LALSimPhenSpinRingDown.c

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/*
 * Copyright (C) 2011 Riccardo Sturani
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with with program; see the file COPYING. If not, write to the
 *  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 *  MA  02110-1301  USA
 */
 
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_interp.h>
#include <gsl/gsl_spline.h>
#include <lal/LALStdlib.h>
#include <lal/LALConstants.h>
 
#ifdef __GNUC__
#define UNUSED __attribute__ ((unused))
#else
#define UNUSED
#endif
 
static int UNUSED XLALSimIMRPhenSpinGenerateQNMFreq(COMPLEX16Vector *modefreqs,
                                      UINT4 l,
                                      INT4  m,
                                      REAL8 finalMass,
                                      REAL8 finalSpin,
                                      REAL8 totalMass)
{
  static const int UNUSED nSpin=107;
  static const int nMode=8;
  if (modefreqs->length>8) {
    XLALPrintError("*** LALSimIMRPhenSpinGenerateQNMFreq ERROR: number of modes limited to %d, %d requested\n",nMode,modefreqs->length);
    XLAL_ERROR(XLAL_EFUNC);
  }
  int idx;
 
  static const double afinallist[107] = {-0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
  -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
  -0.986, -0.984, -0.982, -0.98, -0.975, -0.97, -0.96, -0.95, -0.94, -0.92, -0.9, -0.88, -0.86, -0.84,
  -0.82, -0.8, -0.78, -0.76, -0.74, -0.72, -0.7, -0.65, -0.6, -0.55, -0.5, -0.45, -0.4, -0.35, -0.3,
  -0.25, -0.2, -0.15, -0.1, -0.05, 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6,
  0.65, 0.7, 0.72, 0.74, 0.76, 0.78, 0.8, 0.82, 0.84, 0.86, 0.88, 0.9, 0.92, 0.94, 0.95, 0.96, 0.97,
  0.975, 0.98, 0.982, 0.984, 0.986, 0.988, 0.99, 0.992, 0.994, 0.995, 0.996, 0.997, 0.9975, 0.998,
  0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996};
 
  const double reomegaqnm22[8][107] = {{ 0.270228, 0.276562, 0.280636, 0.285234, 0.287548, 0.288282, 0.288845, 0.289287, 0.289639, 0.289924, 0.290781, 0.291189, 0.291418, 0.291658, 0.291785, 0.291870, 0.291998, 0.292111, 0.292221, 0.292331, 0.292441, 0.292552, 0.292664, 0.292943, 0.293223, 0.293787, 0.294354, 0.294925, 0.296077, 0.297244, 0.298426, 0.299624, 0.300837, 0.302067, 0.303313, 0.304577, 0.305857, 0.307156, 0.308473, 0.309808, 0.313232, 0.316784, 0.320473, 0.324307, 0.328299, 0.332458, 0.336798, 0.341333, 0.346079, 0.351053, 0.356275, 0.361768, 0.367557, 0.373672, 0.380146, 0.387018, 0.394333, 0.402145, 0.410518, 0.419527, 0.429264, 0.439842, 0.451402, 0.464123, 0.478235, 0.494045, 0.511969, 0.532600, 0.541794, 0.551630, 0.562201, 0.573616, 0.586017, 0.599580, 0.614539, 0.631206, 0.650018, 0.671614, 0.696995, 0.727875, 0.746320, 0.767674, 0.793208, 0.808235, 0.825429, 0.833100, 0.841343, 0.850272, 0.860046, 0.870893, 0.883162, 0.897446, 0.905664, 0.914902, 0.925581, 0.931689, 0.938524, 0.946385, 0.948123, 0.949929, 0.951813, 0.953784, 0.955854, 0.960358, 0.965514, 0.968438, 0.971690},
{ 0.243689, 0.247076, 0.248937, 0.250577, 0.251041, 0.251088, 0.251073, 0.251023, 0.250952, 0.250874, 0.250520, 0.250339, 0.250292, 0.250359, 0.250463, 0.250549, 0.250686, 0.250814, 0.250945, 0.251079, 0.251214, 0.251349, 0.251484, 0.251820, 0.252158, 0.252836, 0.253519, 0.254205, 0.255591, 0.256994, 0.258413, 0.259851, 0.261306, 0.262780, 0.264273, 0.265785, 0.267317, 0.268869, 0.270442, 0.272036, 0.276117, 0.280342, 0.284721, 0.289262, 0.293978, 0.298880, 0.303981, 0.309295, 0.314838, 0.320629, 0.326687, 0.333036, 0.339701, 0.346711, 0.354101, 0.361910, 0.370183, 0.378976, 0.388353, 0.398390, 0.409183, 0.420847, 0.433527, 0.447407, 0.462728, 0.479807, 0.499079, 0.521161, 0.530970, 0.541447, 0.552684, 0.564795, 0.577922, 0.592247, 0.608001, 0.625499, 0.645173, 0.667658, 0.693938, 0.725708, 0.744582, 0.766349, 0.792272, 0.807482, 0.824852, 0.832591, 0.840901, 0.849896, 0.859735, 0.870645, 0.882977, 0.897322, 0.905568, 0.914834, 0.925538, 0.931657, 0.938502, 0.946371, 0.948110, 0.949919, 0.951804, 0.953776, 0.955847, 0.960353, 0.965510, 0.968435, 0.971688},
{ 0.191626, 0.188311, 0.185222, 0.182107, 0.182532, 0.183173, 0.183784, 0.184279, 0.184634, 0.184860, 0.184811, 0.184353, 0.184263, 0.184581, 0.184713, 0.184720, 0.184862, 0.185055, 0.185205, 0.185357, 0.185521, 0.185687, 0.185850, 0.186250, 0.186658, 0.187473, 0.188294, 0.189121, 0.190789, 0.192478, 0.194189, 0.195923, 0.197680, 0.199460, 0.201263, 0.203092, 0.204945, 0.206823, 0.208728, 0.210659, 0.215608, 0.220737, 0.226056, 0.231577, 0.237312, 0.243272, 0.249472, 0.255926, 0.262651, 0.269665, 0.276988, 0.284642, 0.292654, 0.301053, 0.309873, 0.319153, 0.328939, 0.339285, 0.350255, 0.361927, 0.374396, 0.387779, 0.402225, 0.417925, 0.435130, 0.454179, 0.475545, 0.499906, 0.510701, 0.522217, 0.534557, 0.547847, 0.562240, 0.577926, 0.595148, 0.614222, 0.635576, 0.659827, 0.687923, 0.721496, 0.741239, 0.763831, 0.790516, 0.806079, 0.823779, 0.831643, 0.840075, 0.849189, 0.859144, 0.870168, 0.882612, 0.897067, 0.905368, 0.914687, 0.925444, 0.931587, 0.938454, 0.946343, 0.948085, 0.949897, 0.951785, 0.953760, 0.955833, 0.960343, 0.965503, 0.968430, 0.971683},
{ 0.127766, 0.134925, 0.137314, 0.135026, 0.132545, 0.132613, 0.133213, 0.133927, 0.134502, 0.134846, 0.134197, 0.133839, 0.134383, 0.134311, 0.134305, 0.134548, 0.134538, 0.134764, 0.134855, 0.134990, 0.135153, 0.135276, 0.135401, 0.135760, 0.136094, 0.136791, 0.137494, 0.138199, 0.139634, 0.141097, 0.142587, 0.144106, 0.145656, 0.147236, 0.148849, 0.150493, 0.152171, 0.153884, 0.155632, 0.157416, 0.162043, 0.166920, 0.172065, 0.177495, 0.183228, 0.189280, 0.195670, 0.202416, 0.209537, 0.217053, 0.224984, 0.233352, 0.242183, 0.251505, 0.261348, 0.271749, 0.282749, 0.294397, 0.306753, 0.319886, 0.333884, 0.348856, 0.364938, 0.382309, 0.401210, 0.421977, 0.445099, 0.471336, 0.482957, 0.495375, 0.508729, 0.523187, 0.538956, 0.556285, 0.575464, 0.596830, 0.620788, 0.647869, 0.678894, 0.715333, 0.736426, 0.760279, 0.788101, 0.804173, 0.822338, 0.830374, 0.838970, 0.848242, 0.858347, 0.869515, 0.882100, 0.896696, 0.905068, 0.914460, 0.925289, 0.931468, 0.938371, 0.946292, 0.948041, 0.949858, 0.951752, 0.953732, 0.955811, 0.960329, 0.965496, 0.968424, 0.971679},
{ 0.111845, 0.106167, 0.107777, 0.111206, 0.108936, 0.108364, 0.108639, 0.109304, 0.109887, 0.110167, 0.109102, 0.109714, 0.109696, 0.109638, 0.109676, 0.109676, 0.109779, 0.109961, 0.109986, 0.110136, 0.110210, 0.110304, 0.110427, 0.110658, 0.110906, 0.111408, 0.111916, 0.112428, 0.113458, 0.114508, 0.115576, 0.116663, 0.117771, 0.118902, 0.120054, 0.121230, 0.122431, 0.123659, 0.124914, 0.126199, 0.129550, 0.133123, 0.136951, 0.141068, 0.145514, 0.150331, 0.155561, 0.161252, 0.167448, 0.174197, 0.181540, 0.189518, 0.198166, 0.207515, 0.217594, 0.228433, 0.240060, 0.252511, 0.265825, 0.280057, 0.295269, 0.311546, 0.328992, 0.347741, 0.367967, 0.389902, 0.413872, 0.440385, 0.451887, 0.464034, 0.476972, 0.490925, 0.506263, 0.523592, 0.543861, 0.568205, 0.597077, 0.629836, 0.666171, 0.707148, 0.730203, 0.755806, 0.785154, 0.801892, 0.820650, 0.828901, 0.837698, 0.847157, 0.857436, 0.868766, 0.881504, 0.896248, 0.904696, 0.914167, 0.925079, 0.931302, 0.938248, 0.946214, 0.947971, 0.949797, 0.951699, 0.953687, 0.955773, 0.960306, 0.965484, 0.968417, 0.971675},
{ 0.097352, 0.098752, 0.095213, 0.097231, 0.096805, 0.095906, 0.095838, 0.096399, 0.096960, 0.097159, 0.096291, 0.096883, 0.096445, 0.096717, 0.096813, 0.096745, 0.096896, 0.097015, 0.097036, 0.097175, 0.097226, 0.097351, 0.097408, 0.097640, 0.097875, 0.098312, 0.098759, 0.099209, 0.100108, 0.101005, 0.101904, 0.102805, 0.103707, 0.104611, 0.105520, 0.106431, 0.107346, 0.108266, 0.109192, 0.110125, 0.112493, 0.114931, 0.117463, 0.120121, 0.122943, 0.125975, 0.129278, 0.132931, 0.137032, 0.141710, 0.147116, 0.153415, 0.160767, 0.169299, 0.179085, 0.190140, 0.202441, 0.215947, 0.230623, 0.246457, 0.263464, 0.281691, 0.301218, 0.322157, 0.344655, 0.368896, 0.395090, 0.423450, 0.435430, 0.447764, 0.460418, 0.473311, 0.486283, 0.499037, 0.511101, 0.522095, 0.532461, 0.536917, 0.527548, 0.521465, 0.518438, 0.515417, 0.512410, 0.510911, 0.509415, 0.508818, 0.508221, 0.507624, 0.507028, 0.506432, 0.505837, 0.505242, 0.504944, 0.504647, 0.504350, 0.504202, 0.504054, 0.503904, 0.503874, 0.503845, 0.503817, 0.503789, 0.503760, 0.503692, 0.503638, 0.503632, 0.503585},
{ 0.084098, 0.086874, 0.087915, 0.085882, 0.087177, 0.086217, 0.085878, 0.086378, 0.086944, 0.087051, 0.086602, 0.086479, 0.086776, 0.086675, 0.086661, 0.086887, 0.086965, 0.087057, 0.087108, 0.087225, 0.087354, 0.087429, 0.087563, 0.087827, 0.088086, 0.088604, 0.089131, 0.089658, 0.090698, 0.091730, 0.092745, 0.093744, 0.094727, 0.095694, 0.096641, 0.097572, 0.098485, 0.099379, 0.100255, 0.101113, 0.103185, 0.105155, 0.107036, 0.108838, 0.110571, 0.112244, 0.113866, 0.115452, 0.117034, 0.118689, 0.120596, 0.123138, 0.127029, 0.133252, 0.142539, 0.154841, 0.169536, 0.185971, 0.203721, 0.222585, 0.242517, 0.263571, 0.285865, 0.309569, 0.334899, 0.362133, 0.391629, 0.423854, 0.437641, 0.452010, 0.467014, 0.482713, 0.499165, 0.516428, 0.534543, 0.553525, 0.573596, 0.602227, 0.649295, 0.697231, 0.722841, 0.750611, 0.781797, 0.799333, 0.818797, 0.827303, 0.836336, 0.846012, 0.856487, 0.867993, 0.880887, 0.895775, 0.904293, 0.913837, 0.924830, 0.931097, 0.938091, 0.946107, 0.947875, 0.949711, 0.951623, 0.953621, 0.955717, 0.960269, 0.965464, 0.968404, 0.971669},
{ 0.078336, 0.073380, 0.076620, 0.074432, 0.076411, 0.075479, 0.074940, 0.075503, 0.076100, 0.076029, 0.075987, 0.075511, 0.075776, 0.075832, 0.075971, 0.075923, 0.076114, 0.076229, 0.076321, 0.076418, 0.076597, 0.076721, 0.076841, 0.077174, 0.077519, 0.078210, 0.078912, 0.079614, 0.081016, 0.082412, 0.083796, 0.085153, 0.086479, 0.087770, 0.089021, 0.090230, 0.091394, 0.092513, 0.093588, 0.094617, 0.096993, 0.099091, 0.100921, 0.102489, 0.103795, 0.104821, 0.105530, 0.105854, 0.105679, 0.104817, 0.102968, 0.099711, 0.094996, 0.092822, 0.102996, 0.122468, 0.144233, 0.166117, 0.187881, 0.209753, 0.232042, 0.255048, 0.279057, 0.304354, 0.331244, 0.360084, 0.391319, 0.425537, 0.440234, 0.455604, 0.471729, 0.488705, 0.506652, 0.525720, 0.546107, 0.568081, 0.592057, 0.618799, 0.650217, 0.691189, 0.716737, 0.745623, 0.778341, 0.796657, 0.816858, 0.825638, 0.834931, 0.844846, 0.855539, 0.867237, 0.880294, 0.895318, 0.903898, 0.913504, 0.924565, 0.930871, 0.937910, 0.945976, 0.947755, 0.949602, 0.951525, 0.953535, 0.955643, 0.960217, 0.965434, 0.968355, 0.971639}};
 
  const double reomegaqnm21[8][107] = {{ 0.336609, 0.339386, 0.340852, 0.342219, 0.342818, 0.343002, 0.343143, 0.343254, 0.343344, 0.343417, 0.343641, 0.343748, 0.343804, 0.343853, 0.343871, 0.343879, 0.343886, 0.343891, 0.343896, 0.343902, 0.343909, 0.343915, 0.343922, 0.343941, 0.343960, 0.344002, 0.344049, 0.344101, 0.344220, 0.344359, 0.344517, 0.344696, 0.344896, 0.345115, 0.345356, 0.345617, 0.345899, 0.346201, 0.346525, 0.346870, 0.347824, 0.348911, 0.350132, 0.351491, 0.352990, 0.354633, 0.356423, 0.358366, 0.360469, 0.362738, 0.365183, 0.367812, 0.370637, 0.373672, 0.376931, 0.380432, 0.384197, 0.388248, 0.392615, 0.397330, 0.402436, 0.407979, 0.414020, 0.420632, 0.427909, 0.435968, 0.444968, 0.455121, 0.459569, 0.464271, 0.469259, 0.474564, 0.480231, 0.486308, 0.492859, 0.499965, 0.507729, 0.516291, 0.525845, 0.536673, 0.542693, 0.549213, 0.556329, 0.560146, 0.564155, 0.565814, 0.567505, 0.569227, 0.570976, 0.572749, 0.574535, 0.576322, 0.577208, 0.578084, 0.578948, 0.579374, 0.579795, 0.580212, 0.580295, 0.580377, 0.580460, 0.580541, 0.580623, 0.580784, 0.580942, 0.581018, 0.581093},
{ 0.313486, 0.314984, 0.315748, 0.316360, 0.316504, 0.316512, 0.316502, 0.316483, 0.316460, 0.316436, 0.316347, 0.316311, 0.316305, 0.316315, 0.316325, 0.316330, 0.316338, 0.316345, 0.316352, 0.316360, 0.316368, 0.316375, 0.316383, 0.316401, 0.316419, 0.316455, 0.316491, 0.316527, 0.316602, 0.316682, 0.316772, 0.316874, 0.316989, 0.317122, 0.317273, 0.317444, 0.317636, 0.317851, 0.318090, 0.318353, 0.319124, 0.320064, 0.321179, 0.322476, 0.323960, 0.325636, 0.327508, 0.329582, 0.331865, 0.334364, 0.337088, 0.340045, 0.343249, 0.346711, 0.350448, 0.354478, 0.358823, 0.363506, 0.368558, 0.374014, 0.379916, 0.386313, 0.393268, 0.400856, 0.409172, 0.418337, 0.428509, 0.439897, 0.444855, 0.450076, 0.455587, 0.461420, 0.467612, 0.474208, 0.481261, 0.488834, 0.497004, 0.505862, 0.515506, 0.526011, 0.531572, 0.537263, 0.542874, 0.545479, 0.547723, 0.548438, 0.548984, 0.549290, 0.549241, 0.548642, 0.547140, 0.544185, 0.542606, 0.542325, 0.541626, 0.540962, 0.540617, 0.540156, 0.540066, 0.539986, 0.539906, 0.539818, 0.539726, 0.539553, 0.539377, 0.539288, 0.539198},
{ 0.270281, 0.269419, 0.268655, 0.267935, 0.267923, 0.268009, 0.268102, 0.268185, 0.268251, 0.268297, 0.268334, 0.268285, 0.268273, 0.268312, 0.268342, 0.268359, 0.268398, 0.268442, 0.268483, 0.268523, 0.268562, 0.268601, 0.268640, 0.268733, 0.268822, 0.268989, 0.269141, 0.269280, 0.269520, 0.269718, 0.269881, 0.270016, 0.270132, 0.270235, 0.270333, 0.270431, 0.270536, 0.270653, 0.270785, 0.270937, 0.271426, 0.272100, 0.272992, 0.274121, 0.275504, 0.277153, 0.279078, 0.281288, 0.283792, 0.286598, 0.289716, 0.293156, 0.296931, 0.301053, 0.305540, 0.310410, 0.315684, 0.321389, 0.327554, 0.334218, 0.341421, 0.349217, 0.357668, 0.366852, 0.376864, 0.387825, 0.399890, 0.413261, 0.419032, 0.425075, 0.431414, 0.438075, 0.445088, 0.452488, 0.460310, 0.468593, 0.477369, 0.486650, 0.496390, 0.506348, 0.511184, 0.515607, 0.519030, 0.519992, 0.520100, 0.519830, 0.519361, 0.518710, 0.517943, 0.517204, 0.516728, 0.516696, 0.516098, 0.513376, 0.509813, 0.508083, 0.506412, 0.504789, 0.504468, 0.504148, 0.503830, 0.503511, 0.503194, 0.502559, 0.501923, 0.501605, 0.501286},
{ 0.212690, 0.214089, 0.215208, 0.215364, 0.214740, 0.214584, 0.214560, 0.214625, 0.214730, 0.214837, 0.214992, 0.214885, 0.214922, 0.215045, 0.215071, 0.215139, 0.215267, 0.215383, 0.215507, 0.215624, 0.215741, 0.215858, 0.215974, 0.216256, 0.216533, 0.217064, 0.217566, 0.218040, 0.218903, 0.219653, 0.220295, 0.220836, 0.221285, 0.221650, 0.221945, 0.222180, 0.222368, 0.222520, 0.222647, 0.222759, 0.223032, 0.223383, 0.223900, 0.224647, 0.225672, 0.227010, 0.228689, 0.230730, 0.233151, 0.235969, 0.239199, 0.242854, 0.246951, 0.251505, 0.256534, 0.262058, 0.268101, 0.274689, 0.281852, 0.289628, 0.298059, 0.307197, 0.317104, 0.327855, 0.339542, 0.352278, 0.366207, 0.381510, 0.388065, 0.394895, 0.402017, 0.409454, 0.417227, 0.425361, 0.433878, 0.442797, 0.452127, 0.461855, 0.471918, 0.482195, 0.487390, 0.492710, 0.498495, 0.501813, 0.505600, 0.507251, 0.508939, 0.510585, 0.512031, 0.513028, 0.513289, 0.512758, 0.512367, 0.512091, 0.511921, 0.511350, 0.509600, 0.507150, 0.506650, 0.506154, 0.505662, 0.505175, 0.504694, 0.503744, 0.502809, 0.502344, 0.501880},
{ 0.171239, 0.169224, 0.168634, 0.170053, 0.169938, 0.169613, 0.169418, 0.169408, 0.169531, 0.169696, 0.169825, 0.169724, 0.169920, 0.169916, 0.170075, 0.170140, 0.170344, 0.170511, 0.170710, 0.170886, 0.171073, 0.171258, 0.171437, 0.171892, 0.172337, 0.173213, 0.174064, 0.174889, 0.176453, 0.177895, 0.179203, 0.180372, 0.181395, 0.182273, 0.183007, 0.183606, 0.184081, 0.184444, 0.184710, 0.184896, 0.185105, 0.185120, 0.185113, 0.185222, 0.185550, 0.186176, 0.187164, 0.188562, 0.190413, 0.192751, 0.195604, 0.199000, 0.202962, 0.207515, 0.212679, 0.218480, 0.224939, 0.232083, 0.239940, 0.248543, 0.257928, 0.268139, 0.279228, 0.291258, 0.304303, 0.318456, 0.333830, 0.350563, 0.357675, 0.365045, 0.372687, 0.380617, 0.388855, 0.397422, 0.406346, 0.415670, 0.425462, 0.435857, 0.447149, 0.459990, 0.467349, 0.475546, 0.484594, 0.489367, 0.494295, 0.496339, 0.498459, 0.500692, 0.503080, 0.505635, 0.508214, 0.510197, 0.510572, 0.510387, 0.509864, 0.509635, 0.509456, 0.508790, 0.508443, 0.507999, 0.507470, 0.506881, 0.506257, 0.504974, 0.503704, 0.503082, 0.502466},
{ 0.136159, 0.137914, 0.137016, 0.136626, 0.137329, 0.137055, 0.136755, 0.136667, 0.136793, 0.136997, 0.136954, 0.137117, 0.137154, 0.137279, 0.137300, 0.137470, 0.137649, 0.137842, 0.138069, 0.138258, 0.138476, 0.138671, 0.138881, 0.139389, 0.139898, 0.140910, 0.141910, 0.142898, 0.144829, 0.146684, 0.148447, 0.150099, 0.151622, 0.153001, 0.154221, 0.155270, 0.156142, 0.156839, 0.157368, 0.157740, 0.158094, 0.157845, 0.157250, 0.156526, 0.155847, 0.155354, 0.155162, 0.155369, 0.156061, 0.157316, 0.159206, 0.161795, 0.165143, 0.169299, 0.174306, 0.180192, 0.186977, 0.194671, 0.203282, 0.212811, 0.223263, 0.234649, 0.246985, 0.260297, 0.274622, 0.290009, 0.306518, 0.324226, 0.331666, 0.339322, 0.347205, 0.355332, 0.363727, 0.372432, 0.381518, 0.391111, 0.401435, 0.412868, 0.425995, 0.441563, 0.450520, 0.460463, 0.471717, 0.477974, 0.484665, 0.487438, 0.490248, 0.493085, 0.495960, 0.498923, 0.502084, 0.505527, 0.507222, 0.508526, 0.508875, 0.508627, 0.508251, 0.507926, 0.507863, 0.507785, 0.507670, 0.507484, 0.507181, 0.506113, 0.504624, 0.503839, 0.503060},
{ 0.114342, 0.113963, 0.115141, 0.114074, 0.114860, 0.114789, 0.114485, 0.114338, 0.114452, 0.114665, 0.114512, 0.114807, 0.114670, 0.114821, 0.114995, 0.115025, 0.115231, 0.115438, 0.115661, 0.115846, 0.116050, 0.116249, 0.116452, 0.116951, 0.117454, 0.118454, 0.119460, 0.120464, 0.122464, 0.124443, 0.126383, 0.128266, 0.130073, 0.131781, 0.133368, 0.134813, 0.136090, 0.137179, 0.138065, 0.138742, 0.139567, 0.139335, 0.138333, 0.136834, 0.135064, 0.133208, 0.131418, 0.129826, 0.128564, 0.127775, 0.127629, 0.128336, 0.130133, 0.133252, 0.137863, 0.144021, 0.151672, 0.160684, 0.170902, 0.182186, 0.194429, 0.207556, 0.221528, 0.236327, 0.251955, 0.268421, 0.285744, 0.303950, 0.311492, 0.319195, 0.327076, 0.335168, 0.343522, 0.352232, 0.361443, 0.371382, 0.382361, 0.394771, 0.409089, 0.426092, 0.436065, 0.447400, 0.460415, 0.467675, 0.475563, 0.478922, 0.482402, 0.485993, 0.489665, 0.493377, 0.497113, 0.500995, 0.503086, 0.505273, 0.507186, 0.507677, 0.507628, 0.507177, 0.507077, 0.506981, 0.506892, 0.506806, 0.506714, 0.506383, 0.505391, 0.504576, 0.503665},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.096761, 0.105267, 0.116748, 0.129817, 0.143719, 0.158124, 0.172920, 0.188094, 0.203673, 0.219697, 0.236201, 0.253208, 0.270727, 0.288784, 0.296181, 0.303707, 0.311404, 0.319342, 0.327628, 0.336416, 0.345907, 0.356330, 0.367923, 0.380968, 0.395965, 0.413866, 0.424377, 0.436366, 0.450442, 0.458506, 0.467375, 0.471171, 0.475126, 0.479254, 0.483568, 0.488052, 0.492639, 0.497232, 0.499557, 0.501993, 0.504598, 0.505838, 0.506697, 0.506742, 0.506649, 0.506536, 0.506410, 0.506281, 0.506156, 0.505924, 0.505541, 0.505047, 0.504219}};
  const double reomegaqnm20[8][107] = {{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.373762, 0.374032, 0.374485, 0.375124, 0.375955, 0.376985, 0.378223, 0.379682, 0.381374, 0.383318, 0.385536, 0.388054, 0.390905, 0.394129, 0.395535, 0.397012, 0.398565, 0.400198, 0.401917, 0.403727, 0.405634, 0.407645, 0.409766, 0.412004, 0.414368, 0.416862, 0.418159, 0.419491, 0.420856, 0.421551, 0.422254, 0.422538, 0.422823, 0.423109, 0.423396, 0.423685, 0.423975, 0.424266, 0.424412, 0.424558, 0.424701, 0.424768, 0.424827, 0.424866, 0.424870, 0.424871, 0.424870, 0.424866, 0.424858, 0.424833, 0.424799, 0.424786, 0.424772},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.346831, 0.347191, 0.347795, 0.348646, 0.349750, 0.351116, 0.352753, 0.354673, 0.356893, 0.359428, 0.362301, 0.365534, 0.369153, 0.373185, 0.374919, 0.376725, 0.378602, 0.380550, 0.382569, 0.384655, 0.386801, 0.388999, 0.391231, 0.393473, 0.395684, 0.397807, 0.398810, 0.399759, 0.400640, 0.401051, 0.401440, 0.401589, 0.401734, 0.401876, 0.402013, 0.402145, 0.402274, 0.402398, 0.402459, 0.402518, 0.402575, 0.402603, 0.402634, 0.402671, 0.402680, 0.402690, 0.402699, 0.402708, 0.402716, 0.402715, 0.402639, 0.402518, 0.402260},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.301226, 0.301745, 0.302612, 0.303832, 0.305410, 0.307356, 0.309677, 0.312384, 0.315491, 0.319010, 0.322953, 0.327329, 0.332140, 0.337367, 0.339564, 0.341813, 0.344104, 0.346423, 0.348751, 0.351062, 0.353316, 0.355458, 0.357410, 0.359064, 0.360277, 0.360891, 0.360932, 0.360787, 0.360457, 0.360224, 0.359947, 0.359824, 0.359695, 0.359558, 0.359416, 0.359266, 0.359111, 0.358949, 0.358866, 0.358781, 0.358695, 0.358653, 0.358612, 0.358564, 0.358551, 0.358536, 0.358520, 0.358503, 0.358487, 0.358477, 0.358557, 0.358656, 0.358763},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.251735, 0.252425, 0.253576, 0.255192, 0.257276, 0.259831, 0.262861, 0.266370, 0.270359, 0.274824, 0.279754, 0.285121, 0.290866, 0.296871, 0.299299, 0.301709, 0.304069, 0.306337, 0.308452, 0.310333, 0.311866, 0.312892, 0.313197, 0.312525, 0.310673, 0.307762, 0.306042, 0.304179, 0.302199, 0.301174, 0.300132, 0.299710, 0.299286, 0.298859, 0.298431, 0.298001, 0.297569, 0.297135, 0.296918, 0.296700, 0.296479, 0.296377, 0.296272, 0.296133, 0.296106, 0.296084, 0.296072, 0.296071, 0.296081, 0.296090, 0.295901, 0.295691, 0.295593},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.207801, 0.208660, 0.210090, 0.212089, 0.214652, 0.217773, 0.221444, 0.225649, 0.230365, 0.235556, 0.241164, 0.247088, 0.253161, 0.259075, 0.261282, 0.263320, 0.265113, 0.266556, 0.267505, 0.267758, 0.267026, 0.264918, 0.260982, 0.255164, 0.249003, 0.243206, 0.240152, 0.237243, 0.234329, 0.232892, 0.231471, 0.230906, 0.230343, 0.229782, 0.229223, 0.228668, 0.228112, 0.227563, 0.227282, 0.227020, 0.226723, 0.226605, 0.226491, 0.226268, 0.226253, 0.226265, 0.226297, 0.226324, 0.226309, 0.226033, 0.225920, 0.226313, 0.226576},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.169657, 0.170725, 0.172497, 0.174959, 0.178090, 0.181864, 0.186246, 0.191189, 0.196629, 0.202475, 0.208593, 0.214773, 0.220670, 0.225672, 0.227190, 0.228272, 0.228756, 0.228412, 0.226904, 0.223732, 0.218155, 0.209323, 0.198745, 0.193577, 0.186305, 0.180463, 0.176827, 0.174111, 0.171249, 0.169885, 0.168502, 0.167948, 0.167413, 0.166876, 0.166340, 0.165810, 0.165288, 0.164746, 0.164515, 0.164209, 0.163984, 0.163792, 0.163805, 0.163455, 0.163488, 0.163585, 0.163680, 0.163676, 0.163501, 0.163097, 0.163828, 0.163493, 0.162468},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.133728, 0.135148, 0.137483, 0.140692, 0.144717, 0.149486, 0.154913, 0.160894, 0.167302, 0.173965, 0.180643, 0.186972, 0.192350, 0.195693, 0.196032, 0.195488, 0.193718, 0.190195, 0.184057, 0.173800, 0.157606, 0.149904, 0.150294, 0.136574, 0.136371, 0.130053, 0.125270, 0.122908, 0.121266, 0.119961, 0.118878, 0.118309, 0.117833, 0.117412, 0.116952, 0.116509, 0.116094, 0.115667, 0.115352, 0.115216, 0.115053, 0.114762, 0.114876, 0.114415, 0.114510, 0.114721, 0.114853, 0.114708, 0.114322, 0.114511, 0.114432, 0.113700, 0.115095},
{ 0.099636, 0.098809, 0.098823, 0.098961, 0.099181, 0.099322, 0.099091, 0.098913, 0.099007, 0.099206, 0.099084, 0.099201, 0.099305, 0.099370, 0.099413, 0.099541, 0.099710, 0.099906, 0.100109, 0.100292, 0.100464, 0.100668, 0.100843, 0.101320, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617, 0.108576, 0.110540, 0.112492, 0.114417, 0.116296, 0.118106, 0.119822, 0.121422, 0.122876, 0.124150, 0.125214, 0.126860, 0.127085, 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.108440, 0.104598, 0.100602, 0.096644, 0.093455, 0.092822, 0.093595, 0.095873, 0.099540, 0.104431, 0.110354, 0.117108, 0.124493, 0.132307, 0.140327, 0.148283, 0.155807, 0.162340, 0.166934, 0.167780, 0.166293, 0.163133, 0.157503, 0.147921, 0.131060, 0.107176, 0.119461, 0.116330, 0.094108, 0.104492, 0.097083, 0.093018, 0.087420, 0.086369, 0.083105, 0.081981, 0.082460, 0.081711, 0.081131, 0.080986, 0.080498, 0.080153, 0.079710, 0.079360, 0.079312, 0.079042, 0.078766, 0.078878, 0.078724, 0.078322, 0.078468, 0.078779, 0.078873, 0.078526, 0.078115, 0.078949, 0.077817, 0.078978, 0.078246}};
  const double reomegaqnm33[8][107] = {{ 0.445768, 0.452799, 0.456948, 0.460943, 0.462462, 0.462842, 0.463095, 0.463269, 0.463394, 0.463488, 0.463746, 0.463886, 0.463989, 0.464144, 0.464267, 0.464374, 0.464572, 0.464763, 0.464952, 0.465140, 0.465329, 0.465518, 0.465707, 0.466182, 0.466657, 0.467612, 0.468573, 0.469540, 0.471491, 0.473465, 0.475464, 0.477487, 0.479535, 0.481609, 0.483709, 0.485837, 0.487991, 0.490174, 0.492386, 0.494627, 0.500363, 0.506300, 0.512449, 0.518826, 0.525445, 0.532323, 0.539479, 0.546934, 0.554710, 0.562834, 0.571335, 0.580244, 0.589600, 0.599443, 0.609823, 0.620796, 0.632425, 0.644787, 0.657972, 0.672086, 0.687260, 0.703650, 0.721455, 0.740921, 0.762369, 0.786223, 0.813057, 0.843687, 0.857254, 0.871717, 0.887201, 0.903860, 0.921885, 0.941521, 0.963088, 0.987016, 1.013906, 1.044637, 1.080583, 1.124097, 1.149983, 1.179862, 1.215469, 1.236367, 1.260229, 1.270858, 1.282268, 1.294616, 1.308117, 1.323083, 1.339991, 1.359648, 1.370944, 1.383632, 1.398286, 1.406660, 1.416026, 1.426791, 1.429170, 1.431642, 1.434220, 1.436917, 1.439748, 1.445906, 1.452953, 1.456948, 1.461390},
{ 0.428357, 0.432238, 0.434351, 0.436362, 0.437184, 0.437404, 0.437552, 0.437654, 0.437725, 0.437773, 0.437868, 0.437898, 0.437929, 0.438015, 0.438115, 0.438217, 0.438421, 0.438623, 0.438826, 0.439030, 0.439233, 0.439437, 0.439641, 0.440152, 0.440665, 0.441694, 0.442729, 0.443771, 0.445872, 0.447999, 0.450150, 0.452328, 0.454532, 0.456764, 0.459023, 0.461311, 0.463627, 0.465974, 0.468350, 0.470758, 0.476918, 0.483289, 0.489884, 0.496717, 0.503805, 0.511164, 0.518814, 0.526776, 0.535074, 0.543734, 0.552785, 0.562261, 0.572200, 0.582644, 0.593642, 0.605250, 0.617535, 0.630573, 0.644453, 0.659285, 0.675198, 0.692352, 0.710943, 0.731221, 0.753507, 0.778225, 0.805952, 0.837504, 0.851449, 0.866295, 0.882167, 0.899220, 0.917645, 0.937687, 0.959667, 0.984015, 1.011333, 1.042500, 1.078890, 1.122855, 1.148968, 1.179073, 1.214906, 1.235913, 1.259884, 1.270555, 1.282006, 1.294395, 1.307936, 1.322940, 1.339885, 1.359577, 1.370888, 1.383591, 1.398259, 1.406639, 1.416011, 1.426781, 1.429161, 1.431634, 1.434213, 1.436910, 1.439742, 1.445902, 1.452950, 1.456946, 1.461388},
{ 0.390162, 0.390933, 0.390855, 0.390130, 0.389593, 0.389452, 0.389377, 0.389349, 0.389352, 0.389374, 0.389533, 0.389627, 0.389680, 0.389780, 0.389896, 0.390013, 0.390243, 0.390473, 0.390704, 0.390935, 0.391167, 0.391398, 0.391630, 0.392211, 0.392793, 0.393963, 0.395139, 0.396321, 0.398706, 0.401118, 0.403557, 0.406025, 0.408522, 0.411048, 0.413604, 0.416191, 0.418810, 0.421460, 0.424144, 0.426861, 0.433807, 0.440980, 0.448397, 0.456071, 0.464019, 0.472260, 0.480815, 0.489704, 0.498954, 0.508590, 0.518645, 0.529153, 0.540151, 0.551685, 0.563804, 0.576567, 0.590041, 0.604302, 0.619445, 0.635578, 0.652833, 0.671371, 0.691391, 0.713145, 0.736956, 0.763249, 0.792606, 0.825846, 0.840483, 0.856032, 0.872619, 0.890397, 0.909560, 0.930355, 0.953102, 0.978234, 1.006355, 1.038346, 1.075582, 1.120416, 1.146970, 1.177518, 1.213791, 1.235015, 1.259198, 1.269953, 1.281487, 1.293956, 1.307576, 1.322655, 1.339673, 1.359433, 1.370776, 1.383509, 1.398204, 1.406597, 1.415981, 1.426761, 1.429142, 1.431618, 1.434198, 1.436897, 1.439731, 1.445894, 1.452945, 1.456942, 1.461385},
{ 0.332321, 0.329612, 0.329447, 0.330998, 0.331533, 0.331485, 0.331367, 0.331244, 0.331151, 0.331101, 0.331226, 0.331354, 0.331387, 0.331504, 0.331643, 0.331766, 0.332024, 0.332280, 0.332537, 0.332795, 0.333053, 0.333311, 0.333569, 0.334216, 0.334865, 0.336168, 0.337478, 0.338796, 0.341454, 0.344143, 0.346863, 0.349614, 0.352398, 0.355215, 0.358066, 0.360951, 0.363872, 0.366829, 0.369823, 0.372855, 0.380605, 0.388612, 0.396890, 0.405455, 0.414327, 0.423525, 0.433070, 0.442986, 0.453300, 0.464039, 0.475237, 0.486928, 0.499155, 0.511962, 0.525402, 0.539534, 0.554428, 0.570163, 0.586836, 0.604556, 0.623460, 0.643711, 0.665511, 0.689115, 0.714850, 0.743145, 0.774586, 0.809998, 0.825530, 0.841991, 0.859506, 0.878231, 0.898362, 0.920146, 0.943908, 0.970086, 0.999286, 1.032398, 1.070804, 1.116860, 1.144045, 1.175233, 1.212147, 1.233689, 1.258185, 1.269061, 1.280716, 1.293303, 1.307039, 1.322230, 1.339355, 1.359216, 1.370608, 1.383385, 1.398122, 1.406534, 1.415935, 1.426730, 1.429115, 1.431593, 1.434176, 1.436878, 1.439714, 1.445882, 1.452937, 1.456936, 1.461381},
{ 0.279748, 0.281425, 0.280003, 0.278496, 0.279479, 0.279701, 0.279679, 0.279534, 0.279380, 0.279284, 0.279511, 0.279556, 0.279569, 0.279745, 0.279852, 0.279994, 0.280246, 0.280507, 0.280766, 0.281026, 0.281285, 0.281546, 0.281806, 0.282459, 0.283115, 0.284431, 0.285757, 0.287091, 0.289787, 0.292519, 0.295288, 0.298095, 0.300940, 0.303825, 0.306751, 0.309717, 0.312725, 0.315776, 0.318871, 0.322011, 0.330062, 0.338415, 0.347087, 0.356096, 0.365463, 0.375210, 0.385359, 0.395936, 0.406968, 0.418488, 0.430528, 0.443126, 0.456326, 0.470174, 0.484725, 0.500042, 0.516195, 0.533269, 0.551359, 0.570583, 0.591077, 0.613010, 0.636588, 0.662069, 0.689786, 0.720173, 0.753822, 0.791564, 0.808064, 0.825515, 0.844044, 0.863808, 0.885005, 0.907885, 0.932779, 0.960131, 0.990559, 1.024965, 1.064751, 1.112293, 1.140263, 1.172260, 1.210000, 1.231954, 1.256856, 1.267892, 1.279704, 1.292446, 1.306332, 1.321670, 1.338934, 1.358928, 1.370382, 1.383219, 1.398011, 1.406448, 1.415873, 1.426690, 1.429078, 1.431560, 1.434147, 1.436852, 1.439692, 1.445866, 1.452926, 1.456927, 1.461375},
{ 0.239992, 0.240995, 0.242946, 0.241560, 0.241854, 0.242213, 0.242269, 0.242117, 0.241939, 0.241855, 0.242174, 0.242080, 0.242226, 0.242298, 0.242438, 0.242546, 0.242783, 0.243024, 0.243261, 0.243498, 0.243736, 0.243974, 0.244213, 0.244811, 0.245412, 0.246621, 0.247840, 0.249069, 0.251558, 0.254089, 0.256662, 0.259279, 0.261940, 0.264647, 0.267400, 0.270200, 0.273049, 0.275948, 0.278897, 0.281899, 0.289636, 0.297725, 0.306186, 0.315041, 0.324312, 0.334027, 0.344210, 0.354891, 0.366101, 0.377873, 0.390245, 0.403257, 0.416954, 0.431386, 0.446612, 0.462696, 0.479713, 0.497750, 0.516906, 0.537303, 0.559082, 0.582416, 0.607517, 0.634649, 0.664150, 0.696462, 0.732182, 0.772150, 0.789586, 0.807999, 0.827516, 0.848298, 0.870543, 0.894505, 0.920521, 0.949042, 0.980704, 1.016433, 1.057669, 1.106837, 1.135700, 1.168643, 1.207370, 1.229826, 1.255224, 1.266456, 1.278461, 1.291392, 1.305463, 1.320979, 1.338415, 1.358571, 1.370101, 1.383011, 1.397871, 1.406340, 1.415794, 1.426639, 1.429032, 1.431519, 1.434110, 1.436820, 1.439664, 1.445846, 1.452913, 1.456917, 1.461368},
{ 0.218840, 0.216298, 0.216633, 0.217244, 0.216888, 0.217233, 0.217329, 0.217189, 0.217034, 0.217006, 0.217217, 0.217255, 0.217293, 0.217414, 0.217505, 0.217599, 0.217807, 0.218016, 0.218223, 0.218427, 0.218635, 0.218841, 0.219050, 0.219570, 0.220094, 0.221148, 0.222212, 0.223288, 0.225470, 0.227696, 0.229966, 0.232282, 0.234646, 0.237057, 0.239517, 0.242028, 0.244591, 0.247207, 0.249877, 0.252604, 0.259674, 0.267128, 0.274991, 0.283291, 0.292057, 0.301319, 0.311110, 0.321465, 0.332419, 0.344012, 0.356285, 0.369284, 0.383057, 0.397660, 0.413152, 0.429604, 0.447094, 0.465712, 0.485563, 0.506772, 0.529486, 0.553883, 0.580183, 0.608655, 0.639647, 0.673609, 0.711146, 0.753105, 0.771386, 0.790674, 0.811095, 0.832808, 0.856013, 0.880965, 0.908002, 0.937583, 0.970359, 1.007288, 1.049872, 1.100643, 1.130440, 1.164419, 1.204272, 1.227311, 1.253296, 1.264760, 1.276993, 1.290148, 1.304437, 1.320164, 1.337802, 1.358147, 1.369768, 1.382763, 1.397703, 1.406210, 1.415699, 1.426576, 1.428976, 1.431468, 1.434066, 1.436781, 1.439630, 1.445822, 1.452897, 1.456905, 1.461349},
{ 0.199814, 0.201353, 0.200132, 0.200956, 0.200467, 0.200722, 0.200829, 0.200716, 0.200604, 0.200626, 0.200705, 0.200826, 0.200822, 0.200914, 0.201004, 0.201103, 0.201273, 0.201448, 0.201625, 0.201800, 0.201975, 0.202153, 0.202329, 0.202773, 0.203220, 0.204121, 0.205032, 0.205953, 0.207826, 0.209742, 0.211702, 0.213706, 0.215757, 0.217854, 0.220001, 0.222198, 0.224447, 0.226749, 0.229105, 0.231518, 0.237809, 0.244492, 0.251597, 0.259160, 0.267216, 0.275804, 0.284965, 0.294742, 0.305178, 0.316322, 0.328221, 0.340928, 0.354499, 0.368992, 0.384475, 0.401019, 0.418708, 0.437635, 0.457910, 0.479661, 0.503040, 0.528232, 0.555461, 0.585008, 0.617226, 0.652577, 0.691676, 0.735379, 0.754411, 0.774477, 0.795706, 0.818253, 0.842317, 0.868149, 0.896082, 0.926573, 0.960272, 0.998162, 1.041815, 1.093935, 1.124603, 1.159629, 1.200706, 1.224407, 1.251066, 1.262799, 1.275299, 1.288715, 1.303258, 1.319229, 1.337099, 1.357662, 1.369384, 1.382477, 1.397508, 1.406057, 1.415588, 1.426502, 1.428909, 1.431409, 1.434013, 1.436734, 1.439590, 1.445793, 1.452879, 1.456891, 1.461338}};
  const double reomegaqnm32[8][107] = {{ 0.506437, 0.510521, 0.512354, 0.513460, 0.513606, 0.513606, 0.513597, 0.513588, 0.513582, 0.513579, 0.513605, 0.513652, 0.513698, 0.513775, 0.513839, 0.513896, 0.514004, 0.514110, 0.514215, 0.514321, 0.514427, 0.514533, 0.514639, 0.514905, 0.515173, 0.515712, 0.516256, 0.516805, 0.517918, 0.519052, 0.520208, 0.521384, 0.522583, 0.523803, 0.525046, 0.526312, 0.527601, 0.528913, 0.530250, 0.531610, 0.535122, 0.538796, 0.542640, 0.546663, 0.550875, 0.555285, 0.559905, 0.564749, 0.569831, 0.575167, 0.580774, 0.586673, 0.592888, 0.599443, 0.606369, 0.613700, 0.621475, 0.629738, 0.638545, 0.647958, 0.658052, 0.668919, 0.680668, 0.693440, 0.707409, 0.722802, 0.739919, 0.759175, 0.767600, 0.776509, 0.785959, 0.796021, 0.806783, 0.818351, 0.830862, 0.844496, 0.859491, 0.876183, 0.895066, 0.916929, 0.929375, 0.943179, 0.958779, 0.967466, 0.976924, 0.980968, 0.985186, 0.989601, 0.994241, 0.999140, 1.004343, 1.009907, 1.012845, 1.015898, 1.019070, 1.020697, 1.022344, 1.023996, 1.024325, 1.024652, 1.024978, 1.025301, 1.025621, 1.026251, 1.026862, 1.027158, 1.027448},
{ 0.488275, 0.490233, 0.491246, 0.492172, 0.492528, 0.492618, 0.492677, 0.492716, 0.492741, 0.492758, 0.492791, 0.492808, 0.492829, 0.492880, 0.492934, 0.492989, 0.493099, 0.493208, 0.493318, 0.493428, 0.493538, 0.493648, 0.493758, 0.494035, 0.494313, 0.494872, 0.495436, 0.496005, 0.497158, 0.498330, 0.499524, 0.500739, 0.501976, 0.503236, 0.504519, 0.505826, 0.507158, 0.508514, 0.509897, 0.511306, 0.514946, 0.518763, 0.522766, 0.526965, 0.531371, 0.535995, 0.540849, 0.545948, 0.551306, 0.556940, 0.562868, 0.569112, 0.575695, 0.582644, 0.589989, 0.597765, 0.606012, 0.614777, 0.624114, 0.634088, 0.644775, 0.656268, 0.668679, 0.682148, 0.696852, 0.713017, 0.730945, 0.751047, 0.759820, 0.769080, 0.778884, 0.789302, 0.800419, 0.812337, 0.825190, 0.839148, 0.854439, 0.871376, 0.890418, 0.912277, 0.924613, 0.938179, 0.953324, 0.961646, 0.970585, 0.974358, 0.978256, 0.982286, 0.986453, 0.990754, 0.995172, 0.999636, 1.001825, 1.003902, 1.005709, 1.006402, 1.006823, 1.006752, 1.006644, 1.006493, 1.006292, 1.006037, 1.005719, 1.004884, 1.003812, 1.003222, 1.002616},
{ 0.453935, 0.454400, 0.454380, 0.454081, 0.453894, 0.453854, 0.453838, 0.453837, 0.453845, 0.453857, 0.453919, 0.453957, 0.453984, 0.454042, 0.454104, 0.454165, 0.454286, 0.454408, 0.454530, 0.454652, 0.454775, 0.454897, 0.455019, 0.455326, 0.455633, 0.456250, 0.456870, 0.457494, 0.458752, 0.460026, 0.461318, 0.462628, 0.463959, 0.465311, 0.466686, 0.468084, 0.469507, 0.470957, 0.472434, 0.473939, 0.477830, 0.481919, 0.486219, 0.490742, 0.495504, 0.500517, 0.505796, 0.511357, 0.517216, 0.523391, 0.529901, 0.536770, 0.544022, 0.551685, 0.559790, 0.568375, 0.577480, 0.587154, 0.597454, 0.608445, 0.620207, 0.632835, 0.646443, 0.661174, 0.677206, 0.694768, 0.714161, 0.735793, 0.745193, 0.755089, 0.765534, 0.776597, 0.788357, 0.800914, 0.814392, 0.828949, 0.844795, 0.862215, 0.881614, 0.903610, 0.915876, 0.929229, 0.943952, 0.951955, 0.960488, 0.964074, 0.967772, 0.971596, 0.975560, 0.979688, 0.984015, 0.988606, 0.991038, 0.993603, 0.996365, 0.997858, 0.999462, 1.001225, 1.001601, 1.001985, 1.002374, 1.002765, 1.003150, 1.003835, 1.004148, 1.003996, 1.003539},
{ 0.404724, 0.403689, 0.403600, 0.404076, 0.404258, 0.404251, 0.404224, 0.404195, 0.404175, 0.404166, 0.404215, 0.404267, 0.404298, 0.404370, 0.404445, 0.404519, 0.404667, 0.404815, 0.404963, 0.405111, 0.405258, 0.405406, 0.405554, 0.405923, 0.406292, 0.407028, 0.407765, 0.408500, 0.409972, 0.411447, 0.412927, 0.414414, 0.415912, 0.417423, 0.418949, 0.420493, 0.422056, 0.423641, 0.425251, 0.426886, 0.431100, 0.435515, 0.440156, 0.445044, 0.450200, 0.455643, 0.461393, 0.467468, 0.473888, 0.480675, 0.487850, 0.495438, 0.503465, 0.511962, 0.520962, 0.530505, 0.540632, 0.551396, 0.562855, 0.575079, 0.588148, 0.602160, 0.617234, 0.633516, 0.651186, 0.670476, 0.691688, 0.715225, 0.725411, 0.736102, 0.747353, 0.759229, 0.771806, 0.785179, 0.799465, 0.814813, 0.831421, 0.849554, 0.869595, 0.892144, 0.904659, 0.918275, 0.933356, 0.941641, 0.950603, 0.954427, 0.958419, 0.962607, 0.967027, 0.971729, 0.976781, 0.982283, 0.985249, 0.988396, 0.991774, 0.993577, 0.995484, 0.997537, 0.997971, 0.998417, 0.998874, 0.999344, 0.999831, 1.000861, 1.001979, 1.002546, 1.003020},
{ 0.352819, 0.353913, 0.353592, 0.352947, 0.353195, 0.353300, 0.353333, 0.353317, 0.353284, 0.353256, 0.353311, 0.353371, 0.353402, 0.353505, 0.353594, 0.353689, 0.353876, 0.354063, 0.354249, 0.354435, 0.354621, 0.354807, 0.354992, 0.355454, 0.355914, 0.356831, 0.357741, 0.358645, 0.360438, 0.362212, 0.363970, 0.365716, 0.367451, 0.369182, 0.370910, 0.372639, 0.374373, 0.376117, 0.377872, 0.379642, 0.384158, 0.388840, 0.393728, 0.398863, 0.404276, 0.409999, 0.416059, 0.422484, 0.429298, 0.436529, 0.444202, 0.452347, 0.460993, 0.470174, 0.479926, 0.490291, 0.501316, 0.513053, 0.525565, 0.538924, 0.553214, 0.568538, 0.585017, 0.602800, 0.622072, 0.643068, 0.666091, 0.691546, 0.702528, 0.714032, 0.726111, 0.738830, 0.752263, 0.766506, 0.781674, 0.797919, 0.815443, 0.834526, 0.855593, 0.879346, 0.892606, 0.907139, 0.923415, 0.932448, 0.942290, 0.946510, 0.950927, 0.955571, 0.960487, 0.965731, 0.971391, 0.977596, 0.980967, 0.984569, 0.988462, 0.990546, 0.992747, 0.995099, 0.995592, 0.996096, 0.996609, 0.997135, 0.997675, 0.998807, 1.000038, 1.000709, 1.001429},
{ 0.307722, 0.307242, 0.308236, 0.308063, 0.307908, 0.308068, 0.308173, 0.308184, 0.308142, 0.308095, 0.308192, 0.308221, 0.308283, 0.308395, 0.308516, 0.308625, 0.308854, 0.309081, 0.309306, 0.309533, 0.309758, 0.309983, 0.310208, 0.310768, 0.311325, 0.312433, 0.313532, 0.314621, 0.316770, 0.318882, 0.320958, 0.323001, 0.325012, 0.326996, 0.328955, 0.330893, 0.332815, 0.334725, 0.336628, 0.338527, 0.343295, 0.348145, 0.353144, 0.358351, 0.363819, 0.369594, 0.375719, 0.382231, 0.389166, 0.396559, 0.404442, 0.412850, 0.421819, 0.431386, 0.441592, 0.452482, 0.464106, 0.476520, 0.489790, 0.503991, 0.519211, 0.535555, 0.553148, 0.572143, 0.592729, 0.615145, 0.639698, 0.666799, 0.678474, 0.690693, 0.703509, 0.716990, 0.731215, 0.746285, 0.762327, 0.779508, 0.798061, 0.818318, 0.840790, 0.866326, 0.880686, 0.896506, 0.914300, 0.924200, 0.935002, 0.939638, 0.944491, 0.949596, 0.955000, 0.960764, 0.966981, 0.973799, 0.977507, 0.981479, 0.985792, 0.988112, 0.990571, 0.993204, 0.993756, 0.994318, 0.994892, 0.995477, 0.996076, 0.997322, 0.998658, 0.999375, 1.000143},
{ 0.271458, 0.270652, 0.270094, 0.270893, 0.270470, 0.270595, 0.270749, 0.270789, 0.270736, 0.270675, 0.270818, 0.270821, 0.270923, 0.271042, 0.271163, 0.271299, 0.271556, 0.271813, 0.272070, 0.272328, 0.272584, 0.272841, 0.273097, 0.273736, 0.274373, 0.275640, 0.276897, 0.278144, 0.280607, 0.283028, 0.285404, 0.287735, 0.290021, 0.292262, 0.294461, 0.296619, 0.298740, 0.300827, 0.302885, 0.304919, 0.309930, 0.314908, 0.319939, 0.325108, 0.330488, 0.336148, 0.342147, 0.348538, 0.355370, 0.362688, 0.370534, 0.378950, 0.387977, 0.397660, 0.408042, 0.419173, 0.431107, 0.443903, 0.457628, 0.472361, 0.488191, 0.505226, 0.523593, 0.543446, 0.564978, 0.588431, 0.614121, 0.642471, 0.654683, 0.667464, 0.680874, 0.694985, 0.709889, 0.725698, 0.742564, 0.760684, 0.780336, 0.801915, 0.826017, 0.853601, 0.869186, 0.886397, 0.905791, 0.916587, 0.928363, 0.933413, 0.938698, 0.944254, 0.950130, 0.956394, 0.963145, 0.970538, 0.974556, 0.978858, 0.983534, 0.986056, 0.988736, 0.991618, 0.992224, 0.992841, 0.993470, 0.994112, 0.994769, 0.996134, 0.997587, 0.998359, 0.999176},
{ 0.239041, 0.240558, 0.239971, 0.240247, 0.239966, 0.239996, 0.240167, 0.240230, 0.240169, 0.240104, 0.240251, 0.240310, 0.240357, 0.240506, 0.240654, 0.240790, 0.241071, 0.241349, 0.241627, 0.241907, 0.242186, 0.242464, 0.242743, 0.243437, 0.244130, 0.245511, 0.246885, 0.248252, 0.250959, 0.253628, 0.256256, 0.258838, 0.261372, 0.263856, 0.266288, 0.268666, 0.270993, 0.273269, 0.275497, 0.277680, 0.282971, 0.288097, 0.293157, 0.298256, 0.303491, 0.308954, 0.314724, 0.320873, 0.327466, 0.334560, 0.342210, 0.350466, 0.359377, 0.368992, 0.379362, 0.390540, 0.402581, 0.415547, 0.429506, 0.444538, 0.460733, 0.478196, 0.497054, 0.517462, 0.539613, 0.563751, 0.590201, 0.619411, 0.632006, 0.645199, 0.659060, 0.673672, 0.689141, 0.705603, 0.723235, 0.742271, 0.763031, 0.785965, 0.811731, 0.841375, 0.858181, 0.876773, 0.897746, 0.909424, 0.922158, 0.927616, 0.933325, 0.939323, 0.945661, 0.952411, 0.959676, 0.967623, 0.971935, 0.976549, 0.981559, 0.984263, 0.987140, 0.990241, 0.990894, 0.991560, 0.992240, 0.992935, 0.993647, 0.995125, 0.996696, 0.997527, 0.998401}};
  const double reomegaqnm31[8][107] = {{ 0.578812, 0.579132, 0.578821, 0.578212, 0.577910, 0.577830, 0.577777, 0.577742, 0.577719, 0.577704, 0.577678, 0.577674, 0.577670, 0.577653, 0.577632, 0.577609, 0.577560, 0.577512, 0.577464, 0.577417, 0.577370, 0.577324, 0.577278, 0.577165, 0.577054, 0.576842, 0.576641, 0.576450, 0.576102, 0.575796, 0.575532, 0.575308, 0.575125, 0.574981, 0.574876, 0.574809, 0.574780, 0.574788, 0.574832, 0.574913, 0.575268, 0.575841, 0.576625, 0.577620, 0.578823, 0.580234, 0.581854, 0.583686, 0.585734, 0.588003, 0.590499, 0.593231, 0.596209, 0.599443, 0.602949, 0.606742, 0.610842, 0.615270, 0.620053, 0.625222, 0.630813, 0.636869, 0.643444, 0.650601, 0.658418, 0.666994, 0.676453, 0.686960, 0.691503, 0.696265, 0.701265, 0.706528, 0.712080, 0.717952, 0.724182, 0.730815, 0.737907, 0.745525, 0.753756, 0.762706, 0.767493, 0.772513, 0.777787, 0.780525, 0.783334, 0.784477, 0.785632, 0.786799, 0.787978, 0.789167, 0.790369, 0.791581, 0.792191, 0.792805, 0.793420, 0.793729, 0.794038, 0.794347, 0.794409, 0.794470, 0.794532, 0.794593, 0.794655, 0.794780, 0.794921, 0.795016, 0.795171},
{ 0.559537, 0.560143, 0.560464, 0.560752, 0.560852, 0.560873, 0.560884, 0.560889, 0.560891, 0.560891, 0.560879, 0.560867, 0.560857, 0.560839, 0.560821, 0.560804, 0.560768, 0.560733, 0.560698, 0.560663, 0.560628, 0.560593, 0.560558, 0.560470, 0.560384, 0.560213, 0.560045, 0.559881, 0.559567, 0.559274, 0.559005, 0.558763, 0.558551, 0.558369, 0.558220, 0.558104, 0.558022, 0.557974, 0.557962, 0.557986, 0.558204, 0.558650, 0.559326, 0.560233, 0.561372, 0.562744, 0.564352, 0.566199, 0.568289, 0.570629, 0.573225, 0.576086, 0.579221, 0.582644, 0.586368, 0.590410, 0.594790, 0.599531, 0.604659, 0.610208, 0.616212, 0.622718, 0.629779, 0.637457, 0.645830, 0.654996, 0.665072, 0.676210, 0.681005, 0.686015, 0.691257, 0.696749, 0.702510, 0.708564, 0.714933, 0.721641, 0.728711, 0.736157, 0.743970, 0.752084, 0.756196, 0.760280, 0.764241, 0.766132, 0.767934, 0.768623, 0.769291, 0.769936, 0.770558, 0.771152, 0.771719, 0.772256, 0.772513, 0.772762, 0.773003, 0.773120, 0.773235, 0.773348, 0.773371, 0.773393, 0.773415, 0.773437, 0.773459, 0.773503, 0.773544, 0.773561, 0.773573},
{ 0.528589, 0.528767, 0.528753, 0.528654, 0.528604, 0.528596, 0.528593, 0.528593, 0.528595, 0.528597, 0.528605, 0.528607, 0.528608, 0.528609, 0.528611, 0.528613, 0.528616, 0.528619, 0.528620, 0.528621, 0.528621, 0.528621, 0.528620, 0.528614, 0.528604, 0.528575, 0.528532, 0.528478, 0.528341, 0.528176, 0.527993, 0.527800, 0.527606, 0.527418, 0.527242, 0.527083, 0.526946, 0.526833, 0.526749, 0.526695, 0.526710, 0.526957, 0.527454, 0.528211, 0.529239, 0.530542, 0.532127, 0.533999, 0.536165, 0.538632, 0.541407, 0.544500, 0.547921, 0.551685, 0.555805, 0.560300, 0.565191, 0.570500, 0.576257, 0.582494, 0.589249, 0.596568, 0.604504, 0.613119, 0.622488, 0.632702, 0.643865, 0.656103, 0.661330, 0.666761, 0.672405, 0.678269, 0.684360, 0.690678, 0.697216, 0.703951, 0.710831, 0.717744, 0.724456, 0.730463, 0.732890, 0.734638, 0.735394, 0.735313, 0.734917, 0.734675, 0.734387, 0.734056, 0.733684, 0.733272, 0.732824, 0.732340, 0.732087, 0.731825, 0.731556, 0.731419, 0.731280, 0.731140, 0.731111, 0.731083, 0.731054, 0.731026, 0.730997, 0.730940, 0.730884, 0.730856, 0.730826},
{ 0.484184, 0.483875, 0.483854, 0.483978, 0.484024, 0.484025, 0.484021, 0.484018, 0.484017, 0.484018, 0.484042, 0.484065, 0.484085, 0.484127, 0.484168, 0.484209, 0.484290, 0.484369, 0.484446, 0.484522, 0.484596, 0.484669, 0.484741, 0.484913, 0.485076, 0.485375, 0.485640, 0.485872, 0.486244, 0.486507, 0.486677, 0.486770, 0.486800, 0.486782, 0.486730, 0.486656, 0.486569, 0.486480, 0.486397, 0.486326, 0.486241, 0.486343, 0.486682, 0.487294, 0.488203, 0.489426, 0.490979, 0.492871, 0.495114, 0.497717, 0.500692, 0.504049, 0.507801, 0.511962, 0.516549, 0.521581, 0.527079, 0.533069, 0.539580, 0.546644, 0.554302, 0.562597, 0.571582, 0.581316, 0.591867, 0.603312, 0.615732, 0.629208, 0.634908, 0.640786, 0.646839, 0.653058, 0.659424, 0.665905, 0.672440, 0.678924, 0.685167, 0.690812, 0.695146, 0.696586, 0.695185, 0.691462, 0.685653, 0.682791, 0.679803, 0.678575, 0.677372, 0.676170, 0.674960, 0.673761, 0.672565, 0.671376, 0.670784, 0.670195, 0.669607, 0.669314, 0.669021, 0.668729, 0.668671, 0.668612, 0.668554, 0.668496, 0.668438, 0.668321, 0.668204, 0.668146, 0.668093},
{ 0.431741, 0.432151, 0.432119, 0.431947, 0.432003, 0.432038, 0.432058, 0.432067, 0.432071, 0.432073, 0.432118, 0.432172, 0.432219, 0.432319, 0.432417, 0.432515, 0.432709, 0.432901, 0.433091, 0.433280, 0.433466, 0.433650, 0.433833, 0.434281, 0.434716, 0.435549, 0.436332, 0.437065, 0.438381, 0.439503, 0.440442, 0.441211, 0.441828, 0.442312, 0.442682, 0.442959, 0.443160, 0.443303, 0.443403, 0.443474, 0.443601, 0.443773, 0.444096, 0.444649, 0.445484, 0.446641, 0.448151, 0.450035, 0.452314, 0.455003, 0.458118, 0.461674, 0.465687, 0.470174, 0.475154, 0.480646, 0.486675, 0.493266, 0.500448, 0.508257, 0.516729, 0.525907, 0.535839, 0.546578, 0.558179, 0.570697, 0.584178, 0.598632, 0.604674, 0.610848, 0.617133, 0.623496, 0.629882, 0.636205, 0.642325, 0.648001, 0.652812, 0.655938, 0.655571, 0.646432, 0.632014, 0.585761, 0.561844, 0.551901, 0.541633, 0.537490, 0.533347, 0.529204, 0.525061, 0.520912, 0.516755, 0.512588, 0.510500, 0.508409, 0.506313, 0.505264, 0.504214, 0.503162, 0.502952, 0.502741, 0.502531, 0.502320, 0.502109, 0.501688, 0.501266, 0.501055, 0.500844},
{ 0.378411, 0.378009, 0.378304, 0.378423, 0.378337, 0.378379, 0.378429, 0.378463, 0.378477, 0.378480, 0.378547, 0.378632, 0.378705, 0.378866, 0.379023, 0.379180, 0.379492, 0.379803, 0.380112, 0.380420, 0.380726, 0.381030, 0.381333, 0.382082, 0.382820, 0.384261, 0.385654, 0.386995, 0.389515, 0.391806, 0.393858, 0.395669, 0.397243, 0.398591, 0.399730, 0.400680, 0.401465, 0.402108, 0.402632, 0.403060, 0.403833, 0.404384, 0.404907, 0.405540, 0.406384, 0.407512, 0.408977, 0.410822, 0.413078, 0.415773, 0.418930, 0.422571, 0.426716, 0.431386, 0.436603, 0.442389, 0.448768, 0.455767, 0.463416, 0.471746, 0.480794, 0.490597, 0.501194, 0.512627, 0.524930, 0.538125, 0.552204, 0.567080, 0.573206, 0.579391, 0.585591, 0.591738, 0.597731, 0.603413, 0.608532, 0.612672, 0.615090, 0.614343, 0.607403, 0.591834, 0.589895, 0.618559, 0.610264, 0.568180, 0.552753, 0.547793, 0.542827, 0.537718, 0.532494, 0.527212, 0.521893, 0.516526, 0.513820, 0.511097, 0.508356, 0.506978, 0.505594, 0.504205, 0.503926, 0.503647, 0.503368, 0.503089, 0.502810, 0.502250, 0.501689, 0.501408, 0.501127},
{ 0.327891, 0.327969, 0.327530, 0.327908, 0.327791, 0.327789, 0.327855, 0.327920, 0.327949, 0.327950, 0.328039, 0.328130, 0.328237, 0.328435, 0.328639, 0.328840, 0.329242, 0.329642, 0.330043, 0.330442, 0.330840, 0.331238, 0.331634, 0.332621, 0.333602, 0.335541, 0.337450, 0.339323, 0.342949, 0.346387, 0.349608, 0.352585, 0.355298, 0.357735, 0.359891, 0.361774, 0.363399, 0.364787, 0.365963, 0.366957, 0.368811, 0.370063, 0.371012, 0.371881, 0.372830, 0.373978, 0.375413, 0.377201, 0.379393, 0.382031, 0.385148, 0.388774, 0.392936, 0.397660, 0.402969, 0.408889, 0.415444, 0.422662, 0.430570, 0.439196, 0.448571, 0.458722, 0.469677, 0.481456, 0.494064, 0.507477, 0.521610, 0.536251, 0.542155, 0.548018, 0.553764, 0.559288, 0.564439, 0.568992, 0.572615, 0.574817, 0.574976, 0.572941, 0.572216, 0.580712, 0.582336, 0.575398, 0.576187, 0.607780, 0.599756, 0.600712, 0.601044, 0.596450, 0.597300, 0.595576, 0.594049, 0.592565, 0.591920, 0.591289, 0.590644, 0.590323, 0.590004, 0.589686, 0.589623, 0.589559, 0.589496, 0.589433, 0.589369, 0.589243, 0.589117, 0.589053, 0.588991},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.374296, 0.380240, 0.386850, 0.394150, 0.402165, 0.410917, 0.420425, 0.430706, 0.441768, 0.453601, 0.466170, 0.479388, 0.493075, 0.506864, 0.512262, 0.517493, 0.522458, 0.527028, 0.531035, 0.534286, 0.536616, 0.538129, 0.539814, 0.544015, 0.551154, 0.555856, 0.559470, 0.567869, 0.567126, 0.562079, 0.566807, 0.560762, 0.551738, 0.544985, 0.538995, 0.532949, 0.526659, 0.520224, 0.516962, 0.513664, 0.510325, 0.508638, 0.506939, 0.505227, 0.504883, 0.504538, 0.504193, 0.503847, 0.503500, 0.502805, 0.502108, 0.501758, 0.501408}};
  const double reomegaqnm30[8][107] = {{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.599562, 0.599920, 0.600519, 0.601364, 0.602462, 0.603820, 0.605450, 0.607365, 0.609583, 0.612123, 0.615010, 0.618276, 0.621957, 0.626099, 0.627897, 0.629782, 0.631760, 0.633834, 0.636010, 0.638296, 0.640697, 0.643221, 0.645877, 0.648674, 0.651621, 0.654730, 0.656348, 0.658011, 0.659719, 0.660591, 0.661475, 0.661832, 0.662191, 0.662551, 0.662914, 0.663279, 0.663646, 0.664014, 0.664199, 0.664385, 0.664569, 0.664660, 0.664749, 0.664839, 0.664859, 0.664880, 0.664904, 0.664934, 0.664972, 0.665109, 0.665498, 0.665982, 0.666966},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.582779, 0.583184, 0.583863, 0.584820, 0.586062, 0.587597, 0.589436, 0.591594, 0.594085, 0.596930, 0.600152, 0.603777, 0.607836, 0.612363, 0.614312, 0.616344, 0.618461, 0.620665, 0.622957, 0.625337, 0.627805, 0.630358, 0.632992, 0.635698, 0.638461, 0.641259, 0.642661, 0.644057, 0.645442, 0.646128, 0.646807, 0.647077, 0.647346, 0.647614, 0.647880, 0.648144, 0.648407, 0.648669, 0.648799, 0.648929, 0.649058, 0.649122, 0.649187, 0.649253, 0.649266, 0.649279, 0.649291, 0.649303, 0.649313, 0.649323, 0.649294, 0.649244, 0.649152},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.551849, 0.552343, 0.553168, 0.554330, 0.555836, 0.557693, 0.559913, 0.562508, 0.565493, 0.568882, 0.572694, 0.576945, 0.581647, 0.586805, 0.588993, 0.591248, 0.593567, 0.595944, 0.598370, 0.600831, 0.603310, 0.605782, 0.608213, 0.610555, 0.612746, 0.614707, 0.615572, 0.616342, 0.617006, 0.617294, 0.617551, 0.617645, 0.617733, 0.617816, 0.617894, 0.617966, 0.618032, 0.618093, 0.618122, 0.618148, 0.618174, 0.618186, 0.618198, 0.618209, 0.618210, 0.618212, 0.618214, 0.618216, 0.618219, 0.618230, 0.618254, 0.618264, 0.618233},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.512162, 0.512763, 0.513767, 0.515179, 0.517004, 0.519250, 0.521925, 0.525038, 0.528599, 0.532614, 0.537089, 0.542016, 0.547375, 0.553111, 0.555487, 0.557894, 0.560315, 0.562730, 0.565110, 0.567417, 0.569602, 0.571599, 0.573324, 0.574673, 0.575528, 0.575774, 0.575639, 0.575325, 0.574828, 0.574511, 0.574151, 0.573994, 0.573831, 0.573660, 0.573483, 0.573299, 0.573109, 0.572912, 0.572811, 0.572709, 0.572605, 0.572552, 0.572499, 0.572445, 0.572435, 0.572425, 0.572415, 0.572405, 0.572395, 0.572369, 0.572328, 0.572320, 0.572370},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.470407, 0.471107, 0.472275, 0.473914, 0.476029, 0.478623, 0.481699, 0.485259, 0.489303, 0.493821, 0.498793, 0.504175, 0.509885, 0.515766, 0.518107, 0.520404, 0.522620, 0.524706, 0.526601, 0.528226, 0.529475, 0.530221, 0.530314, 0.529605, 0.527994, 0.525482, 0.523916, 0.522167, 0.520255, 0.519245, 0.518203, 0.517777, 0.517347, 0.516912, 0.516474, 0.516031, 0.515584, 0.515133, 0.514906, 0.514679, 0.514450, 0.514336, 0.514221, 0.514107, 0.514085, 0.514062, 0.514038, 0.514013, 0.513986, 0.513938, 0.513927, 0.513901, 0.513786},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.431644, 0.432418, 0.433707, 0.435512, 0.437834, 0.440669, 0.444013, 0.447856, 0.452178, 0.456946, 0.462098, 0.467532, 0.473068, 0.478389, 0.480341, 0.482117, 0.483646, 0.484836, 0.485569, 0.485694, 0.485025, 0.483359, 0.480530, 0.476531, 0.471580, 0.465954, 0.462965, 0.459898, 0.456775, 0.455199, 0.453616, 0.452982, 0.452347, 0.451711, 0.451075, 0.450438, 0.449801, 0.449164, 0.448846, 0.448528, 0.448209, 0.448050, 0.447889, 0.447735, 0.447703, 0.447668, 0.447631, 0.447595, 0.447565, 0.447530, 0.447412, 0.447346, 0.447470},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.397933, 0.398754, 0.400121, 0.402029, 0.404472, 0.407440, 0.410914, 0.414868, 0.419255, 0.424004, 0.428999, 0.434048, 0.438831, 0.442785, 0.443930, 0.444691, 0.444941, 0.444515, 0.443201, 0.440739, 0.436855, 0.431399, 0.424647, 0.417293, 0.409623, 0.401877, 0.398025, 0.394206, 0.390427, 0.388555, 0.386695, 0.385955, 0.385217, 0.384480, 0.383746, 0.383014, 0.382285, 0.381557, 0.381194, 0.380831, 0.380468, 0.380291, 0.380104, 0.379937, 0.379896, 0.379849, 0.379803, 0.379771, 0.379760, 0.379683, 0.379573, 0.379702, 0.379469},
{ 0.282233, 0.282890, 0.282956, 0.282808, 0.282895, 0.282817, 0.282871, 0.282969, 0.283015, 0.283004, 0.283121, 0.283198, 0.283332, 0.283555, 0.283776, 0.284000, 0.284453, 0.284905, 0.285356, 0.285808, 0.286259, 0.286710, 0.287161, 0.288288, 0.289414, 0.291659, 0.293895, 0.296117, 0.300508, 0.304798, 0.308952, 0.312931, 0.316696, 0.320211, 0.323444, 0.326372, 0.328986, 0.331286, 0.333289, 0.335018, 0.338331, 0.340577, 0.342167, 0.343420, 0.344573, 0.345802, 0.347235, 0.348969, 0.351079, 0.353624, 0.356651, 0.360199, 0.364303, 0.368992, 0.369276, 0.370125, 0.371535, 0.373496, 0.375995, 0.379009, 0.382504, 0.386428, 0.390703, 0.395206, 0.399746, 0.404011, 0.407482, 0.409242, 0.409125, 0.408309, 0.406575, 0.403632, 0.399118, 0.392662, 0.384204, 0.374776, 0.365847, 0.356745, 0.348034, 0.339576, 0.335477, 0.331464, 0.327534, 0.325598, 0.323683, 0.322922, 0.322164, 0.321409, 0.320658, 0.319909, 0.319163, 0.318421, 0.318049, 0.317679, 0.317312, 0.317127, 0.316938, 0.316781, 0.316729, 0.316663, 0.316616, 0.316616, 0.316630, 0.316423, 0.316583, 0.316299, 0.316258}};
  const double reomegaqnm44[8][107] = {{ 0.603485, 0.613847, 0.619636, 0.623952, 0.624219, 0.623894, 0.623504, 0.623122, 0.622780, 0.622487, 0.621648, 0.621375, 0.621309, 0.621365, 0.621483, 0.621613, 0.621877, 0.622141, 0.622404, 0.622667, 0.622930, 0.623194, 0.623458, 0.624119, 0.624781, 0.626113, 0.627452, 0.628799, 0.631518, 0.634269, 0.637054, 0.639872, 0.642726, 0.645615, 0.648541, 0.651503, 0.654504, 0.657544, 0.660623, 0.663743, 0.671728, 0.679989, 0.688543, 0.697411, 0.706611, 0.716168, 0.726107, 0.736455, 0.747243, 0.758508, 0.770286, 0.782624, 0.795569, 0.809178, 0.823517, 0.838660, 0.854693, 0.871718, 0.889853, 0.909242, 0.930054, 0.952500, 0.976839, 1.003396, 1.032592, 1.064981, 1.101315, 1.142654, 1.160918, 1.180359, 1.201137, 1.223450, 1.247547, 1.273743, 1.302451, 1.334225, 1.369837, 1.410416, 1.457726, 1.514785, 1.548623, 1.587589, 1.633903, 1.661025, 1.691943, 1.705697, 1.720452, 1.736406, 1.753835, 1.773136, 1.794920, 1.820217, 1.834740, 1.851041, 1.869853, 1.880596, 1.892605, 1.906400, 1.909447, 1.912614, 1.915915, 1.919368, 1.922993, 1.930875, 1.939891, 1.945001, 1.950681},
{ 0.592310, 0.596523, 0.598412, 0.599977, 0.600617, 0.600806, 0.600947, 0.601053, 0.601136, 0.601202, 0.601389, 0.601485, 0.601558, 0.601693, 0.601828, 0.601964, 0.602238, 0.602511, 0.602785, 0.603060, 0.603334, 0.603609, 0.603884, 0.604574, 0.605265, 0.606653, 0.608050, 0.609455, 0.612290, 0.615158, 0.618061, 0.620998, 0.623972, 0.626982, 0.630029, 0.633115, 0.636240, 0.639405, 0.642610, 0.645858, 0.654166, 0.662758, 0.671651, 0.680865, 0.690420, 0.700341, 0.710653, 0.721383, 0.732565, 0.744232, 0.756425, 0.769188, 0.782571, 0.796632, 0.811434, 0.827055, 0.843581, 0.861114, 0.879773, 0.899703, 0.921074, 0.944098, 0.969034, 0.996209, 1.026044, 1.059094, 1.096112, 1.138157, 1.156711, 1.176444, 1.197519, 1.220132, 1.244532, 1.271035, 1.300052, 1.332138, 1.368063, 1.408958, 1.456584, 1.513957, 1.547951, 1.587070, 1.633535, 1.660729, 1.691718, 1.705500, 1.720282, 1.736263, 1.753718, 1.773044, 1.794851, 1.820170, 1.834704, 1.851014, 1.869835, 1.880582, 1.892595, 1.906393, 1.909441, 1.912608, 1.915910, 1.919363, 1.922989, 1.930872, 1.939889, 1.945000, 1.950680},
{ 0.559386, 0.561881, 0.562985, 0.563673, 0.563747, 0.563732, 0.563712, 0.563695, 0.563683, 0.563678, 0.563718, 0.563794, 0.563872, 0.564021, 0.564168, 0.564316, 0.564612, 0.564908, 0.565204, 0.565501, 0.565798, 0.566096, 0.566394, 0.567139, 0.567887, 0.569390, 0.570901, 0.572420, 0.575484, 0.578584, 0.581720, 0.584892, 0.588102, 0.591350, 0.594637, 0.597965, 0.601333, 0.604743, 0.608195, 0.611692, 0.620630, 0.629865, 0.639415, 0.649299, 0.659540, 0.670161, 0.681189, 0.692653, 0.704586, 0.717023, 0.730006, 0.743579, 0.757794, 0.772710, 0.788392, 0.804918, 0.822375, 0.840868, 0.860518, 0.881470, 0.903897, 0.928012, 0.954076, 0.982419, 1.013463, 1.047766, 1.086081, 1.129470, 1.148575, 1.168866, 1.190507, 1.213693, 1.238674, 1.265764, 1.295376, 1.328062, 1.364594, 1.406100, 1.454338, 1.512324, 1.546623, 1.586043, 1.632803, 1.660142, 1.691272, 1.705109, 1.719944, 1.735978, 1.753484, 1.772859, 1.794714, 1.820077, 1.834631, 1.850961, 1.869799, 1.880554, 1.892574, 1.906379, 1.909429, 1.912597, 1.915900, 1.919355, 1.922982, 1.930867, 1.939885, 1.944997, 1.950678},
{ 0.514416, 0.513669, 0.512866, 0.512200, 0.512256, 0.512336, 0.512404, 0.512455, 0.512488, 0.512510, 0.512565, 0.512640, 0.512726, 0.512889, 0.513051, 0.513214, 0.513540, 0.513866, 0.514193, 0.514520, 0.514848, 0.515175, 0.515503, 0.516325, 0.517149, 0.518804, 0.520467, 0.522139, 0.525511, 0.528920, 0.532367, 0.535852, 0.539377, 0.542943, 0.546549, 0.550198, 0.553889, 0.557625, 0.561406, 0.565233, 0.575009, 0.585097, 0.595517, 0.606289, 0.617438, 0.628986, 0.640963, 0.653399, 0.666327, 0.679785, 0.693815, 0.708464, 0.723784, 0.739837, 0.756690, 0.774421, 0.793122, 0.812899, 0.833875, 0.856197, 0.880043, 0.905628, 0.933216, 0.963140, 0.995828, 1.031838, 1.071929, 1.117168, 1.137033, 1.158097, 1.180522, 1.204506, 1.230297, 1.258209, 1.288655, 1.322187, 1.359576, 1.401950, 1.451065, 1.509932, 1.544671, 1.584530, 1.631722, 1.659272, 1.690609, 1.704527, 1.719441, 1.735553, 1.753135, 1.772584, 1.794508, 1.819937, 1.834521, 1.850880, 1.869745, 1.880512, 1.892544, 1.906359, 1.909410, 1.912581, 1.915886, 1.919342, 1.922970, 1.930859, 1.939880, 1.944993, 1.950675},
{ 0.454601, 0.454746, 0.455842, 0.456343, 0.456046, 0.455998, 0.456018, 0.456071, 0.456127, 0.456171, 0.456246, 0.456327, 0.456423, 0.456596, 0.456773, 0.456949, 0.457302, 0.457655, 0.458009, 0.458363, 0.458717, 0.459072, 0.459427, 0.460317, 0.461208, 0.462999, 0.464799, 0.466609, 0.470257, 0.473946, 0.477675, 0.481446, 0.485259, 0.489115, 0.493016, 0.496962, 0.500954, 0.504993, 0.509081, 0.513219, 0.523786, 0.534689, 0.545948, 0.557585, 0.569625, 0.582093, 0.595020, 0.608436, 0.622378, 0.636885, 0.652000, 0.667772, 0.684256, 0.701516, 0.719620, 0.738651, 0.758702, 0.779882, 0.802317, 0.826160, 0.851591, 0.878829, 0.908143, 0.939873, 0.974449, 1.012439, 1.054606, 1.102023, 1.122789, 1.144773, 1.168136, 1.193076, 1.219842, 1.248749, 1.280208, 1.314774, 1.353216, 1.396662, 1.446869, 1.506844, 1.542142, 1.582559, 1.630306, 1.658130, 1.689736, 1.703759, 1.718778, 1.734991, 1.752673, 1.772218, 1.794235, 1.819751, 1.834376, 1.850773, 1.869673, 1.880456, 1.892503, 1.906332, 1.909386, 1.912559, 1.915866, 1.919324, 1.922955, 1.930848, 1.939873, 1.944987, 1.950672},
{ 0.405546, 0.404573, 0.403366, 0.404025, 0.404115, 0.403989, 0.403940, 0.403971, 0.404037, 0.404098, 0.404160, 0.404265, 0.404355, 0.404535, 0.404715, 0.404897, 0.405260, 0.405624, 0.405988, 0.406353, 0.406718, 0.407083, 0.407449, 0.408365, 0.409284, 0.411129, 0.412986, 0.414853, 0.418619, 0.422430, 0.426286, 0.430188, 0.434137, 0.438134, 0.442180, 0.446277, 0.450425, 0.454625, 0.458878, 0.463187, 0.474206, 0.485594, 0.497376, 0.509573, 0.522212, 0.535321, 0.548930, 0.563075, 0.577791, 0.593121, 0.609109, 0.625808, 0.643274, 0.661572, 0.680777, 0.700971, 0.722252, 0.744732, 0.768542, 0.793839, 0.820807, 0.849672, 0.880708, 0.914263, 0.950774, 0.990817, 1.035165, 1.084901, 1.106636, 1.129614, 1.153995, 1.179980, 1.207817, 1.237823, 1.270410, 1.306132, 1.345761, 1.390425, 1.441882, 1.503141, 1.539093, 1.580170, 1.628580, 1.656733, 1.688664, 1.702815, 1.717960, 1.734298, 1.752101, 1.771765, 1.793895, 1.819518, 1.834194, 1.850639, 1.869583, 1.880387, 1.892453, 1.906298, 1.909355, 1.912532, 1.915842, 1.919303, 1.922936, 1.930834, 1.939864, 1.944981, 1.950667},
{ 0.359760, 0.362048, 0.362088, 0.361405, 0.361838, 0.361724, 0.361635, 0.361653, 0.361731, 0.361798, 0.361829, 0.361951, 0.362022, 0.362204, 0.362384, 0.362559, 0.362914, 0.363269, 0.363624, 0.363980, 0.364336, 0.364693, 0.365050, 0.365945, 0.366843, 0.368648, 0.370465, 0.372293, 0.375986, 0.379729, 0.383522, 0.387367, 0.391264, 0.395214, 0.399220, 0.403281, 0.407400, 0.411576, 0.415813, 0.420110, 0.431129, 0.442560, 0.454427, 0.466756, 0.479575, 0.492914, 0.506807, 0.521289, 0.536401, 0.552185, 0.568691, 0.585972, 0.604089, 0.623109, 0.643109, 0.664176, 0.686412, 0.709933, 0.734875, 0.761399, 0.789696, 0.819999, 0.852590, 0.887824, 0.926150, 0.968153, 1.014622, 1.066653, 1.089358, 1.113337, 1.138753, 1.165806, 1.194747, 1.225892, 1.259656, 1.296595, 1.337482, 1.383447, 1.436255, 1.498918, 1.535593, 1.577409, 1.626568, 1.655098, 1.687403, 1.701703, 1.716995, 1.733478, 1.751424, 1.771226, 1.793491, 1.819241, 1.833977, 1.850478, 1.869475, 1.880303, 1.892391, 1.906258, 1.909318, 1.912499, 1.915812, 1.919277, 1.922914, 1.930818, 1.939853, 1.944972, 1.950661},
{ 0.330474, 0.328796, 0.329888, 0.329377, 0.329765, 0.329704, 0.329609, 0.329627, 0.329709, 0.329764, 0.329799, 0.329879, 0.329976, 0.330138, 0.330301, 0.330468, 0.330801, 0.331135, 0.331469, 0.331804, 0.332139, 0.332474, 0.332810, 0.333653, 0.334498, 0.336199, 0.337912, 0.339638, 0.343129, 0.346673, 0.350272, 0.353926, 0.357636, 0.361405, 0.365233, 0.369122, 0.373073, 0.377087, 0.381166, 0.385312, 0.395976, 0.407089, 0.418680, 0.430776, 0.443408, 0.456611, 0.470421, 0.484877, 0.500022, 0.515903, 0.532572, 0.550085, 0.568507, 0.587909, 0.608371, 0.629986, 0.652859, 0.677111, 0.702884, 0.730344, 0.759691, 0.791165, 0.825057, 0.861733, 0.901654, 0.945421, 0.993838, 1.048020, 1.071648, 1.096587, 1.123003, 1.151096, 1.181120, 1.213393, 1.248331, 1.286493, 1.328654, 1.375949, 1.430149, 1.494278, 1.531719, 1.574326, 1.624300, 1.653246, 1.685968, 1.700434, 1.715892, 1.732539, 1.750646, 1.770607, 1.793024, 1.818920, 1.833724, 1.850291, 1.869349, 1.880205, 1.892320, 1.906211, 1.909276, 1.912460, 1.915778, 1.919247, 1.922887, 1.930799, 1.939840, 1.944963, 1.950654}};
  const double reomegaqnm43[8][107] = {{ 0.664561, 0.671781, 0.674607, 0.674567, 0.672823, 0.672081, 0.671488, 0.671028, 0.670676, 0.670408, 0.669768, 0.669607, 0.669582, 0.669640, 0.669730, 0.669825, 0.670015, 0.670204, 0.670393, 0.670583, 0.670772, 0.670962, 0.671152, 0.671628, 0.672106, 0.673067, 0.674034, 0.675008, 0.676976, 0.678971, 0.680993, 0.683044, 0.685124, 0.687232, 0.689371, 0.691539, 0.693739, 0.695971, 0.698234, 0.700531, 0.706420, 0.712531, 0.718876, 0.725468, 0.732322, 0.739454, 0.746883, 0.754628, 0.762712, 0.771159, 0.779996, 0.789254, 0.798968, 0.809178, 0.819929, 0.831271, 0.843264, 0.855978, 0.869492, 0.883903, 0.899326, 0.915897, 0.933787, 0.953206, 0.974424, 0.997788, 1.023764, 1.052994, 1.065793, 1.079333, 1.093709, 1.109033, 1.125444, 1.143116, 1.162272, 1.183207, 1.206320, 1.232181, 1.261648, 1.296128, 1.315984, 1.338258, 1.363840, 1.378331, 1.394372, 1.401333, 1.408674, 1.416458, 1.424768, 1.433721, 1.443487, 1.454334, 1.460298, 1.466741, 1.473812, 1.477658, 1.481774, 1.486238, 1.487183, 1.488148, 1.489135, 1.490146, 1.491183, 1.493346, 1.495650, 1.496867, 1.498136},
{ 0.649267, 0.650865, 0.651497, 0.652059, 0.652330, 0.652416, 0.652482, 0.652533, 0.652574, 0.652606, 0.652704, 0.652761, 0.652810, 0.652906, 0.653002, 0.653098, 0.653292, 0.653486, 0.653680, 0.653874, 0.654069, 0.654263, 0.654459, 0.654947, 0.655438, 0.656424, 0.657416, 0.658415, 0.660434, 0.662481, 0.664556, 0.666660, 0.668793, 0.670957, 0.673152, 0.675378, 0.677636, 0.679927, 0.682252, 0.684611, 0.690663, 0.696946, 0.703473, 0.710258, 0.717317, 0.724667, 0.732325, 0.740314, 0.748654, 0.757372, 0.766495, 0.776055, 0.786087, 0.796632, 0.807733, 0.819445, 0.831827, 0.844949, 0.858893, 0.873754, 0.889649, 0.906718, 0.925129, 0.945097, 0.966889, 0.990856, 1.017463, 1.047353, 1.060422, 1.074238, 1.088892, 1.104496, 1.121189, 1.139143, 1.158579, 1.179788, 1.203166, 1.229273, 1.258954, 1.293593, 1.313493, 1.335773, 1.361305, 1.375739, 1.391692, 1.398606, 1.405892, 1.413612, 1.421846, 1.430710, 1.440368, 1.451085, 1.456973, 1.463330, 1.470306, 1.474100, 1.478163, 1.482573, 1.483508, 1.484463, 1.485440, 1.486442, 1.487470, 1.489620, 1.491920, 1.493142, 1.494424},
{ 0.618226, 0.619662, 0.620260, 0.620602, 0.620631, 0.620624, 0.620617, 0.620614, 0.620613, 0.620616, 0.620657, 0.620710, 0.620763, 0.620865, 0.620966, 0.621069, 0.621273, 0.621477, 0.621682, 0.621887, 0.622092, 0.622298, 0.622504, 0.623019, 0.623536, 0.624576, 0.625622, 0.626675, 0.628801, 0.630955, 0.633139, 0.635352, 0.637596, 0.639872, 0.642180, 0.644521, 0.646896, 0.649306, 0.651751, 0.654233, 0.660603, 0.667221, 0.674101, 0.681259, 0.688712, 0.696478, 0.704577, 0.713030, 0.721860, 0.731095, 0.740763, 0.750896, 0.761531, 0.772710, 0.784478, 0.796890, 0.810008, 0.823902, 0.838656, 0.854369, 0.871157, 0.889163, 0.908559, 0.929559, 0.952436, 0.977540, 1.005338, 1.036473, 1.050055, 1.064390, 1.079571, 1.095707, 1.112937, 1.131429, 1.151401, 1.173140, 1.197032, 1.223628, 1.253754, 1.288759, 1.308798, 1.331174, 1.356745, 1.371175, 1.387109, 1.394013, 1.401288, 1.408998, 1.417230, 1.426102, 1.435794, 1.446595, 1.452561, 1.459040, 1.466211, 1.470148, 1.474403, 1.479083, 1.480085, 1.481114, 1.482171, 1.483261, 1.484387, 1.486766, 1.489363, 1.490769, 1.492270},
{ 0.577515, 0.577137, 0.576762, 0.576508, 0.576555, 0.576591, 0.576620, 0.576642, 0.576657, 0.576668, 0.576714, 0.576768, 0.576824, 0.576935, 0.577046, 0.577156, 0.577378, 0.577600, 0.577822, 0.578044, 0.578266, 0.578489, 0.578712, 0.579270, 0.579830, 0.580954, 0.582084, 0.583221, 0.585513, 0.587833, 0.590180, 0.592557, 0.594964, 0.597402, 0.599874, 0.602379, 0.604920, 0.607496, 0.610110, 0.612762, 0.619569, 0.626640, 0.633995, 0.641651, 0.649629, 0.657947, 0.666628, 0.675696, 0.685176, 0.695095, 0.705484, 0.716378, 0.727815, 0.739837, 0.752493, 0.765838, 0.779937, 0.794862, 0.810700, 0.827552, 0.845537, 0.864800, 0.885517, 0.907906, 0.932243, 0.958881, 0.988290, 1.021114, 1.035393, 1.050437, 1.066338, 1.083205, 1.101173, 1.120410, 1.141131, 1.163618, 1.188250, 1.215570, 1.246391, 1.282050, 1.302397, 1.325072, 1.350952, 1.365555, 1.381693, 1.388695, 1.396082, 1.403923, 1.412311, 1.421378, 1.431320, 1.442459, 1.448645, 1.455393, 1.462908, 1.467057, 1.471563, 1.476549, 1.477621, 1.478723, 1.479859, 1.481032, 1.482246, 1.484822, 1.487650, 1.489191, 1.490846},
{ 0.525789, 0.525845, 0.526285, 0.526489, 0.526396, 0.526387, 0.526402, 0.526425, 0.526449, 0.526469, 0.526526, 0.526586, 0.526649, 0.526770, 0.526893, 0.527015, 0.527260, 0.527504, 0.527749, 0.527995, 0.528240, 0.528485, 0.528731, 0.529346, 0.529962, 0.531197, 0.532436, 0.533681, 0.536184, 0.538710, 0.541259, 0.543833, 0.546434, 0.549064, 0.551724, 0.554416, 0.557141, 0.559902, 0.562699, 0.565535, 0.572804, 0.580347, 0.588189, 0.596352, 0.604861, 0.613740, 0.623015, 0.632711, 0.642858, 0.653485, 0.664626, 0.676316, 0.688598, 0.701516, 0.715120, 0.729469, 0.744629, 0.760677, 0.777701, 0.795805, 0.815114, 0.835775, 0.857968, 0.881917, 0.907901, 0.936280, 0.967529, 1.002295, 1.017380, 1.033248, 1.049988, 1.067712, 1.086553, 1.106679, 1.128303, 1.151707, 1.177270, 1.205533, 1.237316, 1.273974, 1.294851, 1.318099, 1.344631, 1.359612, 1.376187, 1.383386, 1.390988, 1.399066, 1.407718, 1.417085, 1.427376, 1.438935, 1.445369, 1.452403, 1.460257, 1.464604, 1.469335, 1.474587, 1.475718, 1.476882, 1.478083, 1.479324, 1.480610, 1.483343, 1.486355, 1.488001, 1.489774},
{ 0.476971, 0.476710, 0.476193, 0.476399, 0.476477, 0.476442, 0.476428, 0.476440, 0.476467, 0.476494, 0.476558, 0.476627, 0.476696, 0.476830, 0.476965, 0.477100, 0.477370, 0.477640, 0.477910, 0.478180, 0.478450, 0.478720, 0.478991, 0.479667, 0.480344, 0.481698, 0.483055, 0.484415, 0.487142, 0.489882, 0.492637, 0.495408, 0.498200, 0.501013, 0.503849, 0.506712, 0.509604, 0.512526, 0.515481, 0.518472, 0.526117, 0.534029, 0.542242, 0.550788, 0.559696, 0.568998, 0.578725, 0.588908, 0.599580, 0.610775, 0.622529, 0.634884, 0.647882, 0.661572, 0.676009, 0.691252, 0.707372, 0.724448, 0.742573, 0.761856, 0.782423, 0.804427, 0.828056, 0.853536, 0.881154, 0.911277, 0.944388, 0.981145, 0.997065, 1.013790, 1.031413, 1.050044, 1.069820, 1.090910, 1.113530, 1.137967, 1.164607, 1.194005, 1.227005, 1.265008, 1.286634, 1.310709, 1.338182, 1.353696, 1.370862, 1.378319, 1.386193, 1.394562, 1.403528, 1.413236, 1.423906, 1.435897, 1.442576, 1.449883, 1.458049, 1.462574, 1.467504, 1.472983, 1.474165, 1.475382, 1.476637, 1.477935, 1.479282, 1.482147, 1.485310, 1.487042, 1.488911},
{ 0.430443, 0.431347, 0.431584, 0.431207, 0.431429, 0.431412, 0.431378, 0.431377, 0.431405, 0.431440, 0.431503, 0.431587, 0.431654, 0.431803, 0.431949, 0.432095, 0.432388, 0.432680, 0.432973, 0.433266, 0.433558, 0.433851, 0.434143, 0.434874, 0.435606, 0.437068, 0.438530, 0.439992, 0.442918, 0.445847, 0.448782, 0.451724, 0.454675, 0.457639, 0.460618, 0.463614, 0.466631, 0.469671, 0.472736, 0.475831, 0.483711, 0.491834, 0.500242, 0.508978, 0.518083, 0.527594, 0.537552, 0.547994, 0.558959, 0.570486, 0.582619, 0.595401, 0.608880, 0.623109, 0.638145, 0.654053, 0.670907, 0.688791, 0.707800, 0.728048, 0.749667, 0.772816, 0.797685, 0.824511, 0.853588, 0.885293, 0.920120, 0.958744, 0.975458, 0.993007, 1.011487, 1.031010, 1.051718, 1.073786, 1.097437, 1.122970, 1.150787, 1.181468, 1.215892, 1.255523, 1.278068, 1.303156, 1.331765, 1.347908, 1.365756, 1.373503, 1.381682, 1.390369, 1.399671, 1.409737, 1.420794, 1.433213, 1.440128, 1.447693, 1.456148, 1.460834, 1.465942, 1.471622, 1.472848, 1.474111, 1.475414, 1.476762, 1.478161, 1.481139, 1.484431, 1.486237, 1.488188},
{ 0.393654, 0.392526, 0.393009, 0.392902, 0.393058, 0.393081, 0.393041, 0.393030, 0.393062, 0.393104, 0.393163, 0.393249, 0.393326, 0.393480, 0.393635, 0.393790, 0.394099, 0.394409, 0.394718, 0.395027, 0.395336, 0.395646, 0.395955, 0.396727, 0.397499, 0.399043, 0.400585, 0.402126, 0.405206, 0.408283, 0.411357, 0.414431, 0.417507, 0.420586, 0.423670, 0.426763, 0.429866, 0.432984, 0.436119, 0.439273, 0.447270, 0.455468, 0.463919, 0.472677, 0.481794, 0.491318, 0.501298, 0.511782, 0.522814, 0.534442, 0.546714, 0.559680, 0.573393, 0.587909, 0.603291, 0.619609, 0.636939, 0.655370, 0.675002, 0.695954, 0.718361, 0.742390, 0.768236, 0.796144, 0.826417, 0.859443, 0.895735, 0.935992, 0.953414, 0.971707, 0.990971, 1.011324, 1.032916, 1.055929, 1.080602, 1.107247, 1.136292, 1.168346, 1.204332, 1.245775, 1.269347, 1.295564, 1.325428, 1.342256, 1.360839, 1.368897, 1.377396, 1.386417, 1.396067, 1.406499, 1.417946, 1.430788, 1.437932, 1.445743, 1.454468, 1.459304, 1.464574, 1.470436, 1.471702, 1.473006, 1.474351, 1.475743, 1.477188, 1.480267, 1.483672, 1.485542, 1.487563}};
  const double reomegaqnm42[8][107] = {{ 0.734414, 0.736680, 0.735600, 0.731902, 0.729696, 0.729070, 0.728636, 0.728333, 0.728117, 0.727963, 0.727630, 0.727557, 0.727547, 0.727572, 0.727608, 0.727645, 0.727718, 0.727792, 0.727866, 0.727940, 0.728015, 0.728090, 0.728165, 0.728354, 0.728546, 0.728935, 0.729332, 0.729738, 0.730574, 0.731442, 0.732344, 0.733278, 0.734246, 0.735247, 0.736280, 0.737348, 0.738448, 0.739582, 0.740750, 0.741952, 0.745108, 0.748482, 0.752080, 0.755907, 0.759972, 0.764284, 0.768851, 0.773686, 0.778801, 0.784212, 0.789935, 0.795988, 0.802395, 0.809178, 0.816368, 0.823994, 0.832096, 0.840715, 0.849903, 0.859717, 0.870227, 0.881516, 0.893686, 0.906859, 0.921188, 0.936870, 0.954157, 0.973389, 0.981725, 0.990483, 0.999708, 1.009452, 1.019779, 1.030763, 1.042500, 1.055107, 1.068735, 1.083586, 1.099933, 1.118171, 1.128177, 1.138907, 1.150500, 1.156676, 1.163142, 1.165816, 1.168543, 1.171326, 1.174167, 1.177067, 1.180028, 1.183050, 1.184585, 1.186134, 1.187698, 1.188486, 1.189277, 1.190071, 1.190231, 1.190390, 1.190550, 1.190709, 1.190869, 1.191189, 1.191511, 1.191675, 1.191848},
{ 0.712955, 0.712958, 0.712987, 0.713105, 0.713200, 0.713233, 0.713258, 0.713278, 0.713293, 0.713305, 0.713340, 0.713361, 0.713380, 0.713418, 0.713456, 0.713494, 0.713571, 0.713647, 0.713725, 0.713802, 0.713880, 0.713957, 0.714036, 0.714232, 0.714430, 0.714832, 0.715240, 0.715655, 0.716507, 0.717387, 0.718298, 0.719238, 0.720210, 0.721214, 0.722250, 0.723319, 0.724421, 0.725557, 0.726727, 0.727932, 0.731100, 0.734496, 0.738126, 0.742000, 0.746125, 0.750512, 0.755170, 0.760113, 0.765353, 0.770907, 0.776791, 0.783024, 0.789629, 0.796632, 0.804059, 0.811946, 0.820329, 0.829251, 0.838765, 0.848928, 0.859813, 0.871502, 0.884097, 0.897721, 0.912529, 0.928713, 0.946524, 0.966294, 0.974847, 0.983819, 0.993255, 1.003202, 1.013720, 1.024877, 1.036759, 1.049467, 1.063130, 1.077905, 1.093991, 1.111627, 1.121100, 1.131030, 1.141374, 1.146648, 1.151921, 1.154007, 1.156065, 1.158081, 1.160039, 1.161916, 1.163689, 1.165332, 1.166096, 1.166819, 1.167499, 1.167821, 1.168132, 1.168431, 1.168489, 1.168547, 1.168605, 1.168662, 1.168718, 1.168829, 1.168939, 1.168993, 1.169046},
{ 0.684948, 0.685604, 0.685862, 0.685990, 0.685994, 0.685991, 0.685989, 0.685988, 0.685989, 0.685992, 0.686012, 0.686034, 0.686056, 0.686100, 0.686143, 0.686186, 0.686273, 0.686360, 0.686447, 0.686534, 0.686621, 0.686708, 0.686796, 0.687015, 0.687234, 0.687676, 0.688120, 0.688569, 0.689479, 0.690407, 0.691357, 0.692330, 0.693329, 0.694355, 0.695410, 0.696495, 0.697611, 0.698761, 0.699944, 0.701163, 0.704371, 0.707818, 0.711519, 0.715485, 0.719728, 0.724260, 0.729094, 0.734242, 0.739721, 0.745546, 0.751735, 0.758310, 0.765293, 0.772710, 0.780590, 0.788969, 0.797884, 0.807381, 0.817511, 0.828336, 0.839927, 0.852369, 0.865765, 0.880239, 0.895943, 0.913069, 0.931859, 0.952631, 0.961585, 0.970954, 0.980778, 0.991098, 1.001965, 1.013435, 1.025573, 1.038451, 1.052150, 1.066743, 1.082273, 1.098644, 1.106992, 1.115198, 1.122744, 1.125910, 1.128265, 1.128859, 1.129181, 1.129177, 1.128807, 1.128080, 1.127083, 1.125883, 1.125214, 1.124508, 1.123769, 1.123389, 1.123003, 1.122610, 1.122531, 1.122452, 1.122372, 1.122293, 1.122213, 1.122052, 1.121891, 1.121810, 1.121729},
{ 0.647990, 0.647822, 0.647676, 0.647600, 0.647625, 0.647639, 0.647649, 0.647657, 0.647663, 0.647668, 0.647693, 0.647720, 0.647748, 0.647803, 0.647858, 0.647913, 0.648023, 0.648133, 0.648243, 0.648352, 0.648461, 0.648570, 0.648679, 0.648950, 0.649221, 0.649759, 0.650295, 0.650828, 0.651891, 0.652954, 0.654019, 0.655093, 0.656179, 0.657281, 0.658401, 0.659544, 0.660713, 0.661909, 0.663135, 0.664394, 0.667697, 0.671244, 0.675059, 0.679160, 0.683567, 0.688296, 0.693363, 0.698785, 0.704579, 0.710763, 0.717358, 0.724385, 0.731869, 0.739837, 0.748320, 0.757354, 0.766979, 0.777242, 0.788196, 0.799903, 0.812438, 0.825885, 0.840350, 0.855954, 0.872851, 0.891225, 0.911311, 0.933401, 0.942880, 0.952766, 0.963093, 0.973893, 0.985204, 0.997064, 1.009510, 1.022572, 1.036258, 1.050524, 1.065176, 1.079598, 1.086192, 1.091620, 1.094299, 1.093339, 1.088849, 1.085066, 1.078826, 1.065901, 1.050163, 1.040584, 1.032493, 1.024579, 1.020564, 1.016511, 1.012427, 1.010375, 1.008316, 1.006250, 1.005835, 1.005421, 1.005006, 1.004591, 1.004175, 1.003343, 1.002510, 1.002092, 1.001675},
{ 0.601499, 0.601533, 0.601690, 0.601760, 0.601739, 0.601742, 0.601751, 0.601762, 0.601772, 0.601782, 0.601819, 0.601857, 0.601896, 0.601972, 0.602048, 0.602124, 0.602276, 0.602428, 0.602578, 0.602729, 0.602878, 0.603028, 0.603176, 0.603546, 0.603912, 0.604635, 0.605347, 0.606049, 0.607423, 0.608764, 0.610080, 0.611377, 0.612660, 0.613937, 0.615213, 0.616494, 0.617784, 0.619089, 0.620413, 0.621761, 0.625254, 0.628967, 0.632939, 0.637206, 0.641797, 0.646736, 0.652047, 0.657752, 0.663873, 0.670430, 0.677447, 0.684949, 0.692962, 0.701516, 0.710643, 0.720381, 0.730772, 0.741865, 0.753714, 0.766384, 0.779950, 0.794500, 0.810136, 0.826982, 0.845188, 0.864931, 0.886430, 0.909952, 0.919996, 0.930438, 0.941299, 0.952604, 0.964373, 0.976623, 0.989359, 1.002561, 1.016156, 1.029960, 1.043523, 1.055685, 1.060352, 1.062953, 1.061689, 1.059014, 1.055963, 1.055545, 1.056757, 1.063454, 1.070851, 1.067367, 1.044575, 1.031316, 1.026188, 1.021151, 1.016017, 1.013408, 1.010774, 1.008118, 1.007584, 1.007049, 1.006513, 1.005977, 1.005439, 1.004360, 1.003277, 1.002734, 1.002190},
{ 0.552601, 0.552551, 0.552370, 0.552435, 0.552479, 0.552476, 0.552478, 0.552488, 0.552501, 0.552516, 0.552570, 0.552623, 0.552677, 0.552784, 0.552891, 0.552998, 0.553210, 0.553422, 0.553633, 0.553842, 0.554051, 0.554260, 0.554467, 0.554981, 0.555491, 0.556493, 0.557475, 0.558437, 0.560304, 0.562100, 0.563833, 0.565508, 0.567135, 0.568721, 0.570275, 0.571804, 0.573315, 0.574817, 0.576317, 0.577820, 0.581634, 0.585594, 0.589768, 0.594213, 0.598977, 0.604097, 0.609608, 0.615541, 0.621924, 0.628785, 0.636151, 0.644050, 0.652513, 0.661572, 0.671264, 0.681627, 0.692705, 0.704551, 0.717219, 0.730778, 0.745301, 0.760879, 0.777614, 0.795629, 0.815066, 0.836096, 0.858919, 0.883769, 0.894334, 0.905279, 0.916621, 0.928371, 0.940536, 0.953109, 0.966066, 0.979341, 0.992803, 1.006179, 1.018929, 1.030017, 1.034492, 1.038274, 1.042328, 1.044870, 1.046874, 1.046988, 1.046512, 1.045620, 1.045029, 1.046766, 1.061806, 1.053066, 1.057122, 1.055044, 1.053047, 1.052074, 1.051228, 1.050375, 1.050254, 1.050082, 1.049951, 1.049799, 1.049650, 1.049361, 1.049070, 1.048925, 1.048781},
{ 0.503269, 0.503552, 0.503720, 0.503584, 0.503679, 0.503691, 0.503690, 0.503695, 0.503710, 0.503730, 0.503802, 0.503875, 0.503945, 0.504088, 0.504229, 0.504371, 0.504653, 0.504935, 0.505215, 0.505494, 0.505772, 0.506049, 0.506326, 0.507011, 0.507690, 0.509029, 0.510341, 0.511626, 0.514118, 0.516507, 0.518795, 0.520990, 0.523096, 0.525123, 0.527077, 0.528969, 0.530808, 0.532603, 0.534363, 0.536098, 0.540379, 0.544679, 0.549101, 0.553732, 0.558643, 0.563892, 0.569530, 0.575600, 0.582139, 0.589184, 0.596769, 0.604928, 0.613696, 0.623109, 0.633206, 0.644029, 0.655627, 0.668051, 0.681360, 0.695621, 0.710913, 0.727322, 0.744951, 0.763918, 0.784362, 0.806439, 0.830331, 0.856234, 0.867202, 0.878534, 0.890237, 0.902314, 0.914759, 0.927554, 0.940658, 0.953997, 0.967447, 0.980821, 0.993913, 1.006815, 1.013500, 1.020569, 1.027727, 1.031190, 1.034877, 1.036509, 1.038140, 1.039449, 1.039885, 1.039184, 1.038655, 1.053066, 1.057122, 1.055044, 1.053047, 1.052073, 1.051227, 1.050376, 1.050254, 1.050082, 1.049951, 1.049799, 1.049650, 1.049361, 1.049070, 1.048925, 1.048781},
{ 0.458276, 0.457751, 0.457881, 0.457945, 0.457989, 0.458029, 0.458033, 0.458033, 0.458048, 0.458074, 0.458160, 0.458253, 0.458338, 0.458513, 0.458688, 0.458863, 0.459211, 0.459558, 0.459904, 0.460249, 0.460594, 0.460937, 0.461279, 0.462130, 0.462975, 0.464645, 0.466288, 0.467904, 0.471049, 0.474076, 0.476984, 0.479771, 0.482441, 0.484996, 0.487443, 0.489788, 0.492042, 0.494213, 0.496312, 0.498350, 0.503245, 0.507984, 0.512709, 0.517542, 0.522584, 0.527919, 0.533617, 0.539736, 0.546328, 0.553439, 0.561112, 0.569387, 0.578306, 0.587909, 0.598239, 0.609341, 0.621266, 0.634068, 0.647807, 0.662552, 0.678378, 0.695373, 0.713636, 0.733279, 0.754431, 0.777236, 0.801852, 0.828439, 0.839660, 0.851226, 0.863141, 0.875405, 0.888012, 0.900947, 0.914190, 0.927720, 0.941538, 0.955735, 0.970632, 0.986868, 0.995669, 1.004963, 1.014867, 1.019991, 1.024971, 1.026899, 1.028851, 1.030914, 1.033082, 1.034847, 1.034943, 1.033977, 1.035495, 1.031710, 1.022650, 1.018972, 1.015358, 1.011667, 1.010917, 1.010162, 1.009404, 1.008642, 1.007876, 1.006334, 1.004777, 1.003992, 1.003203}};
  const double reomegaqnm41[8][107] = {{ 0.812182, 0.808144, 0.804532, 0.801074, 0.799893, 0.799611, 0.799426, 0.799300, 0.799213, 0.799150, 0.799003, 0.798947, 0.798911, 0.798850, 0.798791, 0.798733, 0.798616, 0.798500, 0.798384, 0.798270, 0.798156, 0.798043, 0.797930, 0.797653, 0.797381, 0.796850, 0.796339, 0.795846, 0.794914, 0.794054, 0.793261, 0.792535, 0.791872, 0.791272, 0.790731, 0.790250, 0.789825, 0.789457, 0.789142, 0.788881, 0.788453, 0.788336, 0.788518, 0.788990, 0.789746, 0.790780, 0.792090, 0.793675, 0.795538, 0.797681, 0.800109, 0.802828, 0.805847, 0.809178, 0.812834, 0.816829, 0.821184, 0.825920, 0.831063, 0.836645, 0.842701, 0.849275, 0.856419, 0.864196, 0.872681, 0.881970, 0.892182, 0.903467, 0.908325, 0.913401, 0.918714, 0.924282, 0.930130, 0.936284, 0.942774, 0.949638, 0.956920, 0.964670, 0.972954, 0.981849, 0.986554, 0.991450, 0.996552, 0.999185, 1.001875, 1.002968, 1.004070, 1.005183, 1.006305, 1.007437, 1.008580, 1.009733, 1.010313, 1.010896, 1.011482, 1.011775, 1.012069, 1.012365, 1.012425, 1.012486, 1.012547, 1.012610, 1.012675, 1.012826, 1.013062, 1.013298, 1.013824},
{ 0.787016, 0.786705, 0.786633, 0.786636, 0.786654, 0.786658, 0.786660, 0.786659, 0.786658, 0.786655, 0.786633, 0.786608, 0.786583, 0.786532, 0.786482, 0.786432, 0.786332, 0.786233, 0.786133, 0.786034, 0.785936, 0.785837, 0.785740, 0.785496, 0.785255, 0.784780, 0.784314, 0.783860, 0.782983, 0.782153, 0.781373, 0.780643, 0.779964, 0.779339, 0.778765, 0.778245, 0.777777, 0.777362, 0.776999, 0.776689, 0.776136, 0.775899, 0.775972, 0.776348, 0.777024, 0.777997, 0.779265, 0.780828, 0.782689, 0.784850, 0.787316, 0.790096, 0.793197, 0.796632, 0.800412, 0.804555, 0.809080, 0.814010, 0.819370, 0.825192, 0.831513, 0.838376, 0.845834, 0.853949, 0.862794, 0.872463, 0.883066, 0.894745, 0.899756, 0.904979, 0.910431, 0.916126, 0.922083, 0.928320, 0.934858, 0.941718, 0.948921, 0.956483, 0.964413, 0.972695, 0.976951, 0.981262, 0.985603, 0.987773, 0.989934, 0.990794, 0.991650, 0.992503, 0.993351, 0.994195, 0.995032, 0.995862, 0.996275, 0.996685, 0.997094, 0.997297, 0.997500, 0.997702, 0.997743, 0.997783, 0.997823, 0.997864, 0.997904, 0.997983, 0.998061, 0.998100, 0.998148},
{ 0.762154, 0.762371, 0.762447, 0.762470, 0.762460, 0.762454, 0.762450, 0.762446, 0.762442, 0.762439, 0.762424, 0.762410, 0.762395, 0.762365, 0.762336, 0.762306, 0.762245, 0.762184, 0.762123, 0.762060, 0.761998, 0.761934, 0.761871, 0.761709, 0.761545, 0.761209, 0.760866, 0.760516, 0.759805, 0.759091, 0.758382, 0.757690, 0.757020, 0.756379, 0.755772, 0.755203, 0.754676, 0.754192, 0.753754, 0.753363, 0.752600, 0.752154, 0.752031, 0.752234, 0.752765, 0.753625, 0.754814, 0.756336, 0.758192, 0.760388, 0.762929, 0.765823, 0.769079, 0.772710, 0.776728, 0.781151, 0.785999, 0.791294, 0.797065, 0.803342, 0.810163, 0.817572, 0.825620, 0.834367, 0.843884, 0.854256, 0.865580, 0.877973, 0.883258, 0.888742, 0.894435, 0.900343, 0.906472, 0.912826, 0.919402, 0.926186, 0.933150, 0.940233, 0.947322, 0.954199, 0.957445, 0.960474, 0.963195, 0.964409, 0.965508, 0.965912, 0.966295, 0.966656, 0.966994, 0.967309, 0.967600, 0.967867, 0.967991, 0.968108, 0.968220, 0.968273, 0.968325, 0.968376, 0.968385, 0.968395, 0.968405, 0.968415, 0.968424, 0.968443, 0.968462, 0.968471, 0.968475},
{ 0.727482, 0.727419, 0.727374, 0.727356, 0.727363, 0.727365, 0.727367, 0.727368, 0.727369, 0.727369, 0.727372, 0.727375, 0.727378, 0.727384, 0.727390, 0.727395, 0.727404, 0.727411, 0.727417, 0.727421, 0.727423, 0.727424, 0.727423, 0.727414, 0.727396, 0.727333, 0.727237, 0.727112, 0.726782, 0.726368, 0.725889, 0.725364, 0.724810, 0.724241, 0.723670, 0.723106, 0.722558, 0.722034, 0.721540, 0.721082, 0.720114, 0.719440, 0.719091, 0.719085, 0.719436, 0.720153, 0.721242, 0.722709, 0.724560, 0.726801, 0.729440, 0.732484, 0.735946, 0.739837, 0.744172, 0.748968, 0.754247, 0.760031, 0.766349, 0.773233, 0.780719, 0.788851, 0.797679, 0.807257, 0.817652, 0.828933, 0.841176, 0.854453, 0.860066, 0.865854, 0.871814, 0.877939, 0.884216, 0.890619, 0.897108, 0.903610, 0.910008, 0.916106, 0.921568, 0.925840, 0.927280, 0.928103, 0.928217, 0.927993, 0.927582, 0.927367, 0.927123, 0.926851, 0.926552, 0.926227, 0.925876, 0.925500, 0.925304, 0.925101, 0.924893, 0.924786, 0.924679, 0.924570, 0.924548, 0.924526, 0.924504, 0.924482, 0.924459, 0.924415, 0.924370, 0.924348, 0.924328},
{ 0.683045, 0.683066, 0.683115, 0.683138, 0.683141, 0.683147, 0.683153, 0.683160, 0.683166, 0.683173, 0.683202, 0.683232, 0.683261, 0.683319, 0.683377, 0.683434, 0.683546, 0.683656, 0.683763, 0.683867, 0.683969, 0.684068, 0.684165, 0.684396, 0.684612, 0.684997, 0.685323, 0.685593, 0.685975, 0.686168, 0.686198, 0.686092, 0.685876, 0.685572, 0.685204, 0.684790, 0.684348, 0.683891, 0.683432, 0.682983, 0.681954, 0.681143, 0.680622, 0.680439, 0.680626, 0.681205, 0.682194, 0.683604, 0.685446, 0.687731, 0.690469, 0.693671, 0.697348, 0.701516, 0.706189, 0.711386, 0.717128, 0.723441, 0.730350, 0.737890, 0.746095, 0.755006, 0.764669, 0.775134, 0.786452, 0.798673, 0.811839, 0.825957, 0.831859, 0.837893, 0.844039, 0.850270, 0.856541, 0.862785, 0.868895, 0.874706, 0.879948, 0.884181, 0.886682, 0.886368, 0.884820, 0.882330, 0.879045, 0.877163, 0.875153, 0.874319, 0.873469, 0.872606, 0.871730, 0.870843, 0.869945, 0.869039, 0.868583, 0.868125, 0.867665, 0.867434, 0.867203, 0.866972, 0.866925, 0.866879, 0.866833, 0.866786, 0.866740, 0.866647, 0.866554, 0.866507, 0.866460},
{ 0.632260, 0.632262, 0.632219, 0.632253, 0.632284, 0.632294, 0.632304, 0.632316, 0.632329, 0.632343, 0.632405, 0.632467, 0.632529, 0.632653, 0.632776, 0.632898, 0.633140, 0.633379, 0.633615, 0.633849, 0.634079, 0.634306, 0.634531, 0.635078, 0.635607, 0.636608, 0.637532, 0.638380, 0.639849, 0.641028, 0.641936, 0.642598, 0.643043, 0.643301, 0.643404, 0.643379, 0.643254, 0.643052, 0.642794, 0.642500, 0.641703, 0.640966, 0.640422, 0.640165, 0.640257, 0.640743, 0.641654, 0.643015, 0.644845, 0.647160, 0.649976, 0.653306, 0.657167, 0.661572, 0.666542, 0.672094, 0.678251, 0.685038, 0.692482, 0.700614, 0.709468, 0.719080, 0.729489, 0.740734, 0.752848, 0.765853, 0.779737, 0.794417, 0.800467, 0.806579, 0.812714, 0.818811, 0.824779, 0.830485, 0.835720, 0.840156, 0.843255, 0.844101, 0.841167, 0.832816, 0.827120, 0.821047, 0.814772, 0.811623, 0.808488, 0.807240, 0.805995, 0.804756, 0.803521, 0.802292, 0.801069, 0.799852, 0.799245, 0.798641, 0.798037, 0.797736, 0.797436, 0.797136, 0.797076, 0.797016, 0.796956, 0.796896, 0.796836, 0.796716, 0.796596, 0.796538, 0.796478},
{ 0.577671, 0.577747, 0.577832, 0.577822, 0.577876, 0.577897, 0.577913, 0.577930, 0.577948, 0.577969, 0.578066, 0.578162, 0.578258, 0.578450, 0.578641, 0.578831, 0.579210, 0.579586, 0.579960, 0.580331, 0.580699, 0.581065, 0.581428, 0.582323, 0.583200, 0.584900, 0.586522, 0.588064, 0.590896, 0.593380, 0.595512, 0.597299, 0.598760, 0.599921, 0.600814, 0.601472, 0.601932, 0.602227, 0.602387, 0.602441, 0.602270, 0.601899, 0.601548, 0.601371, 0.601477, 0.601940, 0.602816, 0.604145, 0.605960, 0.608286, 0.611144, 0.614555, 0.618537, 0.623109, 0.628291, 0.634105, 0.640572, 0.647718, 0.655568, 0.664152, 0.673498, 0.683637, 0.694598, 0.706401, 0.719056, 0.732542, 0.746777, 0.761555, 0.767525, 0.773458, 0.779281, 0.784886, 0.790116, 0.794732, 0.798360, 0.800381, 0.799703, 0.794215, 0.779821, 0.761639, 0.752939, 0.745281, 0.737595, 0.733911, 0.730347, 0.728943, 0.727558, 0.726183, 0.724821, 0.723472, 0.722136, 0.720811, 0.720153, 0.719498, 0.718845, 0.718520, 0.718196, 0.717872, 0.717808, 0.717743, 0.717679, 0.717614, 0.717549, 0.717420, 0.717292, 0.717224, 0.717163},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.593214, 0.599185, 0.605845, 0.613217, 0.621327, 0.630197, 0.639852, 0.650311, 0.661589, 0.673683, 0.686569, 0.700168, 0.714307, 0.728612, 0.734225, 0.739661, 0.744800, 0.749470, 0.753412, 0.756227, 0.757257, 0.755324, 0.747973, 0.728096, 0.650476, 0.611311, 0.592090, 0.573322, 0.554778, 0.545580, 0.536421, 0.532767, 0.529117, 0.525471, 0.521828, 0.534982, 0.528313, 0.521510, 0.518051, 0.514548, 0.510997, 0.509203, 0.507394, 0.505570, 0.505203, 0.504836, 0.504468, 0.504099, 0.503730, 0.502990, 0.502247, 0.501874, 0.501501}};
  const double reomegaqnm40[8][107] = {{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.809327, 0.809774, 0.810523, 0.811579, 0.812950, 0.814646, 0.816680, 0.819068, 0.821832, 0.824994, 0.828585, 0.832642, 0.837209, 0.842340, 0.844566, 0.846898, 0.849342, 0.851904, 0.854591, 0.857411, 0.860371, 0.863482, 0.866753, 0.870197, 0.873826, 0.877655, 0.879649, 0.881700, 0.883809, 0.884886, 0.885979, 0.886420, 0.886864, 0.887310, 0.887760, 0.888211, 0.888666, 0.889123, 0.889352, 0.889582, 0.889813, 0.889929, 0.890048, 0.890186, 0.890221, 0.890261, 0.890311, 0.890374, 0.890462, 0.890801, 0.891872, 0.893423, 0.897340},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.796792, 0.797273, 0.798078, 0.799213, 0.800686, 0.802506, 0.804687, 0.807245, 0.810200, 0.813574, 0.817397, 0.821700, 0.826523, 0.831911, 0.834235, 0.836662, 0.839194, 0.841836, 0.844591, 0.847462, 0.850452, 0.853565, 0.856799, 0.860156, 0.863630, 0.867213, 0.869041, 0.870889, 0.872754, 0.873692, 0.874632, 0.875008, 0.875385, 0.875762, 0.876139, 0.876516, 0.876893, 0.877270, 0.877458, 0.877647, 0.877835, 0.877929, 0.878024, 0.878117, 0.878136, 0.878154, 0.878172, 0.878190, 0.878206, 0.878236, 0.878267, 0.878303, 0.878429},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.772891, 0.773436, 0.774349, 0.775634, 0.777299, 0.779355, 0.781814, 0.784691, 0.788004, 0.791775, 0.796025, 0.800780, 0.806065, 0.811904, 0.814397, 0.816982, 0.819656, 0.822419, 0.825266, 0.828192, 0.831188, 0.834241, 0.837333, 0.840435, 0.843512, 0.846511, 0.847960, 0.849364, 0.850709, 0.851356, 0.851984, 0.852229, 0.852471, 0.852710, 0.852944, 0.853175, 0.853402, 0.853625, 0.853735, 0.853843, 0.853951, 0.854005, 0.854058, 0.854111, 0.854121, 0.854132, 0.854142, 0.854153, 0.854164, 0.854187, 0.854205, 0.854201, 0.854163},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.740047, 0.740678, 0.741735, 0.743220, 0.745143, 0.747512, 0.750339, 0.753636, 0.757418, 0.761700, 0.766495, 0.771814, 0.777658, 0.784009, 0.786680, 0.789419, 0.792217, 0.795061, 0.797936, 0.800820, 0.803685, 0.806492, 0.809190, 0.811715, 0.813983, 0.815893, 0.816680, 0.817335, 0.817845, 0.818042, 0.818198, 0.818249, 0.818293, 0.818330, 0.818361, 0.818384, 0.818400, 0.818409, 0.818411, 0.818412, 0.818410, 0.818409, 0.818407, 0.818404, 0.818404, 0.818403, 0.818403, 0.818402, 0.818401, 0.818399, 0.818400, 0.818408, 0.818424},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.701757, 0.702483, 0.703695, 0.705399, 0.707599, 0.710305, 0.713523, 0.717264, 0.721533, 0.726336, 0.731670, 0.737521, 0.743851, 0.750576, 0.753344, 0.756135, 0.758927, 0.761694, 0.764400, 0.766998, 0.769430, 0.771620, 0.773474, 0.774879, 0.775711, 0.775850, 0.775630, 0.775206, 0.774575, 0.774183, 0.773739, 0.773548, 0.773349, 0.773141, 0.772926, 0.772704, 0.772473, 0.772235, 0.772113, 0.771990, 0.771864, 0.771801, 0.771737, 0.771673, 0.771660, 0.771647, 0.771634, 0.771621, 0.771608, 0.771583, 0.771556, 0.771534, 0.771516},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.661843, 0.662654, 0.664009, 0.665910, 0.668360, 0.671365, 0.674926, 0.679045, 0.683719, 0.688936, 0.694669, 0.700864, 0.707423, 0.714165, 0.716846, 0.719476, 0.722013, 0.724408, 0.726595, 0.728492, 0.729996, 0.730981, 0.731307, 0.730830, 0.729436, 0.727079, 0.725549, 0.723799, 0.721846, 0.720799, 0.719709, 0.719262, 0.718808, 0.718348, 0.717882, 0.717410, 0.716932, 0.716449, 0.716206, 0.715961, 0.715715, 0.715591, 0.715468, 0.715343, 0.715318, 0.715294, 0.715269, 0.715244, 0.715220, 0.715168, 0.715118, 0.715104, 0.715080},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.623402, 0.624280, 0.625745, 0.627796, 0.630435, 0.633659, 0.637463, 0.641838, 0.646764, 0.652205, 0.658097, 0.664333, 0.670727, 0.676954, 0.679282, 0.681442, 0.683368, 0.684972, 0.686146, 0.686757, 0.686646, 0.685638, 0.683574, 0.680369, 0.676056, 0.670788, 0.667863, 0.664780, 0.661570, 0.659924, 0.658256, 0.657583, 0.656907, 0.656228, 0.655546, 0.654862, 0.654175, 0.653487, 0.653141, 0.652796, 0.652450, 0.652276, 0.652103, 0.651929, 0.651894, 0.651860, 0.651826, 0.651791, 0.651756, 0.651684, 0.651624, 0.651570, 0.651532},
{ 0.523121, 0.522966, 0.522983, 0.523079, 0.523114, 0.523151, 0.523176, 0.523196, 0.523218, 0.523244, 0.523371, 0.523498, 0.523623, 0.523873, 0.524124, 0.524374, 0.524872, 0.525369, 0.525864, 0.526357, 0.526849, 0.527339, 0.527826, 0.529037, 0.530235, 0.532589, 0.534883, 0.537110, 0.541345, 0.545250, 0.548791, 0.551942, 0.554695, 0.557052, 0.559032, 0.560663, 0.561980, 0.563023, 0.563831, 0.564442, 0.565326, 0.565642, 0.565721, 0.565798, 0.566039, 0.566564, 0.567456, 0.568779, 0.570581, 0.572899, 0.575766, 0.579207, 0.583247, 0.587909, 0.588217, 0.589140, 0.590677, 0.592826, 0.595581, 0.598932, 0.602865, 0.607353, 0.612354, 0.617799, 0.623576, 0.629502, 0.635269, 0.640353, 0.642007, 0.643325, 0.644200, 0.644492, 0.644035, 0.642627, 0.640056, 0.636153, 0.630889, 0.624446, 0.617123, 0.609231, 0.605155, 0.601029, 0.596874, 0.594791, 0.592707, 0.591874, 0.591041, 0.590209, 0.589376, 0.588544, 0.587713, 0.586883, 0.586468, 0.586053, 0.585638, 0.585431, 0.585224, 0.585016, 0.584975, 0.584935, 0.584894, 0.584851, 0.584807, 0.584733, 0.584628, 0.584607, 0.584599}};
 
  const double imomegaqnm22[8][107] = {{ 0.078461, 0.080101, 0.081647, 0.084004, 0.085495, 0.086013, 0.086422, 0.086745, 0.087003, 0.087210, 0.087780, 0.087988, 0.088065, 0.088096, 0.088088, 0.088076, 0.088061, 0.088057, 0.088059, 0.088063, 0.088068, 0.088073, 0.088078, 0.088091, 0.088104, 0.088130, 0.088156, 0.088181, 0.088231, 0.088281, 0.088329, 0.088376, 0.088423, 0.088468, 0.088512, 0.088555, 0.088598, 0.088639, 0.088679, 0.088717, 0.088809, 0.088892, 0.088966, 0.089032, 0.089087, 0.089131, 0.089164, 0.089185, 0.089191, 0.089183, 0.089157, 0.089114, 0.089050, 0.088962, 0.088849, 0.088706, 0.088528, 0.088311, 0.088048, 0.087729, 0.087345, 0.086882, 0.086321, 0.085639, 0.084802, 0.083765, 0.082462, 0.080793, 0.079991, 0.079093, 0.078082, 0.076936, 0.075630, 0.074126, 0.072378, 0.070321, 0.067864, 0.064869, 0.061119, 0.056231, 0.053149, 0.049434, 0.044790, 0.041959, 0.038630, 0.037116, 0.035468, 0.033659, 0.031652, 0.029390, 0.026791, 0.023710, 0.021911, 0.019866, 0.017474, 0.016092, 0.014534, 0.012727, 0.012326, 0.011908, 0.011471, 0.011013, 0.010531, 0.009478, 0.008267, 0.007577, 0.006807},
{ 0.284478, 0.282567, 0.281162, 0.279245, 0.278072, 0.277670, 0.277358, 0.277118, 0.276936, 0.276800, 0.276536, 0.276565, 0.276647, 0.276753, 0.276778, 0.276775, 0.276764, 0.276768, 0.276776, 0.276784, 0.276791, 0.276797, 0.276803, 0.276818, 0.276834, 0.276864, 0.276893, 0.276922, 0.276977, 0.277028, 0.277076, 0.277120, 0.277160, 0.277197, 0.277230, 0.277259, 0.277283, 0.277304, 0.277321, 0.277333, 0.277344, 0.277326, 0.277278, 0.277196, 0.277080, 0.276926, 0.276732, 0.276495, 0.276212, 0.275877, 0.275486, 0.275033, 0.274512, 0.273915, 0.273232, 0.272452, 0.271562, 0.270546, 0.269383, 0.268049, 0.266512, 0.264733, 0.262661, 0.260225, 0.257331, 0.253847, 0.249580, 0.244238, 0.241705, 0.238888, 0.235736, 0.232183, 0.228149, 0.223524, 0.218165, 0.211876, 0.204376, 0.195252, 0.183847, 0.169019, 0.159687, 0.148458, 0.134453, 0.125927, 0.115917, 0.111365, 0.106415, 0.100985, 0.094960, 0.088175, 0.080377, 0.071134, 0.065738, 0.059605, 0.052426, 0.048280, 0.043605, 0.038184, 0.036979, 0.035724, 0.034413, 0.033038, 0.031592, 0.028433, 0.024800, 0.022730, 0.020422},
{ 0.504534, 0.501693, 0.501238, 0.503711, 0.506007, 0.506490, 0.506633, 0.506559, 0.506365, 0.506120, 0.505173, 0.505120, 0.505381, 0.505519, 0.505371, 0.505318, 0.505354, 0.505311, 0.505262, 0.505236, 0.505210, 0.505177, 0.505141, 0.505059, 0.504978, 0.504812, 0.504645, 0.504476, 0.504135, 0.503786, 0.503432, 0.503070, 0.502702, 0.502326, 0.501944, 0.501554, 0.501156, 0.500751, 0.500338, 0.499917, 0.498828, 0.497686, 0.496488, 0.495230, 0.493910, 0.492523, 0.491065, 0.489531, 0.487913, 0.486206, 0.484399, 0.482484, 0.480448, 0.478277, 0.475955, 0.473463, 0.470778, 0.467872, 0.464713, 0.461260, 0.457463, 0.453259, 0.448569, 0.443287, 0.437269, 0.430315, 0.422131, 0.412262, 0.407689, 0.402664, 0.397103, 0.390894, 0.383895, 0.375919, 0.366715, 0.355940, 0.343110, 0.327518, 0.308058, 0.282827, 0.266998, 0.248008, 0.224410, 0.210086, 0.193307, 0.185690, 0.177413, 0.168340, 0.158283, 0.146966, 0.133965, 0.118563, 0.109572, 0.099352, 0.087389, 0.080478, 0.072685, 0.063646, 0.061638, 0.059545, 0.057359, 0.055068, 0.052656, 0.047390, 0.041333, 0.037883, 0.034035},
{ 0.777682, 0.778170, 0.774907, 0.771079, 0.772456, 0.773571, 0.774249, 0.774423, 0.774236, 0.773865, 0.772678, 0.773376, 0.773489, 0.772990, 0.773229, 0.773121, 0.773005, 0.772942, 0.772818, 0.772776, 0.772680, 0.772579, 0.772506, 0.772294, 0.772084, 0.771654, 0.771224, 0.770787, 0.769900, 0.768995, 0.768072, 0.767129, 0.766168, 0.765187, 0.764186, 0.763165, 0.762123, 0.761061, 0.759977, 0.758872, 0.756015, 0.753020, 0.749885, 0.746606, 0.743182, 0.739611, 0.735891, 0.732017, 0.727985, 0.723788, 0.719419, 0.714865, 0.710114, 0.705148, 0.699946, 0.694481, 0.688721, 0.682628, 0.676155, 0.669243, 0.661823, 0.653808, 0.645091, 0.635536, 0.624969, 0.613154, 0.599764, 0.584301, 0.577364, 0.569885, 0.561756, 0.552827, 0.542888, 0.531648, 0.518699, 0.503480, 0.485224, 0.462864, 0.434823, 0.398473, 0.375741, 0.348572, 0.314974, 0.294663, 0.270945, 0.260200, 0.248542, 0.235779, 0.221649, 0.205769, 0.187547, 0.165980, 0.153396, 0.139094, 0.122354, 0.112682, 0.101773, 0.089118, 0.086305, 0.083375, 0.080314, 0.077105, 0.073726, 0.066352, 0.057868, 0.053037, 0.047648},
{ 1.044309, 1.046603, 1.050655, 1.048278, 1.047193, 1.048092, 1.048935, 1.049247, 1.049061, 1.048626, 1.048121, 1.048623, 1.048064, 1.048425, 1.048083, 1.048244, 1.048026, 1.047992, 1.047878, 1.047811, 1.047683, 1.047624, 1.047519, 1.047294, 1.047043, 1.046571, 1.046088, 1.045602, 1.044600, 1.043569, 1.042506, 1.041410, 1.040279, 1.039113, 1.037909, 1.036667, 1.035386, 1.034063, 1.032697, 1.031287, 1.027561, 1.023531, 1.019176, 1.014480, 1.009427, 1.004003, 0.998200, 0.992012, 0.985437, 0.978476, 0.971133, 0.963412, 0.955317, 0.946845, 0.937987, 0.928725, 0.919026, 0.908845, 0.898118, 0.886764, 0.874681, 0.861738, 0.847776, 0.832595, 0.815947, 0.797527, 0.776957, 0.753800, 0.743710, 0.733106, 0.721967, 0.710268, 0.697962, 0.684902, 0.670601, 0.653750, 0.632042, 0.603295, 0.565870, 0.517102, 0.486783, 0.450771, 0.406552, 0.379969, 0.349048, 0.335080, 0.319949, 0.303412, 0.285135, 0.264631, 0.241142, 0.213382, 0.197201, 0.178818, 0.157307, 0.144878, 0.130859, 0.114594, 0.110978, 0.107211, 0.103275, 0.099148, 0.094804, 0.085320, 0.074409, 0.068195, 0.061264},
{ 1.321876, 1.316952, 1.316680, 1.319467, 1.317311, 1.317699, 1.318525, 1.318939, 1.318766, 1.318308, 1.318440, 1.318071, 1.318219, 1.318003, 1.318199, 1.317998, 1.317922, 1.317906, 1.317816, 1.317701, 1.317641, 1.317538, 1.317449, 1.317225, 1.317008, 1.316565, 1.316117, 1.315660, 1.314736, 1.313781, 1.312801, 1.311792, 1.310749, 1.309671, 1.308555, 1.307400, 1.306200, 1.304955, 1.303660, 1.302314, 1.298700, 1.294695, 1.290248, 1.285302, 1.279801, 1.273681, 1.266873, 1.259306, 1.250911, 1.241631, 1.231433, 1.220321, 1.208348, 1.195608, 1.182210, 1.168248, 1.153773, 1.138779, 1.123199, 1.106915, 1.089762, 1.071525, 1.051940, 1.030673, 1.007299, 0.981265, 0.951825, 0.917950, 0.902851, 0.886706, 0.869389, 0.850781, 0.830803, 0.809534, 0.787531, 0.766572, 0.750871, 0.748723, 0.741744, 0.732374, 0.728044, 0.723765, 0.719565, 0.717492, 0.715438, 0.714621, 0.713807, 0.712996, 0.712188, 0.711383, 0.710581, 0.709781, 0.709382, 0.708984, 0.708587, 0.708388, 0.708190, 0.707992, 0.707952, 0.707911, 0.707871, 0.707832, 0.707796, 0.707720, 0.707620, 0.707592, 0.707598},
{ 1.582041, 1.586347, 1.583178, 1.585108, 1.583555, 1.583429, 1.584183, 1.584679, 1.584484, 1.583983, 1.584406, 1.583828, 1.584168, 1.584097, 1.583865, 1.583835, 1.583730, 1.583671, 1.583575, 1.583419, 1.583359, 1.583229, 1.583150, 1.582888, 1.582639, 1.582125, 1.581635, 1.581142, 1.580158, 1.579185, 1.578210, 1.577232, 1.576245, 1.575242, 1.574220, 1.573172, 1.572096, 1.570987, 1.569838, 1.568647, 1.565452, 1.561889, 1.557887, 1.553369, 1.548253, 1.542442, 1.535819, 1.528233, 1.519487, 1.509316, 1.497379, 1.483278, 1.466729, 1.447911, 1.427683, 1.407115, 1.386816, 1.366830, 1.346890, 1.326617, 1.305614, 1.283473, 1.259763, 1.233995, 1.205580, 1.173764, 1.137526, 1.095408, 1.076453, 1.056023, 1.033875, 1.009698, 0.983084, 0.953463, 0.919986, 0.881204, 0.833927, 0.770337, 0.707988, 0.641106, 0.601525, 0.555418, 0.499613, 0.466355, 0.427874, 0.410550, 0.391822, 0.371395, 0.348864, 0.323638, 0.294800, 0.260789, 0.240992, 0.218519, 0.192238, 0.177057, 0.159933, 0.140065, 0.135647, 0.131044, 0.126235, 0.121193, 0.115884, 0.104293, 0.090955, 0.083359, 0.074885},
{ 1.849571, 1.849682, 1.851341, 1.850066, 1.849828, 1.849286, 1.850035, 1.850597, 1.850266, 1.849681, 1.850075, 1.850080, 1.849639, 1.849608, 1.849634, 1.849658, 1.849410, 1.849226, 1.849059, 1.848840, 1.848638, 1.848508, 1.848291, 1.847881, 1.847459, 1.846618, 1.845835, 1.845061, 1.843607, 1.842250, 1.840966, 1.839752, 1.838590, 1.837469, 1.836377, 1.835304, 1.834239, 1.833173, 1.832097, 1.831005, 1.828147, 1.825021, 1.821526, 1.817570, 1.813060, 1.807903, 1.801987, 1.795176, 1.787281, 1.778014, 1.766864, 1.752776, 1.733234, 1.703841, 1.668818, 1.638934, 1.614234, 1.592062, 1.570644, 1.548919, 1.526188, 1.501903, 1.475550, 1.446567, 1.414276, 1.377806, 1.335978, 1.287119, 1.265086, 1.241327, 1.215578, 1.187510, 1.156708, 1.122625, 1.084532, 1.041406, 0.991742, 0.933178, 0.861906, 0.773444, 0.721837, 0.663505, 0.594647, 0.554166, 0.507666, 0.486825, 0.464348, 0.439888, 0.412969, 0.382898, 0.348601, 0.308246, 0.284798, 0.258210, 0.227147, 0.209213, 0.188989, 0.165524, 0.160306, 0.154870, 0.149189, 0.143232, 0.136961, 0.123266, 0.107504, 0.113694, 0.102135}};
  const double imomegaqnm21[8][107] = {{ 0.074312, 0.077266, 0.079182, 0.081281, 0.082265, 0.082556, 0.082768, 0.082926, 0.083045, 0.083135, 0.083360, 0.083430, 0.083456, 0.083471, 0.083481, 0.083492, 0.083519, 0.083551, 0.083583, 0.083616, 0.083648, 0.083680, 0.083713, 0.083792, 0.083870, 0.084024, 0.084174, 0.084319, 0.084599, 0.084865, 0.085117, 0.085356, 0.085583, 0.085799, 0.086003, 0.086198, 0.086383, 0.086558, 0.086725, 0.086884, 0.087247, 0.087566, 0.087846, 0.088091, 0.088302, 0.088484, 0.088637, 0.088763, 0.088862, 0.088935, 0.088983, 0.089004, 0.088997, 0.088962, 0.088897, 0.088798, 0.088664, 0.088489, 0.088268, 0.087995, 0.087662, 0.087257, 0.086767, 0.086173, 0.085450, 0.084564, 0.083466, 0.082085, 0.081430, 0.080703, 0.079893, 0.078983, 0.077955, 0.076785, 0.075439, 0.073874, 0.072027, 0.069804, 0.067061, 0.063549, 0.061372, 0.058791, 0.055644, 0.053776, 0.051643, 0.050698, 0.049691, 0.048614, 0.047457, 0.046208, 0.044856, 0.043388, 0.042607, 0.041794, 0.040950, 0.040517, 0.040078, 0.039632, 0.039542, 0.039452, 0.039362, 0.039271, 0.039180, 0.038997, 0.038811, 0.038714, 0.038609},
{ 0.258785, 0.258526, 0.258215, 0.257703, 0.257385, 0.257284, 0.257210, 0.257158, 0.257123, 0.257101, 0.257089, 0.257133, 0.257178, 0.257248, 0.257304, 0.257357, 0.257465, 0.257574, 0.257683, 0.257791, 0.257898, 0.258005, 0.258112, 0.258376, 0.258637, 0.259149, 0.259649, 0.260137, 0.261076, 0.261967, 0.262812, 0.263613, 0.264372, 0.265089, 0.265768, 0.266410, 0.267016, 0.267589, 0.268130, 0.268640, 0.269792, 0.270782, 0.271629, 0.272346, 0.272945, 0.273434, 0.273821, 0.274112, 0.274309, 0.274415, 0.274430, 0.274354, 0.274183, 0.273915, 0.273543, 0.273058, 0.272452, 0.271711, 0.270819, 0.269754, 0.268489, 0.266992, 0.265218, 0.263108, 0.260587, 0.257547, 0.253838, 0.249238, 0.247078, 0.244692, 0.242045, 0.239089, 0.235766, 0.231999, 0.227686, 0.222686, 0.216800, 0.209731, 0.201006, 0.189803, 0.182820, 0.174484, 0.164205, 0.158029, 0.150891, 0.147700, 0.144280, 0.140606, 0.136657, 0.132444, 0.128112, 0.124511, 0.123925, 0.123321, 0.121670, 0.121162, 0.120732, 0.120140, 0.120048, 0.119951, 0.119844, 0.119734, 0.119631, 0.119429, 0.119227, 0.119127, 0.119027},
{ 0.451082, 0.450126, 0.449946, 0.450393, 0.450836, 0.450954, 0.451016, 0.451037, 0.451032, 0.451015, 0.450927, 0.450953, 0.451028, 0.451151, 0.451242, 0.451336, 0.451538, 0.451736, 0.451932, 0.452129, 0.452326, 0.452521, 0.452716, 0.453201, 0.453683, 0.454634, 0.455570, 0.456489, 0.458275, 0.459989, 0.461626, 0.463185, 0.464665, 0.466067, 0.467390, 0.468636, 0.469808, 0.470906, 0.471935, 0.472897, 0.475022, 0.476783, 0.478216, 0.479352, 0.480220, 0.480840, 0.481231, 0.481407, 0.481377, 0.481149, 0.480726, 0.480109, 0.479294, 0.478277, 0.477047, 0.475592, 0.473893, 0.471929, 0.469669, 0.467076, 0.464104, 0.460691, 0.456761, 0.452210, 0.446903, 0.440653, 0.433196, 0.424144, 0.419951, 0.415358, 0.410300, 0.404693, 0.398434, 0.391383, 0.383355, 0.374094, 0.363227, 0.350188, 0.334044, 0.313093, 0.299808, 0.283583, 0.262719, 0.249472, 0.233119, 0.225306, 0.216483, 0.206365, 0.194563, 0.180538, 0.163450, 0.141483, 0.127310, 0.111596, 0.095488, 0.086832, 0.077419, 0.066857, 0.064554, 0.062171, 0.059699, 0.057125, 0.054435, 0.048632, 0.042066, 0.038376, 0.034303},
{ 0.670736, 0.672092, 0.671812, 0.670663, 0.670549, 0.670730, 0.670927, 0.671078, 0.671164, 0.671189, 0.671021, 0.671075, 0.671219, 0.671310, 0.671427, 0.671572, 0.671807, 0.672062, 0.672309, 0.672557, 0.672808, 0.673057, 0.673305, 0.673929, 0.674552, 0.675799, 0.677043, 0.678283, 0.680743, 0.683166, 0.685536, 0.687840, 0.690067, 0.692205, 0.694247, 0.696187, 0.698020, 0.699744, 0.701359, 0.702865, 0.706165, 0.708833, 0.710915, 0.712460, 0.713510, 0.714105, 0.714277, 0.714053, 0.713452, 0.712490, 0.711176, 0.709516, 0.707509, 0.705148, 0.702423, 0.699317, 0.695803, 0.691851, 0.687416, 0.682445, 0.676867, 0.670592, 0.663504, 0.655451, 0.646227, 0.635554, 0.623036, 0.608090, 0.601244, 0.593791, 0.585630, 0.576638, 0.566651, 0.555455, 0.542760, 0.528156, 0.511038, 0.490465, 0.464847, 0.431189, 0.409563, 0.382936, 0.348824, 0.327730, 0.302947, 0.291759, 0.279694, 0.266590, 0.252176, 0.235931, 0.216835, 0.192946, 0.178198, 0.160681, 0.138951, 0.125667, 0.110911, 0.095128, 0.091773, 0.088322, 0.084758, 0.081061, 0.077210, 0.068928, 0.059584, 0.054342, 0.048559},
{ 0.910592, 0.910063, 0.911380, 0.911832, 0.911012, 0.911003, 0.911199, 0.911439, 0.911606, 0.911660, 0.911352, 0.911585, 0.911648, 0.911704, 0.911854, 0.911933, 0.912192, 0.912425, 0.912663, 0.912897, 0.913141, 0.913376, 0.913616, 0.914220, 0.914830, 0.916061, 0.917309, 0.918574, 0.921148, 0.923769, 0.926420, 0.929083, 0.931738, 0.934365, 0.936941, 0.939446, 0.941862, 0.944173, 0.946367, 0.948436, 0.953025, 0.956761, 0.959656, 0.961747, 0.963080, 0.963701, 0.963651, 0.962967, 0.961680, 0.959815, 0.957389, 0.954417, 0.950902, 0.946845, 0.942236, 0.937057, 0.931283, 0.924873, 0.917775, 0.909918, 0.901208, 0.891524, 0.880707, 0.868545, 0.854753, 0.838939, 0.820547, 0.798756, 0.788822, 0.778034, 0.766250, 0.753290, 0.738922, 0.722836, 0.704612, 0.683652, 0.659084, 0.629562, 0.592913, 0.545420, 0.515651, 0.480063, 0.436051, 0.409334, 0.377864, 0.363486, 0.347803, 0.330563, 0.311454, 0.290066, 0.265802, 0.237412, 0.220683, 0.201065, 0.176930, 0.162373, 0.145371, 0.124789, 0.120176, 0.115422, 0.110541, 0.105527, 0.100358, 0.089395, 0.077178, 0.070358, 0.062849},
{ 1.163133, 1.162051, 1.161016, 1.162363, 1.161800, 1.161553, 1.161645, 1.161909, 1.162120, 1.162171, 1.161849, 1.162143, 1.162003, 1.162223, 1.162278, 1.162400, 1.162612, 1.162792, 1.163001, 1.163209, 1.163415, 1.163621, 1.163836, 1.164362, 1.164893, 1.165982, 1.167096, 1.168236, 1.170596, 1.173058, 1.175616, 1.178263, 1.180984, 1.183762, 1.186579, 1.189408, 1.192222, 1.194992, 1.197689, 1.200289, 1.206244, 1.211270, 1.215276, 1.218241, 1.220174, 1.221102, 1.221052, 1.220056, 1.218138, 1.215325, 1.211642, 1.207111, 1.201759, 1.195608, 1.188677, 1.180978, 1.172507, 1.163245, 1.153145, 1.142130, 1.130089, 1.116863, 1.102237, 1.085922, 1.067530, 1.046522, 1.022136, 0.993243, 0.980058, 0.965724, 0.950047, 0.932779, 0.913601, 0.892095, 0.867699, 0.839644, 0.806856, 0.767797, 0.720146, 0.659944, 0.622848, 0.578732, 0.524237, 0.491317, 0.452927, 0.435542, 0.416661, 0.395943, 0.372912, 0.346898, 0.316949, 0.281670, 0.261342, 0.238436, 0.211307, 0.195088, 0.176156, 0.153337, 0.148132, 0.142654, 0.136869, 0.130747, 0.124273, 0.110319, 0.094939, 0.086464, 0.077185},
{ 1.414276, 1.416039, 1.415596, 1.415363, 1.415597, 1.415238, 1.415194, 1.415427, 1.415648, 1.415679, 1.415505, 1.415544, 1.415631, 1.415658, 1.415791, 1.415907, 1.416079, 1.416241, 1.416430, 1.416629, 1.416797, 1.416999, 1.417174, 1.417648, 1.418130, 1.419109, 1.420112, 1.421142, 1.423282, 1.425540, 1.427915, 1.430412, 1.433028, 1.435759, 1.438595, 1.441525, 1.444529, 1.447581, 1.450649, 1.453695, 1.460994, 1.467516, 1.473003, 1.477325, 1.480421, 1.482261, 1.482821, 1.482069, 1.479966, 1.476459, 1.471497, 1.465052, 1.457153, 1.447911, 1.437516, 1.426190, 1.414119, 1.401396, 1.388008, 1.373845, 1.358718, 1.342365, 1.324453, 1.304557, 1.282128, 1.256434, 1.226447, 1.190653, 1.174220, 1.156285, 1.136589, 1.114807, 1.090529, 1.063232, 1.032247, 0.996712, 0.955487, 0.906959, 0.848541, 0.775494, 0.730792, 0.678016, 0.613349, 0.574379, 0.528885, 0.508284, 0.485946, 0.461517, 0.434493, 0.404108, 0.369135, 0.327547, 0.303278, 0.275875, 0.244209, 0.225953, 0.204982, 0.179727, 0.173965, 0.167908, 0.161519, 0.154752, 0.147552, 0.131555, 0.113035, 0.102763, 0.091610},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 1.685684, 1.667396, 1.650218, 1.634024, 1.618223, 1.602186, 1.585342, 1.567163, 1.547117, 1.524616, 1.498944, 1.469166, 1.433974, 1.391423, 1.371712, 1.350090, 1.326232, 1.299741, 1.270135, 1.236831, 1.199118, 1.156089, 1.106489, 1.048413, 0.978780, 0.892317, 0.839828, 0.778168, 0.702974, 0.657884, 0.605411, 0.581667, 0.555906, 0.527711, 0.496517, 0.461510, 0.421398, 0.373867, 0.346042, 0.314367, 0.277467, 0.256370, 0.232725, 0.204918, 0.198597, 0.191947, 0.184925, 0.177485, 0.169568, 0.151985, 0.131247, 0.119312, 0.106197}};
  const double imomegaqnm20[8][107] = {{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 0.088946, 0.088898, 0.088817, 0.088700, 0.088547, 0.088353, 0.088115, 0.087827, 0.087481, 0.087069, 0.086579, 0.085995, 0.085295, 0.084453, 0.084067, 0.083648, 0.083194, 0.082698, 0.082156, 0.081562, 0.080908, 0.080185, 0.079381, 0.078483, 0.077473, 0.076330, 0.075701, 0.075028, 0.074306, 0.073926, 0.073532, 0.073371, 0.073207, 0.073041, 0.072872, 0.072701, 0.072527, 0.072351, 0.072263, 0.072174, 0.072087, 0.072043, 0.071996, 0.071930, 0.071911, 0.071886, 0.071856, 0.071815, 0.071760, 0.071567, 0.071095, 0.070577, 0.069561},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 0.273860, 0.273694, 0.273414, 0.273014, 0.272487, 0.271821, 0.271003, 0.270014, 0.268831, 0.267421, 0.265747, 0.263754, 0.261372, 0.258507, 0.257198, 0.255780, 0.254240, 0.252564, 0.250736, 0.248735, 0.246539, 0.244119, 0.241444, 0.238480, 0.235186, 0.231528, 0.229555, 0.227483, 0.225314, 0.224195, 0.223053, 0.222591, 0.222125, 0.221655, 0.221182, 0.220707, 0.220228, 0.219746, 0.219504, 0.219261, 0.219017, 0.218894, 0.218769, 0.218646, 0.218624, 0.218602, 0.218583, 0.218567, 0.218555, 0.218550, 0.218576, 0.218586, 0.218541},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 0.478161, 0.477809, 0.477217, 0.476373, 0.475263, 0.473863, 0.472148, 0.470080, 0.467612, 0.464686, 0.461221, 0.457117, 0.452237, 0.446396, 0.443736, 0.440863, 0.437753, 0.434379, 0.430711, 0.426714, 0.422353, 0.417586, 0.412380, 0.406711, 0.400596, 0.394120, 0.390798, 0.387457, 0.384120, 0.382462, 0.380814, 0.380158, 0.379504, 0.378853, 0.378204, 0.377558, 0.376915, 0.376275, 0.375956, 0.375638, 0.375319, 0.375160, 0.375004, 0.374856, 0.374826, 0.374795, 0.374762, 0.374724, 0.374680, 0.374571, 0.374466, 0.374476, 0.374628},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 0.704945, 0.704331, 0.703296, 0.701824, 0.699889, 0.697457, 0.694481, 0.690905, 0.686650, 0.681622, 0.675691, 0.668694, 0.660408, 0.650537, 0.646058, 0.641230, 0.636017, 0.630380, 0.624277, 0.617664, 0.610506, 0.602788, 0.594547, 0.585942, 0.577339, 0.569239, 0.565445, 0.561815, 0.558363, 0.556704, 0.555087, 0.554453, 0.553825, 0.553204, 0.552590, 0.551982, 0.551381, 0.550785, 0.550490, 0.550199, 0.549903, 0.549755, 0.549623, 0.549478, 0.549438, 0.549395, 0.549349, 0.549308, 0.549280, 0.549303, 0.549380, 0.549273, 0.548898},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 0.946541, 0.945626, 0.944084, 0.941891, 0.939010, 0.935394, 0.930976, 0.925674, 0.919380, 0.911953, 0.903214, 0.892924, 0.880767, 0.866316, 0.859772, 0.852729, 0.845140, 0.836957, 0.828139, 0.818665, 0.808571, 0.798035, 0.787576, 0.778347, 0.771240, 0.764674, 0.761819, 0.759101, 0.756567, 0.755353, 0.754178, 0.753717, 0.753262, 0.752812, 0.752366, 0.751927, 0.751490, 0.751064, 0.750845, 0.750633, 0.750426, 0.750296, 0.750238, 0.750094, 0.750035, 0.749986, 0.749967, 0.749993, 0.750061, 0.750126, 0.749650, 0.749564, 0.750138},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 1.195198, 1.193960, 1.191877, 1.188916, 1.185032, 1.180162, 1.174222, 1.167105, 1.158673, 1.148745, 1.137087, 1.123387, 1.107232, 1.088067, 1.079403, 1.070093, 1.060089, 1.049356, 1.037903, 1.025862, 1.013708, 1.002960, 0.997335, 0.993889, 0.987227, 0.983917, 0.982151, 0.980231, 0.978641, 0.977871, 0.977090, 0.976786, 0.976474, 0.976178, 0.975870, 0.975582, 0.975274, 0.974976, 0.974851, 0.974680, 0.974600, 0.974444, 0.974424, 0.974293, 0.974188, 0.974146, 0.974213, 0.974371, 0.974505, 0.974110, 0.974112, 0.974787, 0.974253},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 1.447378, 1.445774, 1.443079, 1.439259, 1.434262, 1.428019, 1.420435, 1.411388, 1.400713, 1.388197, 1.373555, 1.356407, 1.336243, 1.312390, 1.301635, 1.290113, 1.277800, 1.264747, 1.251235, 1.238360, 1.230978, 1.236823, 1.228953, 1.223151, 1.221395, 1.219601, 1.218691, 1.216721, 1.215773, 1.215081, 1.214311, 1.214157, 1.213848, 1.213637, 1.213402, 1.213208, 1.212985, 1.212747, 1.212620, 1.212586, 1.212371, 1.212445, 1.212213, 1.212199, 1.212018, 1.212001, 1.212205, 1.212475, 1.212482, 1.211727, 1.212758, 1.211922, 1.211527},
{ 1.669503, 1.668395, 1.669442, 1.668664, 1.669275, 1.668971, 1.668820, 1.668995, 1.669204, 1.669212, 1.669190, 1.669059, 1.669253, 1.669326, 1.669380, 1.669414, 1.669602, 1.669773, 1.669951, 1.670142, 1.670305, 1.670479, 1.670661, 1.671105, 1.671552, 1.672460, 1.673398, 1.674357, 1.676355, 1.678461, 1.680685, 1.683035, 1.685516, 1.688135, 1.690893, 1.693787, 1.696812, 1.699961, 1.703216, 1.706546, 1.714937, 1.722933, 1.730080, 1.736116, 1.740904, 1.744368, 1.746449, 1.747073, 1.746118, 1.743369, 1.738448, 1.730726, 1.719332, 1.703841, 1.703116, 1.700942, 1.697329, 1.692278, 1.685776, 1.677781, 1.668216, 1.656957, 1.643827, 1.628580, 1.610879, 1.590273, 1.566155, 1.537745, 1.524995, 1.511417, 1.497110, 1.482566, 1.470178, 1.480076, 1.483391, 1.467377, 1.472722, 1.464347, 1.468574, 1.463725, 1.464201, 1.462140, 1.458072, 1.458542, 1.458162, 1.458344, 1.458079, 1.457758, 1.457217, 1.457199, 1.457032, 1.456856, 1.456708, 1.456496, 1.456405, 1.456612, 1.456203, 1.456343, 1.456084, 1.456111, 1.456452, 1.456702, 1.456399, 1.456163, 1.456141, 1.455774, 1.457166}};
  const double imomegaqnm33[8][107] = {{ 0.068612, 0.073535, 0.077498, 0.082919, 0.086037, 0.087057, 0.087838, 0.088440, 0.088909, 0.089277, 0.090269, 0.090639, 0.090797, 0.090910, 0.090941, 0.090952, 0.090960, 0.090966, 0.090973, 0.090980, 0.090987, 0.090994, 0.091001, 0.091020, 0.091038, 0.091074, 0.091110, 0.091146, 0.091217, 0.091287, 0.091356, 0.091424, 0.091492, 0.091558, 0.091624, 0.091688, 0.091751, 0.091814, 0.091875, 0.091934, 0.092078, 0.092214, 0.092339, 0.092455, 0.092558, 0.092649, 0.092726, 0.092787, 0.092830, 0.092854, 0.092856, 0.092834, 0.092784, 0.092703, 0.092587, 0.092430, 0.092228, 0.091973, 0.091656, 0.091267, 0.090793, 0.090218, 0.089521, 0.088676, 0.087647, 0.086385, 0.084821, 0.082856, 0.081925, 0.080892, 0.079741, 0.078451, 0.076995, 0.075339, 0.073436, 0.071223, 0.068611, 0.065463, 0.061565, 0.056537, 0.053388, 0.049609, 0.044905, 0.042044, 0.038688, 0.037163, 0.035505, 0.033687, 0.031671, 0.029403, 0.026797, 0.023711, 0.021911, 0.019865, 0.017473, 0.016091, 0.014533, 0.012727, 0.012325, 0.011907, 0.011470, 0.011012, 0.010530, 0.009477, 0.008266, 0.007576, 0.006807},
{ 0.277496, 0.278402, 0.278809, 0.278955, 0.278824, 0.278742, 0.278664, 0.278594, 0.278534, 0.278482, 0.278334, 0.278289, 0.278281, 0.278294, 0.278307, 0.278318, 0.278336, 0.278354, 0.278373, 0.278391, 0.278409, 0.278427, 0.278446, 0.278491, 0.278537, 0.278627, 0.278716, 0.278805, 0.278980, 0.279153, 0.279323, 0.279489, 0.279653, 0.279813, 0.279970, 0.280123, 0.280273, 0.280419, 0.280561, 0.280699, 0.281026, 0.281324, 0.281591, 0.281825, 0.282020, 0.282175, 0.282285, 0.282345, 0.282350, 0.282293, 0.282168, 0.281967, 0.281681, 0.281298, 0.280807, 0.280191, 0.279434, 0.278515, 0.277407, 0.276080, 0.274494, 0.272602, 0.270340, 0.267630, 0.264363, 0.260394, 0.255518, 0.249435, 0.246568, 0.243397, 0.239871, 0.235928, 0.231489, 0.226451, 0.220675, 0.213971, 0.206071, 0.196570, 0.184822, 0.169692, 0.160224, 0.148867, 0.134739, 0.126150, 0.116076, 0.111499, 0.106524, 0.101069, 0.095019, 0.088212, 0.080393, 0.071135, 0.065734, 0.059597, 0.052418, 0.048273, 0.043599, 0.038180, 0.036976, 0.035721, 0.034410, 0.033036, 0.031590, 0.028432, 0.024799, 0.022729, 0.020420},
{ 0.486993, 0.484741, 0.483427, 0.482389, 0.482301, 0.482372, 0.482460, 0.482542, 0.482611, 0.482664, 0.482744, 0.482718, 0.482702, 0.482709, 0.482722, 0.482729, 0.482743, 0.482759, 0.482774, 0.482789, 0.482804, 0.482819, 0.482834, 0.482871, 0.482907, 0.482980, 0.483051, 0.483121, 0.483256, 0.483386, 0.483511, 0.483630, 0.483742, 0.483849, 0.483949, 0.484043, 0.484130, 0.484210, 0.484283, 0.484348, 0.484477, 0.484555, 0.484575, 0.484535, 0.484428, 0.484247, 0.483987, 0.483638, 0.483192, 0.482640, 0.481968, 0.481164, 0.480211, 0.479093, 0.477786, 0.476267, 0.474506, 0.472466, 0.470105, 0.467369, 0.464195, 0.460500, 0.456181, 0.451103, 0.445090, 0.437899, 0.429190, 0.418467, 0.413455, 0.407937, 0.401829, 0.395030, 0.387407, 0.378790, 0.368950, 0.357573, 0.344212, 0.328195, 0.308447, 0.283082, 0.267235, 0.248247, 0.224647, 0.210309, 0.193501, 0.185866, 0.177568, 0.168469, 0.158382, 0.147032, 0.133998, 0.118564, 0.109560, 0.099331, 0.087366, 0.080456, 0.072667, 0.063634, 0.061627, 0.059535, 0.057351, 0.055061, 0.052650, 0.047387, 0.041331, 0.037882, 0.034034},
{ 0.709974, 0.711601, 0.713499, 0.714385, 0.713785, 0.713546, 0.713418, 0.713383, 0.713411, 0.713468, 0.713655, 0.713595, 0.713563, 0.713584, 0.713571, 0.713561, 0.713550, 0.713535, 0.713522, 0.713507, 0.713493, 0.713479, 0.713465, 0.713428, 0.713392, 0.713317, 0.713241, 0.713162, 0.712999, 0.712828, 0.712649, 0.712461, 0.712264, 0.712058, 0.711843, 0.711618, 0.711383, 0.711138, 0.710882, 0.710616, 0.709899, 0.709105, 0.708229, 0.707264, 0.706201, 0.705033, 0.703748, 0.702336, 0.700785, 0.699079, 0.697202, 0.695135, 0.692855, 0.690337, 0.687550, 0.684459, 0.681020, 0.677183, 0.672887, 0.668056, 0.662599, 0.656401, 0.649315, 0.641153, 0.631664, 0.620511, 0.607221, 0.591101, 0.583641, 0.575473, 0.566484, 0.556529, 0.545428, 0.532943, 0.518759, 0.502439, 0.483360, 0.460589, 0.432625, 0.396831, 0.374520, 0.347819, 0.314676, 0.294558, 0.270986, 0.260282, 0.248651, 0.235902, 0.221769, 0.205870, 0.187614, 0.166001, 0.153393, 0.139070, 0.122317, 0.112642, 0.101735, 0.089089, 0.086278, 0.083351, 0.080292, 0.077086, 0.073710, 0.066342, 0.057864, 0.053035, 0.047648},
{ 0.972477, 0.969229, 0.967660, 0.969029, 0.969442, 0.969155, 0.968886, 0.968746, 0.968738, 0.968815, 0.969029, 0.968878, 0.968919, 0.968877, 0.968857, 0.968828, 0.968768, 0.968706, 0.968649, 0.968589, 0.968529, 0.968470, 0.968410, 0.968260, 0.968110, 0.967806, 0.967500, 0.967190, 0.966561, 0.965920, 0.965265, 0.964597, 0.963916, 0.963220, 0.962509, 0.961784, 0.961043, 0.960287, 0.959514, 0.958725, 0.956678, 0.954518, 0.952237, 0.949827, 0.947277, 0.944577, 0.941715, 0.938677, 0.935446, 0.932005, 0.928331, 0.924401, 0.920185, 0.915649, 0.910755, 0.905456, 0.899695, 0.893406, 0.886510, 0.878908, 0.870479, 0.861073, 0.850501, 0.838516, 0.824795, 0.808901, 0.790225, 0.767883, 0.757639, 0.746483, 0.734270, 0.720819, 0.705900, 0.689212, 0.670355, 0.648776, 0.623682, 0.593881, 0.557455, 0.511016, 0.482143, 0.447640, 0.404868, 0.378929, 0.348555, 0.334768, 0.319791, 0.303378, 0.285189, 0.264731, 0.241246, 0.213447, 0.197233, 0.178815, 0.157271, 0.144831, 0.130807, 0.114545, 0.110932, 0.107167, 0.103234, 0.099111, 0.094772, 0.085297, 0.074397, 0.068188, 0.061261},
{ 1.234880, 1.238501, 1.237567, 1.236381, 1.237353, 1.237185, 1.236888, 1.236715, 1.236725, 1.236844, 1.236889, 1.236862, 1.236868, 1.236807, 1.236739, 1.236707, 1.236605, 1.236507, 1.236413, 1.236315, 1.236219, 1.236121, 1.236024, 1.235780, 1.235534, 1.235039, 1.234539, 1.234033, 1.233006, 1.231956, 1.230884, 1.229790, 1.228672, 1.227531, 1.226366, 1.225176, 1.223961, 1.222721, 1.221454, 1.220161, 1.216809, 1.213278, 1.209559, 1.205642, 1.201516, 1.197169, 1.192585, 1.187749, 1.182642, 1.177243, 1.171527, 1.165464, 1.159019, 1.152151, 1.144813, 1.136947, 1.128483, 1.119340, 1.109418, 1.098594, 1.086720, 1.073606, 1.059017, 1.042646, 1.024094, 1.002820, 0.978074, 0.948772, 0.935434, 0.920971, 0.905209, 0.887929, 0.868853, 0.847622, 0.823753, 0.796583, 0.765161, 0.728048, 0.682917, 0.625639, 0.590118, 0.547732, 0.495250, 0.463448, 0.426230, 0.409344, 0.391005, 0.370913, 0.348652, 0.323623, 0.294897, 0.260904, 0.241081, 0.218564, 0.192229, 0.177023, 0.159881, 0.140004, 0.135587, 0.130985, 0.126178, 0.121138, 0.115834, 0.104253, 0.090930, 0.083341, 0.074875},
{ 1.508123, 1.507143, 1.508863, 1.507649, 1.508328, 1.508308, 1.508054, 1.507900, 1.507943, 1.508075, 1.507959, 1.508051, 1.507942, 1.507906, 1.507868, 1.507795, 1.507680, 1.507563, 1.507448, 1.507330, 1.507211, 1.507093, 1.506973, 1.506674, 1.506374, 1.505766, 1.505151, 1.504528, 1.503256, 1.501952, 1.500614, 1.499242, 1.497835, 1.496393, 1.494914, 1.493399, 1.491846, 1.490254, 1.488623, 1.486953, 1.482598, 1.477977, 1.473078, 1.467888, 1.462391, 1.456574, 1.450419, 1.443908, 1.437021, 1.429733, 1.422014, 1.413833, 1.405148, 1.395912, 1.386070, 1.375552, 1.364277, 1.352147, 1.339041, 1.324812, 1.309279, 1.292214, 1.273331, 1.252260, 1.228516, 1.201450, 1.170160, 1.133351, 1.116676, 1.098649, 1.079064, 1.057665, 1.034127, 1.008030, 0.978819, 0.945725, 0.907651, 0.862934, 0.808869, 0.740600, 0.698384, 0.648072, 0.585828, 0.548130, 0.504030, 0.484027, 0.462309, 0.438520, 0.412171, 0.382553, 0.348572, 0.308374, 0.284937, 0.258319, 0.227191, 0.209218, 0.188957, 0.165464, 0.160243, 0.154805, 0.149123, 0.143167, 0.136898, 0.123211, 0.107464, 0.098495, 0.102103},
{ 1.779474, 1.778289, 1.778279, 1.778446, 1.778602, 1.778683, 1.778496, 1.778376, 1.778435, 1.778543, 1.778425, 1.778411, 1.778415, 1.778342, 1.778265, 1.778203, 1.778078, 1.777952, 1.777827, 1.777701, 1.777572, 1.777445, 1.777316, 1.776993, 1.776668, 1.776009, 1.775340, 1.774660, 1.773268, 1.771834, 1.770354, 1.768830, 1.767260, 1.765643, 1.763977, 1.762263, 1.760499, 1.758683, 1.756815, 1.754894, 1.749851, 1.744448, 1.738667, 1.732489, 1.725894, 1.718862, 1.711372, 1.703401, 1.694926, 1.685918, 1.676347, 1.666175, 1.655359, 1.643845, 1.631569, 1.618456, 1.604409, 1.589315, 1.573032, 1.555388, 1.536168, 1.515101, 1.491847, 1.465968, 1.436889, 1.403838, 1.365752, 1.321105, 1.300933, 1.279162, 1.255553, 1.229810, 1.201558, 1.170316, 1.135450, 1.096094, 1.051014, 0.998352, 0.935078, 0.855690, 0.806777, 0.748562, 0.676569, 0.632966, 0.581960, 0.558828, 0.533715, 0.506213, 0.475757, 0.441533, 0.402280, 0.355861, 0.328804, 0.298080, 0.262156, 0.241415, 0.218035, 0.190926, 0.184902, 0.178626, 0.172070, 0.165197, 0.157962, 0.142169, 0.123998, 0.113649, 0.115718}};
  const double imomegaqnm32[8][107] = {{ 0.069981, 0.075891, 0.079961, 0.084549, 0.086675, 0.087288, 0.087731, 0.088055, 0.088298, 0.088483, 0.088949, 0.089111, 0.089177, 0.089224, 0.089240, 0.089249, 0.089264, 0.089280, 0.089296, 0.089311, 0.089327, 0.089343, 0.089359, 0.089399, 0.089438, 0.089516, 0.089592, 0.089667, 0.089815, 0.089958, 0.090097, 0.090231, 0.090362, 0.090489, 0.090611, 0.090731, 0.090846, 0.090958, 0.091066, 0.091171, 0.091418, 0.091644, 0.091851, 0.092037, 0.092203, 0.092349, 0.092475, 0.092580, 0.092663, 0.092724, 0.092760, 0.092770, 0.092752, 0.092703, 0.092620, 0.092500, 0.092336, 0.092124, 0.091857, 0.091525, 0.091117, 0.090620, 0.090016, 0.089280, 0.088383, 0.087280, 0.085912, 0.084190, 0.083373, 0.082467, 0.081457, 0.080325, 0.079046, 0.077590, 0.075918, 0.073972, 0.071674, 0.068905, 0.065473, 0.061044, 0.058268, 0.054933, 0.050781, 0.048255, 0.045293, 0.043948, 0.042487, 0.040887, 0.039116, 0.037130, 0.034861, 0.032200, 0.030668, 0.028952, 0.026993, 0.025895, 0.024695, 0.023373, 0.023091, 0.022804, 0.022510, 0.022210, 0.021904, 0.021273, 0.020618, 0.020284, 0.019946},
{ 0.269958, 0.271103, 0.271569, 0.271797, 0.271769, 0.271739, 0.271709, 0.271682, 0.271660, 0.271642, 0.271600, 0.271599, 0.271610, 0.271637, 0.271663, 0.271689, 0.271738, 0.271788, 0.271837, 0.271887, 0.271936, 0.271985, 0.272034, 0.272155, 0.272276, 0.272514, 0.272749, 0.272979, 0.273430, 0.273867, 0.274290, 0.274699, 0.275094, 0.275477, 0.275847, 0.276204, 0.276548, 0.276881, 0.277202, 0.277511, 0.278233, 0.278886, 0.279471, 0.279990, 0.280444, 0.280831, 0.281152, 0.281405, 0.281588, 0.281697, 0.281728, 0.281677, 0.281536, 0.281298, 0.280953, 0.280489, 0.279891, 0.279142, 0.278220, 0.277098, 0.275743, 0.274112, 0.272151, 0.269788, 0.266929, 0.263444, 0.259149, 0.253778, 0.251243, 0.248435, 0.245311, 0.241815, 0.237876, 0.233400, 0.228266, 0.222302, 0.215266, 0.206793, 0.196296, 0.182737, 0.174223, 0.163971, 0.151146, 0.143303, 0.134051, 0.129825, 0.125215, 0.120137, 0.114476, 0.108062, 0.100631, 0.091721, 0.086456, 0.080395, 0.073168, 0.068900, 0.063968, 0.058005, 0.056627, 0.055164, 0.053600, 0.051916, 0.050086, 0.045842, 0.040492, 0.037243, 0.033496},
{ 0.467568, 0.466534, 0.465963, 0.465576, 0.465576, 0.465611, 0.465647, 0.465678, 0.465703, 0.465721, 0.465757, 0.465769, 0.465786, 0.465830, 0.465874, 0.465917, 0.466002, 0.466087, 0.466172, 0.466257, 0.466342, 0.466426, 0.466510, 0.466719, 0.466926, 0.467335, 0.467737, 0.468132, 0.468902, 0.469646, 0.470362, 0.471052, 0.471716, 0.472354, 0.472967, 0.473555, 0.474117, 0.474656, 0.475171, 0.475662, 0.476788, 0.477775, 0.478627, 0.479346, 0.479936, 0.480396, 0.480728, 0.480929, 0.480996, 0.480925, 0.480709, 0.480339, 0.479805, 0.479093, 0.478187, 0.477067, 0.475709, 0.474081, 0.472149, 0.469864, 0.467171, 0.463997, 0.460250, 0.455807, 0.450509, 0.444136, 0.436378, 0.426779, 0.422279, 0.417316, 0.411814, 0.405678, 0.398787, 0.390983, 0.382055, 0.371712, 0.359535, 0.344894, 0.326766, 0.303324, 0.288565, 0.270734, 0.248298, 0.234485, 0.218082, 0.210545, 0.202287, 0.193147, 0.182897, 0.171205, 0.157550, 0.141037, 0.131219, 0.119895, 0.106426, 0.098550, 0.089605, 0.079206, 0.076902, 0.074511, 0.072025, 0.069436, 0.066736, 0.060945, 0.054409, 0.050632, 0.046214},
{ 0.676421, 0.677009, 0.677656, 0.677994, 0.677837, 0.677774, 0.677743, 0.677739, 0.677751, 0.677771, 0.677847, 0.677865, 0.677889, 0.677954, 0.678013, 0.678072, 0.678191, 0.678309, 0.678427, 0.678545, 0.678662, 0.678779, 0.678896, 0.679186, 0.679474, 0.680043, 0.680603, 0.681153, 0.682225, 0.683259, 0.684252, 0.685206, 0.686119, 0.686991, 0.687822, 0.688612, 0.689362, 0.690072, 0.690741, 0.691371, 0.692774, 0.693937, 0.694869, 0.695575, 0.696061, 0.696329, 0.696381, 0.696216, 0.695833, 0.695224, 0.694383, 0.693299, 0.691956, 0.690337, 0.688418, 0.686172, 0.683563, 0.680548, 0.677075, 0.673077, 0.668472, 0.663158, 0.657000, 0.649824, 0.641401, 0.631413, 0.619417, 0.604759, 0.597941, 0.590456, 0.582192, 0.573014, 0.562747, 0.551163, 0.537956, 0.522703, 0.504794, 0.483307, 0.456741, 0.422406, 0.400785, 0.374655, 0.341786, 0.321582, 0.297656, 0.286701, 0.274734, 0.261540, 0.246825, 0.230161, 0.210883, 0.187861, 0.174326, 0.158846, 0.140582, 0.129950, 0.117883, 0.103783, 0.100635, 0.097352, 0.093916, 0.090311, 0.086514, 0.078232, 0.068781, 0.063492, 0.057725},
{ 0.909938, 0.908951, 0.908223, 0.908499, 0.908759, 0.908711, 0.908640, 0.908591, 0.908577, 0.908590, 0.908700, 0.908704, 0.908742, 0.908816, 0.908884, 0.908954, 0.909092, 0.909230, 0.909367, 0.909505, 0.909642, 0.909779, 0.909915, 0.910255, 0.910593, 0.911263, 0.911925, 0.912578, 0.913857, 0.915095, 0.916290, 0.917440, 0.918541, 0.919593, 0.920592, 0.921538, 0.922429, 0.923266, 0.924046, 0.924769, 0.926330, 0.927539, 0.928398, 0.928916, 0.929098, 0.928950, 0.928475, 0.927673, 0.926544, 0.925081, 0.923275, 0.921114, 0.918580, 0.915649, 0.912293, 0.908473, 0.904145, 0.899253, 0.893726, 0.887477, 0.880398, 0.872351, 0.863160, 0.852593, 0.840344, 0.825994, 0.808951, 0.788349, 0.778833, 0.768426, 0.756980, 0.744315, 0.730198, 0.714323, 0.696284, 0.675516, 0.651207, 0.622130, 0.586300, 0.540190, 0.511288, 0.476530, 0.433121, 0.406628, 0.375448, 0.361237, 0.345759, 0.328746, 0.309828, 0.288470, 0.263842, 0.234536, 0.217363, 0.197780, 0.174761, 0.161405, 0.146283, 0.128649, 0.124714, 0.120609, 0.116313, 0.111801, 0.107044, 0.096630, 0.084618, 0.077780, 0.070190},
{ 1.152050, 1.153709, 1.153872, 1.153087, 1.153488, 1.153542, 1.153476, 1.153392, 1.153351, 1.153363, 1.153489, 1.153480, 1.153543, 1.153597, 1.153671, 1.153738, 1.153876, 1.154015, 1.154153, 1.154291, 1.154429, 1.154567, 1.154704, 1.155048, 1.155391, 1.156075, 1.156756, 1.157432, 1.158768, 1.160078, 1.161357, 1.162600, 1.163801, 1.164956, 1.166059, 1.167107, 1.168097, 1.169023, 1.169885, 1.170680, 1.172359, 1.173585, 1.174349, 1.174649, 1.174488, 1.173869, 1.172794, 1.171266, 1.169282, 1.166836, 1.163919, 1.160514, 1.156601, 1.152151, 1.147129, 1.141488, 1.135171, 1.128109, 1.120212, 1.111371, 1.101448, 1.090269, 1.077610, 1.063177, 1.046581, 1.027290, 1.004550, 0.977259, 0.964715, 0.951032, 0.936026, 0.919465, 0.901055, 0.880410, 0.857015, 0.830164, 0.798841, 0.761530, 0.715803, 0.657401, 0.621064, 0.577636, 0.523777, 0.491090, 0.452772, 0.435359, 0.416427, 0.395655, 0.372601, 0.346625, 0.316732, 0.281231, 0.260459, 0.236798, 0.209028, 0.192939, 0.174750, 0.153576, 0.148857, 0.143934, 0.138785, 0.133379, 0.127679, 0.115203, 0.100791, 0.092559, 0.083365},
{ 1.406836, 1.405392, 1.406268, 1.406057, 1.406142, 1.406299, 1.406271, 1.406165, 1.406107, 1.406129, 1.406223, 1.406264, 1.406282, 1.406354, 1.406410, 1.406470, 1.406596, 1.406721, 1.406845, 1.406969, 1.407094, 1.407219, 1.407344, 1.407657, 1.407971, 1.408601, 1.409232, 1.409865, 1.411131, 1.412394, 1.413647, 1.414882, 1.416094, 1.417274, 1.418417, 1.419514, 1.420559, 1.421547, 1.422471, 1.423325, 1.425130, 1.426417, 1.427149, 1.427306, 1.426878, 1.425861, 1.424254, 1.422054, 1.419260, 1.415863, 1.411852, 1.407208, 1.401906, 1.395912, 1.389184, 1.381667, 1.373291, 1.363970, 1.353597, 1.342038, 1.329123, 1.314638, 1.298306, 1.279767, 1.258538, 1.233961, 1.205106, 1.170609, 1.154795, 1.137571, 1.118711, 1.097933, 1.074875, 1.049071, 1.019901, 0.986518, 0.947721, 0.901729, 0.845717, 0.774746, 0.730886, 0.678728, 0.614393, 0.575510, 0.530067, 0.509459, 0.487080, 0.462557, 0.435377, 0.404792, 0.369646, 0.327970, 0.303613, 0.275888, 0.243375, 0.224553, 0.203287, 0.178557, 0.173049, 0.167306, 0.161301, 0.154998, 0.148355, 0.133821, 0.117037, 0.107447, 0.096722},
{ 1.662798, 1.663080, 1.662335, 1.662964, 1.662684, 1.662889, 1.662913, 1.662801, 1.662735, 1.662773, 1.662813, 1.662899, 1.662888, 1.662944, 1.663002, 1.663061, 1.663164, 1.663269, 1.663373, 1.663478, 1.663585, 1.663691, 1.663798, 1.664065, 1.664335, 1.664878, 1.665428, 1.665983, 1.667108, 1.668250, 1.669401, 1.670556, 1.671708, 1.672850, 1.673973, 1.675069, 1.676129, 1.677144, 1.678106, 1.679006, 1.680938, 1.682332, 1.683111, 1.683222, 1.682636, 1.681333, 1.679303, 1.676539, 1.673034, 1.668778, 1.663757, 1.657948, 1.651324, 1.643845, 1.635461, 1.626108, 1.615705, 1.604150, 1.591316, 1.577043, 1.561127, 1.543311, 1.523262, 1.500544, 1.474575, 1.444558, 1.409367, 1.367353, 1.348111, 1.327168, 1.304254, 1.279033, 1.251079, 1.219847, 1.184614, 1.144406, 1.097849, 1.042913, 0.976381, 0.892625, 0.841139, 0.780155, 0.705249, 0.660126, 0.607512, 0.583693, 0.557852, 0.529565, 0.498246, 0.463041, 0.422630, 0.374769, 0.346825, 0.315037, 0.277784, 0.256229, 0.231884, 0.203589, 0.197290, 0.190724, 0.183858, 0.176655, 0.169065, 0.152466, 0.133310, 0.122367, 0.110130}};
  const double imomegaqnm31[8][107] = {{ 0.073965, 0.078720, 0.081273, 0.083514, 0.084354, 0.084576, 0.084731, 0.084843, 0.084925, 0.084987, 0.085144, 0.085201, 0.085229, 0.085261, 0.085286, 0.085309, 0.085356, 0.085403, 0.085450, 0.085496, 0.085542, 0.085588, 0.085634, 0.085746, 0.085857, 0.086073, 0.086282, 0.086485, 0.086872, 0.087235, 0.087577, 0.087899, 0.088203, 0.088490, 0.088761, 0.089017, 0.089259, 0.089488, 0.089706, 0.089912, 0.090380, 0.090791, 0.091150, 0.091464, 0.091737, 0.091972, 0.092173, 0.092340, 0.092476, 0.092582, 0.092658, 0.092704, 0.092719, 0.092703, 0.092653, 0.092568, 0.092445, 0.092279, 0.092066, 0.091800, 0.091472, 0.091074, 0.090593, 0.090012, 0.089309, 0.088456, 0.087414, 0.086124, 0.085522, 0.084860, 0.084129, 0.083320, 0.082420, 0.081411, 0.080274, 0.078981, 0.077496, 0.075769, 0.073730, 0.071271, 0.069834, 0.068222, 0.066393, 0.065381, 0.064294, 0.063835, 0.063362, 0.062875, 0.062371, 0.061850, 0.061312, 0.060755, 0.060470, 0.060179, 0.059884, 0.059734, 0.059583, 0.059430, 0.059399, 0.059368, 0.059336, 0.059303, 0.059270, 0.059196, 0.059100, 0.059030, 0.058923},
{ 0.257000, 0.257665, 0.257908, 0.258023, 0.258024, 0.258019, 0.258015, 0.258013, 0.258013, 0.258015, 0.258039, 0.258074, 0.258112, 0.258186, 0.258260, 0.258334, 0.258480, 0.258625, 0.258770, 0.258914, 0.259056, 0.259199, 0.259340, 0.259689, 0.260034, 0.260708, 0.261363, 0.261998, 0.263215, 0.264363, 0.265445, 0.266467, 0.267431, 0.268341, 0.269202, 0.270015, 0.270783, 0.271511, 0.272198, 0.272849, 0.274329, 0.275619, 0.276741, 0.277716, 0.278556, 0.279274, 0.279879, 0.280377, 0.280775, 0.281074, 0.281276, 0.281383, 0.281391, 0.281298, 0.281099, 0.280787, 0.280353, 0.279785, 0.279069, 0.278184, 0.277108, 0.275810, 0.274252, 0.272382, 0.270135, 0.267421, 0.264118, 0.260049, 0.258153, 0.256073, 0.253782, 0.251247, 0.248428, 0.245276, 0.241726, 0.237695, 0.233072, 0.227706, 0.221382, 0.213796, 0.209396, 0.204502, 0.199040, 0.196076, 0.192951, 0.191656, 0.190336, 0.188992, 0.187625, 0.186235, 0.184824, 0.183393, 0.182671, 0.181945, 0.181214, 0.180847, 0.180480, 0.180111, 0.180037, 0.179963, 0.179890, 0.179816, 0.179742, 0.179595, 0.179448, 0.179373, 0.179291},
{ 0.438425, 0.438087, 0.437919, 0.437841, 0.437874, 0.437896, 0.437917, 0.437936, 0.437953, 0.437968, 0.438032, 0.438094, 0.438157, 0.438284, 0.438411, 0.438537, 0.438789, 0.439039, 0.439289, 0.439538, 0.439785, 0.440032, 0.440278, 0.440887, 0.441489, 0.442675, 0.443833, 0.444965, 0.447147, 0.449222, 0.451191, 0.453059, 0.454827, 0.456502, 0.458085, 0.459583, 0.460999, 0.462337, 0.463601, 0.464796, 0.467500, 0.469841, 0.471860, 0.473592, 0.475065, 0.476303, 0.477323, 0.478139, 0.478760, 0.479195, 0.479446, 0.479514, 0.479398, 0.479093, 0.478589, 0.477876, 0.476938, 0.475754, 0.474299, 0.472539, 0.470433, 0.467927, 0.464954, 0.461426, 0.457227, 0.452200, 0.446129, 0.438708, 0.435265, 0.431497, 0.427357, 0.422787, 0.417716, 0.412055, 0.405691, 0.398475, 0.390214, 0.380643, 0.369405, 0.356038, 0.348409, 0.340129, 0.331334, 0.326854, 0.322403, 0.320644, 0.318901, 0.317177, 0.315474, 0.313795, 0.312140, 0.310513, 0.309710, 0.308914, 0.308125, 0.307734, 0.307344, 0.306956, 0.306879, 0.306802, 0.306724, 0.306647, 0.306570, 0.306416, 0.306263, 0.306188, 0.306116},
{ 0.628868, 0.629059, 0.629251, 0.629368, 0.629364, 0.629366, 0.629377, 0.629392, 0.629411, 0.629432, 0.629528, 0.629614, 0.629701, 0.629877, 0.630052, 0.630227, 0.630577, 0.630926, 0.631275, 0.631623, 0.631970, 0.632317, 0.632663, 0.633525, 0.634382, 0.636081, 0.637758, 0.639410, 0.642638, 0.645751, 0.648743, 0.651607, 0.654340, 0.656943, 0.659416, 0.661762, 0.663984, 0.666085, 0.668072, 0.669947, 0.674181, 0.677822, 0.680932, 0.683568, 0.685774, 0.687587, 0.689038, 0.690149, 0.690940, 0.691421, 0.691601, 0.691482, 0.691063, 0.690337, 0.689294, 0.687916, 0.686181, 0.684059, 0.681512, 0.678492, 0.674936, 0.670767, 0.665883, 0.660153, 0.653405, 0.645405, 0.635830, 0.624217, 0.618856, 0.613004, 0.606588, 0.599521, 0.591693, 0.582965, 0.573162, 0.562050, 0.549321, 0.534558, 0.517219, 0.496761, 0.485452, 0.474177, 0.464760, 0.460806, 0.457005, 0.455613, 0.454269, 0.452951, 0.451682, 0.450454, 0.449265, 0.448112, 0.447548, 0.446993, 0.446447, 0.446176, 0.445908, 0.445642, 0.445589, 0.445536, 0.445483, 0.445430, 0.445378, 0.445273, 0.445167, 0.445112, 0.445058},
{ 0.835448, 0.835253, 0.835042, 0.835103, 0.835219, 0.835235, 0.835240, 0.835247, 0.835261, 0.835279, 0.835396, 0.835495, 0.835597, 0.835803, 0.836008, 0.836214, 0.836625, 0.837036, 0.837448, 0.837860, 0.838272, 0.838685, 0.839098, 0.840131, 0.841164, 0.843233, 0.845299, 0.847361, 0.851456, 0.855491, 0.859442, 0.863287, 0.867009, 0.870593, 0.874030, 0.877314, 0.880443, 0.883414, 0.886230, 0.888894, 0.894914, 0.900079, 0.904466, 0.908148, 0.911188, 0.913640, 0.915547, 0.916946, 0.917861, 0.918314, 0.918317, 0.917875, 0.916988, 0.915649, 0.913844, 0.911551, 0.908740, 0.905371, 0.901393, 0.896739, 0.891326, 0.885045, 0.877759, 0.869287, 0.859391, 0.847746, 0.833903, 0.817210, 0.809530, 0.801158, 0.791989, 0.781896, 0.770716, 0.758241, 0.744199, 0.728220, 0.709790, 0.688167, 0.662240, 0.630487, 0.612549, 0.571494, 0.486130, 0.438446, 0.387187, 0.365452, 0.342801, 0.319027, 0.293847, 0.266859, 0.237443, 0.204552, 0.186235, 0.166131, 0.143489, 0.130811, 0.116844, 0.101053, 0.097600, 0.094024, 0.090311, 0.086443, 0.082398, 0.073659, 0.063756, 0.058185, 0.052028},
{ 1.055096, 1.055587, 1.055823, 1.055596, 1.055704, 1.055763, 1.055785, 1.055787, 1.055787, 1.055798, 1.055925, 1.056017, 1.056124, 1.056330, 1.056539, 1.056746, 1.057163, 1.057581, 1.058000, 1.058420, 1.058842, 1.059265, 1.059689, 1.060755, 1.061828, 1.063995, 1.066188, 1.068404, 1.072890, 1.077425, 1.081977, 1.086510, 1.090990, 1.095386, 1.099668, 1.103814, 1.107806, 1.111631, 1.115281, 1.118752, 1.126641, 1.133437, 1.139208, 1.144031, 1.147984, 1.151132, 1.153535, 1.155237, 1.156276, 1.156679, 1.156463, 1.155637, 1.154203, 1.152151, 1.149466, 1.146119, 1.142073, 1.137277, 1.131663, 1.125146, 1.117617, 1.108936, 1.098922, 1.087336, 1.073866, 1.058079, 1.039373, 1.016863, 1.006512, 0.995224, 0.982851, 0.969207, 0.954050, 0.937061, 0.917797, 0.895619, 0.869517, 0.837664, 0.795682, 0.727748, 0.673462, 0.625162, 0.604395, 0.565264, 0.499648, 0.471392, 0.441689, 0.410470, 0.377515, 0.342341, 0.304152, 0.261610, 0.237990, 0.212119, 0.183050, 0.166802, 0.148923, 0.128738, 0.124327, 0.119761, 0.115020, 0.110083, 0.104922, 0.093776, 0.081153, 0.074054, 0.066212},
{ 1.289045, 1.288255, 1.288433, 1.288640, 1.288549, 1.288644, 1.288703, 1.288706, 1.288688, 1.288684, 1.288818, 1.288890, 1.288996, 1.289180, 1.289366, 1.289557, 1.289935, 1.290316, 1.290698, 1.291083, 1.291469, 1.291857, 1.292247, 1.293230, 1.294224, 1.296246, 1.298314, 1.300425, 1.304775, 1.309281, 1.313921, 1.318664, 1.323475, 1.328313, 1.333134, 1.337897, 1.342561, 1.347094, 1.351472, 1.355673, 1.365337, 1.373750, 1.380929, 1.386937, 1.391850, 1.395744, 1.398684, 1.400729, 1.401921, 1.402296, 1.401875, 1.400672, 1.398687, 1.395912, 1.392326, 1.387896, 1.382574, 1.376297, 1.368983, 1.360525, 1.350784, 1.339586, 1.326700, 1.311825, 1.294559, 1.274346, 1.250397, 1.221536, 1.208233, 1.193693, 1.177704, 1.159992, 1.140188, 1.117780, 1.092012, 1.061679, 1.024671, 0.976981, 0.912501, 0.833125, 0.790484, 0.734372, 0.645066, 0.613912, 0.604454, 0.609849, 0.605557, 0.606365, 0.604589, 0.604930, 0.604121, 0.603299, 0.603050, 0.602792, 0.602503, 0.602362, 0.602223, 0.602084, 0.602056, 0.602029, 0.602001, 0.601973, 0.601946, 0.601891, 0.601836, 0.601808, 0.601780},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 1.639383, 1.633891, 1.627312, 1.619571, 1.610568, 1.600172, 1.588217, 1.574486, 1.558699, 1.540482, 1.519332, 1.494548, 1.465118, 1.429498, 1.412999, 1.394890, 1.374865, 1.352518, 1.327280, 1.298333, 1.264444, 1.223753, 1.173773, 1.112633, 1.040469, 0.950308, 0.891893, 0.826341, 0.752817, 0.699230, 0.623128, 0.578017, 0.540747, 0.502810, 0.462361, 0.418819, 0.371581, 0.319165, 0.290138, 0.258403, 0.222812, 0.202950, 0.181119, 0.156500, 0.151124, 0.145560, 0.139786, 0.133773, 0.127489, 0.113925, 0.098570, 0.089940, 0.080407}};
  const double imomegaqnm30[8][107] = {{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 0.092687, 0.092637, 0.092553, 0.092433, 0.092275, 0.092076, 0.091832, 0.091538, 0.091186, 0.090769, 0.090275, 0.089691, 0.088997, 0.088168, 0.087792, 0.087386, 0.086947, 0.086471, 0.085955, 0.085393, 0.084779, 0.084107, 0.083367, 0.082549, 0.081642, 0.080628, 0.080076, 0.079490, 0.078867, 0.078540, 0.078202, 0.078064, 0.077924, 0.077783, 0.077639, 0.077493, 0.077346, 0.077196, 0.077121, 0.077045, 0.076969, 0.076929, 0.076884, 0.076820, 0.076802, 0.076779, 0.076750, 0.076713, 0.076663, 0.076489, 0.076039, 0.075485, 0.074203},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 0.281245, 0.281086, 0.280817, 0.280433, 0.279928, 0.279291, 0.278511, 0.277569, 0.276446, 0.275114, 0.273539, 0.271675, 0.269463, 0.266825, 0.265627, 0.264336, 0.262942, 0.261433, 0.259797, 0.258018, 0.256079, 0.253960, 0.251636, 0.249081, 0.246264, 0.243150, 0.241470, 0.239702, 0.237841, 0.236875, 0.235884, 0.235481, 0.235073, 0.234662, 0.234247, 0.233827, 0.233404, 0.232976, 0.232761, 0.232544, 0.232327, 0.232217, 0.232108, 0.232000, 0.231978, 0.231958, 0.231937, 0.231918, 0.231899, 0.231862, 0.231806, 0.231736, 0.231556},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 0.478993, 0.478693, 0.478187, 0.477465, 0.476516, 0.475321, 0.473856, 0.472093, 0.469991, 0.467502, 0.464563, 0.461092, 0.456981, 0.452089, 0.449873, 0.447487, 0.444914, 0.442135, 0.439128, 0.435869, 0.432331, 0.428485, 0.424299, 0.419744, 0.414795, 0.409439, 0.406611, 0.403687, 0.400675, 0.399138, 0.397582, 0.396955, 0.396325, 0.395693, 0.395058, 0.394421, 0.393782, 0.393140, 0.392819, 0.392497, 0.392175, 0.392013, 0.391852, 0.391691, 0.391658, 0.391625, 0.391592, 0.391559, 0.391525, 0.391457, 0.391405, 0.391405, 0.391445},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 0.690175, 0.689687, 0.688863, 0.687691, 0.686150, 0.684213, 0.681842, 0.678992, 0.675601, 0.671595, 0.666873, 0.661311, 0.654741, 0.646948, 0.643426, 0.639642, 0.635570, 0.631185, 0.626456, 0.621355, 0.615851, 0.609918, 0.603541, 0.596726, 0.589514, 0.581992, 0.578157, 0.574299, 0.570439, 0.568516, 0.566600, 0.565836, 0.565074, 0.564314, 0.563556, 0.562800, 0.562047, 0.561296, 0.560921, 0.560547, 0.560174, 0.559988, 0.559802, 0.559615, 0.559578, 0.559540, 0.559503, 0.559467, 0.559432, 0.559363, 0.559277, 0.559209, 0.559138},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 0.915410, 0.914686, 0.913468, 0.911735, 0.909458, 0.906598, 0.903103, 0.898906, 0.893923, 0.888043, 0.881128, 0.872996, 0.863415, 0.852081, 0.846972, 0.841494, 0.835614, 0.829301, 0.822525, 0.815260, 0.807496, 0.799244, 0.790564, 0.781585, 0.772513, 0.763590, 0.759253, 0.755027, 0.750929, 0.748931, 0.746968, 0.746193, 0.745424, 0.744661, 0.743903, 0.743152, 0.742406, 0.741667, 0.741299, 0.740933, 0.740568, 0.740387, 0.740205, 0.740023, 0.739987, 0.739952, 0.739918, 0.739883, 0.739847, 0.739761, 0.739695, 0.739705, 0.739695},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 1.151824, 1.150837, 1.149175, 1.146812, 1.143709, 1.139814, 1.135056, 1.129348, 1.122576, 1.114592, 1.105211, 1.094192, 1.081227, 1.065919, 1.059035, 1.051666, 1.043780, 1.035350, 1.026359, 1.016818, 1.006788, 0.996417, 0.985980, 0.975863, 0.966386, 0.957682, 0.953634, 0.949785, 0.946128, 0.944368, 0.942653, 0.941979, 0.941311, 0.940651, 0.939997, 0.939349, 0.938708, 0.938073, 0.937758, 0.937445, 0.937132, 0.936977, 0.936822, 0.936667, 0.936639, 0.936611, 0.936580, 0.936544, 0.936504, 0.936448, 0.936428, 0.936315, 0.936219},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 1.395494, 1.394233, 1.392109, 1.389089, 1.385124, 1.380148, 1.374073, 1.366785, 1.358140, 1.347953, 1.335985, 1.321933, 1.305409, 1.285931, 1.277193, 1.267863, 1.257920, 1.247362, 1.236235, 1.224669, 1.212958, 1.201632, 1.191349, 1.182302, 1.174267, 1.167204, 1.163981, 1.160939, 1.158062, 1.156680, 1.155334, 1.154806, 1.154282, 1.153764, 1.153251, 1.152743, 1.152240, 1.151741, 1.151494, 1.151247, 1.151003, 1.150879, 1.150761, 1.150640, 1.150623, 1.150601, 1.150566, 1.150523, 1.150492, 1.150513, 1.150334, 1.150373, 1.150585},
{ 1.529937, 1.530686, 1.530097, 1.530516, 1.530284, 1.530367, 1.530473, 1.530487, 1.530447, 1.530426, 1.530556, 1.530632, 1.530702, 1.530869, 1.531033, 1.531192, 1.531519, 1.531846, 1.532176, 1.532508, 1.532841, 1.533177, 1.533514, 1.534366, 1.535229, 1.536994, 1.538809, 1.540677, 1.544569, 1.548674, 1.552990, 1.557506, 1.562202, 1.567050, 1.572010, 1.577037, 1.582076, 1.587077, 1.591989, 1.596774, 1.607981, 1.617910, 1.626466, 1.633664, 1.639564, 1.644238, 1.647757, 1.650184, 1.651570, 1.651955, 1.651367, 1.649819, 1.647315, 1.643845, 1.643335, 1.641797, 1.639208, 1.635528, 1.630696, 1.624631, 1.617226, 1.608344, 1.597807, 1.585389, 1.570800, 1.553671, 1.533537, 1.509851, 1.499261, 1.488002, 1.476093, 1.463621, 1.450821, 1.438215, 1.426792, 1.417582, 1.409842, 1.402860, 1.396979, 1.391746, 1.389346, 1.387063, 1.384890, 1.383840, 1.382815, 1.382410, 1.382010, 1.381612, 1.381218, 1.380828, 1.380440, 1.380056, 1.379863, 1.379676, 1.379489, 1.379383, 1.379306, 1.379208, 1.379208, 1.379184, 1.379129, 1.379081, 1.379097, 1.379105, 1.379024, 1.379212, 1.378677}};
  const double imomegaqnm44[8][107] = {{ 0.047289, 0.057085, 0.065286, 0.076920, 0.083531, 0.085574, 0.087060, 0.088144, 0.088942, 0.089536, 0.090962, 0.091420, 0.091606, 0.091741, 0.091784, 0.091803, 0.091819, 0.091828, 0.091837, 0.091845, 0.091853, 0.091861, 0.091870, 0.091890, 0.091911, 0.091952, 0.091993, 0.092034, 0.092115, 0.092196, 0.092275, 0.092354, 0.092432, 0.092510, 0.092586, 0.092662, 0.092736, 0.092810, 0.092882, 0.092953, 0.093127, 0.093292, 0.093448, 0.093595, 0.093730, 0.093853, 0.093962, 0.094056, 0.094132, 0.094189, 0.094223, 0.094233, 0.094215, 0.094164, 0.094077, 0.093948, 0.093770, 0.093537, 0.093239, 0.092865, 0.092401, 0.091829, 0.091127, 0.090268, 0.089212, 0.087909, 0.086287, 0.084240, 0.083269, 0.082192, 0.080991, 0.079644, 0.078125, 0.076399, 0.074418, 0.072119, 0.069410, 0.066156, 0.062140, 0.056982, 0.053763, 0.049911, 0.045132, 0.042232, 0.038838, 0.037297, 0.035624, 0.033790, 0.031759, 0.029475, 0.026854, 0.023753, 0.021945, 0.019893, 0.017493, 0.016108, 0.014546, 0.012736, 0.012334, 0.011915, 0.011478, 0.011019, 0.010536, 0.009482, 0.008270, 0.007580, 0.006809},
{ 0.267496, 0.272430, 0.275117, 0.277412, 0.278166, 0.278332, 0.278431, 0.278489, 0.278523, 0.278542, 0.278554, 0.278543, 0.278539, 0.278544, 0.278555, 0.278567, 0.278590, 0.278613, 0.278636, 0.278659, 0.278682, 0.278704, 0.278727, 0.278784, 0.278841, 0.278955, 0.279068, 0.279180, 0.279403, 0.279623, 0.279841, 0.280057, 0.280270, 0.280480, 0.280687, 0.280892, 0.281093, 0.281291, 0.281485, 0.281676, 0.282137, 0.282572, 0.282979, 0.283355, 0.283696, 0.283998, 0.284257, 0.284467, 0.284624, 0.284721, 0.284749, 0.284701, 0.284567, 0.284334, 0.283990, 0.283519, 0.282901, 0.282113, 0.281129, 0.279913, 0.278426, 0.276614, 0.274412, 0.271733, 0.268465, 0.264452, 0.259480, 0.253233, 0.250278, 0.247003, 0.243357, 0.239276, 0.234678, 0.229458, 0.223476, 0.216539, 0.208375, 0.198576, 0.186494, 0.170992, 0.161324, 0.149756, 0.135408, 0.126707, 0.116519, 0.111896, 0.106875, 0.101374, 0.095279, 0.088426, 0.080562, 0.071259, 0.065836, 0.059678, 0.052479, 0.048323, 0.043639, 0.038210, 0.037003, 0.035747, 0.034434, 0.033058, 0.031609, 0.028447, 0.024810, 0.022739, 0.020428},
{ 0.476992, 0.476552, 0.476059, 0.475354, 0.475023, 0.474945, 0.474902, 0.474880, 0.474873, 0.474873, 0.474904, 0.474923, 0.474932, 0.474945, 0.474960, 0.474975, 0.475006, 0.475036, 0.475066, 0.475097, 0.475127, 0.475157, 0.475187, 0.475263, 0.475338, 0.475487, 0.475635, 0.475782, 0.476073, 0.476359, 0.476641, 0.476918, 0.477190, 0.477456, 0.477718, 0.477973, 0.478223, 0.478467, 0.478704, 0.478936, 0.479483, 0.479984, 0.480434, 0.480828, 0.481160, 0.481423, 0.481610, 0.481712, 0.481721, 0.481624, 0.481410, 0.481064, 0.480570, 0.479908, 0.479056, 0.477986, 0.476666, 0.475060, 0.473120, 0.470791, 0.468003, 0.464669, 0.460679, 0.455890, 0.450113, 0.443090, 0.434465, 0.423712, 0.418650, 0.413055, 0.406842, 0.399905, 0.392108, 0.383276, 0.373175, 0.361487, 0.347759, 0.331313, 0.311071, 0.285140, 0.268985, 0.249669, 0.225726, 0.211210, 0.194221, 0.186512, 0.178140, 0.168968, 0.158807, 0.147383, 0.134275, 0.118768, 0.109729, 0.099465, 0.087465, 0.080539, 0.072732, 0.063683, 0.061672, 0.059578, 0.057390, 0.055096, 0.052682, 0.047413, 0.041350, 0.037898, 0.034047},
{ 0.688887, 0.687276, 0.686870, 0.687194, 0.687484, 0.687529, 0.687535, 0.687523, 0.687504, 0.687487, 0.687464, 0.687480, 0.687488, 0.687497, 0.687509, 0.687521, 0.687544, 0.687567, 0.687590, 0.687613, 0.687636, 0.687658, 0.687681, 0.687738, 0.687794, 0.687905, 0.688015, 0.688122, 0.688333, 0.688537, 0.688734, 0.688923, 0.689105, 0.689278, 0.689444, 0.689601, 0.689749, 0.689889, 0.690018, 0.690138, 0.690394, 0.690579, 0.690690, 0.690717, 0.690652, 0.690487, 0.690211, 0.689812, 0.689276, 0.688589, 0.687732, 0.686685, 0.685425, 0.683924, 0.682151, 0.680068, 0.677629, 0.674782, 0.671462, 0.667589, 0.663066, 0.657772, 0.651551, 0.644203, 0.635463, 0.624972, 0.612229, 0.596503, 0.589146, 0.581044, 0.572077, 0.562097, 0.550915, 0.538287, 0.523888, 0.507273, 0.487810, 0.464555, 0.436002, 0.399509, 0.376808, 0.349693, 0.316109, 0.295761, 0.271954, 0.261154, 0.249426, 0.236578, 0.222347, 0.206349, 0.187993, 0.166281, 0.153625, 0.139254, 0.122453, 0.112755, 0.101826, 0.089156, 0.086341, 0.083409, 0.080346, 0.077135, 0.073755, 0.066378, 0.057891, 0.053057, 0.047665},
{ 0.918235, 0.920515, 0.920895, 0.920137, 0.920012, 0.920094, 0.920167, 0.920207, 0.920214, 0.920202, 0.920149, 0.920166, 0.920164, 0.920160, 0.920158, 0.920156, 0.920152, 0.920148, 0.920144, 0.920140, 0.920136, 0.920132, 0.920127, 0.920116, 0.920104, 0.920079, 0.920051, 0.920022, 0.919956, 0.919881, 0.919796, 0.919702, 0.919597, 0.919482, 0.919356, 0.919218, 0.919069, 0.918908, 0.918734, 0.918547, 0.918020, 0.917401, 0.916681, 0.915851, 0.914900, 0.913815, 0.912584, 0.911190, 0.909617, 0.907843, 0.905847, 0.903603, 0.901078, 0.898239, 0.895043, 0.891442, 0.887378, 0.882780, 0.877566, 0.871633, 0.864855, 0.857075, 0.848091, 0.837647, 0.825400, 0.810890, 0.793470, 0.772205, 0.762324, 0.751485, 0.739534, 0.726280, 0.711484, 0.694831, 0.675907, 0.654142, 0.628729, 0.598457, 0.561400, 0.514171, 0.484847, 0.449863, 0.406581, 0.380377, 0.349729, 0.335831, 0.320740, 0.304211, 0.285904, 0.265327, 0.241720, 0.213799, 0.197524, 0.179045, 0.157442, 0.144973, 0.130920, 0.114630, 0.111011, 0.107241, 0.103302, 0.099174, 0.094829, 0.085343, 0.074431, 0.068217, 0.061284},
{ 1.172429, 1.170250, 1.170724, 1.171528, 1.171085, 1.171073, 1.171150, 1.171223, 1.171252, 1.171240, 1.171165, 1.171180, 1.171155, 1.171139, 1.171115, 1.171094, 1.171049, 1.171005, 1.170960, 1.170916, 1.170871, 1.170826, 1.170781, 1.170668, 1.170555, 1.170326, 1.170094, 1.169858, 1.169379, 1.168887, 1.168382, 1.167864, 1.167332, 1.166786, 1.166225, 1.165649, 1.165057, 1.164449, 1.163825, 1.163183, 1.161499, 1.159693, 1.157756, 1.155675, 1.153437, 1.151026, 1.148428, 1.145621, 1.142586, 1.139297, 1.135727, 1.131843, 1.127608, 1.122977, 1.117900, 1.112316, 1.106154, 1.099328, 1.091735, 1.083249, 1.073714, 1.062936, 1.050670, 1.036597, 1.020299, 1.001210, 0.978540, 0.951144, 0.938500, 0.924680, 0.909499, 0.892724, 0.874063, 0.853135, 0.829435, 0.802272, 0.770663, 0.733138, 0.687353, 0.629184, 0.593147, 0.550213, 0.497162, 0.465071, 0.427558, 0.410551, 0.392089, 0.371872, 0.349482, 0.324320, 0.295457, 0.261323, 0.241428, 0.218839, 0.192433, 0.177192, 0.160015, 0.140105, 0.135681, 0.131073, 0.126259, 0.121213, 0.115902, 0.104308, 0.090972, 0.083376, 0.074903},
{ 1.434106, 1.435046, 1.433745, 1.434332, 1.434110, 1.434007, 1.434061, 1.434149, 1.434181, 1.434154, 1.434096, 1.434067, 1.434053, 1.434006, 1.433967, 1.433925, 1.433841, 1.433756, 1.433671, 1.433587, 1.433502, 1.433417, 1.433332, 1.433118, 1.432903, 1.432470, 1.432032, 1.431590, 1.430693, 1.429777, 1.428843, 1.427889, 1.426915, 1.425920, 1.424905, 1.423867, 1.422808, 1.421726, 1.420620, 1.419490, 1.416555, 1.413454, 1.410174, 1.406700, 1.403018, 1.399110, 1.394956, 1.390535, 1.385822, 1.380787, 1.375397, 1.369615, 1.363395, 1.356686, 1.349428, 1.341548, 1.332961, 1.323565, 1.313236, 1.301825, 1.289146, 1.274967, 1.258995, 1.240852, 1.220040, 1.195886, 1.167453, 1.133385, 1.117752, 1.100721, 1.082074, 1.061538, 1.038767, 1.013313, 0.984584, 0.951766, 0.913705, 0.868675, 0.813920, 0.744589, 0.701738, 0.650764, 0.587868, 0.549856, 0.505448, 0.485323, 0.463480, 0.439564, 0.413085, 0.383331, 0.349205, 0.308853, 0.285337, 0.258637, 0.227427, 0.209413, 0.189112, 0.165580, 0.160352, 0.154906, 0.149217, 0.143253, 0.136976, 0.123274, 0.107512, 0.098535, 0.088522},
{ 1.701724, 1.702654, 1.702929, 1.702488, 1.702586, 1.702446, 1.702476, 1.702559, 1.702577, 1.702533, 1.702508, 1.702450, 1.702433, 1.702375, 1.702317, 1.702258, 1.702143, 1.702028, 1.701913, 1.701797, 1.701681, 1.701565, 1.701448, 1.701156, 1.700862, 1.700270, 1.699671, 1.699066, 1.697836, 1.696579, 1.695294, 1.693982, 1.692640, 1.691270, 1.689869, 1.688438, 1.686975, 1.685480, 1.683952, 1.682390, 1.678334, 1.674047, 1.669517, 1.664727, 1.659659, 1.654293, 1.648606, 1.642574, 1.636168, 1.629355, 1.622096, 1.614348, 1.606060, 1.597171, 1.587611, 1.577296, 1.566129, 1.553988, 1.540731, 1.526181, 1.510123, 1.492287, 1.472329, 1.449810, 1.424148, 1.394562, 1.359963, 1.318780, 1.299967, 1.279528, 1.257209, 1.232697, 1.205593, 1.175383, 1.141384, 1.102665, 1.057901, 1.005112, 0.941138, 0.860413, 0.810643, 0.751534, 0.678709, 0.634741, 0.583406, 0.560151, 0.534917, 0.507294, 0.476715, 0.442361, 0.402967, 0.356392, 0.329251, 0.298439, 0.262423, 0.241636, 0.218210, 0.191057, 0.185023, 0.178739, 0.172175, 0.165293, 0.158050, 0.142240, 0.124053, 0.113695, 0.102141}};
  const double imomegaqnm43[8][107] = {{ 0.050967, 0.062587, 0.071427, 0.082053, 0.086727, 0.087934, 0.088737, 0.089284, 0.089666, 0.089939, 0.090561, 0.090757, 0.090839, 0.090902, 0.090925, 0.090937, 0.090952, 0.090965, 0.090977, 0.090990, 0.091003, 0.091015, 0.091028, 0.091059, 0.091090, 0.091152, 0.091213, 0.091273, 0.091393, 0.091510, 0.091625, 0.091738, 0.091848, 0.091956, 0.092062, 0.092166, 0.092267, 0.092367, 0.092464, 0.092559, 0.092786, 0.092999, 0.093198, 0.093382, 0.093550, 0.093702, 0.093836, 0.093952, 0.094048, 0.094123, 0.094175, 0.094201, 0.094198, 0.094164, 0.094095, 0.093985, 0.093831, 0.093624, 0.093357, 0.093020, 0.092601, 0.092084, 0.091449, 0.090670, 0.089712, 0.088528, 0.087053, 0.085187, 0.084300, 0.083315, 0.082216, 0.080981, 0.079586, 0.077998, 0.076170, 0.074044, 0.071530, 0.068498, 0.064738, 0.059879, 0.056829, 0.053157, 0.048569, 0.045767, 0.042466, 0.040960, 0.039319, 0.037514, 0.035505, 0.033234, 0.030612, 0.027485, 0.025648, 0.023550, 0.021079, 0.019644, 0.018017, 0.016120, 0.015696, 0.015255, 0.014793, 0.014308, 0.013797, 0.012678, 0.011388, 0.010652, 0.009830},
{ 0.267208, 0.271308, 0.273219, 0.274661, 0.275084, 0.275171, 0.275221, 0.275250, 0.275266, 0.275275, 0.275283, 0.275284, 0.275289, 0.275306, 0.275325, 0.275344, 0.275382, 0.275420, 0.275458, 0.275495, 0.275533, 0.275570, 0.275608, 0.275701, 0.275793, 0.275977, 0.276159, 0.276339, 0.276694, 0.277041, 0.277381, 0.277714, 0.278040, 0.278358, 0.278669, 0.278973, 0.279270, 0.279560, 0.279842, 0.280118, 0.280775, 0.281387, 0.281952, 0.282469, 0.282937, 0.283353, 0.283715, 0.284019, 0.284261, 0.284436, 0.284538, 0.284561, 0.284496, 0.284334, 0.284064, 0.283670, 0.283138, 0.282446, 0.281571, 0.280483, 0.279144, 0.277507, 0.275512, 0.273080, 0.270109, 0.266454, 0.261917, 0.256203, 0.253495, 0.250490, 0.247140, 0.243383, 0.239143, 0.234319, 0.228777, 0.222332, 0.214721, 0.205548, 0.194178, 0.179489, 0.170264, 0.159161, 0.145275, 0.136787, 0.126779, 0.122211, 0.117228, 0.111743, 0.105633, 0.098719, 0.090720, 0.081161, 0.075534, 0.069090, 0.061475, 0.057034, 0.051986, 0.046068, 0.044743, 0.043358, 0.041905, 0.040378, 0.038763, 0.035212, 0.031077, 0.028696, 0.026012},
{ 0.467961, 0.467928, 0.467721, 0.467392, 0.467251, 0.467223, 0.467210, 0.467207, 0.467209, 0.467213, 0.467240, 0.467258, 0.467274, 0.467304, 0.467335, 0.467366, 0.467428, 0.467490, 0.467551, 0.467613, 0.467674, 0.467735, 0.467796, 0.467948, 0.468099, 0.468399, 0.468695, 0.468987, 0.469562, 0.470123, 0.470670, 0.471203, 0.471723, 0.472229, 0.472721, 0.473200, 0.473665, 0.474117, 0.474555, 0.474980, 0.475982, 0.476899, 0.477729, 0.478470, 0.479120, 0.479676, 0.480131, 0.480483, 0.480722, 0.480843, 0.480834, 0.480685, 0.480382, 0.479908, 0.479245, 0.478369, 0.477252, 0.475861, 0.474154, 0.472081, 0.469580, 0.466571, 0.462953, 0.458595, 0.453321, 0.446894, 0.438977, 0.429080, 0.424409, 0.419240, 0.413489, 0.407057, 0.399812, 0.391586, 0.382153, 0.371204, 0.358294, 0.342758, 0.323524, 0.298692, 0.283102, 0.264334, 0.240854, 0.226493, 0.209553, 0.201816, 0.193377, 0.184084, 0.173730, 0.162011, 0.148455, 0.132258, 0.122731, 0.111831, 0.098972, 0.091490, 0.083002, 0.073087, 0.070872, 0.068561, 0.066141, 0.063599, 0.060917, 0.055039, 0.048237, 0.044343, 0.039981},
{ 0.672249, 0.671448, 0.671290, 0.671459, 0.671573, 0.671589, 0.671592, 0.671589, 0.671585, 0.671583, 0.671597, 0.671622, 0.671642, 0.671683, 0.671725, 0.671766, 0.671849, 0.671931, 0.672013, 0.672095, 0.672177, 0.672258, 0.672340, 0.672542, 0.672743, 0.673140, 0.673532, 0.673919, 0.674676, 0.675411, 0.676124, 0.676815, 0.677484, 0.678131, 0.678756, 0.679359, 0.679940, 0.680499, 0.681036, 0.681551, 0.682741, 0.683793, 0.684705, 0.685475, 0.686100, 0.686575, 0.686895, 0.687052, 0.687038, 0.686842, 0.686450, 0.685846, 0.685012, 0.683924, 0.682556, 0.680873, 0.678838, 0.676402, 0.673507, 0.670082, 0.666037, 0.661260, 0.655609, 0.648898, 0.640878, 0.631213, 0.619430, 0.604832, 0.597984, 0.590428, 0.582049, 0.572704, 0.562209, 0.550324, 0.536732, 0.520992, 0.502477, 0.480242, 0.452767, 0.417355, 0.395150, 0.368437, 0.335051, 0.314653, 0.290615, 0.279647, 0.267693, 0.254542, 0.239906, 0.223365, 0.204271, 0.181520, 0.168174, 0.152942, 0.135027, 0.124632, 0.112868, 0.099165, 0.096110, 0.092924, 0.089591, 0.086093, 0.082405, 0.074336, 0.065019, 0.059696, 0.053742},
{ 0.890457, 0.891421, 0.891587, 0.891311, 0.891280, 0.891313, 0.891341, 0.891358, 0.891365, 0.891365, 0.891375, 0.891404, 0.891428, 0.891476, 0.891524, 0.891572, 0.891669, 0.891765, 0.891860, 0.891956, 0.892051, 0.892146, 0.892240, 0.892476, 0.892709, 0.893171, 0.893625, 0.894073, 0.894945, 0.895787, 0.896599, 0.897380, 0.898130, 0.898849, 0.899536, 0.900191, 0.900814, 0.901405, 0.901963, 0.902490, 0.903662, 0.904630, 0.905391, 0.905943, 0.906283, 0.906405, 0.906302, 0.905967, 0.905388, 0.904551, 0.903440, 0.902035, 0.900311, 0.898239, 0.895783, 0.892901, 0.889542, 0.885644, 0.881130, 0.875907, 0.869859, 0.862840, 0.854663, 0.845086, 0.833786, 0.820324, 0.804084, 0.784160, 0.774872, 0.764659, 0.753372, 0.740824, 0.726777, 0.710918, 0.692834, 0.671952, 0.647457, 0.618121, 0.581970, 0.535513, 0.506452, 0.471562, 0.428069, 0.401560, 0.370386, 0.356189, 0.340731, 0.323748, 0.304876, 0.283583, 0.259050, 0.229886, 0.212810, 0.193352, 0.170509, 0.157275, 0.142315, 0.124914, 0.121039, 0.116998, 0.112773, 0.108340, 0.103669, 0.093454, 0.081672, 0.074946, 0.067429},
{ 1.126859, 1.125834, 1.125954, 1.126319, 1.126176, 1.126168, 1.126195, 1.126225, 1.126243, 1.126248, 1.126253, 1.126286, 1.126307, 1.126359, 1.126409, 1.126459, 1.126559, 1.126659, 1.126759, 1.126858, 1.126957, 1.127056, 1.127154, 1.127399, 1.127642, 1.128122, 1.128594, 1.129058, 1.129961, 1.130829, 1.131662, 1.132458, 1.133215, 1.133934, 1.134612, 1.135250, 1.135845, 1.136399, 1.136910, 1.137378, 1.138355, 1.139054, 1.139470, 1.139598, 1.139435, 1.138972, 1.138204, 1.137119, 1.135705, 1.133945, 1.131820, 1.129304, 1.126368, 1.122977, 1.119085, 1.114642, 1.109583, 1.103831, 1.097292, 1.089849, 1.081358, 1.071637, 1.060455, 1.047509, 1.032398, 1.014577, 0.993280, 0.967385, 0.955381, 0.942227, 0.927737, 0.911678, 0.893755, 0.873583, 0.850650, 0.824251, 0.793379, 0.756525, 0.711269, 0.653346, 0.617238, 0.574013, 0.520310, 0.487672, 0.449379, 0.431968, 0.413032, 0.392253, 0.369188, 0.343199, 0.313298, 0.277807, 0.257054, 0.233428, 0.205721, 0.189684, 0.171568, 0.150512, 0.145825, 0.140939, 0.135831, 0.130473, 0.124828, 0.112489, 0.098264, 0.090147, 0.081079},
{ 1.372466, 1.373275, 1.372701, 1.372840, 1.372836, 1.372781, 1.372788, 1.372825, 1.372853, 1.372859, 1.372859, 1.372887, 1.372910, 1.372957, 1.373005, 1.373052, 1.373147, 1.373241, 1.373335, 1.373428, 1.373522, 1.373615, 1.373707, 1.373939, 1.374168, 1.374622, 1.375069, 1.375509, 1.376365, 1.377189, 1.377976, 1.378725, 1.379434, 1.380101, 1.380722, 1.381298, 1.381825, 1.382302, 1.382728, 1.383101, 1.383798, 1.384146, 1.384132, 1.383747, 1.382982, 1.381828, 1.380274, 1.378309, 1.375916, 1.373076, 1.369766, 1.365955, 1.361610, 1.356686, 1.351132, 1.344884, 1.337866, 1.329985, 1.321128, 1.311153, 1.299886, 1.287108, 1.272539, 1.255814, 1.236450, 1.213789, 1.186908, 1.154456, 1.139486, 1.123126, 1.105153, 1.085290, 1.063183, 1.038372, 1.010246, 0.977967, 0.940341, 0.895582, 0.840838, 0.771099, 0.727798, 0.676120, 0.612136, 0.573358, 0.527953, 0.507339, 0.484939, 0.460381, 0.433149, 0.402495, 0.367263, 0.325492, 0.301088, 0.273325, 0.240789, 0.221967, 0.200716, 0.176027, 0.170533, 0.164807, 0.158821, 0.152543, 0.145930, 0.131477, 0.114820, 0.105319, 0.094706},
{ 1.626688, 1.626751, 1.627193, 1.626831, 1.626996, 1.626921, 1.626905, 1.626944, 1.626977, 1.626979, 1.626985, 1.626995, 1.627023, 1.627062, 1.627102, 1.627143, 1.627225, 1.627306, 1.627387, 1.627469, 1.627550, 1.627630, 1.627711, 1.627912, 1.628112, 1.628508, 1.628900, 1.629286, 1.630041, 1.630769, 1.631466, 1.632130, 1.632756, 1.633340, 1.633881, 1.634374, 1.634816, 1.635205, 1.635538, 1.635812, 1.636228, 1.636233, 1.635804, 1.634922, 1.633571, 1.631734, 1.629398, 1.626546, 1.623158, 1.619211, 1.614677, 1.609522, 1.603703, 1.597171, 1.589863, 1.581706, 1.572609, 1.562462, 1.551132, 1.538451, 1.524214, 1.508161, 1.489960, 1.469181, 1.445251, 1.417395, 1.384523, 1.345045, 1.326899, 1.307110, 1.285418, 1.261497, 1.234937, 1.205201, 1.171580, 1.133104, 1.088396, 1.035401, 0.970849, 0.889002, 0.838381, 0.778147, 0.703806, 0.658863, 0.606333, 0.582515, 0.556653, 0.528321, 0.496929, 0.461622, 0.421075, 0.373046, 0.345006, 0.313120, 0.275774, 0.254178, 0.229802, 0.201493, 0.195195, 0.188631, 0.181771, 0.174575, 0.166996, 0.150436, 0.131355, 0.120473, 0.108320}};
  const double imomegaqnm42[8][107] = {{ 0.058810, 0.071056, 0.078796, 0.085560, 0.087557, 0.087981, 0.088246, 0.088420, 0.088539, 0.088624, 0.088828, 0.088902, 0.088937, 0.088971, 0.088989, 0.089004, 0.089030, 0.089056, 0.089082, 0.089107, 0.089133, 0.089158, 0.089183, 0.089245, 0.089307, 0.089429, 0.089548, 0.089665, 0.089892, 0.090110, 0.090319, 0.090520, 0.090713, 0.090899, 0.091078, 0.091250, 0.091416, 0.091576, 0.091729, 0.091877, 0.092222, 0.092535, 0.092818, 0.093072, 0.093299, 0.093501, 0.093676, 0.093827, 0.093952, 0.094051, 0.094123, 0.094167, 0.094181, 0.094164, 0.094112, 0.094023, 0.093891, 0.093712, 0.093480, 0.093187, 0.092822, 0.092374, 0.091825, 0.091157, 0.090340, 0.089338, 0.088098, 0.086545, 0.085812, 0.085002, 0.084103, 0.083099, 0.081972, 0.080698, 0.079245, 0.077572, 0.075621, 0.073305, 0.070497, 0.066982, 0.064850, 0.062371, 0.059422, 0.057713, 0.055802, 0.054970, 0.054093, 0.053167, 0.052186, 0.051143, 0.050031, 0.048842, 0.048214, 0.047563, 0.046887, 0.046540, 0.046185, 0.045824, 0.045750, 0.045677, 0.045603, 0.045529, 0.045454, 0.045304, 0.045151, 0.045072, 0.044992},
{ 0.264390, 0.266773, 0.267754, 0.268435, 0.268620, 0.268657, 0.268678, 0.268691, 0.268699, 0.268704, 0.268721, 0.268737, 0.268756, 0.268796, 0.268835, 0.268875, 0.268954, 0.269033, 0.269112, 0.269190, 0.269268, 0.269346, 0.269423, 0.269615, 0.269805, 0.270179, 0.270546, 0.270905, 0.271603, 0.272272, 0.272916, 0.273534, 0.274128, 0.274699, 0.275248, 0.275776, 0.276283, 0.276770, 0.277238, 0.277688, 0.278737, 0.279683, 0.280534, 0.281295, 0.281970, 0.282563, 0.283075, 0.283507, 0.283860, 0.284131, 0.284318, 0.284418, 0.284425, 0.284334, 0.284137, 0.283822, 0.283378, 0.282788, 0.282034, 0.281092, 0.279931, 0.278514, 0.276792, 0.274702, 0.272161, 0.269054, 0.265225, 0.260445, 0.258194, 0.255707, 0.252948, 0.249872, 0.246422, 0.242524, 0.238083, 0.232970, 0.227005, 0.219928, 0.211340, 0.200582, 0.194047, 0.186442, 0.177398, 0.172168, 0.166341, 0.163817, 0.161172, 0.158397, 0.155488, 0.152440, 0.149256, 0.145944, 0.144246, 0.142522, 0.140776, 0.139896, 0.139012, 0.138124, 0.137946, 0.137768, 0.137590, 0.137412, 0.137233, 0.136876, 0.136519, 0.136340, 0.136160},
{ 0.454114, 0.454188, 0.454117, 0.453995, 0.453956, 0.453954, 0.453958, 0.453964, 0.453971, 0.453979, 0.454018, 0.454053, 0.454087, 0.454156, 0.454225, 0.454294, 0.454431, 0.454568, 0.454704, 0.454839, 0.454974, 0.455109, 0.455243, 0.455576, 0.455906, 0.456556, 0.457193, 0.457819, 0.459033, 0.460200, 0.461321, 0.462398, 0.463432, 0.464425, 0.465378, 0.466292, 0.467169, 0.468009, 0.468815, 0.469587, 0.471377, 0.472977, 0.474401, 0.475659, 0.476759, 0.477707, 0.478508, 0.479163, 0.479672, 0.480035, 0.480247, 0.480302, 0.480193, 0.479908, 0.479434, 0.478754, 0.477847, 0.476685, 0.475236, 0.473460, 0.471304, 0.468706, 0.465581, 0.461823, 0.457290, 0.451789, 0.445051, 0.436686, 0.432761, 0.428434, 0.423641, 0.418305, 0.412329, 0.405585, 0.397909, 0.389076, 0.378772, 0.366539, 0.351667, 0.332968, 0.321562, 0.308233, 0.292322, 0.283123, 0.272956, 0.268620, 0.264155, 0.259609, 0.255066, 0.250638, 0.246403, 0.242355, 0.240406, 0.238508, 0.236662, 0.235759, 0.234868, 0.233989, 0.233815, 0.233641, 0.233468, 0.233296, 0.233123, 0.232781, 0.232440, 0.232270, 0.232101},
{ 0.648389, 0.648069, 0.648032, 0.648120, 0.648171, 0.648183, 0.648191, 0.648199, 0.648206, 0.648215, 0.648264, 0.648315, 0.648365, 0.648465, 0.648565, 0.648665, 0.648863, 0.649062, 0.649259, 0.649456, 0.649653, 0.649848, 0.650044, 0.650528, 0.651009, 0.651959, 0.652892, 0.653808, 0.655592, 0.657311, 0.658964, 0.660553, 0.662079, 0.663543, 0.664946, 0.666290, 0.667577, 0.668807, 0.669982, 0.671104, 0.673687, 0.675969, 0.677968, 0.679703, 0.681185, 0.682426, 0.683433, 0.684210, 0.684759, 0.685079, 0.685164, 0.685008, 0.684600, 0.683924, 0.682962, 0.681688, 0.680073, 0.678078, 0.675656, 0.672749, 0.669283, 0.665166, 0.660278, 0.654466, 0.647525, 0.639177, 0.629034, 0.616531, 0.610691, 0.604267, 0.597168, 0.589279, 0.580458, 0.570517, 0.559212, 0.546206, 0.531024, 0.512964, 0.490908, 0.462919, 0.445629, 0.425112, 0.399954, 0.384908, 0.367650, 0.360049, 0.352082, 0.342567, 0.318968, 0.290453, 0.258664, 0.222654, 0.202571, 0.180561, 0.155823, 0.141995, 0.126777, 0.109593, 0.105838, 0.101951, 0.097915, 0.093712, 0.089318, 0.079830, 0.069083, 0.063040, 0.056364},
{ 0.853446, 0.853813, 0.853876, 0.853807, 0.853824, 0.853845, 0.853864, 0.853880, 0.853893, 0.853905, 0.853966, 0.854032, 0.854097, 0.854226, 0.854356, 0.854485, 0.854743, 0.855000, 0.855257, 0.855513, 0.855768, 0.856023, 0.856277, 0.856910, 0.857539, 0.858783, 0.860011, 0.861221, 0.863587, 0.865877, 0.868089, 0.870221, 0.872273, 0.874244, 0.876134, 0.877943, 0.879673, 0.881325, 0.882899, 0.884397, 0.887822, 0.890809, 0.893382, 0.895565, 0.897376, 0.898832, 0.899944, 0.900719, 0.901163, 0.901274, 0.901048, 0.900477, 0.899547, 0.898239, 0.896528, 0.894382, 0.891761, 0.888616, 0.884884, 0.880488, 0.875329, 0.869287, 0.862201, 0.853868, 0.844015, 0.832273, 0.818121, 0.800806, 0.792753, 0.783915, 0.774169, 0.763359, 0.751287, 0.737698, 0.722247, 0.704463, 0.683664, 0.658816, 0.628211, 0.588666, 0.563573, 0.532655, 0.491591, 0.463983, 0.427824, 0.409990, 0.389707, 0.367796, 0.356393, 0.346180, 0.324863, 0.280112, 0.254936, 0.227115, 0.195789, 0.178303, 0.159092, 0.137437, 0.132711, 0.127819, 0.122742, 0.117457, 0.111934, 0.100014, 0.086524, 0.078944, 0.070572},
{ 1.072047, 1.071660, 1.071696, 1.071852, 1.071838, 1.071847, 1.071867, 1.071889, 1.071908, 1.071924, 1.071994, 1.072072, 1.072147, 1.072299, 1.072450, 1.072602, 1.072904, 1.073206, 1.073508, 1.073809, 1.074110, 1.074410, 1.074710, 1.075459, 1.076204, 1.077687, 1.079157, 1.080613, 1.083479, 1.086277, 1.089000, 1.091641, 1.094197, 1.096662, 1.099033, 1.101308, 1.103486, 1.105566, 1.107549, 1.109433, 1.113723, 1.117427, 1.120571, 1.123179, 1.125276, 1.126882, 1.128014, 1.128684, 1.128897, 1.128656, 1.127956, 1.126788, 1.125136, 1.122977, 1.120280, 1.117006, 1.113105, 1.108514, 1.103154, 1.096929, 1.089715, 1.081356, 1.071653, 1.060343, 1.047082, 1.031397, 1.012625, 0.989793, 0.979214, 0.967624, 0.954863, 0.940725, 0.924950, 0.907196, 0.887000, 0.863715, 0.836390, 0.803542, 0.762631, 0.708697, 0.673728, 0.630147, 0.573902, 0.539636, 0.500193, 0.482250, 0.462281, 0.439394, 0.412490, 0.380102, 0.351248, 0.347751, 0.343291, 0.343798, 0.342229, 0.342109, 0.341525, 0.341141, 0.341022, 0.340957, 0.340861, 0.340789, 0.340701, 0.340537, 0.340374, 0.340293, 0.340212},
{ 1.300896, 1.301336, 1.301154, 1.301182, 1.301235, 1.301228, 1.301239, 1.301262, 1.301287, 1.301306, 1.301379, 1.301462, 1.301542, 1.301704, 1.301865, 1.302026, 1.302349, 1.302672, 1.302995, 1.303318, 1.303641, 1.303964, 1.304287, 1.305095, 1.305902, 1.307515, 1.309125, 1.310729, 1.313916, 1.317065, 1.320162, 1.323196, 1.326158, 1.329037, 1.331825, 1.334515, 1.337102, 1.339582, 1.341951, 1.344206, 1.349342, 1.353760, 1.357472, 1.360501, 1.362870, 1.364602, 1.365717, 1.366229, 1.366147, 1.365474, 1.364207, 1.362333, 1.359835, 1.356686, 1.352849, 1.348276, 1.342906, 1.336663, 1.329452, 1.321152, 1.311612, 1.300640, 1.287991, 1.273342, 1.256266, 1.236177, 1.212248, 1.183263, 1.169862, 1.155197, 1.139060, 1.121190, 1.101249, 1.078793, 1.053212, 1.023645, 0.988819, 0.946728, 0.894001, 0.824570, 0.780378, 0.727096, 0.660767, 0.620196, 0.572343, 0.550699, 0.527420, 0.502221, 0.474283, 0.441723, 0.401557, 0.347751, 0.343291, 0.343798, 0.342229, 0.342109, 0.341525, 0.341141, 0.341022, 0.340957, 0.340861, 0.340789, 0.340701, 0.340537, 0.340374, 0.340293, 0.340212},
{ 1.539724, 1.539542, 1.539848, 1.539693, 1.539814, 1.539804, 1.539800, 1.539820, 1.539849, 1.539871, 1.539941, 1.540021, 1.540102, 1.540260, 1.540419, 1.540579, 1.540898, 1.541217, 1.541537, 1.541858, 1.542178, 1.542500, 1.542821, 1.543628, 1.544436, 1.546060, 1.547692, 1.549330, 1.552618, 1.555910, 1.559191, 1.562447, 1.565662, 1.568822, 1.571913, 1.574923, 1.577839, 1.580653, 1.583357, 1.585943, 1.591863, 1.596971, 1.601252, 1.604711, 1.607367, 1.609238, 1.610346, 1.610704, 1.610324, 1.609208, 1.607352, 1.604743, 1.601360, 1.597171, 1.592132, 1.586186, 1.579262, 1.571268, 1.562088, 1.551580, 1.539561, 1.525801, 1.510003, 1.491777, 1.470605, 1.445775, 1.416275, 1.380611, 1.364135, 1.346106, 1.326267, 1.304287, 1.279742, 1.252065, 1.220484, 1.183911, 1.140760, 1.088628, 1.023770, 0.940046, 0.887831, 0.825435, 0.748211, 0.701587, 0.647081, 0.622271, 0.595247, 0.565632, 0.533066, 0.497000, 0.455359, 0.402452, 0.368523, 0.320551, 0.276061, 0.251386, 0.224156, 0.193441, 0.186744, 0.179816, 0.172632, 0.165157, 0.157350, 0.140519, 0.121500, 0.110824, 0.099042}};
  const double imomegaqnm41[8][107] = {{ 0.070745, 0.079568, 0.082950, 0.084642, 0.084972, 0.085040, 0.085086, 0.085120, 0.085146, 0.085167, 0.085233, 0.085268, 0.085292, 0.085328, 0.085359, 0.085389, 0.085448, 0.085506, 0.085564, 0.085621, 0.085678, 0.085734, 0.085791, 0.085929, 0.086065, 0.086330, 0.086585, 0.086831, 0.087299, 0.087736, 0.088145, 0.088528, 0.088888, 0.089226, 0.089544, 0.089844, 0.090127, 0.090394, 0.090646, 0.090885, 0.091427, 0.091900, 0.092313, 0.092673, 0.092986, 0.093256, 0.093488, 0.093683, 0.093844, 0.093972, 0.094068, 0.094132, 0.094164, 0.094164, 0.094130, 0.094060, 0.093951, 0.093801, 0.093605, 0.093357, 0.093051, 0.092678, 0.092226, 0.091682, 0.091027, 0.090235, 0.089273, 0.088095, 0.087548, 0.086951, 0.086295, 0.085574, 0.084777, 0.083892, 0.082904, 0.081793, 0.080536, 0.079099, 0.077437, 0.075488, 0.074378, 0.073160, 0.071812, 0.071083, 0.070312, 0.069991, 0.069662, 0.069325, 0.068981, 0.068627, 0.068265, 0.067893, 0.067704, 0.067512, 0.067318, 0.067219, 0.067120, 0.067018, 0.066997, 0.066976, 0.066954, 0.066932, 0.066909, 0.066863, 0.066835, 0.066862, 0.067010},
{ 0.255428, 0.256296, 0.256641, 0.256879, 0.256948, 0.256965, 0.256978, 0.256989, 0.256998, 0.257007, 0.257050, 0.257094, 0.257139, 0.257228, 0.257318, 0.257407, 0.257585, 0.257761, 0.257936, 0.258110, 0.258282, 0.258454, 0.258624, 0.259045, 0.259459, 0.260266, 0.261046, 0.261801, 0.263238, 0.264584, 0.265846, 0.267031, 0.268146, 0.269194, 0.270181, 0.271111, 0.271988, 0.272817, 0.273599, 0.274339, 0.276017, 0.277478, 0.278752, 0.279860, 0.280821, 0.281648, 0.282353, 0.282944, 0.283428, 0.283809, 0.284090, 0.284271, 0.284354, 0.284334, 0.284209, 0.283973, 0.283618, 0.283133, 0.282505, 0.281718, 0.280751, 0.279577, 0.278162, 0.276461, 0.274418, 0.271957, 0.268974, 0.265325, 0.263635, 0.261789, 0.259765, 0.257540, 0.255084, 0.252358, 0.249318, 0.245906, 0.242047, 0.237646, 0.232573, 0.226657, 0.223312, 0.219664, 0.215673, 0.213535, 0.211297, 0.210371, 0.209429, 0.208469, 0.207491, 0.206495, 0.205481, 0.204448, 0.203925, 0.203397, 0.202865, 0.202597, 0.202327, 0.202057, 0.202003, 0.201949, 0.201894, 0.201840, 0.201786, 0.201677, 0.201564, 0.201502, 0.201427},
{ 0.432356, 0.432408, 0.432395, 0.432382, 0.432399, 0.432413, 0.432427, 0.432443, 0.432458, 0.432474, 0.432550, 0.432626, 0.432701, 0.432852, 0.433002, 0.433151, 0.433449, 0.433746, 0.434041, 0.434334, 0.434626, 0.434916, 0.435204, 0.435918, 0.436623, 0.438002, 0.439342, 0.440644, 0.443137, 0.445486, 0.447701, 0.449788, 0.451754, 0.453608, 0.455356, 0.457005, 0.458560, 0.460029, 0.461416, 0.462727, 0.465696, 0.468276, 0.470516, 0.472456, 0.474129, 0.475560, 0.476769, 0.477773, 0.478583, 0.479207, 0.479651, 0.479917, 0.480003, 0.479908, 0.479624, 0.479142, 0.478447, 0.477524, 0.476348, 0.474891, 0.473116, 0.470978, 0.468417, 0.465358, 0.461701, 0.457315, 0.452021, 0.445570, 0.442589, 0.439338, 0.435779, 0.431871, 0.427562, 0.422789, 0.417473, 0.411520, 0.404805, 0.397177, 0.388443, 0.378379, 0.372777, 0.366767, 0.360348, 0.356992, 0.353546, 0.352145, 0.350732, 0.349307, 0.347872, 0.346428, 0.344975, 0.343514, 0.342781, 0.342047, 0.341311, 0.340943, 0.340574, 0.340206, 0.340132, 0.340058, 0.339984, 0.339910, 0.339836, 0.339689, 0.339542, 0.339469, 0.339396},
{ 0.613987, 0.613908, 0.613922, 0.613986, 0.614035, 0.614055, 0.614075, 0.614096, 0.614116, 0.614137, 0.614241, 0.614346, 0.614451, 0.614659, 0.614867, 0.615075, 0.615490, 0.615904, 0.616315, 0.616726, 0.617135, 0.617542, 0.617948, 0.618956, 0.619955, 0.621922, 0.623847, 0.625731, 0.629369, 0.632834, 0.636125, 0.639246, 0.642201, 0.644997, 0.647640, 0.650139, 0.652500, 0.654730, 0.656836, 0.658826, 0.663330, 0.667232, 0.670606, 0.673512, 0.676001, 0.678111, 0.679875, 0.681318, 0.682458, 0.683309, 0.683879, 0.684172, 0.684189, 0.683924, 0.683370, 0.682510, 0.681328, 0.679796, 0.677882, 0.675543, 0.672726, 0.669363, 0.665368, 0.660629, 0.655000, 0.648289, 0.640231, 0.630458, 0.625957, 0.621054, 0.615698, 0.609825, 0.603360, 0.596211, 0.588266, 0.579387, 0.569409, 0.558136, 0.545364, 0.530960, 0.523178, 0.515098, 0.506854, 0.502721, 0.498611, 0.496978, 0.495353, 0.493738, 0.492133, 0.490540, 0.488960, 0.487394, 0.486616, 0.485842, 0.485072, 0.484688, 0.484306, 0.483924, 0.483848, 0.483772, 0.483695, 0.483619, 0.483543, 0.483391, 0.483239, 0.483163, 0.483089},
{ 0.803913, 0.804044, 0.804080, 0.804106, 0.804156, 0.804184, 0.804211, 0.804237, 0.804263, 0.804288, 0.804417, 0.804546, 0.804674, 0.804932, 0.805189, 0.805446, 0.805959, 0.806473, 0.806985, 0.807497, 0.808007, 0.808518, 0.809027, 0.810297, 0.811561, 0.814070, 0.816550, 0.818997, 0.823783, 0.828406, 0.832850, 0.837105, 0.841166, 0.845032, 0.848705, 0.852188, 0.855489, 0.858612, 0.861566, 0.864358, 0.870678, 0.876142, 0.880850, 0.884884, 0.888315, 0.891198, 0.893579, 0.895493, 0.896969, 0.898027, 0.898678, 0.898931, 0.898787, 0.898239, 0.897277, 0.895882, 0.894028, 0.891682, 0.888798, 0.885319, 0.881174, 0.876270, 0.870490, 0.863682, 0.855648, 0.846124, 0.834750, 0.821019, 0.814714, 0.807856, 0.800375, 0.792184, 0.783178, 0.773233, 0.762196, 0.749887, 0.736102, 0.720635, 0.703395, 0.684742, 0.675289, 0.666104, 0.657406, 0.653282, 0.649319, 0.647780, 0.646267, 0.644780, 0.643319, 0.641885, 0.640475, 0.639091, 0.638408, 0.637732, 0.637061, 0.636729, 0.636397, 0.636067, 0.636001, 0.635936, 0.635870, 0.635804, 0.635739, 0.635608, 0.635477, 0.635412, 0.635344},
{ 1.004519, 1.004422, 1.004453, 1.004545, 1.004593, 1.004620, 1.004649, 1.004679, 1.004709, 1.004738, 1.004881, 1.005025, 1.005169, 1.005456, 1.005744, 1.006032, 1.006609, 1.007186, 1.007764, 1.008342, 1.008921, 1.009500, 1.010080, 1.011530, 1.012983, 1.015889, 1.018793, 1.021690, 1.027440, 1.033098, 1.038626, 1.043993, 1.049176, 1.054156, 1.058924, 1.063474, 1.067804, 1.071917, 1.075817, 1.079509, 1.087881, 1.095121, 1.101345, 1.106658, 1.111150, 1.114895, 1.117955, 1.120376, 1.122199, 1.123448, 1.124145, 1.124298, 1.123911, 1.122977, 1.121482, 1.119405, 1.116711, 1.113357, 1.109287, 1.104426, 1.098681, 1.091935, 1.084033, 1.074781, 1.063919, 1.051102, 1.035857, 1.017518, 1.009112, 0.999979, 0.990022, 0.979125, 0.967148, 0.953922, 0.939246, 0.922887, 0.904602, 0.884255, 0.862248, 0.840921, 0.831775, 0.823609, 0.816386, 0.813081, 0.809960, 0.808759, 0.807585, 0.806435, 0.805310, 0.804207, 0.803127, 0.802069, 0.801548, 0.801031, 0.800520, 0.800267, 0.800014, 0.799763, 0.799713, 0.799663, 0.799613, 0.799563, 0.799513, 0.799413, 0.799313, 0.799263, 0.799218},
{ 1.215956, 1.216148, 1.216128, 1.216170, 1.216241, 1.216264, 1.216291, 1.216321, 1.216352, 1.216383, 1.216528, 1.216676, 1.216822, 1.217117, 1.217412, 1.217708, 1.218300, 1.218894, 1.219490, 1.220087, 1.220687, 1.221288, 1.221891, 1.223404, 1.224928, 1.228002, 1.231108, 1.234240, 1.240562, 1.246918, 1.253256, 1.259525, 1.265676, 1.271670, 1.277473, 1.283063, 1.288423, 1.293543, 1.298421, 1.303055, 1.313603, 1.322749, 1.330611, 1.337310, 1.342952, 1.347629, 1.351418, 1.354381, 1.356565, 1.358007, 1.358731, 1.358751, 1.358072, 1.356686, 1.354578, 1.351719, 1.348070, 1.343576, 1.338166, 1.331748, 1.324207, 1.315393, 1.305115, 1.293126, 1.279099, 1.262596, 1.243013, 1.219489, 1.208710, 1.196998, 1.184222, 1.170228, 1.154824, 1.137778, 1.118809, 1.097590, 1.073814, 1.047555, 1.021630, 1.006614, 0.999428, 0.994254, 0.989417, 0.987226, 0.985098, 0.984273, 0.983473, 0.982685, 0.981910, 0.981149, 0.980402, 0.979666, 0.979303, 0.978942, 0.978585, 0.978407, 0.978230, 0.978054, 0.978019, 0.977984, 0.977949, 0.977914, 0.977879, 0.977808, 0.977740, 0.977704, 0.977662},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 1.594416, 1.590734, 1.586076, 1.580376, 1.573548, 1.565481, 1.556033, 1.545023, 1.532216, 1.517307, 1.499894, 1.479430, 1.455158, 1.425982, 1.412595, 1.398026, 1.382103, 1.364610, 1.345276, 1.323754, 1.299592, 1.272190, 1.240773, 1.204723, 1.125253, 0.938477, 0.838838, 0.734651, 0.622895, 0.562606, 0.497864, 0.470296, 0.441499, 0.411211, 0.379069, 0.646318, 0.573546, 0.492714, 0.447938, 0.398980, 0.344066, 0.313415, 0.279721, 0.241717, 0.233418, 0.224829, 0.215913, 0.206630, 0.196927, 0.175980, 0.152268, 0.138939, 0.124215}};
  const double imomegaqnm40[8][107] = {{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 0.094147, 0.094096, 0.094010, 0.093888, 0.093727, 0.093524, 0.093276, 0.092977, 0.092621, 0.092200, 0.091703, 0.091116, 0.090423, 0.089598, 0.089224, 0.088822, 0.088389, 0.087921, 0.087414, 0.086864, 0.086265, 0.085611, 0.084894, 0.084105, 0.083233, 0.082264, 0.081737, 0.081180, 0.080588, 0.080279, 0.079960, 0.079829, 0.079697, 0.079563, 0.079427, 0.079290, 0.079151, 0.079010, 0.078938, 0.078867, 0.078793, 0.078755, 0.078713, 0.078663, 0.078651, 0.078639, 0.078626, 0.078613, 0.078601, 0.078589, 0.078624, 0.078591, 0.077756},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 0.284282, 0.284123, 0.283856, 0.283475, 0.282973, 0.282342, 0.281569, 0.280639, 0.279531, 0.278220, 0.276673, 0.274849, 0.272693, 0.270131, 0.268972, 0.267724, 0.266380, 0.264929, 0.263359, 0.261656, 0.259805, 0.257787, 0.255580, 0.253159, 0.250493, 0.247547, 0.245957, 0.244282, 0.242515, 0.241595, 0.240650, 0.240265, 0.239876, 0.239482, 0.239084, 0.238682, 0.238275, 0.237864, 0.237657, 0.237449, 0.237239, 0.237134, 0.237029, 0.236923, 0.236902, 0.236882, 0.236860, 0.236839, 0.236817, 0.236767, 0.236680, 0.236587, 0.236384},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 0.479814, 0.479529, 0.479050, 0.478367, 0.477469, 0.476339, 0.474956, 0.473292, 0.471312, 0.468970, 0.466209, 0.462957, 0.459115, 0.454557, 0.452497, 0.450282, 0.447898, 0.445327, 0.442550, 0.439545, 0.436285, 0.432744, 0.428889, 0.424686, 0.420099, 0.415093, 0.412423, 0.409638, 0.406737, 0.405243, 0.403720, 0.403102, 0.402480, 0.401854, 0.401223, 0.400587, 0.399947, 0.399303, 0.398979, 0.398654, 0.398328, 0.398165, 0.398001, 0.397837, 0.397804, 0.397771, 0.397738, 0.397705, 0.397672, 0.397608, 0.397552, 0.397528, 0.397490},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 0.683779, 0.683339, 0.682598, 0.681544, 0.680158, 0.678415, 0.676283, 0.673720, 0.670673, 0.667075, 0.662838, 0.657852, 0.651974, 0.645014, 0.641874, 0.638502, 0.634878, 0.630978, 0.626774, 0.622239, 0.617340, 0.612046, 0.606325, 0.600151, 0.593508, 0.586401, 0.582682, 0.578863, 0.574955, 0.572971, 0.570970, 0.570165, 0.569358, 0.568549, 0.567738, 0.566925, 0.566110, 0.565293, 0.564885, 0.564476, 0.564066, 0.563861, 0.563657, 0.563452, 0.563411, 0.563370, 0.563329, 0.563288, 0.563247, 0.563164, 0.563077, 0.563036, 0.563014},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 0.898030, 0.897399, 0.896336, 0.894824, 0.892837, 0.890341, 0.887290, 0.883627, 0.879278, 0.874148, 0.868116, 0.861030, 0.852691, 0.842842, 0.838407, 0.833654, 0.828554, 0.823079, 0.817197, 0.810876, 0.804088, 0.796809, 0.789030, 0.780765, 0.772061, 0.763015, 0.758408, 0.753773, 0.749132, 0.746816, 0.744509, 0.743588, 0.742669, 0.741753, 0.740838, 0.739926, 0.739016, 0.738108, 0.737656, 0.737204, 0.736752, 0.736527, 0.736302, 0.736077, 0.736032, 0.735987, 0.735942, 0.735897, 0.735852, 0.735762, 0.735677, 0.735631, 0.735564},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 1.122693, 1.121836, 1.120394, 1.118342, 1.115648, 1.112266, 1.108136, 1.103182, 1.097304, 1.090380, 1.082250, 1.072712, 1.061506, 1.048301, 1.042369, 1.036021, 1.029226, 1.021952, 1.014170, 1.005854, 0.996995, 0.987606, 0.977740, 0.967503, 0.957067, 0.946652, 0.941522, 0.936480, 0.931545, 0.929125, 0.926737, 0.925792, 0.924853, 0.923919, 0.922991, 0.922069, 0.921152, 0.920242, 0.919789, 0.919338, 0.918888, 0.918664, 0.918440, 0.918216, 0.918172, 0.918127, 0.918082, 0.918037, 0.917993, 0.917906, 0.917810, 0.917765, 0.917749},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 1.356319, 1.355212, 1.353349, 1.350699, 1.347220, 1.342855, 1.337528, 1.331141, 1.323569, 1.314654, 1.304196, 1.291938, 1.277556, 1.260642, 1.253060, 1.244963, 1.236319, 1.227100, 1.217291, 1.206897, 1.195961, 1.184586, 1.172958, 1.161345, 1.150044, 1.139303, 1.134195, 1.129278, 1.124555, 1.122267, 1.120028, 1.119146, 1.118271, 1.117404, 1.116544, 1.115692, 1.114847, 1.114010, 1.113594, 1.113180, 1.112768, 1.112563, 1.112358, 1.112153, 1.112112, 1.112071, 1.112030, 1.111990, 1.111950, 1.111865, 1.111791, 1.111758, 1.111672},
{ 1.438671, 1.438539, 1.438690, 1.438687, 1.438772, 1.438797, 1.438817, 1.438842, 1.438873, 1.438904, 1.439041, 1.439182, 1.439321, 1.439601, 1.439882, 1.440163, 1.440728, 1.441295, 1.441865, 1.442438, 1.443013, 1.443590, 1.444170, 1.445632, 1.447109, 1.450111, 1.453172, 1.456292, 1.462688, 1.469264, 1.475970, 1.482750, 1.489541, 1.496283, 1.502917, 1.509394, 1.515673, 1.521727, 1.527534, 1.533082, 1.545796, 1.556882, 1.566435, 1.574574, 1.581418, 1.587074, 1.591631, 1.595164, 1.597732, 1.599378, 1.600134, 1.600016, 1.599031, 1.597171, 1.596716, 1.595345, 1.593037, 1.589757, 1.585451, 1.580049, 1.573457, 1.565556, 1.556192, 1.545172, 1.532249, 1.517110, 1.499363, 1.478531, 1.469216, 1.459292, 1.448735, 1.437538, 1.425727, 1.413381, 1.400670, 1.387885, 1.375423, 1.363657, 1.352804, 1.342937, 1.338366, 1.334022, 1.329895, 1.327908, 1.325970, 1.325208, 1.324453, 1.323706, 1.322966, 1.322233, 1.321507, 1.320788, 1.320431, 1.320076, 1.319722, 1.319546, 1.319370, 1.319195, 1.319159, 1.319124, 1.319091, 1.319057, 1.319021, 1.318947, 1.318885, 1.318817, 1.318855}};
 
  /* Stuff for interpolating the data */
  gsl_spline    *spline = NULL;
  gsl_interp_accel *acc = NULL;
 
  const double (*reOm)[107] = NULL;
  const double (*imOm)[107] = NULL;
 
  switch ( l ) {
  case (2):
    if ( m == 2 ) {
      reOm = reomegaqnm22;
      imOm = imomegaqnm22;
    }
    else
      if ( m == 1 ) {
        reOm = reomegaqnm21;
        imOm = imomegaqnm21;
      }
      else
        if ( m == 0 ) {
          reOm = reomegaqnm20;
          imOm = imomegaqnm20;
        }
        else {
          XLALPrintError( "Unsupported combination of l, m (%d, %d). It must be 0<=m<=l\n", l, m );
          XLAL_ERROR( XLAL_EINVAL );
        }
    break;
  case (3):
    if ( m == 3 ) {
      reOm = reomegaqnm33;
      imOm = imomegaqnm33;
    }
    else
      if ( m == 2 ) {
        reOm = reomegaqnm32;
        imOm = imomegaqnm32;
      }
      else
        if ( m == 1 ) {
          reOm = reomegaqnm31;
          imOm = imomegaqnm31;
        }
        else
          if ( m == 0 ) {
            reOm = reomegaqnm30;
            imOm = imomegaqnm30;
          }
          else {
            XLALPrintError( "Unsupported combination of l, m (%d, %d). It must be 0<=m<=l\n", l, m );
            XLAL_ERROR( XLAL_EINVAL );
          }
    break;
  case (4):
    if ( m == 4 ) {
      reOm = reomegaqnm44;
      imOm = imomegaqnm44;
    }
    else
      if ( m == 3 ) {
        reOm = reomegaqnm43;
        imOm = imomegaqnm43;
      }
      else
        if ( m == 2 ) {
          reOm = reomegaqnm42;
          imOm = imomegaqnm42;
        }
        else
          if ( m == 1 ) {
            reOm = reomegaqnm41;
            imOm = imomegaqnm41;
          }
          else
            if ( m == 0 ) {
              reOm = reomegaqnm40;
              imOm = imomegaqnm40;
            }
            else {
              XLALPrintError( "Unsupported combination of l, m (%d, %d). It must be 0<=m<=l\n", l, m );
              XLAL_ERROR( XLAL_EINVAL );
            }
    break;
  default:
    XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
    XLAL_ERROR( XLAL_EINVAL );
    break;
  };
 
  spline = gsl_spline_alloc( gsl_interp_cspline, 107 );
  acc    = gsl_interp_accel_alloc();
  for ( idx = 0; idx < (int)modefreqs->length; idx++ ) {
    gsl_spline_init( spline, afinallist, reOm[idx], 107 );
    gsl_interp_accel_reset( acc );
 
    modefreqs->data[idx] = gsl_spline_eval( spline, finalSpin, acc );
 
    gsl_spline_init( spline, afinallist, imOm[idx], 107 );
    gsl_interp_accel_reset( acc );
 
    modefreqs->data[idx] += I*gsl_spline_eval( spline, finalSpin, acc );
 
    /* Scale by the appropriate mass factors */
    modefreqs->data[idx] *= 1./ finalMass / (totalMass * LAL_MTSUN_SI);
  }
  /* Free memory and exit */
 
  gsl_spline_free( spline );
  gsl_interp_accel_free( acc );
 
  return XLAL_SUCCESS;
}