0815200,  1.3141600,  0.9064900,  0.4489300,
  0.2676700,   117.4576200, 94.0368600, 70.6831300, 47.1236300, 35.1066300,
  27.5008100,  22.2441900,  18.4361400, 15.5817300, 13.3811300, 11.6435800,
  10.2434300,  8.1400700,   6.6486900,  5.5460500,  4.7042100,  4.0449500,
  2.9043500,   2.1910300,   1.3783300,  0.9485600,  0.4682100,  0.2786700,
  150.7635300, 117.5979300, 85.0999300, 53.7332400, 38.9845200, 30.1309200,
  24.1804600,  19.9356900,  16.7838100, 14.3694000, 12.4720300, 10.9487800,
  8.6702100,   7.0620600,   5.8774600,  4.9757900,  4.2715100,  3.0572800,
  2.3010400,   1.4429200,   0.9909300,  0.4876200,  0.2897300,
};
static const double refascale99[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount99[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys99[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc99[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 100
static const double refcn100[7]{
  +0.00000000000000,
  +0.81187158823013,
  +1.63818895816803,
  +2.51218342781067,
  +3.33093667030334,
  +4.15018892288208,
  +4.97273159027100,
};
static const double refq100[7]{
  +0.00000000000000,
  +0.30910000000000,
  +0.38670000000000,
  +0.42570000000000,
  +0.44340000000000,
  +0.45430000000000,
  +0.46150000000000,
};
static const double refsq100[7]{
  +0.00000000000000,
  -0.30910000000000,
  -0.19335000000000,
  -0.14190000000000,
  -0.11085000000000,
  -0.09086000000000,
  -0.07690000000000,
};
static const double refalpha100[161]{
  134.5132400, 117.3651100, 86.0922200, 44.8044200, 27.3252700, 19.0895400,
  14.5664700,  11.7577800,  9.8459700,  8.4541400,  7.3899600,  6.5463600,
  5.2877700,   4.3905500,   3.7182100,  3.1964600,  2.7809400,  2.0430800,
  1.5662000,   1.0051900,   0.7001100,  0.3516500,  0.2115700,  123.4197800,
  98.0796000,  67.3261100,  37.7049500, 25.4441800, 19.0089500, 15.0992900,
  12.4780100,  10.5937400,  9.1693800,  8.0521000,  7.1509400,  5.7857800,
  4.8016800,   4.0607900,   3.4850500,  3.0266800,  2.2145000,  1.6918400,
  1.0804100,   0.7499000,   0.3746800,  0.2247500,  49.2489800, 47.1164900,
  42.3467900,  32.0194900,  24.4465800, 19.3482600, 15.8217100, 13.2748600,
  11.3611400,  9.8749900,   8.6897000,  7.7237600,  6.2483100,  5.1791900,
  4.3731500,   3.7469800,   3.2490100,  2.3689400,  1.8048600,  1.1480300,
  0.7947000,   0.3954200,   0.2366200,  48.8289600, 46.7101500, 42.7341700,
  34.2569100,  27.1850100,  21.8934500, 17.9996100, 15.0945700, 12.8774400,
  11.1448400,  9.7612400,   8.6353300,  6.9235800,  5.6936300,  4.7749000,
  4.0677300,   3.5102500,   2.5373800,  1.9230300,  1.2168900,  0.8406700,
  0.4176900,   0.2498100,   89.9278200, 70.7326700, 55.9993400, 40.2168300,
  30.9059100,  24.5634500,  20.0342000, 16.6975800, 14.1706300, 12.2082400,
  10.6500500,  9.3887800,   7.4844400,  6.1272000,  5.1200400,  4.3489600,
  3.7438000,   2.6938500,   2.0351400,  1.2825800,  0.8837900,  0.4375200,
  0.2611500,   116.8173500, 93.2645400, 70.0509200, 46.6547100, 34.7567800,
  27.2346500,  22.0313300,  18.2566300, 15.4237200, 13.2378500, 11.5111700,
  10.1196800,  8.0301600,   6.5502000,  5.4575200,  4.6244600,  3.9729200,
  2.8477600,   2.1456000,   1.3473800,  0.9263400,  0.4570600,  0.2723100,
  135.6122000, 112.6927600, 83.8706100, 53.3717400, 38.7175500, 29.9159300,
  24.0013000,  19.7798800,  16.6432600, 14.2393700, 12.3498800, 10.8330400,
  8.5652100,   6.9665300,   5.7906000,  4.8968900,  4.1998100,  3.0004700,
  2.2553400,   1.4119100,   0.9688000,  0.4766500,  0.2835300,
};
static const double refascale100[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount100[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys100[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc100[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 101
static const double refcn101[5]{
  +0.00000000000000,
  +0.83019560575485,
  +1.67299079895020,
  +2.52414393424988,
  +3.36544203758240,
};
static const double refq101[5]{
  +0.00000000000000,
  +0.12010000000000,
  +0.17910000000000,
  +0.21620000000000,
  +0.23690000000000,
};
static const double refsq101[5]{
  +0.00000000000000,
  -0.12010000000000,
  -0.08955000000000,
  -0.07207000000000,
  -0.05920000000000,
};
static const double refalpha101[115]{
  130.2072000, 114.1115300, 84.3232500,  44.1735800, 26.9219800, 18.7618300,
  14.2890700,  11.5253100,  9.6545200,   8.2988500,  7.2654300,  6.4473300,
  5.2261900,   4.3528300,   3.6953200,   3.1826200,  2.7725000,  2.0398100,
  1.5632300,   1.0001900,   0.6937800,   0.3454500,  0.2067300,  122.3584000,
  96.7485900,  66.8292500,  37.3575000,  25.1065100, 18.6943300, 14.8200100,
  12.2392800,  10.3950300,  9.0069900,   7.9210100,  7.0460100,  5.7195500,
  4.7603300,   4.0350800,   3.4690000,   3.0164800,  2.2102000,  1.6882200,
  1.0750900,   0.7433900,   0.3684100,   0.2198600,  50.5776500, 48.2323300,
  43.1074800,  32.1977700,  24.3573900,  19.1617800, 15.6147000, 13.0800000,
  11.1905700,  9.7313000,   8.5713100,   7.6275000,  6.1859700,  5.1392300,
  4.3474700,   3.7302200,   3.2377200,   2.3633300,  1.8000600,  1.1419300,
  0.7876700,   0.3889300,   0.2316200,   71.2250100, 59.4085900, 48.9787800,
  35.5944200,  27.1964200,  21.5383500,  17.5689600, 14.6827100, 12.5133600,
  10.8340600,  9.5007400,   8.4192200,   6.7771600,  5.5952800,  4.7088100,
  4.0230100,   3.4795100,   2.5235200,   1.9142100,  1.2088600,  0.8319600,
  0.4097500,   0.2436900,   100.3385300, 84.3364300, 64.3830000, 42.1400900,
  30.8493900,  23.9708700,  19.3555900,  16.0717600, 13.6333100, 11.7603700,
  10.2817000,  9.0876400,   7.2841600,   5.9935900,  5.0301200,  4.2876300,
  3.7011600,   2.6742300,   2.0231300,   1.2731600,  0.8742500,  0.4291600,
  0.2547600,
};
static const double refascale101[5]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount101[5]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
};
static const int refsys101[5]{
  1,
  1,
  1,
  1,
  1,
};
static const int refc101[5]{
  3,
  1,
  1,
  1,
  1,
};

// 102
static const double refcn102[7]{
  +0.00000000000000,
  +0.83132714033127,
  +1.67657399177551,
  +2.51869487762451,
  +3.36061143875122,
  +3.62583565711975,
  +3.85555744171143,
};
static const double refq102[7]{
  +0.00000000000000,
  +0.01100000000000,
  +0.01580000000000,
  +0.01860000000000,
  +0.02020000000000,
  +0.02500000000000,
  +0.02900000000000,
};
static const double refsq102[7]{
  +0.00000000000000,
  -0.01100000000000,
  -0.00790000000000,
  -0.00620000000000,
  -0.00500000000000,
  -0.00500000000000,
  -0.00483000000000,
};
static const double refalpha102[161]{
  124.8052800, 110.0045000, 82.1183900,  43.5324100, 26.6190500, 18.5568300,
  14.1261500,  11.3882900,  9.5371900,   8.1977100,  7.1778500,  6.3710900,
  5.1672000,   4.3056400,   3.6562200,   3.1491500,  2.7430100,  2.0161900,
  1.5426600,   0.9830300,   0.6790800,   0.3355800,  0.2000200,  116.7644400,
  95.7311100,  67.1224100,  37.6422800,  25.1782600, 18.6618300, 14.7429700,
  12.1468300,  10.3010700,  8.9177600,   7.8389200,  6.9715600,  5.6589500,
  4.7104300,   3.9930400,   3.4326900,   2.9843700,  2.1845800,  1.6661600,
  1.0570800,   0.7281600,   0.3583200,   0.2130500,  50.1539300, 47.9467800,
  42.8472600,  32.0060400,  24.1919600,  19.0043700, 15.4660100, 12.9435000,
  11.0680800,  9.6229000,   8.4760000,   7.5438000,  6.1208100,  5.0872300,
  4.3047000,   3.6939600,   3.2061100,   2.3386200,  1.7789200,  1.1246200,
  0.7729500,   0.3790900,   0.2249400,   91.3663900, 69.0314800, 53.6426300,
  36.5348500,  27.1761000,  21.2644300,  17.2504600, 14.3838400, 12.2513400,
  10.6102800,  9.3114600,   8.2594600,   6.6624500,  5.5110600,  4.6451400,
  3.9732400,   3.4392500,   2.4961800,   1.8924500,  1.1916000,  0.8171200,
  0.3995300,   0.2366600,   124.2501600, 93.6045400, 66.8688500, 42.1117700,
  30.4955400,  23.5931200,  19.0153800,  15.7803700, 13.3883600, 11.5557700,
  10.1109200,  8.9447300,   7.1826000,   5.9194400,  4.9741900,  4.2439200,
  3.6657200,   2.6498600,   2.0034100,   1.2571400,  0.8603100,  0.4194600,
  0.2480700,   129.4476100, 97.8022200,  70.5399100, 44.9644600, 32.7582600,
  25.4115300,  20.4944800,  17.0008300,  14.4106000, 12.4242700, 10.8583100,
  9.5951500,   7.6891000,   6.3255500,   5.3071500,  4.5217400,  3.9008700,
  2.8126000,   2.1221900,   1.3278300,   0.9068900,  0.4408400,  0.2602500,
  134.8206700, 102.1887200, 74.4006500,  47.9164700, 35.0575700, 27.2357800,
  21.9652600,  18.2071400,  15.4169700,  13.2770900, 11.5910500, 10.2322400,
  8.1848800,   6.7231300,   5.6332500,   4.7939800,  4.1314200,  2.9723400,
  2.2388600,   1.3973400,   0.9527200,   0.4618800,  0.2722400,
};
static const double refascale102[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount102[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys102[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc102[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

// 103
static const double refcn103[7]{
  +0.00000000000000,
  +0.81793087720871,
  +1.64256453514099,
  +2.47565555572510,
  +3.21661520004272,
  +3.99956941604614,
  +4.77920246124268,
};
static const double refq103[7]{
  +0.00000000000000,
  +0.26760000000000,
  +0.30610000000000,
  +0.32020000000000,
  +0.32590000000000,
  +0.32850000000000,
  +0.32990000000000,
};
static const double refsq103[7]{
  +0.00000000000000,
  -0.26760000000000,
  -0.15305000000000,
  -0.10673000000000,
  -0.08150000000000,
  -0.06570000000000,
  -0.05500000000000,
};
static const double refalpha103[161]{
  206.6533200, 83.6937500,  64.8432200,  38.7234300, 25.1567100, 18.0960100,
  14.0318300,  11.4483000,  9.6673800,   8.3601100,  7.3535200,  6.5499200,
  5.3380000,   4.4612000,   3.7954000,   3.2730000,  2.8532900,  2.0999600,
  1.6078600,   1.0246900,   0.7070000,   0.3474600,  0.2059100,  92.3161300,
  82.9673800,  65.8155800,  40.9485200,  27.9903000, 20.6982400, 16.1941600,
  13.1960200,  11.0779900,  9.5086500,   8.3004100,  7.3410300,  5.9114700,
  4.8952500,   4.1354500,   3.5468000,   3.0786100,  2.2486600,  1.7134000,
  1.0857400,   0.7466800,   0.3653500,   0.2160000,  84.5082300, 70.8844100,
  54.6073800,  36.7023400,  26.9875800,  20.8759700, 16.7762200, 13.8910500,
  11.7749600,  10.1664300,  8.9059700,   7.8927900,  6.3660200,  5.2713300,
  4.4497300,   3.8123300,   3.3053600,   2.4078400,  1.8306800,  1.1565000,
  0.7937900,   0.3873200,   0.2286200,   47.5131300, 46.1744600, 42.8144500,
  34.3869400,  27.1100000,  21.6792100,  17.7218900, 14.8050900, 12.6061100,
  10.9063200,  9.5606300,   8.4722600,   6.8249300,  5.6415400,  4.7538100,
  4.0661300,   3.5201400,   2.5565200,   1.9394100,  1.2216400,  0.8370200,
  0.4074000,   0.2401300,   242.4220100, 51.7872100, 46.2957100, 36.7861900,
  29.2534000,  23.5192300,  19.2597900,  16.0851700, 13.6784800, 11.8139300,
  10.3373100,  9.1439400,   7.3414600,   6.0511200,  5.0865400,  4.3417100,
  3.7520400,   2.7154900,   2.0548700,   1.2901200,  0.8821300,  0.4281400,
  0.2519400,   143.6356600, 96.0464200,  68.6157000, 45.5604500, 33.9675300,
  26.5910500,  21.4849100,  17.7937700,  15.0381700, 12.9231500, 11.2595600,
  9.9227000,   7.9177900,   6.4946700,   5.4383800,  4.6275900,  3.9888900,
  2.8734500,   2.1676600,   1.3558600,   0.9251400,  0.4478000,  0.2631500,
  176.3109100, 122.3954600, 83.0180800,  51.6133400, 37.3991000, 28.8827900,
  23.1674700,  19.1031400,  16.0971100,  13.8030600, 12.0054900, 10.5648400,
  8.4103200,   6.8853900,   5.7560900,   4.8909700,  4.2106800,  3.0256600,
  2.2782900,   1.4215700,   0.9684800,   0.4677700,  0.2745500,
};
static const double refascale103[7]{
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
  1.00000000000000,
};
static const double refscount103[7]{
  0.00000000000000,
  1.00000000000000,
  2.00000000000000,
  3.00000000000000,
  4.00000000000000,
  5.00000000000000,
  6.00000000000000,
};
static const int refsys103[7]{
  1,
  1,
  1,
  1,
  1,
  1,
  1,
};
static const int refc103[7]{
  3,
  1,
  1,
  1,
  1,
  1,
  1,
};

////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////

static const double *refcn[MAXELEMENT]{
  nullptr, refcn1,  refcn2,  refcn3,  refcn4,   refcn5,   refcn6,   refcn7,
  refcn8,  refcn9,  refcn10, refcn11, refcn12,  refcn13,  refcn14,  refcn15,
  refcn16, refcn17, refcn18, refcn19, refcn20,  refcn21,  refcn22,  refcn23,
  refcn24, refcn25, refcn26, refcn27, refcn28,  refcn29,  refcn30,  refcn31,
  refcn32, refcn33, refcn34, refcn35, refcn36,  refcn37,  refcn38,  refcn39,
  refcn40, refcn41, refcn42, refcn43, refcn44,  refcn45,  refcn46,  refcn47,
  refcn48, refcn49, refcn50, refcn51, refcn52,  refcn53,  refcn54,  refcn55,
  refcn56, refcn57, refcn58, refcn59, refcn60,  refcn61,  refcn62,  refcn63,
  refcn64, refcn65, refcn66, refcn67, refcn68,  refcn69,  refcn70,  refcn71,
  refcn72, refcn73, refcn74, refcn75, refcn76,  refcn77,  refcn78,  refcn79,
  refcn80, refcn81, refcn82, refcn83, refcn84,  refcn85,  refcn86,  refcn87,
  refcn88, refcn89, refcn90, refcn91, refcn92,  refcn93,  refcn94,  refcn95,
  refcn96, refcn97, refcn98, refcn99, refcn100, refcn101, refcn102, refcn103,
};
static const double *refq[MAXELEMENT]{
  nullptr, refq1,   refq2,   refq3,   refq4,   refq5,  refq6,  refq7,  refq8,
  refq9,   refq10,  refq11,  refq12,  refq13,  refq14, refq15, refq16, refq17,
  refq18,  refq19,  refq20,  refq21,  refq22,  refq23, refq24, refq25, refq26,
  refq27,  refq28,  refq29,  refq30,  refq31,  refq32, refq33, refq34, refq35,
  refq36,  refq37,  refq38,  refq39,  refq40,  refq41, refq42, refq43, refq44,
  refq45,  refq46,  refq47,  refq48,  refq49,  refq50, refq51, refq52, refq53,
  refq54,  refq55,  refq56,  refq57,  refq58,  refq59, refq60, refq61, refq62,
  refq63,  refq64,  refq65,  refq66,  refq67,  refq68, refq69, refq70, refq71,
  refq72,  refq73,  refq74,  refq75,  refq76,  refq77, refq78, refq79, refq80,
  refq81,  refq82,  refq83,  refq84,  refq85,  refq86, refq87, refq88, refq89,
  refq90,  refq91,  refq92,  refq93,  refq94,  refq95, refq96, refq97, refq98,
  refq99,  refq100, refq101, refq102, refq103,
};
static const double *refsq[MAXELEMENT]{
  nullptr, refsq1,  refsq2,  refsq3,  refsq4,   refsq5,   refsq6,   refsq7,
  refsq8,  refsq9,  refsq10, refsq11, refsq12,  refsq13,  refsq14,  refsq15,
  refsq16, refsq17, refsq18, refsq19, refsq20,  refsq21,  refsq22,  refsq23,
  refsq24, refsq25, refsq26, refsq27, refsq28,  refsq29,  refsq30,  refsq31,
  refsq32, refsq33, refsq34, refsq35, refsq36,  refsq37,  refsq38,  refsq39,
  refsq40, refsq41, refsq42, refsq43, refsq44,  refsq45,  refsq46,  refsq47,
  refsq48, refsq49, refsq50, refsq51, refsq52,  refsq53,  refsq54,  refsq55,
  refsq56, refsq57, refsq58, refsq59, refsq60,  refsq61,  refsq62,  refsq63,
  refsq64, refsq65, refsq66, refsq67, refsq68,  refsq69,  refsq70,  refsq71,
  refsq72, refsq73, refsq74, refsq75, refsq76,  refsq77,  refsq78,  refsq79,
  refsq80, refsq81, refsq82, refsq83, refsq84,  refsq85,  refsq86,  refsq87,
  refsq88, refsq89, refsq90, refsq91, refsq92,  refsq93,  refsq94,  refsq95,
  refsq96, refsq97, refsq98, refsq99, refsq100, refsq101, refsq102, refsq103,
};
static const double *refalpha[MAXELEMENT]{
  nullptr,     refalpha1,   refalpha2,  refalpha3,  refalpha4,   refalpha5,
  refalpha6,   refalpha7,   refalpha8,  refalpha9,  refalpha10,  refalpha11,
  refalpha12,  refalpha13,  refalpha14, refalpha15, refalpha16,  refalpha17,
  refalpha18,  refalpha19,  refalpha20, refalpha21, refalpha22,  refalpha23,
  refalpha24,  refalpha25,  refalpha26, refalpha27, refalpha28,  refalpha29,
  refalpha30,  refalpha31,  refalpha32, refalpha33, refalpha34,  refalpha35,
  refalpha36,  refalpha37,  refalpha38, refalpha39, refalpha40,  refalpha41,
  refalpha42,  refalpha43,  refalpha44, refalpha45, refalpha46,  refalpha47,
  refalpha48,  refalpha49,  refalpha50, refalpha51, refalpha52,  refalpha53,
  refalpha54,  refalpha55,  refalpha56, refalpha57, refalpha58,  refalpha59,
  refalpha60,  refalpha61,  refalpha62, refalpha63, refalpha64,  refalpha65,
  refalpha66,  refalpha67,  refalpha68, refalpha69, refalpha70,  refalpha71,
  refalpha72,  refalpha73,  refalpha74, refalpha75, refalpha76,  refalpha77,
  refalpha78,  refalpha79,  refalpha80, refalpha81, refalpha82,  refalpha83,
  refalpha84,  refalpha85,  refalpha86, refalpha87, refalpha88,  refalpha89,
  refalpha90,  refalpha91,  refalpha92, refalpha93, refalpha94,  refalpha95,
  refalpha96,  refalpha97,  refalpha98, refalpha99, refalpha100, refalpha101,
  refalpha102, refalpha103,
};
static const double *refascale[MAXELEMENT]{
  nullptr,      refascale1,   refascale2,   refascale3,   refascale4,
  refascale5,   refascale6,   refascale7,   refascale8,   refascale9,
  refascale10,  refascale11,  refascale12,  refascale13,  refascale14,
  refascale15,  refascale16,  refascale17,  refascale18,  refascale19,
  refascale20,  refascale21,  refascale22,  refascale23,  refascale24,
  refascale25,  refascale26,  refascale27,  refascale28,  refascale29,
  refascale30,  refascale31,  refascale32,  refascale33,  refascale34,
  refascale35,  refascale36,  refascale37,  refascale38,  refascale39,
  refascale40,  refascale41,  refascale42,  refascale43,  refascale44,
  refascale45,  refascale46,  refascale47,  refascale48,  refascale49,
  refascale50,  refascale51,  refascale52,  refascale53,  refascale54,
  refascale55,  refascale56,  refascale57,  refascale58,  refascale59,
  refascale60,  refascale61,  refascale62,  refascale63,  refascale64,
  refascale65,  refascale66,  refascale67,  refascale68,  refascale69,
  refascale70,  refascale71,  refascale72,  refascale73,  refascale74,
  refascale75,  refascale76,  refascale77,  refascale78,  refascale79,
  refascale80,  refascale81,  refascale82,  refascale83,  refascale84,
  refascale85,  refascale86,  refascale87,  refascale88,  refascale89,
  refascale90,  refascale91,  refascale92,  refascale93,  refascale94,
  refascale95,  refascale96,  refascale97,  refascale98,  refascale99,
  refascale100, refascale101, refascale102, refascale103,
};
static const double *refscount[MAXELEMENT]{
  nullptr,      refscount1,   refscount2,   refscount3,   refscount4,
  refscount5,   refscount6,   refscount7,   refscount8,   refscount9,
  refscount10,  refscount11,  refscount12,  refscount13,  refscount14,
  refscount15,  refscount16,  refscount17,  refscount18,  refscount19,
  refscount20,  refscount21,  refscount22,  refscount23,  refscount24,
  refscount25,  refscount26,  refscount27,  refscount28,  refscount29,
  refscount30,  refscount31,  refscount32,  refscount33,  refscount34,
  refscount35,  refscount36,  refscount37,  refscount38,  refscount39,
  refscount40,  refscount41,  refscount42,  refscount43,  refscount44,
  refscount45,  refscount46,  refscount47,  refscount48,  refscount49,
  refscount50,  refscount51,  refscount52,  refscount53,  refscount54,
  refscount55,  refscount56,  refscount57,  refscount58,  refscount59,
  refscount60,  refscount61,  refscount62,  refscount63,  refscount64,
  refscount65,  refscount66,  refscount67,  refscount68,  refscount69,
  refscount70,  refscount71,  refscount72,  refscount73,  refscount74,
  refscount75,  refscount76,  refscount77,  refscount78,  refscount79,
  refscount80,  refscount81,  refscount82,  refscount83,  refscount84,
  refscount85,  refscount86,  refscount87,  refscount88,  refscount89,
  refscount90,  refscount91,  refscount92,  refscount93,  refscount94,
  refscount95,  refscount96,  refscount97,  refscount98,  refscount99,
  refscount100, refscount101, refscount102, refscount103,
};
static const int *refsys[MAXELEMENT]{
  nullptr,  refsys1,  refsys2,   refsys3,   refsys4,   refsys5,   refsys6,
  refsys7,  refsys8,  refsys9,   refsys10,  refsys11,  refsys12,  refsys13,
  refsys14, refsys15, refsys16,  refsys17,  refsys18,  refsys19,  refsys20,
  refsys21, refsys22, refsys23,  refsys24,  refsys25,  refsys26,  refsys27,
  refsys28, refsys29, refsys30,  refsys31,  refsys32,  refsys33,  refsys34,
  refsys35, refsys36, refsys37,  refsys38,  refsys39,  refsys40,  refsys41,
  refsys42, refsys43, refsys44,  refsys45,  refsys46,  refsys47,  refsys48,
  refsys49, refsys50, refsys51,  refsys52,  refsys53,  refsys54,  refsys55,
  refsys56, refsys57, refsys58,  refsys59,  refsys60,  refsys61,  refsys62,
  refsys63, refsys64, refsys65,  refsys66,  refsys67,  refsys68,  refsys69,
  refsys70, refsys71, refsys72,  refsys73,  refsys74,  refsys75,  refsys76,
  refsys77, refsys78, refsys79,  refsys80,  refsys81,  refsys82,  refsys83,
  refsys84, refsys85, refsys86,  refsys87,  refsys88,  refsys89,  refsys90,
  refsys91, refsys92, refsys93,  refsys94,  refsys95,  refsys96,  refsys97,
  refsys98, refsys99, refsys100, refsys101, refsys102, refsys103,
};
static const int *refc[MAXELEMENT]{
  nullptr, refc1,   refc2,   refc3,   refc4,   refc5,  refc6,  refc7,  refc8,
  refc9,   refc10,  refc11,  refc12,  refc13,  refc14, refc15, refc16, refc17,
  refc18,  refc19,  refc20,  refc21,  refc22,  refc23, refc24, refc25, refc26,
  refc27,  refc28,  refc29,  refc30,  refc31,  refc32, refc33, refc34, refc35,
  refc36,  refc37,  refc38,  refc39,  refc40,  refc41, refc42, refc43, refc44,
  refc45,  refc46,  refc47,  refc48,  refc49,  refc50, refc51, refc52, refc53,
  refc54,  refc55,  refc56,  refc57,  refc58,  refc59, refc60, refc61, refc62,
  refc63,  refc64,  refc65,  refc66,  refc67,  refc68, refc69, refc70, refc71,
  refc72,  refc73,  refc74,  refc75,  refc76,  refc77, refc78, refc79, refc80,
  refc81,  refc82,  refc83,  refc84,  refc85,  refc86, refc87, refc88, refc89,
  refc90,  refc91,  refc92,  refc93,  refc94,  refc95, refc96, refc97, refc98,
  refc99,  refc100, refc101, refc102, refc103,
};

// sec. 1
static const double secalpha1[23]{
  5.4415160, 5.3912720, 5.2466780, 4.7462570, 4.1122050, 3.4827990,
  2.9256260, 2.4586020, 2.0763900, 1.7660350, 1.5138980, 1.3080740,
  0.9987770, 0.7833600, 0.6286810, 0.5145050, 0.4281480, 0.2867670,
  0.2047270, 0.1187560, 0.0772270, 0.0349350, 0.0197880,
};
static const double secscale1{
  0.50000000000000,
};

// sec. 2
static const double secalpha2[23]{
  5.4415160, 5.3912720, 5.2466780, 4.7462570, 4.1122050, 3.4827990,
  2.9256260, 2.4586020, 2.0763900, 1.7660350, 1.5138980, 1.3080740,
  0.9987770, 0.7833600, 0.6286810, 0.5145050, 0.4281480, 0.2867670,
  0.2047270, 0.1187560, 0.0772270, 0.0349350, 0.0197880,
};
static const double secscale2{
  0.00000000000000,
};

// sec. 3
static const double secalpha3[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale3{
  0.00000000000000,
};

// sec. 4
static const double secalpha4[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale4{
  0.00000000000000,
};

// sec. 5
static const double secalpha5[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale5{
  0.00000000000000,
};

// sec. 6
static const double secalpha6[23]{
  68.5832590, 67.5115260, 64.6123080, 56.1286650, 47.4318310, 39.9459190,
  33.7814890, 28.7553020, 24.6561470, 21.2992860, 18.5340330, 16.2406480,
  12.7133690, 10.1832050, 8.3194640,  6.9133790,  5.8298100,  4.0106600,
  2.9230920,  1.7494800,  1.1654830,  0.5523060,  0.3242020,
};
static const double secscale6{
  0.16666670000000,
};

// sec. 7
static const double secalpha7[23]{
  13.8928580, 13.7335660, 13.2948950, 11.9342710, 10.4022050, 8.9706190,
  7.7218140,  6.6635680,  5.7772340,  5.0371340,  4.4181730,  3.8984410,
  3.0872240,  2.4956330,  2.0539790,  1.7170460,  1.4549570,  1.0095450,
  0.7395630,  0.4445600,  0.2961500,  0.1392520,  0.0809340,
};
static const double secscale7{
  1.00000000000000,
};

// sec. 8
static const double secalpha8[23]{
  12.9390420, 12.8215110, 12.4887870, 11.3861750, 10.0547130, 8.7593060,
  7.6055220,  6.6166590,  5.7823860,  5.0816990,  4.4924840,  3.9949630,
  3.2117190,  2.6333830,  2.1960400,  1.8580780,  1.5918740,  1.1306230,
  0.8437390,  0.5212300,  0.3539970,  0.1716310,  0.1015580,
};
static const double secscale8{
  1.00000000000000,
};

// sec. 9
static const double secalpha9[23]{
  10.3975870, 10.3144230, 10.0802310, 9.3150480, 8.4027020, 7.5095120,
  6.6939110,  5.9700690,  5.3361820,  4.7845300, 4.3054570, 3.8891980,
  3.2100590,  2.6878840,  2.2798670,  1.9559530, 1.6950280, 1.2295900,
  0.9306730,  0.5848620,  0.4008950,  0.1959850, 0.1160240,
};
static const double secscale9{
  0.50000000000000,
};

// sec. 10
static const double secalpha10[23]{
  11.6125430, 11.5410500, 11.3332410, 10.5895270, 9.5886300, 8.5228410,
  7.5106350,  6.6043140,  5.8164280,  5.1406550,  4.5636850, 4.0709240,
  3.2858130,  2.6994530,  2.2527560,  1.9059510,  1.6320270, 1.1565830,
  0.8609730,  0.5294970,  0.3582750,  0.1725840,  0.1018070,
};
static const double secscale10{
  0.50000000000000,
};

// sec. 11
static const double secalpha11[23]{
  8.1455493, 8.1058081, 7.9903083, 7.5756433, 7.0109396, 6.3972855,
  5.7985381, 5.2452249, 4.7476246, 4.3059510, 3.9161167, 3.5725710,
  3.0018411, 2.5535671, 2.1967930, 1.9088609, 1.6733812, 1.2435728,
  0.9590400, 0.6186562, 0.4313276, 0.2159017, 0.1291912,
};
static const double secscale11{
  0.50000000000000,
};

// sec. 12
static const double secalpha12[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale12{
  0.00000000000000,
};

// sec. 13
static const double secalpha13[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale13{
  0.00000000000000,
};

// sec. 14
static const double secalpha14[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale14{
  0.00000000000000,
};

// sec. 15
static const double secalpha15[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale15{
  0.00000000000000,
};

// sec. 16
static const double secalpha16[23]{
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
  0.0000000, 0.0000000, 0.0000000, 0.0000000, 0.0000000,
};
static const double secscale16{
  0.00000000000000,
};

// sec. 17
static const double secalpha17[23]{
  30.5968154, 30.2907908, 29.4281025, 26.5588368, 23.0571447, 19.6470649,
  16.6420247, 14.1130996, 12.0267253, 10.3165485, 8.9140109,  7.7590140,
  6.0042243,  4.7671234,  3.8705622,  3.2039005,  2.6965878,  1.8588040,
  1.3665825,  0.8411737,  0.5795824,  0.2981883,  0.1870572,
};
static const double secscale17{
  0.50000000000000,
};

static const double *secalpha[18]{
  nullptr,
  secalpha1,
  secalpha2,
  secalpha3,
  secalpha4,
  secalpha5,
  secalpha6,
  secalpha7,
  secalpha8,
  secalpha9,
  secalpha10,
  secalpha11,
  secalpha12,
  secalpha13,
  secalpha14,
  secalpha15,
  secalpha16,
  secalpha17,
};
static const double secscale[18]{
  0,
  secscale1,
  secscale2,
  secscale3,
  secscale4,
  secscale5,
  secscale6,
  secscale7,
  secscale8,
  secscale9,
  secscale10,
  secscale11,
  secscale12,
  secscale13,
  secscale14,
  secscale15,
  secscale16,
  secscale17,
};

} // namespace dftd4