LALSimulation  5.4.0.1-fe68b98
LALSimBlackHoleRingdownPrec.c
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1 #include <stdlib.h>
2 #include <gsl/gsl_vector.h>
3 #include <gsl/gsl_multiroots.h>
4 #include <gsl/gsl_integration.h>
5 
6 //#include <lal/LALDatatypes.h>
7 //#include <lal/LALStdlib.h>
8 #include <lal/LALConstants.h>
9 //#include <lal/TimeSeries.h>
10 //#include <lal/Units.h>
11 
12 #include <LALSimBlackHoleRingdown.h>
13 #include <LALSimBlackHoleRingdownPrec.h>
14 
15 /* note: use double-precision variables, but demand single-precision accuracy */
16 #define EPS LAL_REAL4_EPS
17 #define TINY LAL_REAL4_MIN
18 #define MAXITER 16384
19 
20 
21 #ifdef __GNUC__
22 #define UNUSED __attribute__ ((unused))
23 #else
24 #define UNUSED
25 #endif
26 
27 
28 /**
29  * Computes the final mass and spin of the black hole resulting from merger.
30  * They are given by fittings of NR simulations results. Specifically,
31  * for EOBNR, Table I of Buonanno et al. PRD76, 104049;
32  * for EOBNRv2 and EOBNRv2HM, Eqs. 29a and 29b of Pan et al. PRD84, 124052;
33  * for SEOBNRv1, SEOBNRv2, Eq. 8 of Tichy and Marronetti PRD78, 081501 and
34  * Eqs. 1 and 3 of Barausse and Rezzolla ApJ704, L40. Complemented by https://dcc.ligo.org/T1400476.
35  * For SEOBNRv4P: i) the final mass comes from Eq(3) in https://dcc.ligo.org/T1400476, but
36  * we use q<=1; ii) the final spin comes from Eq(13-16) for Hofmann et al,
37  * https://iopscience.iop.org/article/10.3847/2041-8205/825/2/L19/meta [arxiv:1605.01938]
38  */
39 INT4 XLALSimIMREOBFinalMassSpinPrec(
40  REAL8 *finalMass, /**<< OUTPUT, the final mass (scaled by original total mass) */
41  REAL8 *finalSpin, /**<< OUTPUT, the final spin (scaled by final mass) */
42  const REAL8 mass1, /**<< The mass of the 1st component of the system */
43  const REAL8 mass2, /**<< The mass of the 2nd component of the system */
44  const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
45  const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
46  Approximant approximant /**<< The waveform approximant being used */
47 )
48 {
49  REAL8 LISCO,csi,aeff, a_tot_prec,fitpart,alpha,beta,gamma,epsilon_beta,epsilon_gamma;
50  UNUSED REAL8 epsilon_alpha;
51  static const REAL8 root9ovr8minus1 = -0.057190958417936644;
52  static const REAL8 root12 = 3.4641016151377544;
53 
54  /* Constants used for the spinning EOB model */
55  static const REAL8 p0 = 0.04826;
56  static const REAL8 p1 = 0.01559;
57  static const REAL8 p2 = 0.00485;
58  static const REAL8 t0 = -2.8904;
59  static const REAL8 t2 = -3.5171;
60  static const REAL8 t3 = 2.5763;
61  static const REAL8 s4 = -0.1229;
62  static const REAL8 s5 = 0.4537;
63 
64  static const REAL8 s9 = 2.763032781169752;
65  static const REAL8 s8 = -2.6081232221537394;
66  static const REAL8 s7 = 1.2657111864932808;
67  static const REAL8 s6 = -0.7835007857591175;
68  static const REAL8 s5v2 = -0.3264724801557159;
69  static const REAL8 s4v2 = -0.27506210736300474;
70  static const REAL8 t0v2 = -2.649826989941522;
71  static const REAL8 t3v2 = 3.910637513328723;
72 // static const REAL8 t2v2 = 16.* (-0.17958273605461628 - 0.015625*t3v2);
73  static const REAL8 t2v2 = -3.850983155206041;
74 
75  UNUSED INT4 debugout=0;
76  REAL8 totalMass;
77  REAL8 eta, eta2, eta3;
78  REAL8 a1, a2, chiS, q;
79  REAL8 z1, z2, rISCO, eISCO, atl, tmpVar;
80  REAL8 UNUSED cosa, cosb, cosg, a1a2norm, a1a2L, lnorm;
81  REAL8 UNUSED q2,chi1, chi2, theta1, theta2, phi1, phi2, swapvar;
82 
83  /* get a local copy of the intrinsic parameters */
84  totalMass = mass1 + mass2;
85  eta = mass1 * mass2 / (totalMass*totalMass);
86  eta2 = eta * eta;
87  eta3 = eta2 * eta;
88 //XLAL_PRINT_INFO("Approximant: %d\n",approximant);
89 
90  switch ( approximant )
91  {
92  case EOBNRv2:
93  case EOBNRv2HM:
94  eta3 = eta2 * eta;
95  /* Final mass and spin given by Eqs. 29a and 29b of Pan et al. PRD84, 124052 */
96  *finalMass = 1. + root9ovr8minus1 * eta - 0.4333 * eta2 - 0.4392 * eta3;
97  *finalSpin = root12 * eta - 3.871 * eta2 + 4.028 * eta3;
98  break;
99  case EOBNR:
100  /* Final mass and spin given by Table I of Buonanno et al. PRD76, 104049 */
101  *finalMass = 1 - 0.057191 * eta - 0.498 * eta2;
102  *finalSpin = 3.464102 * eta - 2.9 * eta2;
103  break;
104  case SEOBNRv2:
105  /* See page 3 of the dcc document T1400476-v3, quantities MFinal and aFinal, for expressions below. */
106  a1 = spin1[2];
107  a2 = spin2[2];
108  q = mass1 / mass2;
109  atl = ( a1 + a2 /q/q) / (1.+1./q)/(1.+ 1./q);
110  tmpVar = ( a1 + a2 /q/q) / (1.+1./q/q);
111  z1 = 1. + pow( 1.-atl*atl, 1./3.) * ( pow( 1.+atl, 1./3. ) + pow( 1.-atl, 1./3. ) );
112  z2 = sqrt( 3.*atl*atl + z1*z1 );
113  rISCO = 3. + z2 - ( atl<0. ? -1. : 1. ) * sqrt( (3.-z1) * (3.+z1+2.*z2) );
114  eISCO = sqrt( 1. - 2./(3.*rISCO) );
115  *finalMass = 1. - ( (1.-eISCO)*eta
116  + 16.*eta*eta*( 0.00258 - 0.0773/(1./((1.+1/q/q)/(1.+1/q)/(1.+1/q))*atl-1.6939) - 0.25*(1.-eISCO)) );
117  *finalSpin = tmpVar + tmpVar*eta*( s9*eta*tmpVar*tmpVar + s8*eta*eta*tmpVar + s7*eta*tmpVar
118  + s6*tmpVar*tmpVar + s4v2*tmpVar + s5v2*eta + t0v2)
119  + eta*( 2.*sqrt(3.) + t2v2*eta + t3v2 *eta*eta );
120  break;
121  case SEOBNRv1:
122  /* Final mass/spin comes from Eq. 8 of Tichy and Marronetti PRD78, 081501
123  and from Eqs. 1 and 3 of Barausse and Rezzolla ApJ704, L40 */
124  a1 = spin1[2];
125  a2 = spin2[2];
126 
127  chiS = 0.5 * ( a1 + a2 );
128  q = mass1 / mass2;
129  *finalMass = 1. - p0 + 2.*p1 * chiS + 4.*p2*chiS*chiS;
130  *finalMass = 1. + (0.9515 - 1.0)*4.*eta - 0.013*16.*eta2*(a1+a2);
131  tmpVar = ( a1 + a2 /q/q) / ( 1. + 1/q/q);
132  *finalSpin = tmpVar + tmpVar * eta * (s4 * tmpVar + s5 * eta + t0 ) + eta * (2. * sqrt(3.) + t2*eta + t3*eta*eta );
133  break;
134  case SEOBNRv3_opt:
135  case SEOBNRv3:
136  // Precessing spins (Barausse & Rezzolla 2009, Eqs (6-10))
137  chi1 = sqrt( spin1[0]*spin1[0] + spin1[1]*spin1[1] + spin1[2]*spin1[2] );
138  chi2 = sqrt( spin2[0]*spin2[0] + spin2[1]*spin2[1] + spin2[2]*spin2[2] );
139  if ( chi1 < 1.0e-15 )
140  { theta1 = 0.; }
141  else
142  { theta1 = acos( spin1[2] / chi1 ); }
143  if ( chi2 < 1.0e-15 )
144  { theta2 = 0.; }
145  else
146  { theta2 = acos( spin2[2] / chi2 ); }
147  phi1 = atan2( spin1[1], spin1[0] );
148  phi2 = atan2( spin2[1], spin2[0] );
149  if ( mass1 > mass2 )
150  {
151  q = mass2 / mass1;
152  }
153  else
154  {
155  q = mass1 / mass2;
156  swapvar = chi1; chi1 = chi2; chi2 = swapvar;
157  swapvar = theta1; theta1 = theta2; theta2 = swapvar;
158  swapvar = phi1; phi1 = phi2; phi2 = swapvar;
159  }
160  q2 = q * q;
161  /* Stas: this is v2 appraoch applied to s1.J s2.J az z-components of spin1/2*/
162  q = mass1 / mass2;
163  a1 = spin1[2];
164  a2 = spin2[2];
165  atl = ( a1 + a2 /q/q) / (1.+1./q)/(1.+ 1./q);
166  tmpVar = ( a1 + a2 /q/q) / (1.+1./q/q);
167  z1 = 1. + pow( 1.-atl*atl, 1./3.) * ( pow( 1.+atl, 1./3. ) + pow( 1.-atl, 1./3. ) );
168  z2 = sqrt( 3.*atl*atl + z1*z1 );
169  rISCO = 3. + z2 - ( atl<0. ? -1. : 1. ) * sqrt( (3.-z1) * (3.+z1+2.*z2) );
170  eISCO = sqrt( 1. - 2./(3.*rISCO) );
171  *finalMass = 1. - ( (1.-eISCO)*eta
172  + 16.*eta*eta*( 0.00258 - 0.0773/(1./((1.+1/q/q)/(1.+1/q)/(1.+1/q))*atl-1.6939) - 0.25*(1.-eISCO)) );
173  *finalSpin = tmpVar + tmpVar*eta*( s9*eta*tmpVar*tmpVar + s8*eta*eta*tmpVar + s7*eta*tmpVar
174  + s6*tmpVar*tmpVar + s4v2*tmpVar + s5v2*eta + t0v2)
175  + eta*( 2.*sqrt(3.) + t2v2*eta + t3v2 *eta*eta );
176  break;
177  case SEOBNRv4P:
178  case SEOBNRv4PHM:
179  /* Depending on which mass is larger, compute q. Note that below
180  we always use the convention that q=mass2/mass1<=1. Thus for
181  us, internally mass1 is always the primary. */
182  q = mass2 / mass1;
183  a1 = spin1[2];
184  a2 = spin2[2];
185  if (mass1 < mass2)
186  {
187  q = mass1 / mass2;
188  // We need to flip the spins as well, because spin1 should be primary,
189  // and spin2 should be secondary.
190  swapvar = a2;
191  a2 = a1;
192  a1 = swapvar;
193  }
194 
195  /* This comes from SEOBNRv4 in XLALSimIMREOBFinalMassSpin. Note that
196  we have swapped conventions for q! */
197 
198  REAL8 OnePlusQ = 1. + q;
199 
200  atl = (a1 + a2 * q * q) / (OnePlusQ * OnePlusQ);
201  rISCO = XLALSimRadiusKerrISCO(atl);
202  eISCO = XLALSimEnergyKerrISCO(rISCO);
203  /* See page 3 of the dcc document T1400476-v3, quantity MFinal, for expression below.
204  Note that in this reference it was assumed that q>=1*/
205  *finalMass = 1. - ((1. - eISCO) * eta + 16. * eta * eta * (0.00258 - 0.0773 / (1. / ((1. + q * q) / (OnePlusQ * OnePlusQ)) * atl - 1.6939) - 0.25 * (1. - eISCO)));
206  // Final spin fit for precessing spins (Hofmann et al, 2015)
207  chi1 = sqrt(spin1[0] * spin1[0] + spin1[1] * spin1[1] + spin1[2] * spin1[2]);
208  chi2 = sqrt(spin2[0] * spin2[0] + spin2[1] * spin2[1] + spin2[2] * spin2[2]);
209 
210  alpha = 0.0; // Angle between the 2 spins
211  beta = 0.0; // The angle between spin1 and Newtonian orbital angular momentum
212  gamma = 0.0; // The angle between spin2 and Newtonian orbital angular momentum
213 
214  if (chi1 > 1e-6)
215  {
216  beta = acos(spin1[2] / chi1);
217  }
218 
219  if (chi2 > 1e-6)
220  {
221  gamma = acos(spin2[2] / chi2);
222  }
223 
224  // Dot product between the 2 spins
225  REAL8 tmp = spin1[0] * spin2[0] + spin1[1] * spin2[1] + spin1[2] * spin2[2];
226 
227  // alpha only makes sense if both spins are non-zero
228  if (chi1 > 1e-4 && chi2 > 1e-4)
229 
230  {
231  tmp /= chi1;
232  tmp /= chi2;
233  if (tmp > 1. && tmp <= 1. + 1e-4)
234  tmp = 1.;
235  if (tmp < -1. && tmp >= -1. - 1e-4)
236  tmp = -1.;
237  alpha = acos(tmp);
238  }
239 
240  // See below Eq(18) in Hofmann et al 2015.
241  epsilon_beta = 0.024;
242  epsilon_gamma = 0.024;
243  // Eq(18) in Hofmann et al, 2015.
244  beta = beta + epsilon_beta * sin(beta);
245  gamma = gamma + epsilon_gamma * sin(gamma);
246 
247  // If mass2 > mass1 we need to swap things.
248  // Since alpha is the angle between the spins it is not affected.
249 
250  if (mass2 > mass1)
251  {
252  swapvar = gamma;
253  gamma = beta;
254  beta = swapvar;
255  swapvar = chi2;
256  chi2 = chi1;
257  chi1 = swapvar;
258  }
259 
260  /* Final spin expressions from Hofmann et al, 2015. */
261  // See Table I for the n_M=3, n_J=4 fit and expression for aeff below.
262  csi = 0.474046; //This is $\xi$ in the paper.
263  // Eq(14) in Hofmann et al.
264  a_tot_prec = (chi1 * cos(beta) + chi2 * cos(gamma) * q * q) / ((1.0 + q) * (1.0 + q));
265  // Eq(15) in Hofmann et al.
266  aeff = a_tot_prec + csi * eta * (chi1 * cos(beta) + chi2 * cos(gamma));
267  // These are standard Kerr expressions for quantities at ISCO. See e.g
268  // Bardeen et al. 1972, ApJ 178 347, Hofmann et al 2015, Eqs(2-6)
269  rISCO = XLALSimRadiusKerrISCO(aeff);
270  eISCO = XLALSimEnergyKerrISCO(rISCO);
271  LISCO = XLALSimAngMomKerrISCO(rISCO);
272  /* The k00, k01, ... coefficients are defined in LALSimBlackHoleRingdown.h */
273  REAL8 eta4 = eta * eta3;
274 
275  if (fabs(aeff) > 0.)
276  {
277  REAL8 aeff2 = aeff * aeff;
278  REAL8 aeff3 = aeff * aeff2;
279  REAL8 aeff4 = aeff * aeff3;
280  fitpart = k00 * eta + k01 * aeff * eta + k02 * aeff2 * eta + k03 * aeff3 * eta + k04 * aeff4 * eta +
281  k10 * eta2 + k11 * aeff * eta2 + k12 * aeff2 * eta2 + k13 * aeff3 * eta2 + k14 * aeff4 * eta2 +
282  k20 * eta3 + k21 * aeff * eta3 + k22 * aeff2 * eta3 + k23 * aeff3 * eta3 + k24 * aeff4 * eta3 +
283  k30 * eta4 + k31 * aeff * eta4 + k32 * aeff2 * eta4 + k33 * aeff3 * eta4 + k34 * aeff4 * eta4;
284  }
285  else
286  {
287  // If there is no effective spin, use a simpler expression.
288  fitpart = k00 * eta + k10 * eta2 + k20 * eta3 + k30 * eta4;
289  }
290  // Eq(13) in Hofmann et al.
291  REAL8 ell_norm = fabs(LISCO - 2 * a_tot_prec * (eISCO - 1.0) + fitpart);
292  // Next 2 equations are combined to get Eq(16) in Hofmann et al.
293  REAL8 prefactor = 1. / ((1 + q) * (1 + q));
294  REAL8 inside_sqrt = pow(chi1, 2) + pow(chi2, 2) * pow(q, 4) + 2 * chi1 * chi2 * pow(q, 2) * cos(alpha) +
295  2 * (chi1 * cos(beta) + chi2 * pow(q, 2) * cos(gamma)) * ell_norm * q + pow(ell_norm, 2) * pow(q, 2);
296  // Guard against NANs inside the fit
297  if (inside_sqrt < 0)
298  {
299  XLAL_PRINT_WARNING("Warning: in the final spin fit, argument of sqrt was negative. Truncating the spin to 0.\n");
300  inside_sqrt = 0.0;
301  }
302  *finalSpin = prefactor * sqrt(inside_sqrt);
303  // If somehow we have gone above the Kerr limit, don't.
304  if (*finalSpin > 1)
305  {
306  *finalSpin = 1 - 1e-6;
307  }
308  break; // End of SEOBNRv4P
309  default:
310  XLALPrintError("XLAL Error %s - Unsupported approximant.\n", __func__);
311  XLAL_ERROR(XLAL_EINVAL);
312  }
313 
314  //XLAL_PRINT_INFO( "Final mass = %e, Final spin = %e\n", *finalMass, *finalSpin );
315  return XLAL_SUCCESS;
316 }
317 
318 
319 /**
320  * This function generates the quasinormal mode frequencies for a black
321  * hole ringdown. At present, this function works for the 22, 21, 33, 44
322  * and 55 modes, and includes 8 overtones. The final frequencies are
323  * computed by interpolating the data found on the webpage of
324  * Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
325  * In this page, frequecy data are given for positive final spins only.
326  * For a negative final spin chi<0 case, the (l,m) mode frequency is given by
327  * the (l,-m) mode frequency of the positive final spin -chi case.
328  */
329 INT4 XLALSimIMREOBGenerateQNMFreqV2Prec(
330  COMPLEX16Vector *modefreqs, /**<< OUTPUT, complex freqs of overtones in unit of Hz */
331  const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
332  const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
333  const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
334  const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
335  UINT4 l, /**<< The l value of the mode in question */
336  INT4 m, /**<< The m value of the mode in question */
337  UINT4 nmodes, /**<< The number of overtones that should be included (max 8) */
338  Approximant approximant/**<< The waveform approximant being used */
339  )
340 {
341 
342  /* Data for interpolating the quasinormal mode frequencies is taken from
343  * The webpage of Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
344  * In the spin range of (-0.995, 0.999),
345  * interpolation error within 5e-5 for the first 3 overtones of the 22 mode
346  * interpolation error within 0.005 for the first 8 overtones of the 22 mode
347  * On the data points, interpolation error is within 1e-5, except for the
348  * highest overtone of the (4,4) and (5,5) modes.
349  */
350 
351  static const double afinallist[107] = {-0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
352  -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
353  -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,
354  -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,
355  -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,
356  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,
357  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,
358  0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996};
359 
360  /* 2, 2 mode */
361 
362  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, 0.29187, 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, 0.5326, 0.541794, 0.55163, 0.562201, 0.573616, 0.586017, 0.59958, 0.614539, 0.631206, 0.650018, 0.671614, 0.696995, 0.727875, 0.74632, 0.767674, 0.793208, 0.808235, 0.825429, 0.8331, 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, 0.97169},
363 {0.243689, 0.247076, 0.248937, 0.250577, 0.251041, 0.251088, 0.251073, 0.251023, 0.250952, 0.250874, 0.25052, 0.250339, 0.250292, 0.250359, 0.250463, 0.250549, 0.250686, 0.250814, 0.250945, 0.251079, 0.251214, 0.251349, 0.251484, 0.25182, 0.252158, 0.252836, 0.253519, 0.254205, 0.255591, 0.256994, 0.258413, 0.259851, 0.261306, 0.26278, 0.264273, 0.265785, 0.267317, 0.268869, 0.270442, 0.272036, 0.276117, 0.280342, 0.284721, 0.289262, 0.293978, 0.29888, 0.303981, 0.309295, 0.314838, 0.320629, 0.326687, 0.333036, 0.339701, 0.346711, 0.354101, 0.36191, 0.370183, 0.378976, 0.388353, 0.39839, 0.409183, 0.420847, 0.433527, 0.447407, 0.462728, 0.479807, 0.499079, 0.521161, 0.53097, 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, 0.94811, 0.949919, 0.951804, 0.953776, 0.955847, 0.960353, 0.96551, 0.968435, 0.971688},
364 {0.191626, 0.188311, 0.185222, 0.182107, 0.182532, 0.183173, 0.183784, 0.184279, 0.184634, 0.18486, 0.184811, 0.184353, 0.184263, 0.184581, 0.184713, 0.18472, 0.184862, 0.185055, 0.185205, 0.185357, 0.185521, 0.185687, 0.18585, 0.18625, 0.186658, 0.187473, 0.188294, 0.189121, 0.190789, 0.192478, 0.194189, 0.195923, 0.19768, 0.19946, 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, 0.43513, 0.454179, 0.475545, 0.499906, 0.510701, 0.522217, 0.534557, 0.547847, 0.56224, 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, 0.95376, 0.955833, 0.960343, 0.965503, 0.96843, 0.971683},
365 {0.127766, 0.134925, 0.137314, 0.135026, 0.132545, 0.132613, 0.133213, 0.133927, 0.134502, 0.134846, 0.134197,
366 0.133839, 0.134383, 0.134311, 0.134305, 0.134548, 0.134538, 0.134764, 0.134855, 0.13499, 0.135153, 0.135276, 0.135401, 0.13576, 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, 0.16692, 0.172065, 0.177495, 0.183228, 0.18928, 0.19567, 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, 0.40121, 0.421977, 0.445099, 0.471336, 0.482957, 0.495375, 0.508729, 0.523187, 0.538956, 0.556285, 0.575464, 0.59683, 0.620788, 0.647869, 0.678894, 0.715333, 0.736426, 0.760279, 0.788101, 0.804173, 0.822338, 0.830374, 0.83897, 0.848242, 0.858347, 0.869515, 0.8821, 0.896696, 0.905068, 0.91446, 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},
367 {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, 0.11021, 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, 0.12123, 0.122431, 0.123659, 0.124914, 0.126199, 0.12955, 0.133123, 0.136951, 0.141068, 0.145514, 0.150331, 0.155561, 0.161252, 0.167448, 0.174197, 0.18154, 0.189518, 0.198166, 0.207515, 0.217594, 0.228433, 0.24006, 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, 0.82065, 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},
368 {0.0973518, 0.0987518, 0.0952128, 0.097231, 0.0968051, 0.0959061, 0.0958383, 0.0963991, 0.0969597, 0.0971588, 0.0962907, 0.0968828, 0.0964446, 0.0967173, 0.0968133, 0.0967445, 0.0968961, 0.0970152, 0.0970355, 0.0971754, 0.0972259, 0.0973507, 0.097408, 0.0976397, 0.0978753, 0.0983115, 0.0987594, 0.099209, 0.100108, 0.101005, 0.101904, 0.102805, 0.103707, 0.104611, 0.10552, 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, 0.14171, 0.147116, 0.153415, 0.160767, 0.169299, 0.179085, 0.19014, 0.202441, 0.215947, 0.230623, 0.246457, 0.263464, 0.281691, 0.301218, 0.322157, 0.344655, 0.368896, 0.39509, 0.42345, 0.43543, 0.447764, 0.460418, 0.473311, 0.486283, 0.499037,
369 0.511101, 0.522095, 0.532461, 0.536917, 0.527548, 0.521465, 0.518438, 0.515417, 0.51241, 0.510911, 0.509415, 0.508818, 0.508221, 0.507624, 0.507028, 0.506432, 0.505837, 0.505242, 0.504944, 0.504647, 0.50435, 0.504202, 0.504054, 0.503904, 0.503874, 0.503845, 0.503817, 0.503789, 0.50376, 0.503692, 0.503638, 0.503632, 0.503585},
370 {0.084098, 0.0868741, 0.0879148, 0.0858816, 0.0871769, 0.0862173, 0.0858779, 0.0863779, 0.0869438, 0.0870509, 0.0866021, 0.0864788, 0.0867758, 0.0866752, 0.0866613, 0.0868868, 0.086965, 0.0870574, 0.0871075, 0.0872251, 0.0873545, 0.0874293, 0.087563, 0.0878271, 0.088086, 0.0886037, 0.0891314, 0.0896576, 0.0906978, 0.0917299, 0.0927446, 0.093744, 0.0947274, 0.0956935, 0.0966414, 0.0975719, 0.0984848, 0.0993786, 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, 0.45201, 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,
371 0.818797, 0.827303, 0.836336, 0.846012, 0.856487, 0.867993, 0.880887, 0.895775, 0.904293, 0.913837, 0.92483, 0.931097, 0.938091, 0.946107, 0.947875, 0.949711, 0.951623, 0.953621, 0.955717, 0.960269, 0.965464, 0.968404, 0.971669},
372 {0.0783357, 0.0733796, 0.0766204, 0.0744319, 0.0764107, 0.0754793, 0.0749396, 0.0755031, 0.0761004, 0.0760294, 0.0759874, 0.075511, 0.0757765, 0.0758322, 0.0759714, 0.0759232, 0.0761145, 0.0762289, 0.0763205, 0.0764184, 0.0765972, 0.0767207, 0.0768409, 0.0771736, 0.0775187, 0.07821, 0.0789117, 0.0796137, 0.0810158, 0.0824117, 0.0837964, 0.0851528, 0.0864792, 0.0877698, 0.0890208, 0.0902295, 0.0913937, 0.0925132, 0.0935883, 0.0946171, 0.0969926, 0.0990908, 0.100921, 0.102489, 0.103795, 0.104821, 0.10553, 0.105854, 0.105679, 0.104817, 0.102968, 0.0997112, 0.094996, 0.0928224, 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, 0.52572, 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, 0.93791, 0.945976, 0.947755, 0.949602, 0.951525, 0.953535, 0.955643, 0.960217, 0.965434, 0.968355, 0.971639}};
373 
374  const double imomegaqnm22[8][107] = {{0.0784607, 0.0801007, 0.0816472, 0.0840037, 0.0854954, 0.0860129, 0.0864215, 0.0867455, 0.0870035, 0.08721, 0.0877802, 0.0879878, 0.088065, 0.0880965, 0.0880878, 0.0880757, 0.0880612, 0.0880574, 0.0880589, 0.0880627, 0.0880675, 0.0880727, 0.088078, 0.0880913, 0.0881045, 0.0881304, 0.088156, 0.0881813, 0.0882315, 0.0882807, 0.0883289, 0.0883763, 0.0884226, 0.0884679, 0.0885122, 0.0885555, 0.0885976, 0.0886386, 0.0886785, 0.0887172, 0.0888085, 0.0888917, 0.0889663, 0.0890315, 0.0890868, 0.0891313, 0.0891643, 0.0891846, 0.0891911, 0.0891825, 0.0891574, 0.0891138, 0.0890496, 0.0889623, 0.0888489, 0.0887057, 0.0885283, 0.0883112, 0.0880477, 0.0877293, 0.0873453, 0.086882, 0.0863212, 0.0856388, 0.0848021, 0.0837652, 0.0824618, 0.0807929, 0.0799908, 0.0790927, 0.0780817, 0.0769364, 0.0756296, 0.0741258, 0.072378, 0.0703215, 0.0678642, 0.0648692, 0.0611186, 0.0562313, 0.053149, 0.0494336, 0.0447904, 0.0419586, 0.0386302, 0.0371155, 0.0354676, 0.033659, 0.0316516, 0.0293904, 0.0267908, 0.0237095, 0.0219107, 0.0198661, 0.0174737, 0.0160919, 0.014534, 0.0127274, 0.0123259, 0.0119077, 0.0114708, 0.0110127, 0.0105306, 0.00947799, 0.00826689, 0.00757704, 0.0068074},
375 {0.284478, 0.282567, 0.281162, 0.279245, 0.278072, 0.27767, 0.277358, 0.277118, 0.276936, 0.2768, 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, 0.27712, 0.27716, 0.277197, 0.27723, 0.277259, 0.277283, 0.277304, 0.277321, 0.277333, 0.277344, 0.277326, 0.277278, 0.277196, 0.27708, 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, 0.24958, 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, 0.0949599, 0.0881754, 0.080377, 0.0711342, 0.0657383, 0.0596046, 0.0524264, 0.04828, 0.043605, 0.0381837, 0.0369789, 0.0357239, 0.0344128, 0.0330384, 0.0315916, 0.0284334, 0.0247999, 0.0227304, 0.0204216},
376 {0.504534, 0.501693, 0.501238, 0.503711, 0.506007, 0.50649, 0.506633, 0.506559, 0.506365, 0.50612, 0.505173, 0.50512, 0.505381, 0.505519, 0.505371, 0.505318, 0.505354, 0.505311, 0.505262, 0.505236, 0.50521, 0.505177, 0.505141, 0.505059, 0.504978, 0.504812, 0.504645, 0.504476, 0.504135, 0.503786, 0.503432, 0.50307, 0.502702, 0.502326, 0.501944, 0.501554, 0.501156, 0.500751, 0.500338, 0.499917, 0.498828, 0.497686, 0.496488, 0.49523, 0.49391, 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, 0.46126, 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, 0.35594, 0.34311, 0.327518, 0.308058, 0.282827, 0.266998, 0.248008, 0.22441, 0.210086, 0.193307, 0.18569, 0.177413, 0.16834, 0.158283, 0.146966, 0.133965, 0.118563, 0.109572, 0.0993515, 0.0873891, 0.0804781, 0.0726848, 0.0636465, 0.0616378, 0.0595453, 0.0573593, 0.0550676, 0.0526555, 0.0473899, 0.0413327, 0.037883, 0.0340348},
377 {0.777682, 0.77817, 0.774907, 0.771079, 0.772456, 0.773571, 0.774249, 0.774423, 0.774236, 0.773865, 0.772678, 0.773376, 0.773489, 0.77299, 0.773229, 0.773121, 0.773005, 0.772942, 0.772818, 0.772776, 0.77268, 0.772579, 0.772506, 0.772294, 0.772084, 0.771654, 0.771224, 0.770787, 0.7699, 0.768995, 0.768072, 0.767129, 0.766168, 0.765187, 0.764186, 0.763165, 0.762123, 0.761061, 0.759977, 0.758872, 0.756015, 0.75302, 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, 0.50348, 0.485224, 0.462864, 0.434823, 0.398473, 0.375741, 0.348572, 0.314974, 0.294663, 0.270945, 0.2602, 0.248542, 0.235779, 0.221649, 0.205769, 0.187547, 0.16598, 0.153396, 0.139094, 0.122354, 0.112682, 0.101773, 0.0891181, 0.0863053, 0.0833752, 0.0803139, 0.0771045, 0.0737264, 0.0663517, 0.0578682, 0.053037, 0.0476481},
378 {1.04431, 1.0466, 1.05065, 1.04828, 1.04719, 1.04809, 1.04894, 1.04925, 1.04906, 1.04863, 1.04812, 1.04862, 1.04806, 1.04843, 1.04808, 1.04824, 1.04803, 1.04799, 1.04788, 1.04781, 1.04768, 1.04762, 1.04752, 1.04729, 1.04704, 1.04657, 1.04609, 1.0456, 1.0446, 1.04357, 1.04251, 1.04141, 1.04028, 1.03911, 1.03791, 1.03667, 1.03539, 1.03406, 1.0327, 1.03129, 1.02756, 1.02353, 1.01918, 1.01448, 1.00943, 1.004, 0.9982, 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, 0.7538, 0.74371, 0.733106, 0.721967, 0.710268, 0.697962, 0.684902, 0.670601, 0.65375, 0.632042, 0.603295, 0.56587, 0.517102, 0.486783, 0.450771, 0.406552, 0.379969, 0.349048, 0.33508, 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, 0.0948041, 0.0853202, 0.0744092, 0.0681953, 0.0612642},
379 {1.32188, 1.31695, 1.31668, 1.31947, 1.31731, 1.3177, 1.31852, 1.31894, 1.31877, 1.31831, 1.31844, 1.31807, 1.31822, 1.318, 1.3182, 1.318, 1.31792, 1.31791, 1.31782, 1.3177, 1.31764, 1.31754, 1.31745, 1.31723, 1.31701, 1.31656, 1.31612, 1.31566, 1.31474, 1.31378, 1.3128, 1.31179, 1.31075, 1.30967, 1.30856, 1.3074, 1.3062, 1.30495, 1.30366, 1.30231, 1.2987, 1.2947, 1.29025, 1.2853, 1.2798, 1.27368, 1.26687, 1.25931, 1.25091, 1.24163, 1.23143, 1.22032, 1.20835, 1.19561, 1.18221, 1.16825, 1.15377, 1.13878, 1.1232, 1.10691, 1.08976, 1.07153, 1.05194, 1.03067, 1.0073, 0.981265, 0.951825, 0.91795, 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, 0.70819, 0.707992, 0.707952, 0.707911, 0.707871, 0.707832, 0.707796, 0.70772, 0.70762, 0.707592, 0.707598},
380 {1.58204, 1.58635, 1.58318, 1.58511, 1.58355, 1.58343, 1.58418, 1.58468, 1.58448, 1.58398, 1.58441, 1.58383, 1.58417, 1.5841, 1.58387, 1.58384, 1.58373, 1.58367, 1.58357, 1.58342, 1.58336, 1.58323, 1.58315, 1.58289, 1.58264, 1.58213, 1.58164, 1.58114, 1.58016, 1.57919, 1.57821, 1.57723, 1.57624, 1.57524, 1.57422, 1.57317, 1.5721, 1.57099, 1.56984, 1.56865, 1.56545, 1.56189, 1.55789, 1.55337, 1.54825, 1.54244, 1.53582, 1.52823, 1.51949, 1.50932, 1.49738, 1.48328, 1.46673, 1.44791, 1.42768, 1.40711, 1.38682, 1.36683, 1.34689, 1.32662, 1.30561, 1.28347, 1.25976, 1.234, 1.20558, 1.17376, 1.13753, 1.09541, 1.07645, 1.05602, 1.03387, 1.0097, 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, 0.41055, 0.391822, 0.371395, 0.348864, 0.323638, 0.2948, 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, 0.0909554, 0.0833586, 0.0748845},
381 {1.84957, 1.84968, 1.85134, 1.85007, 1.84983, 1.84929, 1.85004, 1.8506, 1.85027, 1.84968, 1.85008, 1.85008, 1.84964, 1.84961, 1.84963, 1.84966, 1.84941, 1.84923, 1.84906, 1.84884, 1.84864, 1.84851, 1.84829, 1.84788, 1.84746, 1.84662, 1.84583, 1.84506, 1.84361, 1.84225, 1.84097, 1.83975, 1.83859, 1.83747, 1.83638, 1.8353, 1.83424, 1.83317, 1.8321, 1.831, 1.82815, 1.82502, 1.82153, 1.81757, 1.81306, 1.8079, 1.80199, 1.79518, 1.78728, 1.77801, 1.76686, 1.75278, 1.73323, 1.70384, 1.66882, 1.63893, 1.61423, 1.59206, 1.57064, 1.54892, 1.52619, 1.5019, 1.47555, 1.44657, 1.41428, 1.37781, 1.33598, 1.28712, 1.26509, 1.24133, 1.21558, 1.18751, 1.15671, 1.12263, 1.08453, 1.04141, 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, 0.25821, 0.227147, 0.209213, 0.188989, 0.165524, 0.160306, 0.15487, 0.149189, 0.143232, 0.136961, 0.123266, 0.107504, 0.113694, 0.102135}};
382 
383  /* 2, 1 mode */
384 
385  const double reomegaqnm21[8][107] = {{0.336609, 0.339386, 0.340852, 0.342219, 0.342818, 0.343002,
386  0.343143, 0.343254, 0.343344, 0.343417, 0.343641, 0.343748,
387  0.343804, 0.343853, 0.343871, 0.343879, 0.343886, 0.343891,
388  0.343896, 0.343902, 0.343909, 0.343915, 0.343922, 0.343941, 0.34396,
389  0.344002, 0.344049, 0.344101, 0.34422, 0.344359, 0.344517,
390  0.344696, 0.344896, 0.345115, 0.345356, 0.345617, 0.345899,
391  0.346201, 0.346525, 0.34687, 0.347824, 0.348911, 0.350132, 0.351491,
392  0.35299, 0.354633, 0.356423, 0.358366, 0.360469, 0.362738,
393  0.365183, 0.367812, 0.370637, 0.373672, 0.376931, 0.380432,
394  0.384197, 0.388248, 0.392615, 0.39733, 0.402436, 0.407979, 0.41402,
395  0.420632, 0.427909, 0.435968, 0.444968, 0.455121, 0.459569,
396  0.464271, 0.469259, 0.474564, 0.480231, 0.486308, 0.492859,
397  0.499965, 0.507729, 0.516291, 0.525845, 0.536673, 0.542693,
398  0.549213, 0.556329, 0.560146, 0.564155, 0.565814, 0.567505,
399  0.569227, 0.570976, 0.572749, 0.574535, 0.576322, 0.577208,
400  0.578084, 0.578948, 0.579374, 0.579795, 0.580212, 0.580295,
401  0.580377, 0.58046, 0.580541, 0.580623, 0.580784, 0.580942, 0.581018,
402  0.581093}, {0.313486, 0.314984, 0.315748, 0.31636, 0.316504,
403  0.316512, 0.316502, 0.316483, 0.31646, 0.316436, 0.316347, 0.316311,
404  0.316305, 0.316315, 0.316325, 0.31633, 0.316338, 0.316345,
405  0.316352, 0.31636, 0.316368, 0.316375, 0.316383, 0.316401, 0.316419,
406  0.316455, 0.316491, 0.316527, 0.316602, 0.316682, 0.316772,
407  0.316874, 0.316989, 0.317122, 0.317273, 0.317444, 0.317636,
408  0.317851, 0.31809, 0.318353, 0.319124, 0.320064, 0.321179, 0.322476,
409  0.32396, 0.325636, 0.327508, 0.329582, 0.331865, 0.334364,
410  0.337088, 0.340045, 0.343249, 0.346711, 0.350448, 0.354478,
411  0.358823, 0.363506, 0.368558, 0.374014, 0.379916, 0.386313,
412  0.393268, 0.400856, 0.409172, 0.418337, 0.428509, 0.439897,
413  0.444855, 0.450076, 0.455587, 0.46142, 0.467612, 0.474208, 0.481261,
414  0.488834, 0.497004, 0.505862, 0.515506, 0.526011, 0.531572,
415  0.537263, 0.542874, 0.545479, 0.547723, 0.548438, 0.548984, 0.54929,
416  0.549241, 0.548642, 0.54714, 0.544185, 0.542606, 0.542325,
417  0.541626, 0.540962, 0.540617, 0.540156, 0.540066, 0.539986,
418  0.539906, 0.539818, 0.539726, 0.539553, 0.539377, 0.539288,
419  0.539198}, {0.270281, 0.269419, 0.268655, 0.267935, 0.267923,
420  0.268009, 0.268102, 0.268185, 0.268251, 0.268297, 0.268334,
421  0.268285, 0.268273, 0.268312, 0.268342, 0.268359, 0.268398,
422  0.268442, 0.268483, 0.268523, 0.268562, 0.268601, 0.26864, 0.268733,
423  0.268822, 0.268989, 0.269141, 0.26928, 0.26952, 0.269718, 0.269881,
424  0.270016, 0.270132, 0.270235, 0.270333, 0.270431, 0.270536,
425  0.270653, 0.270785, 0.270937, 0.271426, 0.2721, 0.272992, 0.274121,
426  0.275504, 0.277153, 0.279078, 0.281288, 0.283792, 0.286598,
427  0.289716, 0.293156, 0.296931, 0.301053, 0.30554, 0.31041, 0.315684,
428  0.321389, 0.327554, 0.334218, 0.341421, 0.349217, 0.357668,
429  0.366852, 0.376864, 0.387825, 0.39989, 0.413261, 0.419032, 0.425075,
430  0.431414, 0.438075, 0.445088, 0.452488, 0.46031, 0.468593,
431  0.477369, 0.48665, 0.49639, 0.506348, 0.511184, 0.515607, 0.51903,
432  0.519992, 0.5201, 0.51983, 0.519361, 0.51871, 0.517943, 0.517204,
433  0.516728, 0.516696, 0.516098, 0.513376, 0.509813, 0.508083,
434  0.506412, 0.504789, 0.504468, 0.504148, 0.50383, 0.503511, 0.503194,
435  0.502559, 0.501923, 0.501605, 0.501286}, {0.21269, 0.214089,
436  0.215208, 0.215364, 0.21474, 0.214584, 0.21456, 0.214625, 0.21473,
437  0.214837, 0.214992, 0.214885, 0.214922, 0.215045, 0.215071,
438  0.215139, 0.215267, 0.215383, 0.215507, 0.215624, 0.215741,
439  0.215858, 0.215974, 0.216256, 0.216533, 0.217064, 0.217566, 0.21804,
440  0.218903, 0.219653, 0.220295, 0.220836, 0.221285, 0.22165,
441  0.221945, 0.22218, 0.222368, 0.22252, 0.222647, 0.222759, 0.223032,
442  0.223383, 0.2239, 0.224647, 0.225672, 0.22701, 0.228689, 0.23073,
443  0.233151, 0.235969, 0.239199, 0.242854, 0.246951, 0.251505,
444  0.256534, 0.262058, 0.268101, 0.274689, 0.281852, 0.289628,
445  0.298059, 0.307197, 0.317104, 0.327855, 0.339542, 0.352278,
446  0.366207, 0.38151, 0.388065, 0.394895, 0.402017, 0.409454, 0.417227,
447  0.425361, 0.433878, 0.442797, 0.452127, 0.461855, 0.471918,
448  0.482195, 0.48739, 0.49271, 0.498495, 0.501813, 0.5056, 0.507251,
449  0.508939, 0.510585, 0.512031, 0.513028, 0.513289, 0.512758,
450  0.512367, 0.512091, 0.511921, 0.51135, 0.5096, 0.50715, 0.50665,
451  0.506154, 0.505662, 0.505175, 0.504694, 0.503744, 0.502809,
452  0.502344, 0.50188}, {0.171239, 0.169224, 0.168634, 0.170053,
453  0.169938, 0.169613, 0.169418, 0.169408, 0.169531, 0.169696,
454  0.169825, 0.169724, 0.16992, 0.169916, 0.170075, 0.17014, 0.170344,
455  0.170511, 0.17071, 0.170886, 0.171073, 0.171258, 0.171437, 0.171892,
456  0.172337, 0.173213, 0.174064, 0.174889, 0.176453, 0.177895,
457  0.179203, 0.180372, 0.181395, 0.182273, 0.183007, 0.183606,
458  0.184081, 0.184444, 0.18471, 0.184896, 0.185105, 0.18512, 0.185113,
459  0.185222, 0.18555, 0.186176, 0.187164, 0.188562, 0.190413, 0.192751,
460  0.195604, 0.199, 0.202962, 0.207515, 0.212679, 0.21848, 0.224939,
461  0.232083, 0.23994, 0.248543, 0.257928, 0.268139, 0.279228, 0.291258,
462  0.304303, 0.318456, 0.33383, 0.350563, 0.357675, 0.365045,
463  0.372687, 0.380617, 0.388855, 0.397422, 0.406346, 0.41567, 0.425462,
464  0.435857, 0.447149, 0.45999, 0.467349, 0.475546, 0.484594,
465  0.489367, 0.494295, 0.496339, 0.498459, 0.500692, 0.50308, 0.505635,
466  0.508214, 0.510197, 0.510572, 0.510387, 0.509864, 0.509635,
467  0.509456, 0.50879, 0.508443, 0.507999, 0.50747, 0.506881, 0.506257,
468  0.504974, 0.503704, 0.503082, 0.502466}, {0.136159, 0.137914,
469  0.137016, 0.136626, 0.137329, 0.137055, 0.136755, 0.136667,
470  0.136793, 0.136997, 0.136954, 0.137117, 0.137154, 0.137279, 0.1373,
471  0.13747, 0.137649, 0.137842, 0.138069, 0.138258, 0.138476, 0.138671,
472  0.138881, 0.139389, 0.139898, 0.14091, 0.14191, 0.142898, 0.144829,
473  0.146684, 0.148447, 0.150099, 0.151622, 0.153001, 0.154221,
474  0.15527, 0.156142, 0.156839, 0.157368, 0.15774, 0.158094, 0.157845,
475  0.15725, 0.156526, 0.155847, 0.155354, 0.155162, 0.155369, 0.156061,
476  0.157316, 0.159206, 0.161795, 0.165143, 0.169299, 0.174306,
477  0.180192, 0.186977, 0.194671, 0.203282, 0.212811, 0.223263,
478  0.234649, 0.246985, 0.260297, 0.274622, 0.290009, 0.306518,
479  0.324226, 0.331666, 0.339322, 0.347205, 0.355332, 0.363727,
480  0.372432, 0.381518, 0.391111, 0.401435, 0.412868, 0.425995,
481  0.441563, 0.45052, 0.460463, 0.471717, 0.477974, 0.484665, 0.487438,
482  0.490248, 0.493085, 0.49596, 0.498923, 0.502084, 0.505527,
483  0.507222, 0.508526, 0.508875, 0.508627, 0.508251, 0.507926,
484  0.507863, 0.507785, 0.50767, 0.507484, 0.507181, 0.506113, 0.504624,
485  0.503839, 0.50306}, {0.114342, 0.113963, 0.115141, 0.114074,
486  0.11486, 0.114789, 0.114485, 0.114338, 0.114452, 0.114665, 0.114512,
487  0.114807, 0.11467, 0.114821, 0.114995, 0.115025, 0.115231,
488  0.115438, 0.115661, 0.115846, 0.11605, 0.116249, 0.116452, 0.116951,
489  0.117454, 0.118454, 0.11946, 0.120464, 0.122464, 0.124443,
490  0.126383, 0.128266, 0.130073, 0.131781, 0.133368, 0.134813, 0.13609,
491  0.137179, 0.138065, 0.138742, 0.139567, 0.139335, 0.138333,
492  0.136834, 0.135064, 0.133208, 0.131418, 0.129826, 0.128564,
493  0.127775, 0.127629, 0.128336, 0.130133, 0.133252, 0.137863,
494  0.144021, 0.151672, 0.160684, 0.170902, 0.182186, 0.194429,
495  0.207556, 0.221528, 0.236327, 0.251955, 0.268421, 0.285744, 0.30395,
496  0.311492, 0.319195, 0.327076, 0.335168, 0.343522, 0.352232,
497  0.361443, 0.371382, 0.382361, 0.394771, 0.409089, 0.426092,
498  0.436065, 0.4474, 0.460415, 0.467675, 0.475563, 0.478922, 0.482402,
499  0.485993, 0.489665, 0.493377, 0.497113, 0.500995, 0.503086,
500  0.505273, 0.507186, 0.507677, 0.507628, 0.507177, 0.507077,
501  0.506981, 0.506892, 0.506806, 0.506714, 0.506383, 0.505391,
502  0.504576, 0.503665}, {0.0996362, 0.098809, 0.0988228, 0.0989612,
503  0.0991812, 0.0993225, 0.0990912, 0.0989133, 0.0990066, 0.0992056,
504  0.0990844, 0.0992013, 0.0993046, 0.0993698, 0.0994135, 0.0995406,
505  0.0997102, 0.0999057, 0.100109, 0.100292, 0.100464, 0.100668,
506  0.100843, 0.10132, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617,
507  0.108576, 0.11054, 0.112492, 0.114417, 0.116296, 0.118106,
508  0.119822, 0.121422, 0.122876, 0.12415, 0.125214, 0.12686, 0.127085,
509  0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.10844,
510  0.104598, 0.100602, 0.0966436, 0.0934548, 0.0928224, 0.0967608,
511  0.105267, 0.116748, 0.129817, 0.143719, 0.158124, 0.17292, 0.188094,
512  0.203673, 0.219697, 0.236201, 0.253208, 0.270727, 0.288784,
513  0.296181, 0.303707, 0.311404, 0.319342, 0.327628, 0.336416,
514  0.345907, 0.35633, 0.367923, 0.380968, 0.395965, 0.413866, 0.424377,
515  0.436366, 0.450442, 0.458506, 0.467375, 0.471171, 0.475126,
516  0.479254, 0.483568, 0.488052, 0.492639, 0.497232, 0.499557,
517  0.501993, 0.504598, 0.505838, 0.506697, 0.506742, 0.506649,
518  0.506536, 0.50641, 0.506281, 0.506156, 0.505924, 0.505541, 0.505047,
519  0.504219}};
520 
521  const double imomegaqnm21[8][107] = {{0.0743116, 0.0772659, 0.0791824, 0.0812815, 0.0822652, 0.082556,
522  0.0827684, 0.082926, 0.0830445, 0.0831347, 0.0833596, 0.0834304,
523  0.0834555, 0.0834714, 0.0834806, 0.0834917, 0.0835195, 0.0835507,
524  0.0835831, 0.0836156, 0.0836481, 0.0836804, 0.0837126, 0.083792,
525  0.0838704, 0.0840241, 0.0841737, 0.0843193, 0.0845994, 0.084865,
526  0.085117, 0.0853561, 0.0855831, 0.0857987, 0.0860035, 0.086198,
527  0.0863828, 0.0865584, 0.0867253, 0.086884, 0.087247, 0.0875662,
528  0.0878462, 0.0880906, 0.0883025, 0.088484, 0.088637, 0.0887628,
529  0.0888621, 0.0889354, 0.0889828, 0.0890037, 0.0889973, 0.0889623,
530  0.0888968, 0.0887983, 0.0886636, 0.0884885, 0.0882679, 0.0879952,
531  0.0876618, 0.0872571, 0.086767, 0.086173, 0.0854501, 0.0845642,
532  0.0834665, 0.0820852, 0.0814304, 0.0807035, 0.0798926, 0.0789827,
533  0.077955, 0.0767847, 0.0754394, 0.0738744, 0.072027, 0.0698043,
534  0.067061, 0.0635492, 0.0613721, 0.058791, 0.0556436, 0.0537759,
535  0.0516427, 0.0506978, 0.0496908, 0.0486136, 0.0474565, 0.0462084,
536  0.0448564, 0.0433879, 0.0426068, 0.0417939, 0.0409501, 0.0405173,
537  0.0400777, 0.0396319, 0.039542, 0.0394519, 0.0393616, 0.039271,
538  0.0391802, 0.0389974, 0.0388111, 0.038714, 0.0386091}, {0.258785,
539  0.258526, 0.258215, 0.257703, 0.257385, 0.257284, 0.25721, 0.257158,
540  0.257123, 0.257101, 0.257089, 0.257133, 0.257178, 0.257248,
541  0.257304, 0.257357, 0.257465, 0.257574, 0.257683, 0.257791,
542  0.257898, 0.258005, 0.258112, 0.258376, 0.258637, 0.259149,
543  0.259649, 0.260137, 0.261076, 0.261967, 0.262812, 0.263613,
544  0.264372, 0.265089, 0.265768, 0.26641, 0.267016, 0.267589, 0.26813,
545  0.26864, 0.269792, 0.270782, 0.271629, 0.272346, 0.272945, 0.273434,
546  0.273821, 0.274112, 0.274309, 0.274415, 0.27443, 0.274354,
547  0.274183, 0.273915, 0.273543, 0.273058, 0.272452, 0.271711,
548  0.270819, 0.269754, 0.268489, 0.266992, 0.265218, 0.263108,
549  0.260587, 0.257547, 0.253838, 0.249238, 0.247078, 0.244692,
550  0.242045, 0.239089, 0.235766, 0.231999, 0.227686, 0.222686, 0.2168,
551  0.209731, 0.201006, 0.189803, 0.18282, 0.174484, 0.164205, 0.158029,
552  0.150891, 0.1477, 0.14428, 0.140606, 0.136657, 0.132444, 0.128112,
553  0.124511, 0.123925, 0.123321, 0.12167, 0.121162, 0.120732, 0.12014,
554  0.120048, 0.119951, 0.119844, 0.119734, 0.119631, 0.119429,
555  0.119227, 0.119127, 0.119027}, {0.451082, 0.450126, 0.449946,
556  0.450393, 0.450836, 0.450954, 0.451016, 0.451037, 0.451032,
557  0.451015, 0.450927, 0.450953, 0.451028, 0.451151, 0.451242,
558  0.451336, 0.451538, 0.451736, 0.451932, 0.452129, 0.452326,
559  0.452521, 0.452716, 0.453201, 0.453683, 0.454634, 0.45557, 0.456489,
560  0.458275, 0.459989, 0.461626, 0.463185, 0.464665, 0.466067,
561  0.46739, 0.468636, 0.469808, 0.470906, 0.471935, 0.472897, 0.475022,
562  0.476783, 0.478216, 0.479352, 0.48022, 0.48084, 0.481231, 0.481407,
563  0.481377, 0.481149, 0.480726, 0.480109, 0.479294, 0.478277,
564  0.477047, 0.475592, 0.473893, 0.471929, 0.469669, 0.467076,
565  0.464104, 0.460691, 0.456761, 0.45221, 0.446903, 0.440653, 0.433196,
566  0.424144, 0.419951, 0.415358, 0.4103, 0.404693, 0.398434, 0.391383,
567  0.383355, 0.374094, 0.363227, 0.350188, 0.334044, 0.313093,
568  0.299808, 0.283583, 0.262719, 0.249472, 0.233119, 0.225306,
569  0.216483, 0.206365, 0.194563, 0.180538, 0.16345, 0.141483, 0.12731,
570  0.111596, 0.0954876, 0.0868316, 0.0774193, 0.066857, 0.0645541,
571  0.0621712, 0.0596988, 0.057125, 0.0544355, 0.0486318, 0.0420655,
572  0.0383765, 0.0343031}, {0.670736, 0.672092, 0.671812, 0.670663,
573  0.670549, 0.67073, 0.670927, 0.671078, 0.671164, 0.671189, 0.671021,
574  0.671075, 0.671219, 0.67131, 0.671427, 0.671572, 0.671807,
575  0.672062, 0.672309, 0.672557, 0.672808, 0.673057, 0.673305,
576  0.673929, 0.674552, 0.675799, 0.677043, 0.678283, 0.680743,
577  0.683166, 0.685536, 0.68784, 0.690067, 0.692205, 0.694247, 0.696187,
578  0.69802, 0.699744, 0.701359, 0.702865, 0.706165, 0.708833,
579  0.710915, 0.71246, 0.71351, 0.714105, 0.714277, 0.714053, 0.713452,
580  0.71249, 0.711176, 0.709516, 0.707509, 0.705148, 0.702423, 0.699317,
581  0.695803, 0.691851, 0.687416, 0.682445, 0.676867, 0.670592,
582  0.663504, 0.655451, 0.646227, 0.635554, 0.623036, 0.60809, 0.601244,
583  0.593791, 0.58563, 0.576638, 0.566651, 0.555455, 0.54276, 0.528156,
584  0.511038, 0.490465, 0.464847, 0.431189, 0.409563, 0.382936,
585  0.348824, 0.32773, 0.302947, 0.291759, 0.279694, 0.26659, 0.252176,
586  0.235931, 0.216835, 0.192946, 0.178198, 0.160681, 0.138951,
587  0.125667, 0.110911, 0.095128, 0.0917732, 0.0883219, 0.0847576,
588  0.0810612, 0.0772103, 0.0689279, 0.0595841, 0.0543422,
589  0.048559}, {0.910592, 0.910063, 0.91138, 0.911832, 0.911012,
590  0.911003, 0.911199, 0.911439, 0.911606, 0.91166, 0.911352, 0.911585,
591  0.911648, 0.911704, 0.911854, 0.911933, 0.912192, 0.912425,
592  0.912663, 0.912897, 0.913141, 0.913376, 0.913616, 0.91422, 0.91483,
593  0.916061, 0.917309, 0.918574, 0.921148, 0.923769, 0.92642, 0.929083,
594  0.931738, 0.934365, 0.936941, 0.939446, 0.941862, 0.944173,
595  0.946367, 0.948436, 0.953025, 0.956761, 0.959656, 0.961747, 0.96308,
596  0.963701, 0.963651, 0.962967, 0.96168, 0.959815, 0.957389,
597  0.954417, 0.950902, 0.946845, 0.942236, 0.937057, 0.931283,
598  0.924873, 0.917775, 0.909918, 0.901208, 0.891524, 0.880707,
599  0.868545, 0.854753, 0.838939, 0.820547, 0.798756, 0.788822,
600  0.778034, 0.76625, 0.75329, 0.738922, 0.722836, 0.704612, 0.683652,
601  0.659084, 0.629562, 0.592913, 0.54542, 0.515651, 0.480063, 0.436051,
602  0.409334, 0.377864, 0.363486, 0.347803, 0.330563, 0.311454,
603  0.290066, 0.265802, 0.237412, 0.220683, 0.201065, 0.17693, 0.162373,
604  0.145371, 0.124789, 0.120176, 0.115422, 0.110541, 0.105527,
605  0.100358, 0.0893955, 0.0771778, 0.0703585, 0.0628494}, {1.16313,
606  1.16205, 1.16102, 1.16236, 1.1618, 1.16155, 1.16165, 1.16191,
607  1.16212, 1.16217, 1.16185, 1.16214, 1.162, 1.16222, 1.16228, 1.1624,
608  1.16261, 1.16279, 1.163, 1.16321, 1.16342, 1.16362, 1.16384,
609  1.16436, 1.16489, 1.16598, 1.1671, 1.16824, 1.1706, 1.17306,
610  1.17562, 1.17826, 1.18098, 1.18376, 1.18658, 1.18941, 1.19222,
611  1.19499, 1.19769, 1.20029, 1.20624, 1.21127, 1.21528, 1.21824,
612  1.22017, 1.2211, 1.22105, 1.22006, 1.21814, 1.21533, 1.21164,
613  1.20711, 1.20176, 1.19561, 1.18868, 1.18098, 1.17251, 1.16324,
614  1.15314, 1.14213, 1.13009, 1.11686, 1.10224, 1.08592, 1.06753,
615  1.04652, 1.02214, 0.993243, 0.980058, 0.965724, 0.950047, 0.932779,
616  0.913601, 0.892095, 0.867699, 0.839644, 0.806856, 0.767797,
617  0.720146, 0.659944, 0.622848, 0.578732, 0.524237, 0.491317,
618  0.452927, 0.435542, 0.416661, 0.395943, 0.372912, 0.346898,
619  0.316949, 0.28167, 0.261342, 0.238436, 0.211307, 0.195088, 0.176156,
620  0.153337, 0.148132, 0.142654, 0.136869, 0.130747, 0.124273,
621  0.110319, 0.0949385, 0.0864639, 0.0771851}, {1.41428, 1.41604,
622  1.4156, 1.41536, 1.4156, 1.41524, 1.41519, 1.41543, 1.41565,
623  1.41568, 1.41551, 1.41554, 1.41563, 1.41566, 1.41579, 1.41591,
624  1.41608, 1.41624, 1.41643, 1.41663, 1.4168, 1.417, 1.41717, 1.41765,
625  1.41813, 1.41911, 1.42011, 1.42114, 1.42328, 1.42554, 1.42792,
626  1.43041, 1.43303, 1.43576, 1.4386, 1.44152, 1.44453, 1.44758,
627  1.45065, 1.45369, 1.46099, 1.46752, 1.473, 1.47733, 1.48042,
628  1.48226, 1.48282, 1.48207, 1.47997, 1.47646, 1.4715, 1.46505,
629  1.45715, 1.44791, 1.43752, 1.42619, 1.41412, 1.4014, 1.38801,
630  1.37384, 1.35872, 1.34237, 1.32445, 1.30456, 1.28213, 1.25643,
631  1.22645, 1.19065, 1.17422, 1.15628, 1.13659, 1.11481, 1.09053,
632  1.06323, 1.03225, 0.996712, 0.955487, 0.906959, 0.848541, 0.775494,
633  0.730792, 0.678016, 0.613349, 0.574379, 0.528885, 0.508284,
634  0.485946, 0.461517, 0.434493, 0.404108, 0.369135, 0.327547,
635  0.303278, 0.275875, 0.244209, 0.225953, 0.204982, 0.179727,
636  0.173965, 0.167908, 0.161519, 0.154752, 0.147552, 0.131555,
637  0.113035, 0.102763, 0.09161}, {1.6695, 1.6684, 1.66944, 1.66866,
638  1.66927, 1.66897, 1.66882, 1.66899, 1.6692, 1.66921, 1.66919,
639  1.66906, 1.66925, 1.66933, 1.66938, 1.66941, 1.6696, 1.66977,
640  1.66995, 1.67014, 1.67031, 1.67048, 1.67066, 1.6711, 1.67155,
641  1.67246, 1.6734, 1.67436, 1.67635, 1.67846, 1.68069, 1.68303,
642  1.68552, 1.68814, 1.69089, 1.69379, 1.69681, 1.69996, 1.70322,
643  1.70655, 1.71494, 1.72293, 1.73008, 1.73612, 1.7409, 1.74437,
644  1.74645, 1.74707, 1.74612, 1.74337, 1.73845, 1.73073, 1.71933,
645  1.70384, 1.68568, 1.6674, 1.65022, 1.63402, 1.61822, 1.60219,
646  1.58534, 1.56716, 1.54712, 1.52462, 1.49894, 1.46917, 1.43397,
647  1.39142, 1.37171, 1.35009, 1.32623, 1.29974, 1.27014, 1.23683,
648  1.19912, 1.15609, 1.10649, 1.04841, 0.97878, 0.892317, 0.839828,
649  0.778168, 0.702974, 0.657884, 0.605411, 0.581667, 0.555906,
650  0.527711, 0.496517, 0.46151, 0.421398, 0.373867, 0.346042, 0.314367,
651  0.277467, 0.25637, 0.232725, 0.204918, 0.198597, 0.191947,
652  0.184925, 0.177485, 0.169568, 0.151985, 0.131247, 0.119312,
653  0.106197}};
654 
655  /* 2, 0 mode */
656  const double reomegaqnm20[8][107] = {{0.4247721439, 0.4247863113, 0.4247985972, 0.4248325877,
657  0.4248584259, 0.4248659433, 0.4248700764, 0.4248712306,
658  0.4248698326, 0.4248662798, 0.4248267198, 0.4247676547,
659  0.4247005042, 0.424557753, 0.4244119723, 0.4242658712, 0.4239745379,
660  0.4236846241, 0.4233960302, 0.4231086991, 0.4228226189,
661  0.4225377956, 0.4222542405, 0.4215509794, 0.420855887, 0.4194906865,
662  0.4181592598, 0.4168617799, 0.4143677184, 0.4120044663,
663  0.4097658509, 0.40764485, 0.4056343086, 0.4037273098, 0.4019173509,
664  0.4001984114, 0.3985649653, 0.3970119631, 0.3955348022,
665  0.3941292897, 0.3909047276, 0.3880539184, 0.3855360484, 0.383318276,
666  0.3813740024, 0.3796815867, 0.3782233906, 0.3769850625,
667  0.3759550001, 0.3751239445, 0.3744846758, 0.3740317881,
668  0.3737615278, 0.3736716844, 0.3737615278, 0.3740317881,
669  0.3744846758, 0.3751239445, 0.3759550001, 0.3769850625,
670  0.3782233906, 0.3796815867, 0.3813740024, 0.383318276, 0.3855360484,
671  0.3880539184, 0.3909047276, 0.3941292897, 0.3955348022,
672  0.3970119631, 0.3985649653, 0.4001984114, 0.4019173509,
673  0.4037273098, 0.4056343086, 0.40764485, 0.4097658509, 0.4120044663,
674  0.4143677184, 0.4168617799, 0.4181592598, 0.4194906865, 0.420855887,
675  0.4215509794, 0.4222542405, 0.4225377956, 0.4228226189,
676  0.4231086991, 0.4233960302, 0.4236846241, 0.4239745379,
677  0.4242658712, 0.4244119723, 0.424557753, 0.4247005042, 0.4247676547,
678  0.4248267198, 0.4248662798, 0.4248698326, 0.4248712306,
679  0.4248700764, 0.4248659433, 0.4248584259, 0.4248325877,
680  0.4247985972, 0.4247863113, 0.4247721439}, {0.4022595044,
681  0.4025176372, 0.4026385253, 0.402714655, 0.4027157267, 0.4027081834,
682  0.4026990446, 0.4026895027, 0.4026801424, 0.4026712204,
683  0.4026338048, 0.4026034279, 0.402574986, 0.4025177609, 0.4024587579,
684  0.4023983315, 0.4022740572, 0.402145468, 0.4020126089,
685  0.4018755539, 0.4017344007, 0.4015892521, 0.401440212, 0.4010512734,
686  0.4006403236, 0.3997591492, 0.3988102405, 0.397806802,
687  0.3956841928, 0.3934728792, 0.3912313515, 0.3889989525,
688  0.3868012743, 0.3846545743, 0.3825688955, 0.3805501632,
689  0.3786015741, 0.3767245157, 0.3749191785, 0.3731849675,
690  0.3691526314, 0.3655335386, 0.3623007731, 0.3594283374,
691  0.3568927266, 0.3546733772, 0.3527526583, 0.3511156895,
692  0.3497501098, 0.348645853, 0.34779495, 0.3471913675, 0.3468308827,
693  0.3467109969, 0.3468308827, 0.3471913675, 0.34779495, 0.348645853,
694  0.3497501098, 0.3511156895, 0.3527526583, 0.3546733772,
695  0.3568927266, 0.3594283374, 0.3623007731, 0.3655335386,
696  0.3691526314, 0.3731849675, 0.3749191785, 0.3767245157,
697  0.3786015741, 0.3805501632, 0.3825688955, 0.3846545743,
698  0.3868012743, 0.3889989525, 0.3912313515, 0.3934728792,
699  0.3956841928, 0.397806802, 0.3988102405, 0.3997591492, 0.4006403236,
700  0.4010512734, 0.401440212, 0.4015892521, 0.4017344007,
701  0.4018755539, 0.4020126089, 0.402145468, 0.4022740572, 0.4023983315,
702  0.4024587579, 0.4025177609, 0.402574986, 0.4026034279,
703  0.4026338048, 0.4026712204, 0.4026801424, 0.4026895027,
704  0.4026990446, 0.4027081834, 0.4027157267, 0.402714655, 0.4026385253,
705  0.4025176372, 0.4022595044}, {0.3587631202, 0.3586562755,
706  0.3585571621, 0.3584767648, 0.3584871698, 0.3585031359, 0.358520196,
707  0.3585364516, 0.3585511443, 0.3585641498, 0.3586123314,
708  0.3586525789, 0.3586945293, 0.358781211, 0.3588663108, 0.3589493444,
709  0.3591108827, 0.3592664061, 0.3594155854, 0.3595583252,
710  0.3596945387, 0.3598241205, 0.3599469676, 0.3602240117,
711  0.3604570682, 0.3607872733, 0.3609323176, 0.360891042, 0.3602774401,
712  0.3590639204, 0.3574099949, 0.3554578534, 0.3533158689,
713  0.3510620393, 0.3487514511, 0.3464228554, 0.3441035438,
714  0.3418127732, 0.3395641339, 0.337367187, 0.332139771, 0.3273292258,
715  0.3229529922, 0.3190100679, 0.3154913069, 0.3123844448,
716  0.3096766084, 0.3073555756, 0.3054103975, 0.30383169, 0.3026117559,
717  0.3017446212, 0.3012260348, 0.3010534545, 0.3012260348,
718  0.3017446212, 0.3026117559, 0.30383169, 0.3054103975, 0.3073555756,
719  0.3096766084, 0.3123844448, 0.3154913069, 0.3190100679,
720  0.3229529922, 0.3273292258, 0.332139771, 0.337367187, 0.3395641339,
721  0.3418127732, 0.3441035438, 0.3464228554, 0.3487514511,
722  0.3510620393, 0.3533158689, 0.3554578534, 0.3574099949,
723  0.3590639204, 0.3602774401, 0.360891042, 0.3609323176, 0.3607872733,
724  0.3604570682, 0.3602240117, 0.3599469676, 0.3598241205,
725  0.3596945387, 0.3595583252, 0.3594155854, 0.3592664061,
726  0.3591108827, 0.3589493444, 0.3588663108, 0.358781211, 0.3586945293,
727  0.3586525789, 0.3586123314, 0.3585641498, 0.3585511443,
728  0.3585364516, 0.358520196, 0.3585031359, 0.3584871698, 0.3584767648,
729  0.3585571621, 0.3586562755, 0.3587631202}, {0.2955931981,
730  0.2956911763, 0.2959013663, 0.2960902804, 0.2960805341, 0.296070603,
731  0.2960715835, 0.2960841755, 0.2961057593, 0.2961328408,
732  0.2962715691, 0.2963767257, 0.2964791366, 0.2967001479,
733  0.2969184558, 0.2971346512, 0.2975687544, 0.2980006488,
734  0.2984308575, 0.2988593119, 0.2992856405, 0.2997097563,
735  0.3001315265, 0.3011744976, 0.3021986114, 0.3041793062, 0.306042046,
736  0.30776228, 0.3106733357, 0.3125253856, 0.3131974762, 0.3128916813,
737  0.311865866, 0.3103333453, 0.3084523863, 0.306337079, 0.304069452,
738  0.301708867, 0.2992986826, 0.2968708711, 0.2908660077, 0.2851210461,
739  0.2797541132, 0.2748239607, 0.2703586352, 0.2663699371,
740  0.2628610658, 0.2598308118, 0.2572759173, 0.25519243, 0.2535764879,
741  0.2524247751, 0.2517347842, 0.2515049622, 0.2517347842,
742  0.2524247751, 0.2535764879, 0.25519243, 0.2572759173, 0.2598308118,
743  0.2628610658, 0.2663699371, 0.2703586352, 0.2748239607,
744  0.2797541132, 0.2851210461, 0.2908660077, 0.2968708711,
745  0.2992986826, 0.301708867, 0.304069452, 0.306337079, 0.3084523863,
746  0.3103333453, 0.311865866, 0.3128916813, 0.3131974762, 0.3125253856,
747  0.3106733357, 0.30776228, 0.306042046, 0.3041793062, 0.3021986114,
748  0.3011744976, 0.3001315265, 0.2997097563, 0.2992856405,
749  0.2988593119, 0.2984308575, 0.2980006488, 0.2975687544,
750  0.2971346512, 0.2969184558, 0.2967001479, 0.2964791366,
751  0.2963767257, 0.2962715691, 0.2961328408, 0.2961057593,
752  0.2960841755, 0.2960715835, 0.296070603, 0.2960805341, 0.2960902804,
753  0.2959013663, 0.2956911763, 0.2955931981}, {0.2265759655,
754  0.2263134666, 0.2259201107, 0.226033261, 0.2263091114, 0.2263241376,
755  0.2262966437, 0.2262653635, 0.2262534991, 0.2262677342,
756  0.2264910301, 0.226604597, 0.2267226381, 0.2270204493, 0.2272816677,
757  0.2275628966, 0.2281119757, 0.2286682789, 0.2292233708,
758  0.2297821291, 0.2303431133, 0.2309055008, 0.2314706692, 0.232891702,
759  0.2343288764, 0.2372425752, 0.2401516712, 0.2432064357,
760  0.2490028794, 0.2551643774, 0.2609821536, 0.2649179918,
761  0.2670263535, 0.2677578325, 0.2675054998, 0.2665561482,
762  0.2651128405, 0.2633200598, 0.2612820783, 0.2590753625,
763  0.2531607164, 0.2470884185, 0.2411635985, 0.2355561825,
764  0.2303648137, 0.2256486007, 0.2214438733, 0.2177734415,
765  0.2146518936, 0.2120886995, 0.2100900575, 0.2086599993,
766  0.2078010452, 0.2075145798, 0.2078010452, 0.2086599993,
767  0.2100900575, 0.2120886995, 0.2146518936, 0.2177734415,
768  0.2214438733, 0.2256486007, 0.2303648137, 0.2355561825,
769  0.2411635985, 0.2470884185, 0.2531607164, 0.2590753625,
770  0.2612820783, 0.2633200598, 0.2651128405, 0.2665561482,
771  0.2675054998, 0.2677578325, 0.2670263535, 0.2649179918,
772  0.2609821536, 0.2551643774, 0.2490028794, 0.2432064357,
773  0.2401516712, 0.2372425752, 0.2343288764, 0.232891702, 0.2314706692,
774  0.2309055008, 0.2303431133, 0.2297821291, 0.2292233708,
775  0.2286682789, 0.2281119757, 0.2275628966, 0.2272816677,
776  0.2270204493, 0.2267226381, 0.226604597, 0.2264910301, 0.2262677342,
777  0.2262534991, 0.2262653635, 0.2262966437, 0.2263241376,
778  0.2263091114, 0.226033261, 0.2259201107, 0.2263134666,
779  0.2265759655}, {0.162467714, 0.1634934248, 0.1638277421,
780  0.1630968281, 0.1635010049, 0.1636759976, 0.1636803676,
781  0.1635845741, 0.163488315, 0.1634553864, 0.1638050393, 0.163791891,
782  0.1639844275, 0.1642094594, 0.1645146073, 0.1647460864, 0.165288291,
783  0.1658098185, 0.1663401778, 0.1668757036, 0.1674133259,
784  0.1679475306, 0.1685023684, 0.1698847398, 0.1712487246,
785  0.1741108365, 0.1768267467, 0.1804631771, 0.18630515, 0.1935771765,
786  0.1987452707, 0.2093226733, 0.2181547856, 0.2237317269,
787  0.2269036596, 0.2284118203, 0.228756399, 0.2282723907, 0.2271898972,
788  0.2256715181, 0.2206696442, 0.2147729564, 0.2085926425,
789  0.2024747303, 0.1966287474, 0.1911890101, 0.1862461282,
790  0.1818640842, 0.178089795, 0.1749585446, 0.1724970437, 0.1707251041,
791  0.1696565048, 0.1692994034, 0.1696565048, 0.1707251041,
792  0.1724970437, 0.1749585446, 0.178089795, 0.1818640842, 0.1862461282,
793  0.1911890101, 0.1966287474, 0.2024747303, 0.2085926425,
794  0.2147729564, 0.2206696442, 0.2256715181, 0.2271898972,
795  0.2282723907, 0.228756399, 0.2284118203, 0.2269036596, 0.2237317269,
796  0.2181547856, 0.2093226733, 0.1987452707, 0.1935771765, 0.18630515,
797  0.1804631771, 0.1768267467, 0.1741108365, 0.1712487246,
798  0.1698847398, 0.1685023684, 0.1679475306, 0.1674133259,
799  0.1668757036, 0.1663401778, 0.1658098185, 0.165288291, 0.1647460864,
800  0.1645146073, 0.1642094594, 0.1639844275, 0.163791891,
801  0.1638050393, 0.1634553864, 0.163488315, 0.1635845741, 0.1636803676,
802  0.1636759976, 0.1635010049, 0.1630968281, 0.1638277421,
803  0.1634934248, 0.162467714}, {0.1150947175, 0.1136995811,
804  0.1144317617, 0.1145108329, 0.1143223733, 0.1147075752,
805  0.1148529865, 0.1147211083, 0.1145101899, 0.1144146127,
806  0.1148757124, 0.1147623558, 0.1150527078, 0.1152162011,
807  0.1153522163, 0.1156670599, 0.1160937605, 0.1165085059,
808  0.1169521137, 0.1174121457, 0.1178333408, 0.1183089991,
809  0.1188779907, 0.1199614936, 0.1212661221, 0.122907988, 0.1252696237,
810  0.1300527498, 0.136371485, 0.1365743504, 0.1502937555,
811  0.1499042247, 0.1576063359, 0.1737999474, 0.1840565193,
812  0.1901954481, 0.1937178657, 0.1954878977, 0.1960322476,
813  0.1956928755, 0.1923495252, 0.1869716004, 0.1806432357,
814  0.1739650338, 0.167302038, 0.1608944901, 0.1549126532, 0.1494856455,
815  0.1447169546, 0.1406923509, 0.1374833382, 0.1351476926,
816  0.1337284518, 0.1332523443, 0.1337284518, 0.1351476926,
817  0.1374833382, 0.1406923509, 0.1447169546, 0.1494856455,
818  0.1549126532, 0.1608944901, 0.167302038, 0.1739650338, 0.1806432357,
819  0.1869716004, 0.1923495252, 0.1956928755, 0.1960322476,
820  0.1954878977, 0.1937178657, 0.1901954481, 0.1840565193,
821  0.1737999474, 0.1576063359, 0.1499042247, 0.1502937555,
822  0.1365743504, 0.136371485, 0.1300527498, 0.1252696237, 0.122907988,
823  0.1212661221, 0.1199614936, 0.1188779907, 0.1183089991,
824  0.1178333408, 0.1174121457, 0.1169521137, 0.1165085059,
825  0.1160937605, 0.1156670599, 0.1153522163, 0.1152162011,
826  0.1150527078, 0.1147623558, 0.1148757124, 0.1144146127,
827  0.1145101899, 0.1147211083, 0.1148529865, 0.1147075752,
828  0.1143223733, 0.1145108329, 0.1144317617, 0.1136995811,
829  0.1150947175}, {0.07824594797, 0.07897765236, 0.07781656751,
830  0.07894919224, 0.07811549687, 0.07852555182, 0.0788734926,
831  0.07877853969, 0.0784682439, 0.07832233515, 0.0787241668,
832  0.07887758159, 0.07876636539, 0.07904172864, 0.07931185989,
833  0.07935962619, 0.07970963786, 0.08015321455, 0.08049831171,
834  0.08098647273, 0.08113113975, 0.08171084479, 0.08245975407,
835  0.08198058103, 0.08310489532, 0.08636947463, 0.08742026462,
836  0.09301825285, 0.09708260702, 0.1044921151, 0.09410791221,
837  0.1163296909, 0.1194610774, 0.1071758642, 0.131059966, 0.1479210288,
838  0.1575029326, 0.1631326584, 0.1662931627, 0.1677797021,
839  0.1669344646, 0.162339839, 0.1558069565, 0.1482827082, 0.1403267639,
840  0.1323069592, 0.1244931384, 0.1171075385, 0.1103537661,
841  0.1044314061, 0.09954024628, 0.0958728709, 0.09359533547,
842  0.09282239791, 0.09359533547, 0.0958728709, 0.09954024628,
843  0.1044314061, 0.1103537661, 0.1171075385, 0.1244931384,
844  0.1323069592, 0.1403267639, 0.1482827082, 0.1558069565, 0.162339839,
845  0.1669344646, 0.1677797021, 0.1662931627, 0.1631326584,
846  0.1575029326, 0.1479210288, 0.131059966, 0.1071758642, 0.1194610774,
847  0.1163296909, 0.09410791221, 0.1044921151, 0.09708260702,
848  0.09301825285, 0.08742026462, 0.08636947463, 0.08310489532,
849  0.08198058103, 0.08245975407, 0.08171084479, 0.08113113975,
850  0.08098647273, 0.08049831171, 0.08015321455, 0.07970963786,
851  0.07935962619, 0.07931185989, 0.07904172864, 0.07876636539,
852  0.07887758159, 0.0787241668, 0.07832233515, 0.0784682439,
853  0.07877853969, 0.0788734926, 0.07852555182, 0.07811549687,
854  0.07894919224, 0.07781656751, 0.07897765236, 0.07824594797}};
855  const double imomegaqnm20[8][107] = {{0.06956111286, 0.07057665227, 0.07109516199, 0.07156667263,
856  0.07176004502, 0.0718151936, 0.07185564256, 0.071886392,
857  0.07191058835, 0.07193027264, 0.07199608801, 0.07204342275,
858  0.07208725348, 0.07217445117, 0.07226259362, 0.07235103048,
859  0.07252698509, 0.07270070919, 0.07287193971, 0.07304067834,
860  0.07320697034, 0.0733708643, 0.07353240627, 0.07392625431,
861  0.07430631954, 0.07502754477, 0.07570073722, 0.076330175,
862  0.07747297842, 0.07848269543, 0.07938083725, 0.08018464701,
863  0.08090799941, 0.08156214052, 0.08215626528, 0.08269795953,
864  0.08319353674, 0.08364829544, 0.08406671695, 0.08445261881,
865  0.0852954969, 0.08599466937, 0.08657885062, 0.08706905134,
866  0.0874809756, 0.08782655405, 0.08811495632, 0.08835327799,
867  0.08854701612, 0.08870040374, 0.08881664656, 0.08889809023,
868  0.08894633586, 0.08896231569, 0.08894633586, 0.08889809023,
869  0.08881664656, 0.08870040374, 0.08854701612, 0.08835327799,
870  0.08811495632, 0.08782655405, 0.0874809756, 0.08706905134,
871  0.08657885062, 0.08599466937, 0.0852954969, 0.08445261881,
872  0.08406671695, 0.08364829544, 0.08319353674, 0.08269795953,
873  0.08215626528, 0.08156214052, 0.08090799941, 0.08018464701,
874  0.07938083725, 0.07848269543, 0.07747297842, 0.076330175,
875  0.07570073722, 0.07502754477, 0.07430631954, 0.07392625431,
876  0.07353240627, 0.0733708643, 0.07320697034, 0.07304067834,
877  0.07287193971, 0.07270070919, 0.07252698509, 0.07235103048,
878  0.07226259362, 0.07217445117, 0.07208725348, 0.07204342275,
879  0.07199608801, 0.07193027264, 0.07191058835, 0.071886392,
880  0.07185564256, 0.0718151936, 0.07176004502, 0.07156667263,
881  0.07109516199, 0.07057665227, 0.06956111286}, {0.2185411094,
882  0.2185862168, 0.2185760597, 0.2185502469, 0.2185551556,
883  0.2185670597, 0.2185832072, 0.2186023833, 0.2186236698,
884  0.2186463949, 0.2187689601, 0.21889384, 0.219017296, 0.2192613118,
885  0.2195038699, 0.219745778, 0.2202276534, 0.2207065981, 0.2211824488,
886  0.2216551307, 0.2221245734, 0.2225907052, 0.2230534566,
887  0.2241951244, 0.2253143564, 0.2274827082, 0.2295545126,
888  0.2315282566, 0.2351860943, 0.2384795534, 0.2414444658,
889  0.2441189781, 0.2465387707, 0.2487354182, 0.2507361819,
890  0.2525643629, 0.2542398214, 0.2557795018, 0.2571979034,
891  0.2585074823, 0.2613723978, 0.2637535915, 0.2657465547,
892  0.2674214198, 0.2688307276, 0.2700144584, 0.2710033792,
893  0.2718213228, 0.2724867699, 0.273013963, 0.2734136955, 0.2736938697,
894  0.2738598819, 0.2739148753, 0.2738598819, 0.2736938697,
895  0.2734136955, 0.273013963, 0.2724867699, 0.2718213228, 0.2710033792,
896  0.2700144584, 0.2688307276, 0.2674214198, 0.2657465547,
897  0.2637535915, 0.2613723978, 0.2585074823, 0.2571979034,
898  0.2557795018, 0.2542398214, 0.2525643629, 0.2507361819,
899  0.2487354182, 0.2465387707, 0.2441189781, 0.2414444658,
900  0.2384795534, 0.2351860943, 0.2315282566, 0.2295545126,
901  0.2274827082, 0.2253143564, 0.2241951244, 0.2230534566,
902  0.2225907052, 0.2221245734, 0.2216551307, 0.2211824488,
903  0.2207065981, 0.2202276534, 0.219745778, 0.2195038699, 0.2192613118,
904  0.219017296, 0.21889384, 0.2187689601, 0.2186463949, 0.2186236698,
905  0.2186023833, 0.2185832072, 0.2185670597, 0.2185551556,
906  0.2185502469, 0.2185760597, 0.2185862168,
907  0.2185411094}, {0.3746283234, 0.3744760286, 0.3744655082,
908  0.3745713459, 0.3746804416, 0.3747239651, 0.3747616125,
909  0.3747951976, 0.3748262688, 0.3748559959, 0.3750036033,
910  0.3751595179, 0.3753190966, 0.3756378976, 0.3759558332,
911  0.3762746082, 0.3769149521, 0.3775582079, 0.3782042318,
912  0.3788529456, 0.3795041978, 0.3801578285, 0.3808136809,
913  0.3824619707, 0.3841204813, 0.3874566765, 0.3907983942,
914  0.3941199491, 0.4005962971, 0.4067113438, 0.4123795696,
915  0.4175861754, 0.422352588, 0.426714443, 0.4307106786, 0.4343787455,
916  0.4377527783, 0.4408631174, 0.4437364171, 0.4463959791,
917  0.4522370945, 0.4571173234, 0.4612213527, 0.4646855141,
918  0.4676122255, 0.4700795615, 0.47214769, 0.4738632779, 0.4752625561,
919  0.4763734789, 0.4772172535, 0.4778094206, 0.4781606008,
920  0.4782769831, 0.4781606008, 0.4778094206, 0.4772172535,
921  0.4763734789, 0.4752625561, 0.4738632779, 0.47214769, 0.4700795615,
922  0.4676122255, 0.4646855141, 0.4612213527, 0.4571173234,
923  0.4522370945, 0.4463959791, 0.4437364171, 0.4408631174,
924  0.4377527783, 0.4343787455, 0.4307106786, 0.426714443, 0.422352588,
925  0.4175861754, 0.4123795696, 0.4067113438, 0.4005962971,
926  0.3941199491, 0.3907983942, 0.3874566765, 0.3841204813,
927  0.3824619707, 0.3808136809, 0.3801578285, 0.3795041978,
928  0.3788529456, 0.3782042318, 0.3775582079, 0.3769149521,
929  0.3762746082, 0.3759558332, 0.3756378976, 0.3753190966,
930  0.3751595179, 0.3750036033, 0.3748559959, 0.3748262688,
931  0.3747951976, 0.3747616125, 0.3747239651, 0.3746804416,
932  0.3745713459, 0.3744655082, 0.3744760286,
933  0.3746283234}, {0.5488977566, 0.5492725578, 0.5493796167,
934  0.5493030521, 0.5492800515, 0.5493081779, 0.5493493533,
935  0.5493946353, 0.549438419, 0.5494780738, 0.5496229054, 0.5497549686,
936  0.5499025591, 0.5501989882, 0.5504901744, 0.5507853393,
937  0.5513807914, 0.5519818189, 0.552589775, 0.5532041749, 0.5538251797,
938  0.5544529382, 0.5550874672, 0.5567036937, 0.5583633611,
939  0.5618146957, 0.5654450115, 0.5692386679, 0.5773386388,
940  0.5859421423, 0.5945472028, 0.602787763, 0.6105064194, 0.6176644895,
941  0.624277053, 0.6303804075, 0.6360171698, 0.641229749, 0.6460576806,
942  0.6505367243, 0.6604082105, 0.6686938222, 0.6756913514,
943  0.6816215439, 0.6866504101, 0.6909045159, 0.6944813958,
944  0.6974567098, 0.6998892223, 0.7018243015, 0.7032963922,
945  0.7043307557, 0.7049446682, 0.7051482024, 0.7049446682,
946  0.7043307557, 0.7032963922, 0.7018243015, 0.6998892223,
947  0.6974567098, 0.6944813958, 0.6909045159, 0.6866504101,
948  0.6816215439, 0.6756913514, 0.6686938222, 0.6604082105,
949  0.6505367243, 0.6460576806, 0.641229749, 0.6360171698, 0.6303804075,
950  0.624277053, 0.6176644895, 0.6105064194, 0.602787763, 0.5945472028,
951  0.5859421423, 0.5773386388, 0.5692386679, 0.5654450115,
952  0.5618146957, 0.5583633611, 0.5567036937, 0.5550874672,
953  0.5544529382, 0.5538251797, 0.5532041749, 0.552589775, 0.5519818189,
954  0.5513807914, 0.5507853393, 0.5504901744, 0.5501989882,
955  0.5499025591, 0.5497549686, 0.5496229054, 0.5494780738, 0.549438419,
956  0.5493946353, 0.5493493533, 0.5493081779, 0.5492800515,
957  0.5493030521, 0.5493796167, 0.5492725578,
958  0.5488977566}, {0.7501379784, 0.7495636806, 0.749650308,
959  0.7501258019, 0.7500613683, 0.7499927446, 0.7499667401, 0.749986257,
960  0.7500353707, 0.7500943083, 0.7502378208, 0.7502955686,
961  0.7504262429, 0.7506329733, 0.7508454096, 0.7510636293,
962  0.7514901194, 0.7519267005, 0.7523658758, 0.75281185, 0.7532615237,
963  0.7537170118, 0.7541777199, 0.7553533494, 0.7565672969,
964  0.7591011388, 0.7618191441, 0.7646738706, 0.771240475, 0.7783465723,
965  0.7875759366, 0.7980345082, 0.8085705185, 0.8186647248,
966  0.8281387322, 0.8369567431, 0.8451396344, 0.8527290961,
967  0.8597724928, 0.8663164947, 0.8807666598, 0.8929239587,
968  0.9032139277, 0.9119531958, 0.9193796679, 0.9256743556,
969  0.9309764881, 0.9353939337, 0.9390104311, 0.9418906437,
970  0.9440837035, 0.9456256811, 0.946541273, 0.9468448909, 0.946541273,
971  0.9456256811, 0.9440837035, 0.9418906437, 0.9390104311,
972  0.9353939337, 0.9309764881, 0.9256743556, 0.9193796679,
973  0.9119531958, 0.9032139277, 0.8929239587, 0.8807666598,
974  0.8663164947, 0.8597724928, 0.8527290961, 0.8451396344,
975  0.8369567431, 0.8281387322, 0.8186647248, 0.8085705185,
976  0.7980345082, 0.7875759366, 0.7783465723, 0.771240475, 0.7646738706,
977  0.7618191441, 0.7591011388, 0.7565672969, 0.7553533494,
978  0.7541777199, 0.7537170118, 0.7532615237, 0.75281185, 0.7523658758,
979  0.7519267005, 0.7514901194, 0.7510636293, 0.7508454096,
980  0.7506329733, 0.7504262429, 0.7502955686, 0.7502378208,
981  0.7500943083, 0.7500353707, 0.749986257, 0.7499667401, 0.7499927446,
982  0.7500613683, 0.7501258019, 0.749650308, 0.7495636806,
983  0.7501379784}, {0.9742529776, 0.9747874524, 0.9741123398,
984  0.9741101898, 0.9745054107, 0.9743713094, 0.9742131924,
985  0.9741459996, 0.9741878531, 0.9742927333, 0.9744241227,
986  0.9744440584, 0.9745998745, 0.9746798313, 0.9748508069,
987  0.9749764636, 0.9752738201, 0.9755817532, 0.9758699637,
988  0.9761776339, 0.9764736452, 0.9767861418, 0.9770899129,
989  0.9778706747, 0.9786413703, 0.9802309584, 0.982150519, 0.9839171716,
990  0.987227465, 0.9938892699, 0.9973348177, 1.002960092, 1.013708296,
991  1.025861928, 1.037903138, 1.049355648, 1.060088661, 1.07009284,
992  1.079402597, 1.088066636, 1.107231852, 1.123387254, 1.137086935,
993  1.148745393, 1.158673191, 1.167105446, 1.174222093, 1.180161946,
994  1.185032451, 1.188916455, 1.191876898, 1.193960032, 1.195197574,
995  1.195608054, 1.195197574, 1.193960032, 1.191876898, 1.188916455,
996  1.185032451, 1.180161946, 1.174222093, 1.167105446, 1.158673191,
997  1.148745393, 1.137086935, 1.123387254, 1.107231852, 1.088066636,
998  1.079402597, 1.07009284, 1.060088661, 1.049355648, 1.037903138,
999  1.025861928, 1.013708296, 1.002960092, 0.9973348177, 0.9938892699,
1000  0.987227465, 0.9839171716, 0.982150519, 0.9802309584, 0.9786413703,
1001  0.9778706747, 0.9770899129, 0.9767861418, 0.9764736452,
1002  0.9761776339, 0.9758699637, 0.9755817532, 0.9752738201,
1003  0.9749764636, 0.9748508069, 0.9746798313, 0.9745998745,
1004  0.9744440584, 0.9744241227, 0.9742927333, 0.9741878531,
1005  0.9741459996, 0.9742131924, 0.9743713094, 0.9745054107,
1006  0.9741101898, 0.9741123398, 0.9747874524,
1007  0.9742529776}, {1.211526857, 1.211922483, 1.212758151, 1.211726992,
1008  1.212482465, 1.212475394, 1.212205486, 1.212000716, 1.212018349,
1009  1.212199008, 1.212212997, 1.212444728, 1.212370608, 1.2125862,
1010  1.212619732, 1.212746897, 1.212984684, 1.213207534, 1.213402392,
1011  1.213636737, 1.213847925, 1.214157158, 1.214311053, 1.21508082,
1012  1.215773219, 1.216721426, 1.218690906, 1.219600693, 1.221394824,
1013  1.223150892, 1.228953387, 1.236823174, 1.230978076, 1.238359914,
1014  1.251235241, 1.264746546, 1.277799572, 1.290112987, 1.301635176,
1015  1.312389501, 1.33624286, 1.356406755, 1.373555087, 1.388197376,
1016  1.400713453, 1.411387828, 1.420435218, 1.428018603, 1.434261866,
1017  1.439258803, 1.443079447, 1.445774471, 1.447378225, 1.447910632,
1018  1.447378225, 1.445774471, 1.443079447, 1.439258803, 1.434261866,
1019  1.428018603, 1.420435218, 1.411387828, 1.400713453, 1.388197376,
1020  1.373555087, 1.356406755, 1.33624286, 1.312389501, 1.301635176,
1021  1.290112987, 1.277799572, 1.264746546, 1.251235241, 1.238359914,
1022  1.230978076, 1.236823174, 1.228953387, 1.223150892, 1.221394824,
1023  1.219600693, 1.218690906, 1.216721426, 1.215773219, 1.21508082,
1024  1.214311053, 1.214157158, 1.213847925, 1.213636737, 1.213402392,
1025  1.213207534, 1.212984684, 1.212746897, 1.212619732, 1.2125862,
1026  1.212370608, 1.212444728, 1.212212997, 1.212199008, 1.212018349,
1027  1.212000716, 1.212205486, 1.212475394, 1.212482465, 1.211726992,
1028  1.212758151, 1.211922483, 1.211526857}, {1.457166384, 1.455774437,
1029  1.45614065, 1.456163388, 1.456398915, 1.456702444, 1.456452029,
1030  1.456111048, 1.456084183, 1.456343126, 1.456203267, 1.456611834,
1031  1.456405008, 1.456495794, 1.456708475, 1.456856113, 1.45703245,
1032  1.457199255, 1.457216831, 1.457758397, 1.458078952, 1.458344132,
1033  1.458161964, 1.458541639, 1.4580717, 1.462140395, 1.464201092,
1034  1.463724506, 1.468574149, 1.46434673, 1.472722297, 1.467376603,
1035  1.483390561, 1.480075895, 1.470177613, 1.482565512, 1.497109984,
1036  1.511416992, 1.524995064, 1.537744972, 1.566154575, 1.590272672,
1037  1.610878824, 1.628579645, 1.643827476, 1.656957371, 1.668215944,
1038  1.677781064, 1.685775835, 1.692277814, 1.697328618, 1.700942134,
1039  1.7031156, 1.703841327, 1.7031156, 1.700942134, 1.697328618,
1040  1.692277814, 1.685775835, 1.677781064, 1.668215944, 1.656957371,
1041  1.643827476, 1.628579645, 1.610878824, 1.590272672, 1.566154575,
1042  1.537744972, 1.524995064, 1.511416992, 1.497109984, 1.482565512,
1043  1.470177613, 1.480075895, 1.483390561, 1.467376603, 1.472722297,
1044  1.46434673, 1.468574149, 1.463724506, 1.464201092, 1.462140395,
1045  1.4580717, 1.458541639, 1.458161964, 1.458344132, 1.458078952,
1046  1.457758397, 1.457216831, 1.457199255, 1.45703245, 1.456856113,
1047  1.456708475, 1.456495794, 1.456405008, 1.456611834, 1.456203267,
1048  1.456343126, 1.456084183, 1.456111048, 1.456452029, 1.456702444,
1049  1.456398915, 1.456163388, 1.45614065, 1.455774437, 1.457166384}};
1050 
1051  /* 3, 3 mode */
1052  const double reomegaqnm33[8][107] = {{0.445768, 0.452799, 0.456948, 0.460943, 0.462462, 0.462842,
1053  0.463095, 0.463269, 0.463394, 0.463488, 0.463746, 0.463886,
1054  0.463989, 0.464144, 0.464267, 0.464374, 0.464572, 0.464763,
1055  0.464952, 0.46514, 0.465329, 0.465518, 0.465707, 0.466182, 0.466657,
1056  0.467612, 0.468573, 0.46954, 0.471491, 0.473465, 0.475464,
1057  0.477487, 0.479535, 0.481609, 0.483709, 0.485837, 0.487991,
1058  0.490174, 0.492386, 0.494627, 0.500363, 0.5063, 0.512449, 0.518826,
1059  0.525445, 0.532323, 0.539479, 0.546934, 0.55471, 0.562834, 0.571335,
1060  0.580244, 0.5896, 0.599443, 0.609823, 0.620796, 0.632425, 0.644787,
1061  0.657972, 0.672086, 0.68726, 0.70365, 0.721455, 0.740921, 0.762369,
1062  0.786223, 0.813057, 0.843687, 0.857254, 0.871717, 0.887201,
1063  0.90386, 0.921885, 0.941521, 0.963088, 0.987016, 1.01391, 1.04464,
1064  1.08058, 1.1241, 1.14998, 1.17986, 1.21547, 1.23637, 1.26023,
1065  1.27086, 1.28227, 1.29462, 1.30812, 1.32308, 1.33999, 1.35965,
1066  1.37094, 1.38363, 1.39829, 1.40666, 1.41603, 1.42679, 1.42917,
1067  1.43164, 1.43422, 1.43692, 1.43975, 1.44591, 1.45295, 1.45695,
1068  1.46139}, {0.428357, 0.432238, 0.434351, 0.436362, 0.437184,
1069  0.437404, 0.437552, 0.437654, 0.437725, 0.437773, 0.437868,
1070  0.437898, 0.437929, 0.438015, 0.438115, 0.438217, 0.438421,
1071  0.438623, 0.438826, 0.43903, 0.439233, 0.439437, 0.439641, 0.440152,
1072  0.440665, 0.441694, 0.442729, 0.443771, 0.445872, 0.447999,
1073  0.45015, 0.452328, 0.454532, 0.456764, 0.459023, 0.461311, 0.463627,
1074  0.465974, 0.46835, 0.470758, 0.476918, 0.483289, 0.489884,
1075  0.496717, 0.503805, 0.511164, 0.518814, 0.526776, 0.535074,
1076  0.543734, 0.552785, 0.562261, 0.5722, 0.582644, 0.593642, 0.60525,
1077  0.617535, 0.630573, 0.644453, 0.659285, 0.675198, 0.692352,
1078  0.710943, 0.731221, 0.753507, 0.778225, 0.805952, 0.837504,
1079  0.851449, 0.866295, 0.882167, 0.89922, 0.917645, 0.937687, 0.959667,
1080  0.984015, 1.01133, 1.0425, 1.07889, 1.12285, 1.14897, 1.17907,
1081  1.21491, 1.23591, 1.25988, 1.27055, 1.28201, 1.2944, 1.30794,
1082  1.32294, 1.33989, 1.35958, 1.37089, 1.38359, 1.39826, 1.40664,
1083  1.41601, 1.42678, 1.42916, 1.43163, 1.43421, 1.43691, 1.43974,
1084  1.4459, 1.45295, 1.45695, 1.46139}, {0.390162, 0.390933, 0.390855,
1085  0.39013, 0.389593, 0.389452, 0.389377, 0.389349, 0.389352, 0.389374,
1086  0.389533, 0.389627, 0.38968, 0.38978, 0.389896, 0.390013, 0.390243,
1087  0.390473, 0.390704, 0.390935, 0.391167, 0.391398, 0.39163,
1088  0.392211, 0.392793, 0.393963, 0.395139, 0.396321, 0.398706,
1089  0.401118, 0.403557, 0.406025, 0.408522, 0.411048, 0.413604,
1090  0.416191, 0.41881, 0.42146, 0.424144, 0.426861, 0.433807, 0.44098,
1091  0.448397, 0.456071, 0.464019, 0.47226, 0.480815, 0.489704, 0.498954,
1092  0.50859, 0.518645, 0.529153, 0.540151, 0.551685, 0.563804,
1093  0.576567, 0.590041, 0.604302, 0.619445, 0.635578, 0.652833,
1094  0.671371, 0.691391, 0.713145, 0.736956, 0.763249, 0.792606,
1095  0.825846, 0.840483, 0.856032, 0.872619, 0.890397, 0.90956, 0.930355,
1096  0.953102, 0.978234, 1.00636, 1.03835, 1.07558, 1.12042, 1.14697,
1097  1.17752, 1.21379, 1.23502, 1.2592, 1.26995, 1.28149, 1.29396,
1098  1.30758, 1.32266, 1.33967, 1.35943, 1.37078, 1.38351, 1.3982,
1099  1.4066, 1.41598, 1.42676, 1.42914, 1.43162, 1.4342, 1.4369, 1.43973,
1100  1.44589, 1.45294, 1.45694, 1.46139}, {0.332321, 0.329612, 0.329447,
1101  0.330998, 0.331533, 0.331485, 0.331367, 0.331244, 0.331151,
1102  0.331101, 0.331226, 0.331354, 0.331387, 0.331504, 0.331643,
1103  0.331766, 0.332024, 0.33228, 0.332537, 0.332795, 0.333053, 0.333311,
1104  0.333569, 0.334216, 0.334865, 0.336168, 0.337478, 0.338796,
1105  0.341454, 0.344143, 0.346863, 0.349614, 0.352398, 0.355215,
1106  0.358066, 0.360951, 0.363872, 0.366829, 0.369823, 0.372855,
1107  0.380605, 0.388612, 0.39689, 0.405455, 0.414327, 0.423525, 0.43307,
1108  0.442986, 0.4533, 0.464039, 0.475237, 0.486928, 0.499155, 0.511962,
1109  0.525402, 0.539534, 0.554428, 0.570163, 0.586836, 0.604556, 0.62346,
1110  0.643711, 0.665511, 0.689115, 0.71485, 0.743145, 0.774586,
1111  0.809998, 0.82553, 0.841991, 0.859506, 0.878231, 0.898362, 0.920146,
1112  0.943908, 0.970086, 0.999286, 1.0324, 1.0708, 1.11686, 1.14404,
1113  1.17523, 1.21215, 1.23369, 1.25818, 1.26906, 1.28072, 1.2933,
1114  1.30704, 1.32223, 1.33936, 1.35922, 1.37061, 1.38339, 1.39812,
1115  1.40653, 1.41593, 1.42673, 1.42911, 1.43159, 1.43418, 1.43688,
1116  1.43971, 1.44588, 1.45294, 1.45694, 1.46138}, {0.279748, 0.281425,
1117  0.280003, 0.278496, 0.279479, 0.279701, 0.279679, 0.279534, 0.27938,
1118  0.279284, 0.279511, 0.279556, 0.279569, 0.279745, 0.279852,
1119  0.279994, 0.280246, 0.280507, 0.280766, 0.281026, 0.281285,
1120  0.281546, 0.281806, 0.282459, 0.283115, 0.284431, 0.285757,
1121  0.287091, 0.289787, 0.292519, 0.295288, 0.298095, 0.30094, 0.303825,
1122  0.306751, 0.309717, 0.312725, 0.315776, 0.318871, 0.322011,
1123  0.330062, 0.338415, 0.347087, 0.356096, 0.365463, 0.37521, 0.385359,
1124  0.395936, 0.406968, 0.418488, 0.430528, 0.443126, 0.456326,
1125  0.470174, 0.484725, 0.500042, 0.516195, 0.533269, 0.551359,
1126  0.570583, 0.591077, 0.61301, 0.636588, 0.662069, 0.689786, 0.720173,
1127  0.753822, 0.791564, 0.808064, 0.825515, 0.844044, 0.863808,
1128  0.885005, 0.907885, 0.932779, 0.960131, 0.990559, 1.02497, 1.06475,
1129  1.11229, 1.14026, 1.17226, 1.21, 1.23195, 1.25686, 1.26789, 1.2797,
1130  1.29245, 1.30633, 1.32167, 1.33893, 1.35893, 1.37038, 1.38322,
1131  1.39801, 1.40645, 1.41587, 1.42669, 1.42908, 1.43156, 1.43415,
1132  1.43685, 1.43969, 1.44587, 1.45293, 1.45693, 1.46137}, {0.239992,
1133  0.240995, 0.242946, 0.24156, 0.241854, 0.242213, 0.242269, 0.242117,
1134  0.241939, 0.241855, 0.242174, 0.24208, 0.242226, 0.242298,
1135  0.242438, 0.242546, 0.242783, 0.243024, 0.243261, 0.243498,
1136  0.243736, 0.243974, 0.244213, 0.244811, 0.245412, 0.246621, 0.24784,
1137  0.249069, 0.251558, 0.254089, 0.256662, 0.259279, 0.26194,
1138  0.264647, 0.2674, 0.2702, 0.273049, 0.275948, 0.278897, 0.281899,
1139  0.289636, 0.297725, 0.306186, 0.315041, 0.324312, 0.334027, 0.34421,
1140  0.354891, 0.366101, 0.377873, 0.390245, 0.403257, 0.416954,
1141  0.431386, 0.446612, 0.462696, 0.479713, 0.49775, 0.516906, 0.537303,
1142  0.559082, 0.582416, 0.607517, 0.634649, 0.66415, 0.696462,
1143  0.732182, 0.77215, 0.789586, 0.807999, 0.827516, 0.848298, 0.870543,
1144  0.894505, 0.920521, 0.949042, 0.980704, 1.01643, 1.05767, 1.10684,
1145  1.1357, 1.16864, 1.20737, 1.22983, 1.25522, 1.26646, 1.27846,
1146  1.29139, 1.30546, 1.32098, 1.33842, 1.35857, 1.3701, 1.38301,
1147  1.39787, 1.40634, 1.41579, 1.42664, 1.42903, 1.43152, 1.43411,
1148  1.43682, 1.43966, 1.44585, 1.45291, 1.45692, 1.46137}, {0.21884,
1149  0.216298, 0.216633, 0.217244, 0.216888, 0.217233, 0.217329,
1150  0.217189, 0.217034, 0.217006, 0.217217, 0.217255, 0.217293,
1151  0.217414, 0.217505, 0.217599, 0.217807, 0.218016, 0.218223,
1152  0.218427, 0.218635, 0.218841, 0.21905, 0.21957, 0.220094, 0.221148,
1153  0.222212, 0.223288, 0.22547, 0.227696, 0.229966, 0.232282, 0.234646,
1154  0.237057, 0.239517, 0.242028, 0.244591, 0.247207, 0.249877,
1155  0.252604, 0.259674, 0.267128, 0.274991, 0.283291, 0.292057,
1156  0.301319, 0.31111, 0.321465, 0.332419, 0.344012, 0.356285, 0.369284,
1157  0.383057, 0.39766, 0.413152, 0.429604, 0.447094, 0.465712,
1158  0.485563, 0.506772, 0.529486, 0.553883, 0.580183, 0.608655,
1159  0.639647, 0.673609, 0.711146, 0.753105, 0.771386, 0.790674,
1160  0.811095, 0.832808, 0.856013, 0.880965, 0.908002, 0.937583,
1161  0.970359, 1.00729, 1.04987, 1.10064, 1.13044, 1.16442, 1.20427,
1162  1.22731, 1.2533, 1.26476, 1.27699, 1.29015, 1.30444, 1.32016,
1163  1.3378, 1.35815, 1.36977, 1.38276, 1.3977, 1.40621, 1.4157, 1.42658,
1164  1.42898, 1.43147, 1.43407, 1.43678, 1.43963, 1.44582, 1.4529,
1165  1.45691, 1.46135}, {0.199814, 0.201353, 0.200132, 0.200956,
1166  0.200467, 0.200722, 0.200829, 0.200716, 0.200604, 0.200626,
1167  0.200705, 0.200826, 0.200822, 0.200914, 0.201004, 0.201103,
1168  0.201273, 0.201448, 0.201625, 0.2018, 0.201975, 0.202153, 0.202329,
1169  0.202773, 0.20322, 0.204121, 0.205032, 0.205953, 0.207826, 0.209742,
1170  0.211702, 0.213706, 0.215757, 0.217854, 0.220001, 0.222198,
1171  0.224447, 0.226749, 0.229105, 0.231518, 0.237809, 0.244492,
1172  0.251597, 0.25916, 0.267216, 0.275804, 0.284965, 0.294742, 0.305178,
1173  0.316322, 0.328221, 0.340928, 0.354499, 0.368992, 0.384475,
1174  0.401019, 0.418708, 0.437635, 0.45791, 0.479661, 0.50304, 0.528232,
1175  0.555461, 0.585008, 0.617226, 0.652577, 0.691676, 0.735379,
1176  0.754411, 0.774477, 0.795706, 0.818253, 0.842317, 0.868149,
1177  0.896082, 0.926573, 0.960272, 0.998162, 1.04182, 1.09394, 1.1246,
1178  1.15963, 1.20071, 1.22441, 1.25107, 1.2628, 1.2753, 1.28872,
1179  1.30326, 1.31923, 1.3371, 1.35766, 1.36938, 1.38248, 1.39751,
1180  1.40606, 1.41559, 1.4265, 1.42891, 1.43141, 1.43401, 1.43673,
1181  1.43959, 1.44579, 1.45288, 1.45689, 1.46134}};
1182 
1183  const double imomegaqnm33[8][107] = {{0.068612, 0.0735351, 0.0774984, 0.0829193, 0.0860369, 0.0870572,
1184  0.0878377, 0.0884398, 0.0889085, 0.0892767, 0.0902685, 0.0906386,
1185  0.0907974, 0.0909101, 0.0909414, 0.090952, 0.0909603, 0.0909664,
1186  0.0909729, 0.0909798, 0.090987, 0.0909942, 0.0910015, 0.0910197,
1187  0.0910378, 0.091074, 0.09111, 0.0911457, 0.0912166, 0.0912867,
1188  0.091356, 0.0914243, 0.0914917, 0.0915582, 0.0916236, 0.091688,
1189  0.0917514, 0.0918136, 0.0918746, 0.0919344, 0.0920784, 0.0922137,
1190  0.0923394, 0.0924547, 0.0925583, 0.0926492, 0.0927258, 0.0927867,
1191  0.0928302, 0.0928541, 0.0928562, 0.0928338, 0.092784, 0.092703,
1192  0.0925869, 0.0924305, 0.0922281, 0.0919726, 0.0916556, 0.0912666,
1193  0.0907928, 0.0902179, 0.0895213, 0.0886763, 0.087647, 0.0863849,
1194  0.0848213, 0.0828557, 0.0819248, 0.0808922, 0.0797413, 0.0784512,
1195  0.0769953, 0.075339, 0.0734361, 0.0712234, 0.0686106, 0.0654629,
1196  0.0615646, 0.056537, 0.0533881, 0.0496087, 0.0449046, 0.0420439,
1197  0.0386881, 0.0371631, 0.0355053, 0.0336873, 0.0316714, 0.0294027,
1198  0.0267968, 0.023711, 0.0219107, 0.0198652, 0.0174725, 0.0160908,
1199  0.014533, 0.0127266, 0.0123252, 0.011907, 0.0114701, 0.011012,
1200  0.0105299, 0.00947732, 0.00826624, 0.0075764,
1201  0.00680679}, {0.277496, 0.278402, 0.278809, 0.278955, 0.278824,
1202  0.278742, 0.278664, 0.278594, 0.278534, 0.278482, 0.278334,
1203  0.278289, 0.278281, 0.278294, 0.278307, 0.278318, 0.278336,
1204  0.278354, 0.278373, 0.278391, 0.278409, 0.278427, 0.278446,
1205  0.278491, 0.278537, 0.278627, 0.278716, 0.278805, 0.27898, 0.279153,
1206  0.279323, 0.279489, 0.279653, 0.279813, 0.27997, 0.280123,
1207  0.280273, 0.280419, 0.280561, 0.280699, 0.281026, 0.281324,
1208  0.281591, 0.281825, 0.28202, 0.282175, 0.282285, 0.282345, 0.28235,
1209  0.282293, 0.282168, 0.281967, 0.281681, 0.281298, 0.280807,
1210  0.280191, 0.279434, 0.278515, 0.277407, 0.27608, 0.274494, 0.272602,
1211  0.27034, 0.26763, 0.264363, 0.260394, 0.255518, 0.249435, 0.246568,
1212  0.243397, 0.239871, 0.235928, 0.231489, 0.226451, 0.220675,
1213  0.213971, 0.206071, 0.19657, 0.184822, 0.169692, 0.160224, 0.148867,
1214  0.134739, 0.12615, 0.116076, 0.111499, 0.106524, 0.101069,
1215  0.0950193, 0.088212, 0.0803933, 0.0711348, 0.0657335, 0.0595967,
1216  0.0524182, 0.0482728, 0.0435993, 0.03818, 0.0369756, 0.0357211,
1217  0.0344103, 0.0330362, 0.0315898, 0.028432, 0.0247987, 0.0227292,
1218  0.0204204}, {0.486993, 0.484741, 0.483427, 0.482389, 0.482301,
1219  0.482372, 0.48246, 0.482542, 0.482611, 0.482664, 0.482744, 0.482718,
1220  0.482702, 0.482709, 0.482722, 0.482729, 0.482743, 0.482759,
1221  0.482774, 0.482789, 0.482804, 0.482819, 0.482834, 0.482871,
1222  0.482907, 0.48298, 0.483051, 0.483121, 0.483256, 0.483386, 0.483511,
1223  0.48363, 0.483742, 0.483849, 0.483949, 0.484043, 0.48413, 0.48421,
1224  0.484283, 0.484348, 0.484477, 0.484555, 0.484575, 0.484535,
1225  0.484428, 0.484247, 0.483987, 0.483638, 0.483192, 0.48264, 0.481968,
1226  0.481164, 0.480211, 0.479093, 0.477786, 0.476267, 0.474506,
1227  0.472466, 0.470105, 0.467369, 0.464195, 0.4605, 0.456181, 0.451103,
1228  0.44509, 0.437899, 0.42919, 0.418467, 0.413455, 0.407937, 0.401829,
1229  0.39503, 0.387407, 0.37879, 0.36895, 0.357573, 0.344212, 0.328195,
1230  0.308447, 0.283082, 0.267235, 0.248247, 0.224647, 0.210309,
1231  0.193501, 0.185866, 0.177568, 0.168469, 0.158382, 0.147032,
1232  0.133998, 0.118564, 0.10956, 0.0993313, 0.0873659, 0.0804562,
1233  0.0726665, 0.0636339, 0.0616265, 0.0595355, 0.0573509, 0.0550606,
1234  0.0526499, 0.0473868, 0.0413313, 0.0378821, 0.034034}, {0.709974,
1235  0.711601, 0.713499, 0.714385, 0.713785, 0.713546, 0.713418,
1236  0.713383, 0.713411, 0.713468, 0.713655, 0.713595, 0.713563,
1237  0.713584, 0.713571, 0.713561, 0.71355, 0.713535, 0.713522, 0.713507,
1238  0.713493, 0.713479, 0.713465, 0.713428, 0.713392, 0.713317,
1239  0.713241, 0.713162, 0.712999, 0.712828, 0.712649, 0.712461,
1240  0.712264, 0.712058, 0.711843, 0.711618, 0.711383, 0.711138,
1241  0.710882, 0.710616, 0.709899, 0.709105, 0.708229, 0.707264,
1242  0.706201, 0.705033, 0.703748, 0.702336, 0.700785, 0.699079,
1243  0.697202, 0.695135, 0.692855, 0.690337, 0.68755, 0.684459, 0.68102,
1244  0.677183, 0.672887, 0.668056, 0.662599, 0.656401, 0.649315,
1245  0.641153, 0.631664, 0.620511, 0.607221, 0.591101, 0.583641,
1246  0.575473, 0.566484, 0.556529, 0.545428, 0.532943, 0.518759,
1247  0.502439, 0.48336, 0.460589, 0.432625, 0.396831, 0.37452, 0.347819,
1248  0.314676, 0.294558, 0.270986, 0.260282, 0.248651, 0.235902,
1249  0.221769, 0.20587, 0.187614, 0.166001, 0.153393, 0.13907, 0.122317,
1250  0.112642, 0.101735, 0.0890889, 0.0862783, 0.0833507, 0.080292,
1251  0.0770855, 0.0737103, 0.0663418, 0.057864, 0.053035,
1252  0.0476477}, {0.972477, 0.969229, 0.96766, 0.969029, 0.969442,
1253  0.969155, 0.968886, 0.968746, 0.968738, 0.968815, 0.969029,
1254  0.968878, 0.968919, 0.968877, 0.968857, 0.968828, 0.968768,
1255  0.968706, 0.968649, 0.968589, 0.968529, 0.96847, 0.96841, 0.96826,
1256  0.96811, 0.967806, 0.9675, 0.96719, 0.966561, 0.96592, 0.965265,
1257  0.964597, 0.963916, 0.96322, 0.962509, 0.961784, 0.961043, 0.960287,
1258  0.959514, 0.958725, 0.956678, 0.954518, 0.952237, 0.949827,
1259  0.947277, 0.944577, 0.941715, 0.938677, 0.935446, 0.932005,
1260  0.928331, 0.924401, 0.920185, 0.915649, 0.910755, 0.905456,
1261  0.899695, 0.893406, 0.88651, 0.878908, 0.870479, 0.861073, 0.850501,
1262  0.838516, 0.824795, 0.808901, 0.790225, 0.767883, 0.757639,
1263  0.746483, 0.73427, 0.720819, 0.7059, 0.689212, 0.670355, 0.648776,
1264  0.623682, 0.593881, 0.557455, 0.511016, 0.482143, 0.44764, 0.404868,
1265  0.378929, 0.348555, 0.334768, 0.319791, 0.303378, 0.285189,
1266  0.264731, 0.241246, 0.213447, 0.197233, 0.178815, 0.157271,
1267  0.144831, 0.130807, 0.114545, 0.110932, 0.107167, 0.103234,
1268  0.0991113, 0.0947715, 0.0852972, 0.0743968, 0.068188,
1269  0.0612614}, {1.23488, 1.2385, 1.23757, 1.23638, 1.23735, 1.23719,
1270  1.23689, 1.23671, 1.23672, 1.23684, 1.23689, 1.23686, 1.23687,
1271  1.23681, 1.23674, 1.23671, 1.2366, 1.23651, 1.23641, 1.23631,
1272  1.23622, 1.23612, 1.23602, 1.23578, 1.23553, 1.23504, 1.23454,
1273  1.23403, 1.23301, 1.23196, 1.23088, 1.22979, 1.22867, 1.22753,
1274  1.22637, 1.22518, 1.22396, 1.22272, 1.22145, 1.22016, 1.21681,
1275  1.21328, 1.20956, 1.20564, 1.20152, 1.19717, 1.19258, 1.18775,
1276  1.18264, 1.17724, 1.17153, 1.16546, 1.15902, 1.15215, 1.14481,
1277  1.13695, 1.12848, 1.11934, 1.10942, 1.09859, 1.08672, 1.07361,
1278  1.05902, 1.04265, 1.02409, 1.00282, 0.978074, 0.948772, 0.935434,
1279  0.920971, 0.905209, 0.887929, 0.868853, 0.847622, 0.823753,
1280  0.796583, 0.765161, 0.728048, 0.682917, 0.625639, 0.590118,
1281  0.547732, 0.49525, 0.463448, 0.42623, 0.409344, 0.391005, 0.370913,
1282  0.348652, 0.323623, 0.294897, 0.260904, 0.241081, 0.218564,
1283  0.192229, 0.177023, 0.159881, 0.140004, 0.135587, 0.130985,
1284  0.126178, 0.121138, 0.115834, 0.104253, 0.09093, 0.0833412,
1285  0.0748751}, {1.50812, 1.50714, 1.50886, 1.50765, 1.50833, 1.50831,
1286  1.50805, 1.5079, 1.50794, 1.50808, 1.50796, 1.50805, 1.50794,
1287  1.50791, 1.50787, 1.50779, 1.50768, 1.50756, 1.50745, 1.50733,
1288  1.50721, 1.50709, 1.50697, 1.50667, 1.50637, 1.50577, 1.50515,
1289  1.50453, 1.50326, 1.50195, 1.50061, 1.49924, 1.49784, 1.49639,
1290  1.49491, 1.4934, 1.49185, 1.49025, 1.48862, 1.48695, 1.4826,
1291  1.47798, 1.47308, 1.46789, 1.46239, 1.45657, 1.45042, 1.44391,
1292  1.43702, 1.42973, 1.42201, 1.41383, 1.40515, 1.39591, 1.38607,
1293  1.37555, 1.36428, 1.35215, 1.33904, 1.32481, 1.30928, 1.29221,
1294  1.27333, 1.25226, 1.22852, 1.20145, 1.17016, 1.13335, 1.11668,
1295  1.09865, 1.07906, 1.05766, 1.03413, 1.00803, 0.978819, 0.945725,
1296  0.907651, 0.862934, 0.808869, 0.7406, 0.698384, 0.648072, 0.585828,
1297  0.54813, 0.50403, 0.484027, 0.462309, 0.43852, 0.412171, 0.382553,
1298  0.348572, 0.308374, 0.284937, 0.258319, 0.227191, 0.209218,
1299  0.188957, 0.165464, 0.160243, 0.154805, 0.149123, 0.143167,
1300  0.136898, 0.123211, 0.107464, 0.0984948, 0.102103}, {1.77947,
1301  1.77829, 1.77828, 1.77845, 1.7786, 1.77868, 1.7785, 1.77838,
1302  1.77844, 1.77854, 1.77842, 1.77841, 1.77841, 1.77834, 1.77827,
1303  1.7782, 1.77808, 1.77795, 1.77783, 1.7777, 1.77757, 1.77744,
1304  1.77732, 1.77699, 1.77667, 1.77601, 1.77534, 1.77466, 1.77327,
1305  1.77183, 1.77035, 1.76883, 1.76726, 1.76564, 1.76398, 1.76226,
1306  1.7605, 1.75868, 1.75682, 1.75489, 1.74985, 1.74445, 1.73867,
1307  1.73249, 1.72589, 1.71886, 1.71137, 1.7034, 1.69493, 1.68592,
1308  1.67635, 1.66618, 1.65536, 1.64384, 1.63157, 1.61846, 1.60441,
1309  1.58931, 1.57303, 1.55539, 1.53617, 1.5151, 1.49185, 1.46597,
1310  1.43689, 1.40384, 1.36575, 1.32111, 1.30093, 1.27916, 1.25555,
1311  1.22981, 1.20156, 1.17032, 1.13545, 1.09609, 1.05101, 0.998352,
1312  0.935078, 0.85569, 0.806777, 0.748562, 0.676569, 0.632966, 0.58196,
1313  0.558828, 0.533715, 0.506213, 0.475757, 0.441533, 0.40228, 0.355861,
1314  0.328804, 0.29808, 0.262156, 0.241415, 0.218035, 0.190926,
1315  0.184902, 0.178626, 0.17207, 0.165197, 0.157962, 0.142169, 0.123998,
1316  0.113649, 0.115718}};
1317 
1318 
1319  /* 4, 4 mode */
1320  const double reomegaqnm44[8][107] = {{0.603485, 0.613847, 0.619636, 0.623952, 0.624219, 0.623894,
1321  0.623504, 0.623122, 0.62278, 0.622487, 0.621648, 0.621375, 0.621309,
1322  0.621365, 0.621483, 0.621613, 0.621877, 0.622141, 0.622404,
1323  0.622667, 0.62293, 0.623194, 0.623458, 0.624119, 0.624781, 0.626113,
1324  0.627452, 0.628799, 0.631518, 0.634269, 0.637054, 0.639872,
1325  0.642726, 0.645615, 0.648541, 0.651503, 0.654504, 0.657544,
1326  0.660623, 0.663743, 0.671728, 0.679989, 0.688543, 0.697411,
1327  0.706611, 0.716168, 0.726107, 0.736455, 0.747243, 0.758508,
1328  0.770286, 0.782624, 0.795569, 0.809178, 0.823517, 0.83866, 0.854693,
1329  0.871718, 0.889853, 0.909242, 0.930054, 0.9525, 0.976839, 1.0034,
1330  1.03259, 1.06498, 1.10131, 1.14265, 1.16092, 1.18036, 1.20114,
1331  1.22345, 1.24755, 1.27374, 1.30245, 1.33422, 1.36984, 1.41042,
1332  1.45773, 1.51478, 1.54862, 1.58759, 1.6339, 1.66102, 1.69194,
1333  1.7057, 1.72045, 1.73641, 1.75384, 1.77314, 1.79492, 1.82022,
1334  1.83474, 1.85104, 1.86985, 1.8806, 1.8926, 1.9064, 1.90945, 1.91261,
1335  1.91592, 1.91937, 1.92299, 1.93088, 1.93989, 1.945,
1336  1.95068}, {0.59231, 0.596523, 0.598412, 0.599977, 0.600617,
1337  0.600806, 0.600947, 0.601053, 0.601136, 0.601202, 0.601389,
1338  0.601485, 0.601558, 0.601693, 0.601828, 0.601964, 0.602238,
1339  0.602511, 0.602785, 0.60306, 0.603334, 0.603609, 0.603884, 0.604574,
1340  0.605265, 0.606653, 0.60805, 0.609455, 0.61229, 0.615158, 0.618061,
1341  0.620998, 0.623972, 0.626982, 0.630029, 0.633115, 0.63624,
1342  0.639405, 0.64261, 0.645858, 0.654166, 0.662758, 0.671651, 0.680865,
1343  0.69042, 0.700341, 0.710653, 0.721383, 0.732565, 0.744232,
1344  0.756425, 0.769188, 0.782571, 0.796632, 0.811434, 0.827055,
1345  0.843581, 0.861114, 0.879773, 0.899703, 0.921074, 0.944098,
1346  0.969034, 0.996209, 1.02604, 1.05909, 1.09611, 1.13816, 1.15671,
1347  1.17644, 1.19752, 1.22013, 1.24453, 1.27103, 1.30005, 1.33214,
1348  1.36806, 1.40896, 1.45658, 1.51396, 1.54795, 1.58707, 1.63353,
1349  1.66073, 1.69172, 1.7055, 1.72028, 1.73626, 1.75372, 1.77304,
1350  1.79485, 1.82017, 1.8347, 1.85101, 1.86983, 1.88058, 1.89259,
1351  1.90639, 1.90944, 1.91261, 1.91591, 1.91936, 1.92299, 1.93087,
1352  1.93989, 1.945, 1.95068}, {0.559386, 0.561881, 0.562985, 0.563673,
1353  0.563747, 0.563732, 0.563712, 0.563695, 0.563683, 0.563678,
1354  0.563718, 0.563794, 0.563872, 0.564021, 0.564168, 0.564316,
1355  0.564612, 0.564908, 0.565204, 0.565501, 0.565798, 0.566096,
1356  0.566394, 0.567139, 0.567887, 0.56939, 0.570901, 0.57242, 0.575484,
1357  0.578584, 0.58172, 0.584892, 0.588102, 0.59135, 0.594637, 0.597965,
1358  0.601333, 0.604743, 0.608195, 0.611692, 0.62063, 0.629865, 0.639415,
1359  0.649299, 0.65954, 0.670161, 0.681189, 0.692653, 0.704586,
1360  0.717023, 0.730006, 0.743579, 0.757794, 0.77271, 0.788392, 0.804918,
1361  0.822375, 0.840868, 0.860518, 0.88147, 0.903897, 0.928012,
1362  0.954076, 0.982419, 1.01346, 1.04777, 1.08608, 1.12947, 1.14857,
1363  1.16887, 1.19051, 1.21369, 1.23867, 1.26576, 1.29538, 1.32806,
1364  1.36459, 1.4061, 1.45434, 1.51232, 1.54662, 1.58604, 1.6328,
1365  1.66014, 1.69127, 1.70511, 1.71994, 1.73598, 1.75348, 1.77286,
1366  1.79471, 1.82008, 1.83463, 1.85096, 1.8698, 1.88055, 1.89257,
1367  1.90638, 1.90943, 1.9126, 1.9159, 1.91935, 1.92298, 1.93087,
1368  1.93989, 1.945, 1.95068}, {0.514416, 0.513669, 0.512866, 0.5122,
1369  0.512256, 0.512336, 0.512404, 0.512455, 0.512488, 0.51251, 0.512565,
1370  0.51264, 0.512726, 0.512889, 0.513051, 0.513214, 0.51354, 0.513866,
1371  0.514193, 0.51452, 0.514848, 0.515175, 0.515503, 0.516325,
1372  0.517149, 0.518804, 0.520467, 0.522139, 0.525511, 0.52892, 0.532367,
1373  0.535852, 0.539377, 0.542943, 0.546549, 0.550198, 0.553889,
1374  0.557625, 0.561406, 0.565233, 0.575009, 0.585097, 0.595517,
1375  0.606289, 0.617438, 0.628986, 0.640963, 0.653399, 0.666327,
1376  0.679785, 0.693815, 0.708464, 0.723784, 0.739837, 0.75669, 0.774421,
1377  0.793122, 0.812899, 0.833875, 0.856197, 0.880043, 0.905628,
1378  0.933216, 0.96314, 0.995828, 1.03184, 1.07193, 1.11717, 1.13703,
1379  1.1581, 1.18052, 1.20451, 1.2303, 1.25821, 1.28866, 1.32219,
1380  1.35958, 1.40195, 1.45106, 1.50993, 1.54467, 1.58453, 1.63172,
1381  1.65927, 1.69061, 1.70453, 1.71944, 1.73555, 1.75313, 1.77258,
1382  1.79451, 1.81994, 1.83452, 1.85088, 1.86975, 1.88051, 1.89254,
1383  1.90636, 1.90941, 1.91258, 1.91589, 1.91934, 1.92297, 1.93086,
1384  1.93988, 1.94499, 1.95068}, {0.454601, 0.454746, 0.455842, 0.456343,
1385  0.456046, 0.455998, 0.456018, 0.456071, 0.456127, 0.456171,
1386  0.456246, 0.456327, 0.456423, 0.456596, 0.456773, 0.456949,
1387  0.457302, 0.457655, 0.458009, 0.458363, 0.458717, 0.459072,
1388  0.459427, 0.460317, 0.461208, 0.462999, 0.464799, 0.466609,
1389  0.470257, 0.473946, 0.477675, 0.481446, 0.485259, 0.489115,
1390  0.493016, 0.496962, 0.500954, 0.504993, 0.509081, 0.513219,
1391  0.523786, 0.534689, 0.545948, 0.557585, 0.569625, 0.582093, 0.59502,
1392  0.608436, 0.622378, 0.636885, 0.652, 0.667772, 0.684256, 0.701516,
1393  0.71962, 0.738651, 0.758702, 0.779882, 0.802317, 0.82616, 0.851591,
1394  0.878829, 0.908143, 0.939873, 0.974449, 1.01244, 1.05461, 1.10202,
1395  1.12279, 1.14477, 1.16814, 1.19308, 1.21984, 1.24875, 1.28021,
1396  1.31477, 1.35322, 1.39666, 1.44687, 1.50684, 1.54214, 1.58256,
1397  1.63031, 1.65813, 1.68974, 1.70376, 1.71878, 1.73499, 1.75267,
1398  1.77222, 1.79424, 1.81975, 1.83438, 1.85077, 1.86967, 1.88046,
1399  1.8925, 1.90633, 1.90939, 1.91256, 1.91587, 1.91932, 1.92296,
1400  1.93085, 1.93987, 1.94499, 1.95067}, {0.405546, 0.404573, 0.403366,
1401  0.404025, 0.404115, 0.403989, 0.40394, 0.403971, 0.404037, 0.404098,
1402  0.40416, 0.404265, 0.404355, 0.404535, 0.404715, 0.404897, 0.40526,
1403  0.405624, 0.405988, 0.406353, 0.406718, 0.407083, 0.407449,
1404  0.408365, 0.409284, 0.411129, 0.412986, 0.414853, 0.418619, 0.42243,
1405  0.426286, 0.430188, 0.434137, 0.438134, 0.44218, 0.446277,
1406  0.450425, 0.454625, 0.458878, 0.463187, 0.474206, 0.485594,
1407  0.497376, 0.509573, 0.522212, 0.535321, 0.54893, 0.563075, 0.577791,
1408  0.593121, 0.609109, 0.625808, 0.643274, 0.661572, 0.680777,
1409  0.700971, 0.722252, 0.744732, 0.768542, 0.793839, 0.820807,
1410  0.849672, 0.880708, 0.914263, 0.950774, 0.990817, 1.03516, 1.0849,
1411  1.10664, 1.12961, 1.15399, 1.17998, 1.20782, 1.23782, 1.27041,
1412  1.30613, 1.34576, 1.39042, 1.44188, 1.50314, 1.53909, 1.58017,
1413  1.62858, 1.65673, 1.68866, 1.70281, 1.71796, 1.7343, 1.7521,
1414  1.77176, 1.7939, 1.81952, 1.83419, 1.85064, 1.86958, 1.88039,
1415  1.89245, 1.9063, 1.90936, 1.91253, 1.91584, 1.9193, 1.92294,
1416  1.93083, 1.93986, 1.94498, 1.95067}, {0.35976, 0.362048, 0.362088,
1417  0.361405, 0.361838, 0.361724, 0.361635, 0.361653, 0.361731,
1418  0.361798, 0.361829, 0.361951, 0.362022, 0.362204, 0.362384,
1419  0.362559, 0.362914, 0.363269, 0.363624, 0.36398, 0.364336, 0.364693,
1420  0.36505, 0.365945, 0.366843, 0.368648, 0.370465, 0.372293,
1421  0.375986, 0.379729, 0.383522, 0.387367, 0.391264, 0.395214, 0.39922,
1422  0.403281, 0.4074, 0.411576, 0.415813, 0.42011, 0.431129, 0.44256,
1423  0.454427, 0.466756, 0.479575, 0.492914, 0.506807, 0.521289,
1424  0.536401, 0.552185, 0.568691, 0.585972, 0.604089, 0.623109,
1425  0.643109, 0.664176, 0.686412, 0.709933, 0.734875, 0.761399,
1426  0.789696, 0.819999, 0.85259, 0.887824, 0.92615, 0.968153, 1.01462,
1427  1.06665, 1.08936, 1.11334, 1.13875, 1.16581, 1.19475, 1.22589,
1428  1.25966, 1.29659, 1.33748, 1.38345, 1.43625, 1.49892, 1.53559,
1429  1.57741, 1.62657, 1.6551, 1.6874, 1.7017, 1.717, 1.73348, 1.75142,
1430  1.77123, 1.79349, 1.81924, 1.83398, 1.85048, 1.86948, 1.8803,
1431  1.89239, 1.90626, 1.90932, 1.9125, 1.91581, 1.91928, 1.92291,
1432  1.93082, 1.93985, 1.94497, 1.95066},
1433 {0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72}};
1434 
1435  const double imomegaqnm44[8][107] = {{0.0472887, 0.0570846, 0.0652857, 0.0769202, 0.0835313, 0.0855743,
1436  0.0870596, 0.0881437, 0.0889418, 0.0895359, 0.0909619, 0.0914196,
1437  0.0916056, 0.091741, 0.0917845, 0.0918026, 0.0918186, 0.0918281,
1438  0.0918366, 0.0918448, 0.0918531, 0.0918614, 0.0918696, 0.0918903,
1439  0.0919109, 0.0919521, 0.0919931, 0.092034, 0.0921151, 0.0921956,
1440  0.0922753, 0.0923543, 0.0924324, 0.0925097, 0.0925861, 0.0926616,
1441  0.0927361, 0.0928096, 0.0928821, 0.0929535, 0.0931268, 0.093292,
1442  0.0934484, 0.0935949, 0.0937302, 0.0938532, 0.0939623, 0.0940559,
1443  0.0941321, 0.0941887, 0.0942233, 0.094233, 0.0942145, 0.094164,
1444  0.0940768, 0.0939478, 0.0937705, 0.0935374, 0.0932393, 0.092865,
1445  0.0924006, 0.0918287, 0.0911274, 0.0902679, 0.0892124, 0.0879094,
1446  0.086287, 0.0842401, 0.0832692, 0.0821917, 0.0809905, 0.0796442,
1447  0.0781255, 0.0763992, 0.0744185, 0.0721192, 0.0694103, 0.066156,
1448  0.0621396, 0.056982, 0.0537633, 0.0499111, 0.0451315, 0.0422323,
1449  0.0388376, 0.037297, 0.0356236, 0.0337901, 0.0317587, 0.0294747,
1450  0.0268536, 0.0237529, 0.0219453, 0.0198926, 0.0174928, 0.0161075,
1451  0.0145463, 0.0127365, 0.0123344, 0.0119155, 0.0114779, 0.0110192,
1452  0.0105364, 0.00948248, 0.00827008, 0.00757959,
1453  0.00680933}, {0.267496, 0.27243, 0.275117, 0.277412, 0.278166,
1454  0.278332, 0.278431, 0.278489, 0.278523, 0.278542, 0.278554,
1455  0.278543, 0.278539, 0.278544, 0.278555, 0.278567, 0.27859, 0.278613,
1456  0.278636, 0.278659, 0.278682, 0.278704, 0.278727, 0.278784,
1457  0.278841, 0.278955, 0.279068, 0.27918, 0.279403, 0.279623, 0.279841,
1458  0.280057, 0.28027, 0.28048, 0.280687, 0.280892, 0.281093, 0.281291,
1459  0.281485, 0.281676, 0.282137, 0.282572, 0.282979, 0.283355,
1460  0.283696, 0.283998, 0.284257, 0.284467, 0.284624, 0.284721,
1461  0.284749, 0.284701, 0.284567, 0.284334, 0.28399, 0.283519, 0.282901,
1462  0.282113, 0.281129, 0.279913, 0.278426, 0.276614, 0.274412,
1463  0.271733, 0.268465, 0.264452, 0.25948, 0.253233, 0.250278, 0.247003,
1464  0.243357, 0.239276, 0.234678, 0.229458, 0.223476, 0.216539,
1465  0.208375, 0.198576, 0.186494, 0.170992, 0.161324, 0.149756,
1466  0.135408, 0.126707, 0.116519, 0.111896, 0.106875, 0.101374,
1467  0.0952787, 0.0884259, 0.0805622, 0.0712595, 0.0658364, 0.0596782,
1468  0.0524786, 0.0483228, 0.043639, 0.0382095, 0.0370031, 0.0357465,
1469  0.0344338, 0.0330576, 0.0316092, 0.0284475, 0.0248103, 0.0227388,
1470  0.020428}, {0.476992, 0.476552, 0.476059, 0.475354, 0.475023,
1471  0.474945, 0.474902, 0.47488, 0.474873, 0.474873, 0.474904, 0.474923,
1472  0.474932, 0.474945, 0.47496, 0.474975, 0.475006, 0.475036,
1473  0.475066, 0.475097, 0.475127, 0.475157, 0.475187, 0.475263,
1474  0.475338, 0.475487, 0.475635, 0.475782, 0.476073, 0.476359,
1475  0.476641, 0.476918, 0.47719, 0.477456, 0.477718, 0.477973, 0.478223,
1476  0.478467, 0.478704, 0.478936, 0.479483, 0.479984, 0.480434,
1477  0.480828, 0.48116, 0.481423, 0.48161, 0.481712, 0.481721, 0.481624,
1478  0.48141, 0.481064, 0.48057, 0.479908, 0.479056, 0.477986, 0.476666,
1479  0.47506, 0.47312, 0.470791, 0.468003, 0.464669, 0.460679, 0.45589,
1480  0.450113, 0.44309, 0.434465, 0.423712, 0.41865, 0.413055, 0.406842,
1481  0.399905, 0.392108, 0.383276, 0.373175, 0.361487, 0.347759,
1482  0.331313, 0.311071, 0.28514, 0.268985, 0.249669, 0.225726, 0.21121,
1483  0.194221, 0.186512, 0.17814, 0.168968, 0.158807, 0.147383, 0.134275,
1484  0.118768, 0.109729, 0.099465, 0.0874652, 0.0805385, 0.072732,
1485  0.0636828, 0.0616721, 0.0595777, 0.0573898, 0.0550962, 0.0526822,
1486  0.0474125, 0.0413505, 0.037898, 0.0340467}, {0.688887, 0.687276,
1487  0.68687, 0.687194, 0.687484, 0.687529, 0.687535, 0.687523, 0.687504,
1488  0.687487, 0.687464, 0.68748, 0.687488, 0.687497, 0.687509,
1489  0.687521, 0.687544, 0.687567, 0.68759, 0.687613, 0.687636, 0.687658,
1490  0.687681, 0.687738, 0.687794, 0.687905, 0.688015, 0.688122,
1491  0.688333, 0.688537, 0.688734, 0.688923, 0.689105, 0.689278,
1492  0.689444, 0.689601, 0.689749, 0.689889, 0.690018, 0.690138,
1493  0.690394, 0.690579, 0.69069, 0.690717, 0.690652, 0.690487, 0.690211,
1494  0.689812, 0.689276, 0.688589, 0.687732, 0.686685, 0.685425,
1495  0.683924, 0.682151, 0.680068, 0.677629, 0.674782, 0.671462,
1496  0.667589, 0.663066, 0.657772, 0.651551, 0.644203, 0.635463,
1497  0.624972, 0.612229, 0.596503, 0.589146, 0.581044, 0.572077,
1498  0.562097, 0.550915, 0.538287, 0.523888, 0.507273, 0.48781, 0.464555,
1499  0.436002, 0.399509, 0.376808, 0.349693, 0.316109, 0.295761,
1500  0.271954, 0.261154, 0.249426, 0.236578, 0.222347, 0.206349,
1501  0.187993, 0.166281, 0.153625, 0.139254, 0.122453, 0.112755,
1502  0.101826, 0.0891563, 0.0863413, 0.0834091, 0.080346, 0.0771349,
1503  0.0737552, 0.0663776, 0.0578907, 0.0530572, 0.0476654}, {0.918235,
1504  0.920515, 0.920895, 0.920137, 0.920012, 0.920094, 0.920167,
1505  0.920207, 0.920214, 0.920202, 0.920149, 0.920166, 0.920164, 0.92016,
1506  0.920158, 0.920156, 0.920152, 0.920148, 0.920144, 0.92014,
1507  0.920136, 0.920132, 0.920127, 0.920116, 0.920104, 0.920079,
1508  0.920051, 0.920022, 0.919956, 0.919881, 0.919796, 0.919702,
1509  0.919597, 0.919482, 0.919356, 0.919218, 0.919069, 0.918908,
1510  0.918734, 0.918547, 0.91802, 0.917401, 0.916681, 0.915851, 0.9149,
1511  0.913815, 0.912584, 0.91119, 0.909617, 0.907843, 0.905847, 0.903603,
1512  0.901078, 0.898239, 0.895043, 0.891442, 0.887378, 0.88278,
1513  0.877566, 0.871633, 0.864855, 0.857075, 0.848091, 0.837647, 0.8254,
1514  0.81089, 0.79347, 0.772205, 0.762324, 0.751485, 0.739534, 0.72628,
1515  0.711484, 0.694831, 0.675907, 0.654142, 0.628729, 0.598457, 0.5614,
1516  0.514171, 0.484847, 0.449863, 0.406581, 0.380377, 0.349729,
1517  0.335831, 0.32074, 0.304211, 0.285904, 0.265327, 0.24172, 0.213799,
1518  0.197524, 0.179045, 0.157442, 0.144973, 0.13092, 0.11463, 0.111011,
1519  0.107241, 0.103302, 0.0991739, 0.0948285, 0.0853429, 0.0744311,
1520  0.0682165, 0.0612841}, {1.17243, 1.17025, 1.17072, 1.17153, 1.17109,
1521  1.17107, 1.17115, 1.17122, 1.17125, 1.17124, 1.17116, 1.17118,
1522  1.17115, 1.17114, 1.17112, 1.17109, 1.17105, 1.171, 1.17096,
1523  1.17092, 1.17087, 1.17083, 1.17078, 1.17067, 1.17055, 1.17033,
1524  1.17009, 1.16986, 1.16938, 1.16889, 1.16838, 1.16786, 1.16733,
1525  1.16679, 1.16622, 1.16565, 1.16506, 1.16445, 1.16382, 1.16318,
1526  1.1615, 1.15969, 1.15776, 1.15567, 1.15344, 1.15103, 1.14843,
1527  1.14562, 1.14259, 1.1393, 1.13573, 1.13184, 1.12761, 1.12298,
1528  1.1179, 1.11232, 1.10615, 1.09933, 1.09174, 1.08325, 1.07371,
1529  1.06294, 1.05067, 1.0366, 1.0203, 1.00121, 0.97854, 0.951144,
1530  0.9385, 0.92468, 0.909499, 0.892724, 0.874063, 0.853135, 0.829435,
1531  0.802272, 0.770663, 0.733138, 0.687353, 0.629184, 0.593147,
1532  0.550213, 0.497162, 0.465071, 0.427558, 0.410551, 0.392089,
1533  0.371872, 0.349482, 0.32432, 0.295457, 0.261323, 0.241428, 0.218839,
1534  0.192433, 0.177192, 0.160015, 0.140105, 0.135681, 0.131073,
1535  0.126259, 0.121213, 0.115902, 0.104308, 0.0909715, 0.0833759,
1536  0.0749029}, {1.43411, 1.43505, 1.43374, 1.43433, 1.43411, 1.43401,
1537  1.43406, 1.43415, 1.43418, 1.43415, 1.4341, 1.43407, 1.43405,
1538  1.43401, 1.43397, 1.43393, 1.43384, 1.43376, 1.43367, 1.43359,
1539  1.4335, 1.43342, 1.43333, 1.43312, 1.4329, 1.43247, 1.43203,
1540  1.43159, 1.43069, 1.42978, 1.42884, 1.42789, 1.42691, 1.42592,
1541  1.4249, 1.42387, 1.42281, 1.42173, 1.42062, 1.41949, 1.41656,
1542  1.41345, 1.41017, 1.4067, 1.40302, 1.39911, 1.39496, 1.39054,
1543  1.38582, 1.38079, 1.3754, 1.36961, 1.36339, 1.35669, 1.34943,
1544  1.34155, 1.33296, 1.32356, 1.31324, 1.30183, 1.28915, 1.27497,
1545  1.259, 1.24085, 1.22004, 1.19589, 1.16745, 1.13339, 1.11775,
1546  1.10072, 1.08207, 1.06154, 1.03877, 1.01331, 0.984584, 0.951766,
1547  0.913705, 0.868675, 0.81392, 0.744589, 0.701738, 0.650764, 0.587868,
1548  0.549856, 0.505448, 0.485323, 0.46348, 0.439564, 0.413085,
1549  0.383331, 0.349205, 0.308853, 0.285337, 0.258637, 0.227427,
1550  0.209413, 0.189112, 0.16558, 0.160352, 0.154906, 0.149217, 0.143253,
1551  0.136976, 0.123274, 0.107512, 0.0985354, 0.0885218},
1552 {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
1553 
1554  /* 5, 5 mode */
1555  const double reomegaqnm55[8][107] = {{0.752532, 0.769133, 0.779179, 0.78709, 0.786149, 0.784329, 0.782338,
1556  0.780485, 0.778903, 0.777615, 0.774286, 0.773282, 0.772966,
1557  0.77289, 0.772999, 0.773149, 0.773476, 0.77381, 0.774145, 0.77448,
1558  0.774816, 0.775152, 0.775488, 0.776331, 0.777176, 0.778874,
1559  0.780582, 0.782299, 0.785766, 0.789274, 0.792825, 0.79642, 0.800059,
1560  0.803743, 0.807474, 0.811253, 0.81508, 0.818956, 0.822883,
1561  0.826863, 0.837046, 0.847582, 0.858493, 0.869802, 0.881536,
1562  0.893724, 0.906398, 0.919594, 0.93335, 0.947712, 0.962728, 0.978454,
1563  0.994953, 1.0123, 1.03056, 1.04985, 1.07027, 1.09194, 1.11502,
1564  1.13968, 1.16614, 1.19467, 1.22558, 1.25928, 1.29631, 1.33734,
1565  1.38332, 1.43555, 1.45861, 1.48313, 1.50932, 1.53742, 1.56774,
1566  1.60067, 1.63671, 1.67655, 1.72115, 1.77188, 1.83092, 1.90197,
1567  1.94403, 1.99239, 2.04977, 2.08333, 2.12154, 2.13852, 2.15673,
1568  2.17641, 2.1979, 2.22168, 2.24849, 2.27961, 2.29746, 2.31749,
1569  2.34058, 2.35377, 2.3685, 2.38542, 2.38915, 2.39303, 2.39708,
1570  2.40131, 2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.753001,
1571  0.757208, 0.757533, 0.756804, 0.756468, 0.756414, 0.756397,
1572  0.756401, 0.756417, 0.756438, 0.756561, 0.756667, 0.756761,
1573  0.756937, 0.757109, 0.75728, 0.757623, 0.757967, 0.758311, 0.758656,
1574  0.759001, 0.759346, 0.759692, 0.760558, 0.761427, 0.763172,
1575  0.764927, 0.766693, 0.770255, 0.77386, 0.777508, 0.7812, 0.784938,
1576  0.788722, 0.792553, 0.796433, 0.800362, 0.804341, 0.808372,
1577  0.812456, 0.822904, 0.833711, 0.844898, 0.85649, 0.868513, 0.880997,
1578  0.893974, 0.90748, 0.921555, 0.936243, 0.951594, 0.967664,
1579  0.984515, 1.00222, 1.02086, 1.04054, 1.06135, 1.08343, 1.10693,
1580  1.13203, 1.15894, 1.18793, 1.21932, 1.25352, 1.29105, 1.33262,
1581  1.37915, 1.43196, 1.45525, 1.48001, 1.50644, 1.53478, 1.56534,
1582  1.59852, 1.63481, 1.67491, 1.71976, 1.77074, 1.83004, 1.90134,
1583  1.94352, 1.992, 2.0495, 2.08311, 2.12137, 2.13838, 2.15661, 2.17631,
1584  2.19781, 2.22161, 2.24844, 2.27957, 2.29743, 2.31747, 2.34057,
1585  2.35376, 2.36849, 2.38541, 2.38915, 2.39303, 2.39708, 2.40131,
1586  2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.7196, 0.722567,
1587  0.723924, 0.725024, 0.725386, 0.725467, 0.725518, 0.725552,
1588  0.725576, 0.725595, 0.725675, 0.72576, 0.725849, 0.72603, 0.726211,
1589  0.726392, 0.726754, 0.727117, 0.72748, 0.727843, 0.728207, 0.728571,
1590  0.728936, 0.729849, 0.730765, 0.732605, 0.734456, 0.736316,
1591  0.740071, 0.743868, 0.747711, 0.751599, 0.755534, 0.759516,
1592  0.763547, 0.767627, 0.771759, 0.775942, 0.780178, 0.784469,
1593  0.795442, 0.806783, 0.818514, 0.830662, 0.843253, 0.856316,
1594  0.869886, 0.883998, 0.898692, 0.914015, 0.930016, 0.946752,
1595  0.964288, 0.982696, 1.00206, 1.02247, 1.04405, 1.06692, 1.09123,
1596  1.11716, 1.14494, 1.17482, 1.20713, 1.24229, 1.28082, 1.32342,
1597  1.37101, 1.42493, 1.44867, 1.47389, 1.50078, 1.5296, 1.56064,
1598  1.5943, 1.63108, 1.67167, 1.71702, 1.7685, 1.82829, 1.90008, 1.9425,
1599  1.99122, 2.04895, 2.08267, 2.12104, 2.13809, 2.15636, 2.1761,
1600  2.19764, 2.22147, 2.24834, 2.27951, 2.29738, 2.31743, 2.34054,
1601  2.35374, 2.36848, 2.3854, 2.38914, 2.39302, 2.39707, 2.4013,
1602  2.40575, 2.41541, 2.42645, 2.43271, 2.43966}, {0.680361, 0.681655,
1603  0.681927, 0.681788, 0.681669, 0.681657, 0.681664, 0.681682,
1604  0.681705, 0.681729, 0.681838, 0.681934, 0.682031, 0.682225, 0.68242,
1605  0.682614, 0.683004, 0.683394, 0.683784, 0.684175, 0.684566,
1606  0.684957, 0.685349, 0.686331, 0.687316, 0.689293, 0.69128, 0.693279,
1607  0.69731, 0.701387, 0.705509, 0.709679, 0.713897, 0.718164,
1608  0.722481, 0.72685, 0.731271, 0.735746, 0.740276, 0.744863, 0.756582,
1609  0.768683, 0.781187, 0.794122, 0.807514, 0.821395, 0.835799,
1610  0.850762, 0.866327, 0.88254, 0.899452, 0.917122, 0.935614, 0.955004,
1611  0.975376, 0.996827, 1.01947, 1.04344, 1.06888, 1.09599, 1.12497,
1612  1.1561, 1.18971, 1.22621, 1.26614, 1.31018, 1.35928, 1.41476,
1613  1.43915, 1.46502, 1.49258, 1.52208, 1.5538, 1.58816, 1.62564,
1614  1.66694, 1.713, 1.76521, 1.82572, 1.89823, 1.941, 1.99007, 2.04813,
1615  2.08202, 2.12055, 2.13766, 2.15599, 2.17578, 2.19738, 2.22127,
1616  2.24819, 2.2794, 2.2973, 2.31737, 2.34051, 2.35371, 2.36846,
1617  2.38539, 2.38913, 2.39301, 2.39706, 2.40129, 2.40574, 2.4154,
1618  2.42645, 2.43271, 2.43966}, {0.630475, 0.629154, 0.628652, 0.628812,
1619  0.628995, 0.62902, 0.629028, 0.629035, 0.629045, 0.629061,
1620  0.629172, 0.629277, 0.629381, 0.629592, 0.629802, 0.630012,
1621  0.630433, 0.630855, 0.631277, 0.631699, 0.632122, 0.632545,
1622  0.632968, 0.634029, 0.635093, 0.637229, 0.639376, 0.641534,
1623  0.645886, 0.650284, 0.65473, 0.659225, 0.66377, 0.668366, 0.673014,
1624  0.677716, 0.682472, 0.687284, 0.692153, 0.69708, 0.709663, 0.722641,
1625  0.73604, 0.749885, 0.764206, 0.779035, 0.794407, 0.81036, 0.826938,
1626  0.844188, 0.862164, 0.880925, 0.900539, 0.921082, 0.94264,
1627  0.965314, 0.989218, 1.01449, 1.04128, 1.06978, 1.1002, 1.13284,
1628  1.168, 1.20613, 1.24774, 1.29355, 1.34449, 1.4019, 1.42708, 1.45377,
1629  1.48215, 1.51248, 1.54506, 1.58029, 1.61866, 1.66085, 1.70782,
1630  1.76095, 1.82238, 1.89581, 1.93904, 1.98856, 2.04706, 2.08116,
1631  2.1199, 2.13709, 2.1555, 2.17537, 2.19704, 2.221, 2.24799, 2.27927,
1632  2.29719, 2.31729, 2.34045, 2.35367, 2.36843, 2.38537, 2.38911,
1633  2.39299, 2.39704, 2.40128, 2.40573, 2.41539, 2.42644, 2.4327,
1634  2.43966}, {0.571708, 0.573132, 0.573635, 0.573297, 0.573329,
1635  0.573398, 0.573443, 0.573465, 0.573477, 0.573488, 0.5736, 0.573712,
1636  0.573823, 0.574048, 0.574272, 0.574496, 0.574944, 0.575393,
1637  0.575843, 0.576292, 0.576743, 0.577194, 0.577645, 0.578775,
1638  0.579908, 0.582183, 0.58447, 0.586768, 0.591402, 0.596085, 0.600818,
1639  0.605603, 0.61044, 0.61533, 0.620276, 0.625278, 0.630337, 0.635455,
1640  0.640632, 0.645871, 0.659247, 0.673038, 0.687272, 0.701975,
1641  0.717178, 0.732914, 0.74922, 0.766136, 0.783707, 0.801983, 0.821018,
1642  0.840873, 0.86162, 0.883336, 0.90611, 0.930046, 0.955261, 0.981893,
1643  1.0101, 1.04008, 1.07205, 1.10629, 1.14315, 1.18304, 1.22651,
1644  1.27427, 1.32727, 1.38685, 1.41293, 1.44053, 1.46986, 1.50115,
1645  1.53471, 1.57094, 1.61033, 1.65357, 1.70161, 1.75581, 1.81834,
1646  1.89287, 1.93665, 1.98671, 2.04575, 2.08011, 2.1191, 2.13638,
1647  2.15489, 2.17486, 2.19662, 2.22067, 2.24774, 2.2791, 2.29706,
1648  2.31719, 2.34039, 2.35362, 2.36839, 2.38534, 2.38909, 2.39297,
1649  2.39703, 2.40126, 2.40571, 2.41538, 2.42643, 2.4327,
1650  2.43966}, {0.522196, 0.520579, 0.52057, 0.521087, 0.52093, 0.520981,
1651  0.521047, 0.521087, 0.521102, 0.52111, 0.521228, 0.521338,
1652  0.521456, 0.521686, 0.521918, 0.522149, 0.522613, 0.523077,
1653  0.523541, 0.524006, 0.524471, 0.524937, 0.525404, 0.526572,
1654  0.527743, 0.530095, 0.53246, 0.534837, 0.539631, 0.544478, 0.549379,
1655  0.554335, 0.559348, 0.564418, 0.569547, 0.574737, 0.579987,
1656  0.585301, 0.590679, 0.596123, 0.61003, 0.624382, 0.639206, 0.654532,
1657  0.670391, 0.686819, 0.703853, 0.721535, 0.739912, 0.759036,
1658  0.778963, 0.799758, 0.821493, 0.844248, 0.868117, 0.893205,
1659  0.919633, 0.947544, 0.977101, 1.0085, 1.04198, 1.07781, 1.11634,
1660  1.15802, 1.20338, 1.25315, 1.30829, 1.37015, 1.39719, 1.42578,
1661  1.45611, 1.48844, 1.52307, 1.56039, 1.6009, 1.64529, 1.69451,
1662  1.74992, 1.81368, 1.88946, 1.93386, 1.98455, 2.0442, 2.07886,
1663  2.11815, 2.13555, 2.15417, 2.17425, 2.19612, 2.22028, 2.24745,
1664  2.2789, 2.29691, 2.31708, 2.34031, 2.35356, 2.36835, 2.38531,
1665  2.38906, 2.39295, 2.39701, 2.40125, 2.4057, 2.41537, 2.42643,
1666  2.43269, 2.43965},
1667 {0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9}};
1668 
1669  const double imomegaqnm55[8][107] = {{0.0151971, 0.02987, 0.0432352, 0.064849, 0.0789971, 0.0834521,
1670  0.0865117, 0.0885261, 0.0898184, 0.090638, 0.0919286, 0.0920896,
1671  0.0921222, 0.0921485, 0.0921652, 0.0921765, 0.092191, 0.0922013,
1672  0.0922106, 0.0922195, 0.0922283, 0.0922371, 0.0922459, 0.0922679,
1673  0.0922898, 0.0923335, 0.092377, 0.0924205, 0.0925068, 0.0925926,
1674  0.0926777, 0.092762, 0.0928457, 0.0929286, 0.0930106, 0.0930918,
1675  0.0931722, 0.0932516, 0.09333, 0.0934074, 0.0935961, 0.0937773,
1676  0.09395, 0.0941133, 0.094266, 0.0944066, 0.0945339, 0.094646,
1677  0.0947411, 0.0948169, 0.0948709, 0.0949002, 0.0949014, 0.0948705,
1678  0.094803, 0.0946932, 0.0945348, 0.0943198, 0.0940389, 0.0936804,
1679  0.0932301, 0.09267, 0.0919774, 0.0911228, 0.0900671, 0.0887575,
1680  0.0871199, 0.0850466, 0.0840612, 0.0829665, 0.0817451, 0.0803751,
1681  0.0788289, 0.0770706, 0.0750526, 0.0727103, 0.0699513, 0.0666388,
1682  0.0625545, 0.0573174, 0.054054, 0.0501531, 0.0453206, 0.0423931,
1683  0.038969, 0.0374162, 0.0357305, 0.0338844, 0.0318402, 0.0295431,
1684  0.0269089, 0.0237947, 0.0219803, 0.0199207, 0.017514, 0.0161252,
1685  0.0145605, 0.0127472, 0.0123443, 0.0119247, 0.0114865, 0.011027,
1686  0.0105435, 0.00948819, 0.00827437, 0.00758316,
1687  0.00681219}, {0.25166, 0.264251, 0.270831, 0.275931, 0.277491,
1688  0.277846, 0.278073, 0.278222, 0.278323, 0.278391, 0.278527,
1689  0.278556, 0.278565, 0.278576, 0.278588, 0.2786, 0.278625, 0.27865,
1690  0.278676, 0.278701, 0.278726, 0.278751, 0.278776, 0.278839,
1691  0.278901, 0.279026, 0.27915, 0.279273, 0.279519, 0.279763, 0.280005,
1692  0.280244, 0.280481, 0.280716, 0.280948, 0.281177, 0.281404,
1693  0.281627, 0.281847, 0.282065, 0.282593, 0.283097, 0.283575,
1694  0.284023, 0.284438, 0.284817, 0.285154, 0.285444, 0.285682,
1695  0.285862, 0.285974, 0.286011, 0.285963, 0.285817, 0.28556, 0.285175,
1696  0.284643, 0.28394, 0.283038, 0.281902, 0.280489, 0.278746,
1697  0.276603, 0.273974, 0.27074, 0.266744, 0.261763, 0.255474, 0.252491,
1698  0.249179, 0.245488, 0.24135, 0.236685, 0.231383, 0.225304,
1699  0.218251, 0.20995, 0.199989, 0.187715, 0.171984, 0.162185, 0.150475,
1700  0.135971, 0.127186, 0.116912, 0.112252, 0.107194, 0.101656,
1701  0.0955223, 0.0886307, 0.0807275, 0.0713845, 0.0659411, 0.0597624,
1702  0.0525421, 0.0483758, 0.0436815, 0.0382415, 0.037033, 0.0357743,
1703  0.0344594, 0.0330811, 0.0316306, 0.0284646, 0.0248231, 0.0227495,
1704  0.0204366}, {0.467579, 0.470028, 0.470942, 0.471348, 0.471322,
1705  0.47129, 0.471261, 0.471239, 0.471223, 0.471213, 0.471201, 0.47121,
1706  0.471221, 0.47124, 0.471258, 0.471277, 0.471314, 0.471351, 0.471388,
1707  0.471425, 0.471462, 0.471499, 0.471536, 0.471628, 0.47172,
1708  0.471904, 0.472086, 0.472268, 0.472628, 0.472984, 0.473336,
1709  0.473684, 0.474028, 0.474367, 0.474701, 0.475031, 0.475355,
1710  0.475674, 0.475987, 0.476294, 0.477036, 0.477735, 0.478387,
1711  0.478987, 0.479529, 0.480006, 0.480411, 0.480735, 0.480968,
1712  0.481101, 0.481119, 0.481008, 0.480751, 0.480328, 0.479717,
1713  0.478889, 0.477812, 0.476446, 0.474745, 0.472651, 0.470091,
1714  0.466978, 0.463197, 0.4586, 0.452993, 0.446112, 0.437588, 0.426883,
1715  0.421821, 0.416213, 0.409971, 0.402987, 0.395124, 0.386201,
1716  0.375984, 0.364147, 0.350231, 0.333554, 0.313026, 0.286746,
1717  0.270386, 0.250845, 0.226651, 0.212, 0.194868, 0.1871, 0.178668,
1718  0.169434, 0.15921, 0.147722, 0.134549, 0.118976, 0.109903,
1719  0.0996047, 0.0875705, 0.0806266, 0.0728027, 0.063736, 0.0617217,
1720  0.0596238, 0.0574324, 0.0551353, 0.0527177, 0.047441, 0.0413719,
1721  0.0379158, 0.034061}, {0.676801, 0.675633, 0.67493, 0.67443, 0.6744,
1722  0.674422, 0.674445, 0.674462, 0.674474, 0.674481, 0.67449,
1723  0.674497, 0.674508, 0.674528, 0.674548, 0.674568, 0.674609,
1724  0.674649, 0.674689, 0.674729, 0.674769, 0.674809, 0.674849,
1725  0.674948, 0.675048, 0.675245, 0.675441, 0.675635, 0.67602, 0.676399,
1726  0.676771, 0.677137, 0.677496, 0.677847, 0.678192, 0.678529,
1727  0.678858, 0.679179, 0.679492, 0.679795, 0.680514, 0.681168,
1728  0.681753, 0.68226, 0.682681, 0.683008, 0.683228, 0.683332, 0.683303,
1729  0.683128, 0.682788, 0.682263, 0.681529, 0.680557, 0.679315,
1730  0.677766, 0.675862, 0.673549, 0.67076, 0.667416, 0.663415, 0.658633,
1731  0.65291, 0.64604, 0.637751, 0.627674, 0.615292, 0.599856, 0.592588,
1732  0.584557, 0.575639, 0.565684, 0.554498, 0.541831, 0.527355,
1733  0.510615, 0.490971, 0.467468, 0.438585, 0.401662, 0.378702,
1734  0.351292, 0.317377, 0.296847, 0.272846, 0.261966, 0.250155,
1735  0.237224, 0.222906, 0.20682, 0.188374, 0.16657, 0.153867, 0.139448,
1736  0.1226, 0.112878, 0.101924, 0.0892306, 0.0864106, 0.0834736,
1737  0.0804055, 0.0771896, 0.0738049, 0.0664175, 0.0579207, 0.0530822,
1738  0.0476854}, {0.891895, 0.89147, 0.891863, 0.892311, 0.89227,
1739  0.892236, 0.892217, 0.892213, 0.892217, 0.892223, 0.892242,
1740  0.892246, 0.892254, 0.892269, 0.892283, 0.892298, 0.892327,
1741  0.892357, 0.892386, 0.892415, 0.892444, 0.892473, 0.892502,
1742  0.892574, 0.892646, 0.892788, 0.892927, 0.893065, 0.893335,
1743  0.893597, 0.89385, 0.894094, 0.894329, 0.894554, 0.89477, 0.894975,
1744  0.89517, 0.895353, 0.895526, 0.895686, 0.896031, 0.896291, 0.896458,
1745  0.896521, 0.89647, 0.896292, 0.895974, 0.895501, 0.894855,
1746  0.894014, 0.892957, 0.891657, 0.890083, 0.888198, 0.88596, 0.88332,
1747  0.880219, 0.876586, 0.872336, 0.867364, 0.86154, 0.854705, 0.846653,
1748  0.83712, 0.825754, 0.812083, 0.795442, 0.774871, 0.765236,
1749  0.754619, 0.742864, 0.729775, 0.715106, 0.698537, 0.679644,
1750  0.657847, 0.632324, 0.601851, 0.564477, 0.516789, 0.487173,
1751  0.451846, 0.408167, 0.381741, 0.350856, 0.336857, 0.321664, 0.30503,
1752  0.286614, 0.265926, 0.242205, 0.214167, 0.197833, 0.179293,
1753  0.15763, 0.14513, 0.131046, 0.114725, 0.1111, 0.107324, 0.103379,
1754  0.099244, 0.0948923, 0.085394, 0.0744695, 0.0682486,
1755  0.0613098}, {1.12614, 1.12697, 1.12642, 1.12612, 1.12629, 1.12629,
1756  1.12627, 1.12625, 1.12624, 1.12624, 1.12626, 1.12625, 1.12626,
1757  1.12626, 1.12626, 1.12626, 1.12626, 1.12626, 1.12627, 1.12627,
1758  1.12627, 1.12627, 1.12628, 1.12628, 1.12628, 1.12629, 1.12629,
1759  1.1263, 1.12629, 1.12628, 1.12625, 1.12622, 1.12617, 1.12611,
1760  1.12604, 1.12595, 1.12586, 1.12574, 1.12562, 1.12548, 1.12505,
1761  1.12453, 1.12388, 1.1231, 1.12219, 1.12111, 1.11986, 1.11841,
1762  1.11675, 1.11485, 1.11267, 1.1102, 1.10738, 1.10418, 1.10054,
1763  1.09641, 1.0917, 1.08634, 1.08021, 1.07319, 1.06513, 1.05582,
1764  1.04501, 1.03238, 1.0175, 0.999787, 0.978439, 0.952276, 0.940091,
1765  0.926705, 0.911928, 0.895521, 0.877184, 0.856528, 0.833035, 0.806,
1766  0.774421, 0.736806, 0.690779, 0.632177, 0.595837, 0.552533,
1767  0.499038, 0.466693, 0.428905, 0.411781, 0.393199, 0.372856,
1768  0.350338, 0.325043, 0.296043, 0.261768, 0.241802, 0.219141,
1769  0.192661, 0.177383, 0.160169, 0.140221, 0.135789, 0.131174,
1770  0.126352, 0.121299, 0.11598, 0.104371, 0.0910184, 0.083415,
1771  0.0749342}, {1.3749, 1.37446, 1.37529, 1.37504, 1.37506, 1.37511,
1772  1.37511, 1.37508, 1.37506, 1.37506, 1.37507, 1.37505, 1.37505,
1773  1.37503, 1.37501, 1.37499, 1.37496, 1.37492, 1.37488, 1.37485,
1774  1.37481, 1.37478, 1.37474, 1.37465, 1.37456, 1.37437, 1.37418,
1775  1.37399, 1.37359, 1.37319, 1.37277, 1.37233, 1.37188, 1.37142,
1776  1.37094, 1.37045, 1.36993, 1.36941, 1.36886, 1.36829, 1.3668,
1777  1.36517, 1.36339, 1.36145, 1.35934, 1.35704, 1.35452, 1.35177,
1778  1.34875, 1.34544, 1.3418, 1.33779, 1.33338, 1.3285, 1.32309,
1779  1.31709, 1.3104, 1.30292, 1.29452, 1.28507, 1.27436, 1.26216,
1780  1.24818, 1.23202, 1.2132, 1.19101, 1.1645, 1.13228, 1.11735,
1781  1.10101, 1.08301, 1.06309, 1.04089, 1.01595, 0.987663, 0.955194,
1782  0.917365, 0.872418, 0.817554, 0.747869, 0.704729, 0.653377,
1783  0.590005, 0.551715, 0.507, 0.486743, 0.464764, 0.440707, 0.41408,
1784  0.384173, 0.34989, 0.309375, 0.285775, 0.25899, 0.227694, 0.209637,
1785  0.189292, 0.165716, 0.160479, 0.155024, 0.149326, 0.143353,
1786  0.137067, 0.123347, 0.107567, 0.0985815, 0.0885587},
1787 {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
1788 
1789  /* To actually calculate the ringdown, we will use the following pointers to point to the correct mode */
1790  const double (*reomegaqnm)[107] = NULL;
1791  const double (*imomegaqnm)[107] = NULL;
1792 
1793  REAL8 totalMass, finalMass, finalSpin;
1794 
1795  /* Stuff for interpolating the data */
1796  gsl_spline *spline = NULL;
1797  gsl_interp_accel *acc = NULL;
1798 
1799  UINT4 i;
1800  REAL8 signm = m < 0 ? -1.0 : 1.0;
1801 
1802  /* Check we do not require more overtones than we have */
1803  if ( nmodes > 8 )
1804  {
1805  XLALPrintError( "Requesting more overtones than we have data to generate!\n");
1806  XLAL_ERROR( XLAL_EINVAL );
1807  }
1808 
1809  /* Choose the appropriate data bases on the user requested l an m */
1810  switch ( l )
1811  {
1812  case 2:
1813  if ( abs(m) == 2 )
1814  {
1815  reomegaqnm = reomegaqnm22;
1816  imomegaqnm = imomegaqnm22;
1817  }
1818  else if ( abs(m) == 1 )
1819  {
1820  reomegaqnm = reomegaqnm21;
1821  imomegaqnm = imomegaqnm21;
1822  }
1823  else if ( abs(m) == 0 )
1824  {
1825  reomegaqnm = reomegaqnm20;
1826  imomegaqnm = imomegaqnm20;
1827  }
1828  else
1829  {
1830  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
1831  XLAL_ERROR( XLAL_EINVAL );
1832  }
1833  break;
1834  case 3:
1835  if ( l == 3 )
1836  {
1837  reomegaqnm = reomegaqnm33;
1838  imomegaqnm = imomegaqnm33;
1839  }
1840  else
1841  {
1842  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
1843  XLAL_ERROR( XLAL_EINVAL );
1844  }
1845  break;
1846  case 4:
1847  if ( l == 4 )
1848  {
1849  reomegaqnm = reomegaqnm44;
1850  imomegaqnm = imomegaqnm44;
1851  }
1852  else
1853  {
1854  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
1855  XLAL_ERROR( XLAL_EINVAL );
1856  }
1857  break;
1858  case 5:
1859  if ( l == 5 )
1860  {
1861  reomegaqnm = reomegaqnm55;
1862  imomegaqnm = imomegaqnm55;
1863  }
1864  else
1865  {
1866  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
1867  XLAL_ERROR( XLAL_EINVAL );
1868  }
1869  break;
1870  default:
1871  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
1872  XLAL_ERROR( XLAL_EINVAL );
1873  break;
1874  }
1875 
1876  spline = gsl_spline_alloc( gsl_interp_cspline, 107 );
1877  acc = gsl_interp_accel_alloc();
1878 
1879  totalMass = mass1 + mass2;
1880 
1881  /* Call XLALSimIMREOBFinalMassSpinPrec() to get mass and spin of the final black hole */
1882  if ( XLALSimIMREOBFinalMassSpinPrec(&finalMass, &finalSpin, mass1, mass2, spin1, spin2, approximant) == XLAL_FAILURE )
1883  {
1884  XLAL_ERROR( XLAL_EFUNC );
1885  }
1886 
1887  /* finalSpin interpolation is available only between -0.9996 and 0.9996 */
1888  /* Set finalSpin to +/- 0.9996 if it is out of this range */
1889  if ( finalSpin < -0.9996 ) finalSpin = -0.9996;
1890  if ( finalSpin > 0.9996 ) finalSpin = 0.9996;
1891  /* Now get the QNM frequencies from interpolating the above data */
1892  for ( i = 0; i < nmodes; i++ )
1893  {
1894  gsl_spline_init( spline, afinallist, reomegaqnm[i], 107 );
1895  gsl_interp_accel_reset( acc );
1896 
1897  modefreqs->data[i] = signm*gsl_spline_eval( spline, signm*finalSpin, acc );
1898 
1899  gsl_spline_init( spline, afinallist, imomegaqnm[i], 107 );
1900  gsl_interp_accel_reset( acc );
1901 
1902  modefreqs->data[i] += I*gsl_spline_eval( spline, signm*finalSpin, acc );
1903 
1904  /* Scale by the appropriate mass factors */
1905  modefreqs->data[i] *= 1./ finalMass / (totalMass * LAL_MTSUN_SI);
1906  }
1907  /* Free memory and exit */
1908  gsl_spline_free( spline );
1909  gsl_interp_accel_free( acc );
1910 
1911  return XLAL_SUCCESS;
1912 }
1913 
1914 
1915 
1916 /**
1917  * This function generates the quasinormal mode frequencies for a black
1918  * hole ringdown. At present, this function works for the 22, 21, 33, 44
1919  * and 55 modes, and includes 8 overtones. The final frequencies are
1920  * computed by interpolating the data found on the webpage of
1921  * Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
1922  * In this page, frequecy data are given for positive final spins only.
1923  * For a negative final spin chi<0 case, the (l,m) mode frequency is given by
1924  * the (l,-m) mode frequency of the positive final spin -chi case.
1925  */
1926 INT4 XLALSimIMREOBGenerateQNMFreqV2FromFinalPrec(
1927  COMPLEX16Vector *modefreqs, /**<< OUTPUT, complex freqs of overtones in unit of Hz */
1928  const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
1929  const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
1930  const REAL8 finalMass, /**<< The mass of the final BH (scaled by original total mass) */
1931  REAL8 finalSpin, /**<< The dimensionless spin of the final BH */
1932  UINT4 l, /**<< The l value of the mode in question */
1933  INT4 m, /**<< The m value of the mode in question */
1934  UINT4 nmodes /**<< The number of overtones that should be included (max 8) */
1935  )
1936 {
1937 
1938  /* Data for interpolating the quasinormal mode frequencies is taken from
1939  * The webpage of Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
1940  * In the spin range of (-0.995, 0.999),
1941  * interpolation error within 5e-5 for the first 3 overtones of the 22 mode
1942  * interpolation error within 0.005 for the first 8 overtones of the 22 mode
1943  * On the data points, interpolation error is within 1e-5, except for the
1944  * highest overtone of the (4,4) and (5,5) modes.
1945  */
1946 
1947  static const double afinallist[107] = {-0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
1948  -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
1949  -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,
1950  -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,
1951  -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,
1952  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,
1953  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,
1954  0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996};
1955 
1956  /* 2, 2 mode */
1957 
1958  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, 0.29187, 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, 0.5326, 0.541794, 0.55163, 0.562201, 0.573616, 0.586017, 0.59958, 0.614539, 0.631206, 0.650018, 0.671614, 0.696995, 0.727875, 0.74632, 0.767674, 0.793208, 0.808235, 0.825429, 0.8331, 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, 0.97169},
1959 {0.243689, 0.247076, 0.248937, 0.250577, 0.251041, 0.251088, 0.251073, 0.251023, 0.250952, 0.250874, 0.25052, 0.250339, 0.250292, 0.250359, 0.250463, 0.250549, 0.250686, 0.250814, 0.250945, 0.251079, 0.251214, 0.251349, 0.251484, 0.25182, 0.252158, 0.252836, 0.253519, 0.254205, 0.255591, 0.256994, 0.258413, 0.259851, 0.261306, 0.26278, 0.264273, 0.265785, 0.267317, 0.268869, 0.270442, 0.272036, 0.276117, 0.280342, 0.284721, 0.289262, 0.293978, 0.29888, 0.303981, 0.309295, 0.314838, 0.320629, 0.326687, 0.333036, 0.339701, 0.346711, 0.354101, 0.36191, 0.370183, 0.378976, 0.388353, 0.39839, 0.409183, 0.420847, 0.433527, 0.447407, 0.462728, 0.479807, 0.499079, 0.521161, 0.53097, 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, 0.94811, 0.949919, 0.951804, 0.953776, 0.955847, 0.960353, 0.96551, 0.968435, 0.971688},
1960 {0.191626, 0.188311, 0.185222, 0.182107, 0.182532, 0.183173, 0.183784, 0.184279, 0.184634, 0.18486, 0.184811, 0.184353, 0.184263, 0.184581, 0.184713, 0.18472, 0.184862, 0.185055, 0.185205, 0.185357, 0.185521, 0.185687, 0.18585, 0.18625, 0.186658, 0.187473, 0.188294, 0.189121, 0.190789, 0.192478, 0.194189, 0.195923, 0.19768, 0.19946, 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, 0.43513, 0.454179, 0.475545, 0.499906, 0.510701, 0.522217, 0.534557, 0.547847, 0.56224, 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, 0.95376, 0.955833, 0.960343, 0.965503, 0.96843, 0.971683},
1961 {0.127766, 0.134925, 0.137314, 0.135026, 0.132545, 0.132613, 0.133213, 0.133927, 0.134502, 0.134846, 0.134197,
1962 0.133839, 0.134383, 0.134311, 0.134305, 0.134548, 0.134538, 0.134764, 0.134855, 0.13499, 0.135153, 0.135276, 0.135401, 0.13576, 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, 0.16692, 0.172065, 0.177495, 0.183228, 0.18928, 0.19567, 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, 0.40121, 0.421977, 0.445099, 0.471336, 0.482957, 0.495375, 0.508729, 0.523187, 0.538956, 0.556285, 0.575464, 0.59683, 0.620788, 0.647869, 0.678894, 0.715333, 0.736426, 0.760279, 0.788101, 0.804173, 0.822338, 0.830374, 0.83897, 0.848242, 0.858347, 0.869515, 0.8821, 0.896696, 0.905068, 0.91446, 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},
1963 {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, 0.11021, 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, 0.12123, 0.122431, 0.123659, 0.124914, 0.126199, 0.12955, 0.133123, 0.136951, 0.141068, 0.145514, 0.150331, 0.155561, 0.161252, 0.167448, 0.174197, 0.18154, 0.189518, 0.198166, 0.207515, 0.217594, 0.228433, 0.24006, 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, 0.82065, 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},
1964 {0.0973518, 0.0987518, 0.0952128, 0.097231, 0.0968051, 0.0959061, 0.0958383, 0.0963991, 0.0969597, 0.0971588, 0.0962907, 0.0968828, 0.0964446, 0.0967173, 0.0968133, 0.0967445, 0.0968961, 0.0970152, 0.0970355, 0.0971754, 0.0972259, 0.0973507, 0.097408, 0.0976397, 0.0978753, 0.0983115, 0.0987594, 0.099209, 0.100108, 0.101005, 0.101904, 0.102805, 0.103707, 0.104611, 0.10552, 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, 0.14171, 0.147116, 0.153415, 0.160767, 0.169299, 0.179085, 0.19014, 0.202441, 0.215947, 0.230623, 0.246457, 0.263464, 0.281691, 0.301218, 0.322157, 0.344655, 0.368896, 0.39509, 0.42345, 0.43543, 0.447764, 0.460418, 0.473311, 0.486283, 0.499037,
1965 0.511101, 0.522095, 0.532461, 0.536917, 0.527548, 0.521465, 0.518438, 0.515417, 0.51241, 0.510911, 0.509415, 0.508818, 0.508221, 0.507624, 0.507028, 0.506432, 0.505837, 0.505242, 0.504944, 0.504647, 0.50435, 0.504202, 0.504054, 0.503904, 0.503874, 0.503845, 0.503817, 0.503789, 0.50376, 0.503692, 0.503638, 0.503632, 0.503585},
1966 {0.084098, 0.0868741, 0.0879148, 0.0858816, 0.0871769, 0.0862173, 0.0858779, 0.0863779, 0.0869438, 0.0870509, 0.0866021, 0.0864788, 0.0867758, 0.0866752, 0.0866613, 0.0868868, 0.086965, 0.0870574, 0.0871075, 0.0872251, 0.0873545, 0.0874293, 0.087563, 0.0878271, 0.088086, 0.0886037, 0.0891314, 0.0896576, 0.0906978, 0.0917299, 0.0927446, 0.093744, 0.0947274, 0.0956935, 0.0966414, 0.0975719, 0.0984848, 0.0993786, 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, 0.45201, 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,
1967 0.818797, 0.827303, 0.836336, 0.846012, 0.856487, 0.867993, 0.880887, 0.895775, 0.904293, 0.913837, 0.92483, 0.931097, 0.938091, 0.946107, 0.947875, 0.949711, 0.951623, 0.953621, 0.955717, 0.960269, 0.965464, 0.968404, 0.971669},
1968 {0.0783357, 0.0733796, 0.0766204, 0.0744319, 0.0764107, 0.0754793, 0.0749396, 0.0755031, 0.0761004, 0.0760294, 0.0759874, 0.075511, 0.0757765, 0.0758322, 0.0759714, 0.0759232, 0.0761145, 0.0762289, 0.0763205, 0.0764184, 0.0765972, 0.0767207, 0.0768409, 0.0771736, 0.0775187, 0.07821, 0.0789117, 0.0796137, 0.0810158, 0.0824117, 0.0837964, 0.0851528, 0.0864792, 0.0877698, 0.0890208, 0.0902295, 0.0913937, 0.0925132, 0.0935883, 0.0946171, 0.0969926, 0.0990908, 0.100921, 0.102489, 0.103795, 0.104821, 0.10553, 0.105854, 0.105679, 0.104817, 0.102968, 0.0997112, 0.094996, 0.0928224, 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, 0.52572, 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, 0.93791, 0.945976, 0.947755, 0.949602, 0.951525, 0.953535, 0.955643, 0.960217, 0.965434, 0.968355, 0.971639}};
1969 
1970  const double imomegaqnm22[8][107] = {{0.0784607, 0.0801007, 0.0816472, 0.0840037, 0.0854954, 0.0860129, 0.0864215, 0.0867455, 0.0870035, 0.08721, 0.0877802, 0.0879878, 0.088065, 0.0880965, 0.0880878, 0.0880757, 0.0880612, 0.0880574, 0.0880589, 0.0880627, 0.0880675, 0.0880727, 0.088078, 0.0880913, 0.0881045, 0.0881304, 0.088156, 0.0881813, 0.0882315, 0.0882807, 0.0883289, 0.0883763, 0.0884226, 0.0884679, 0.0885122, 0.0885555, 0.0885976, 0.0886386, 0.0886785, 0.0887172, 0.0888085, 0.0888917, 0.0889663, 0.0890315, 0.0890868, 0.0891313, 0.0891643, 0.0891846, 0.0891911, 0.0891825, 0.0891574, 0.0891138, 0.0890496, 0.0889623, 0.0888489, 0.0887057, 0.0885283, 0.0883112, 0.0880477, 0.0877293, 0.0873453, 0.086882, 0.0863212, 0.0856388, 0.0848021, 0.0837652, 0.0824618, 0.0807929, 0.0799908, 0.0790927, 0.0780817, 0.0769364, 0.0756296, 0.0741258, 0.072378, 0.0703215, 0.0678642, 0.0648692, 0.0611186, 0.0562313, 0.053149, 0.0494336, 0.0447904, 0.0419586, 0.0386302, 0.0371155, 0.0354676, 0.033659, 0.0316516, 0.0293904, 0.0267908, 0.0237095, 0.0219107, 0.0198661, 0.0174737, 0.0160919, 0.014534, 0.0127274, 0.0123259, 0.0119077, 0.0114708, 0.0110127, 0.0105306, 0.00947799, 0.00826689, 0.00757704, 0.0068074},
1971 {0.284478, 0.282567, 0.281162, 0.279245, 0.278072, 0.27767, 0.277358, 0.277118, 0.276936, 0.2768, 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, 0.27712, 0.27716, 0.277197, 0.27723, 0.277259, 0.277283, 0.277304, 0.277321, 0.277333, 0.277344, 0.277326, 0.277278, 0.277196, 0.27708, 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, 0.24958, 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, 0.0949599, 0.0881754, 0.080377, 0.0711342, 0.0657383, 0.0596046, 0.0524264, 0.04828, 0.043605, 0.0381837, 0.0369789, 0.0357239, 0.0344128, 0.0330384, 0.0315916, 0.0284334, 0.0247999, 0.0227304, 0.0204216},
1972 {0.504534, 0.501693, 0.501238, 0.503711, 0.506007, 0.50649, 0.506633, 0.506559, 0.506365, 0.50612, 0.505173, 0.50512, 0.505381, 0.505519, 0.505371, 0.505318, 0.505354, 0.505311, 0.505262, 0.505236, 0.50521, 0.505177, 0.505141, 0.505059, 0.504978, 0.504812, 0.504645, 0.504476, 0.504135, 0.503786, 0.503432, 0.50307, 0.502702, 0.502326, 0.501944, 0.501554, 0.501156, 0.500751, 0.500338, 0.499917, 0.498828, 0.497686, 0.496488, 0.49523, 0.49391, 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, 0.46126, 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, 0.35594, 0.34311, 0.327518, 0.308058, 0.282827, 0.266998, 0.248008, 0.22441, 0.210086, 0.193307, 0.18569, 0.177413, 0.16834, 0.158283, 0.146966, 0.133965, 0.118563, 0.109572, 0.0993515, 0.0873891, 0.0804781, 0.0726848, 0.0636465, 0.0616378, 0.0595453, 0.0573593, 0.0550676, 0.0526555, 0.0473899, 0.0413327, 0.037883, 0.0340348},
1973 {0.777682, 0.77817, 0.774907, 0.771079, 0.772456, 0.773571, 0.774249, 0.774423, 0.774236, 0.773865, 0.772678, 0.773376, 0.773489, 0.77299, 0.773229, 0.773121, 0.773005, 0.772942, 0.772818, 0.772776, 0.77268, 0.772579, 0.772506, 0.772294, 0.772084, 0.771654, 0.771224, 0.770787, 0.7699, 0.768995, 0.768072, 0.767129, 0.766168, 0.765187, 0.764186, 0.763165, 0.762123, 0.761061, 0.759977, 0.758872, 0.756015, 0.75302, 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, 0.50348, 0.485224, 0.462864, 0.434823, 0.398473, 0.375741, 0.348572, 0.314974, 0.294663, 0.270945, 0.2602, 0.248542, 0.235779, 0.221649, 0.205769, 0.187547, 0.16598, 0.153396, 0.139094, 0.122354, 0.112682, 0.101773, 0.0891181, 0.0863053, 0.0833752, 0.0803139, 0.0771045, 0.0737264, 0.0663517, 0.0578682, 0.053037, 0.0476481},
1974 {1.04431, 1.0466, 1.05065, 1.04828, 1.04719, 1.04809, 1.04894, 1.04925, 1.04906, 1.04863, 1.04812, 1.04862, 1.04806, 1.04843, 1.04808, 1.04824, 1.04803, 1.04799, 1.04788, 1.04781, 1.04768, 1.04762, 1.04752, 1.04729, 1.04704, 1.04657, 1.04609, 1.0456, 1.0446, 1.04357, 1.04251, 1.04141, 1.04028, 1.03911, 1.03791, 1.03667, 1.03539, 1.03406, 1.0327, 1.03129, 1.02756, 1.02353, 1.01918, 1.01448, 1.00943, 1.004, 0.9982, 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, 0.7538, 0.74371, 0.733106, 0.721967, 0.710268, 0.697962, 0.684902, 0.670601, 0.65375, 0.632042, 0.603295, 0.56587, 0.517102, 0.486783, 0.450771, 0.406552, 0.379969, 0.349048, 0.33508, 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, 0.0948041, 0.0853202, 0.0744092, 0.0681953, 0.0612642},
1975 {1.32188, 1.31695, 1.31668, 1.31947, 1.31731, 1.3177, 1.31852, 1.31894, 1.31877, 1.31831, 1.31844, 1.31807, 1.31822, 1.318, 1.3182, 1.318, 1.31792, 1.31791, 1.31782, 1.3177, 1.31764, 1.31754, 1.31745, 1.31723, 1.31701, 1.31656, 1.31612, 1.31566, 1.31474, 1.31378, 1.3128, 1.31179, 1.31075, 1.30967, 1.30856, 1.3074, 1.3062, 1.30495, 1.30366, 1.30231, 1.2987, 1.2947, 1.29025, 1.2853, 1.2798, 1.27368, 1.26687, 1.25931, 1.25091, 1.24163, 1.23143, 1.22032, 1.20835, 1.19561, 1.18221, 1.16825, 1.15377, 1.13878, 1.1232, 1.10691, 1.08976, 1.07153, 1.05194, 1.03067, 1.0073, 0.981265, 0.951825, 0.91795, 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, 0.70819, 0.707992, 0.707952, 0.707911, 0.707871, 0.707832, 0.707796, 0.70772, 0.70762, 0.707592, 0.707598},
1976 {1.58204, 1.58635, 1.58318, 1.58511, 1.58355, 1.58343, 1.58418, 1.58468, 1.58448, 1.58398, 1.58441, 1.58383, 1.58417, 1.5841, 1.58387, 1.58384, 1.58373, 1.58367, 1.58357, 1.58342, 1.58336, 1.58323, 1.58315, 1.58289, 1.58264, 1.58213, 1.58164, 1.58114, 1.58016, 1.57919, 1.57821, 1.57723, 1.57624, 1.57524, 1.57422, 1.57317, 1.5721, 1.57099, 1.56984, 1.56865, 1.56545, 1.56189, 1.55789, 1.55337, 1.54825, 1.54244, 1.53582, 1.52823, 1.51949, 1.50932, 1.49738, 1.48328, 1.46673, 1.44791, 1.42768, 1.40711, 1.38682, 1.36683, 1.34689, 1.32662, 1.30561, 1.28347, 1.25976, 1.234, 1.20558, 1.17376, 1.13753, 1.09541, 1.07645, 1.05602, 1.03387, 1.0097, 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, 0.41055, 0.391822, 0.371395, 0.348864, 0.323638, 0.2948, 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, 0.0909554, 0.0833586, 0.0748845},
1977 {1.84957, 1.84968, 1.85134, 1.85007, 1.84983, 1.84929, 1.85004, 1.8506, 1.85027, 1.84968, 1.85008, 1.85008, 1.84964, 1.84961, 1.84963, 1.84966, 1.84941, 1.84923, 1.84906, 1.84884, 1.84864, 1.84851, 1.84829, 1.84788, 1.84746, 1.84662, 1.84583, 1.84506, 1.84361, 1.84225, 1.84097, 1.83975, 1.83859, 1.83747, 1.83638, 1.8353, 1.83424, 1.83317, 1.8321, 1.831, 1.82815, 1.82502, 1.82153, 1.81757, 1.81306, 1.8079, 1.80199, 1.79518, 1.78728, 1.77801, 1.76686, 1.75278, 1.73323, 1.70384, 1.66882, 1.63893, 1.61423, 1.59206, 1.57064, 1.54892, 1.52619, 1.5019, 1.47555, 1.44657, 1.41428, 1.37781, 1.33598, 1.28712, 1.26509, 1.24133, 1.21558, 1.18751, 1.15671, 1.12263, 1.08453, 1.04141, 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, 0.25821, 0.227147, 0.209213, 0.188989, 0.165524, 0.160306, 0.15487, 0.149189, 0.143232, 0.136961, 0.123266, 0.107504, 0.113694, 0.102135}};
1978 
1979  /* 2, 1 mode */
1980 
1981  const double reomegaqnm21[8][107] = {{0.336609, 0.339386, 0.340852, 0.342219, 0.342818, 0.343002,
1982  0.343143, 0.343254, 0.343344, 0.343417, 0.343641, 0.343748,
1983  0.343804, 0.343853, 0.343871, 0.343879, 0.343886, 0.343891,
1984  0.343896, 0.343902, 0.343909, 0.343915, 0.343922, 0.343941, 0.34396,
1985  0.344002, 0.344049, 0.344101, 0.34422, 0.344359, 0.344517,
1986  0.344696, 0.344896, 0.345115, 0.345356, 0.345617, 0.345899,
1987  0.346201, 0.346525, 0.34687, 0.347824, 0.348911, 0.350132, 0.351491,
1988  0.35299, 0.354633, 0.356423, 0.358366, 0.360469, 0.362738,
1989  0.365183, 0.367812, 0.370637, 0.373672, 0.376931, 0.380432,
1990  0.384197, 0.388248, 0.392615, 0.39733, 0.402436, 0.407979, 0.41402,
1991  0.420632, 0.427909, 0.435968, 0.444968, 0.455121, 0.459569,
1992  0.464271, 0.469259, 0.474564, 0.480231, 0.486308, 0.492859,
1993  0.499965, 0.507729, 0.516291, 0.525845, 0.536673, 0.542693,
1994  0.549213, 0.556329, 0.560146, 0.564155, 0.565814, 0.567505,
1995  0.569227, 0.570976, 0.572749, 0.574535, 0.576322, 0.577208,
1996  0.578084, 0.578948, 0.579374, 0.579795, 0.580212, 0.580295,
1997  0.580377, 0.58046, 0.580541, 0.580623, 0.580784, 0.580942, 0.581018,
1998  0.581093}, {0.313486, 0.314984, 0.315748, 0.31636, 0.316504,
1999  0.316512, 0.316502, 0.316483, 0.31646, 0.316436, 0.316347, 0.316311,
2000  0.316305, 0.316315, 0.316325, 0.31633, 0.316338, 0.316345,
2001  0.316352, 0.31636, 0.316368, 0.316375, 0.316383, 0.316401, 0.316419,
2002  0.316455, 0.316491, 0.316527, 0.316602, 0.316682, 0.316772,
2003  0.316874, 0.316989, 0.317122, 0.317273, 0.317444, 0.317636,
2004  0.317851, 0.31809, 0.318353, 0.319124, 0.320064, 0.321179, 0.322476,
2005  0.32396, 0.325636, 0.327508, 0.329582, 0.331865, 0.334364,
2006  0.337088, 0.340045, 0.343249, 0.346711, 0.350448, 0.354478,
2007  0.358823, 0.363506, 0.368558, 0.374014, 0.379916, 0.386313,
2008  0.393268, 0.400856, 0.409172, 0.418337, 0.428509, 0.439897,
2009  0.444855, 0.450076, 0.455587, 0.46142, 0.467612, 0.474208, 0.481261,
2010  0.488834, 0.497004, 0.505862, 0.515506, 0.526011, 0.531572,
2011  0.537263, 0.542874, 0.545479, 0.547723, 0.548438, 0.548984, 0.54929,
2012  0.549241, 0.548642, 0.54714, 0.544185, 0.542606, 0.542325,
2013  0.541626, 0.540962, 0.540617, 0.540156, 0.540066, 0.539986,
2014  0.539906, 0.539818, 0.539726, 0.539553, 0.539377, 0.539288,
2015  0.539198}, {0.270281, 0.269419, 0.268655, 0.267935, 0.267923,
2016  0.268009, 0.268102, 0.268185, 0.268251, 0.268297, 0.268334,
2017  0.268285, 0.268273, 0.268312, 0.268342, 0.268359, 0.268398,
2018  0.268442, 0.268483, 0.268523, 0.268562, 0.268601, 0.26864, 0.268733,
2019  0.268822, 0.268989, 0.269141, 0.26928, 0.26952, 0.269718, 0.269881,
2020  0.270016, 0.270132, 0.270235, 0.270333, 0.270431, 0.270536,
2021  0.270653, 0.270785, 0.270937, 0.271426, 0.2721, 0.272992, 0.274121,
2022  0.275504, 0.277153, 0.279078, 0.281288, 0.283792, 0.286598,
2023  0.289716, 0.293156, 0.296931, 0.301053, 0.30554, 0.31041, 0.315684,
2024  0.321389, 0.327554, 0.334218, 0.341421, 0.349217, 0.357668,
2025  0.366852, 0.376864, 0.387825, 0.39989, 0.413261, 0.419032, 0.425075,
2026  0.431414, 0.438075, 0.445088, 0.452488, 0.46031, 0.468593,
2027  0.477369, 0.48665, 0.49639, 0.506348, 0.511184, 0.515607, 0.51903,
2028  0.519992, 0.5201, 0.51983, 0.519361, 0.51871, 0.517943, 0.517204,
2029  0.516728, 0.516696, 0.516098, 0.513376, 0.509813, 0.508083,
2030  0.506412, 0.504789, 0.504468, 0.504148, 0.50383, 0.503511, 0.503194,
2031  0.502559, 0.501923, 0.501605, 0.501286}, {0.21269, 0.214089,
2032  0.215208, 0.215364, 0.21474, 0.214584, 0.21456, 0.214625, 0.21473,
2033  0.214837, 0.214992, 0.214885, 0.214922, 0.215045, 0.215071,
2034  0.215139, 0.215267, 0.215383, 0.215507, 0.215624, 0.215741,
2035  0.215858, 0.215974, 0.216256, 0.216533, 0.217064, 0.217566, 0.21804,
2036  0.218903, 0.219653, 0.220295, 0.220836, 0.221285, 0.22165,
2037  0.221945, 0.22218, 0.222368, 0.22252, 0.222647, 0.222759, 0.223032,
2038  0.223383, 0.2239, 0.224647, 0.225672, 0.22701, 0.228689, 0.23073,
2039  0.233151, 0.235969, 0.239199, 0.242854, 0.246951, 0.251505,
2040  0.256534, 0.262058, 0.268101, 0.274689, 0.281852, 0.289628,
2041  0.298059, 0.307197, 0.317104, 0.327855, 0.339542, 0.352278,
2042  0.366207, 0.38151, 0.388065, 0.394895, 0.402017, 0.409454, 0.417227,
2043  0.425361, 0.433878, 0.442797, 0.452127, 0.461855, 0.471918,
2044  0.482195, 0.48739, 0.49271, 0.498495, 0.501813, 0.5056, 0.507251,
2045  0.508939, 0.510585, 0.512031, 0.513028, 0.513289, 0.512758,
2046  0.512367, 0.512091, 0.511921, 0.51135, 0.5096, 0.50715, 0.50665,
2047  0.506154, 0.505662, 0.505175, 0.504694, 0.503744, 0.502809,
2048  0.502344, 0.50188}, {0.171239, 0.169224, 0.168634, 0.170053,
2049  0.169938, 0.169613, 0.169418, 0.169408, 0.169531, 0.169696,
2050  0.169825, 0.169724, 0.16992, 0.169916, 0.170075, 0.17014, 0.170344,
2051  0.170511, 0.17071, 0.170886, 0.171073, 0.171258, 0.171437, 0.171892,
2052  0.172337, 0.173213, 0.174064, 0.174889, 0.176453, 0.177895,
2053  0.179203, 0.180372, 0.181395, 0.182273, 0.183007, 0.183606,
2054  0.184081, 0.184444, 0.18471, 0.184896, 0.185105, 0.18512, 0.185113,
2055  0.185222, 0.18555, 0.186176, 0.187164, 0.188562, 0.190413, 0.192751,
2056  0.195604, 0.199, 0.202962, 0.207515, 0.212679, 0.21848, 0.224939,
2057  0.232083, 0.23994, 0.248543, 0.257928, 0.268139, 0.279228, 0.291258,
2058  0.304303, 0.318456, 0.33383, 0.350563, 0.357675, 0.365045,
2059  0.372687, 0.380617, 0.388855, 0.397422, 0.406346, 0.41567, 0.425462,
2060  0.435857, 0.447149, 0.45999, 0.467349, 0.475546, 0.484594,
2061  0.489367, 0.494295, 0.496339, 0.498459, 0.500692, 0.50308, 0.505635,
2062  0.508214, 0.510197, 0.510572, 0.510387, 0.509864, 0.509635,
2063  0.509456, 0.50879, 0.508443, 0.507999, 0.50747, 0.506881, 0.506257,
2064  0.504974, 0.503704, 0.503082, 0.502466}, {0.136159, 0.137914,
2065  0.137016, 0.136626, 0.137329, 0.137055, 0.136755, 0.136667,
2066  0.136793, 0.136997, 0.136954, 0.137117, 0.137154, 0.137279, 0.1373,
2067  0.13747, 0.137649, 0.137842, 0.138069, 0.138258, 0.138476, 0.138671,
2068  0.138881, 0.139389, 0.139898, 0.14091, 0.14191, 0.142898, 0.144829,
2069  0.146684, 0.148447, 0.150099, 0.151622, 0.153001, 0.154221,
2070  0.15527, 0.156142, 0.156839, 0.157368, 0.15774, 0.158094, 0.157845,
2071  0.15725, 0.156526, 0.155847, 0.155354, 0.155162, 0.155369, 0.156061,
2072  0.157316, 0.159206, 0.161795, 0.165143, 0.169299, 0.174306,
2073  0.180192, 0.186977, 0.194671, 0.203282, 0.212811, 0.223263,
2074  0.234649, 0.246985, 0.260297, 0.274622, 0.290009, 0.306518,
2075  0.324226, 0.331666, 0.339322, 0.347205, 0.355332, 0.363727,
2076  0.372432, 0.381518, 0.391111, 0.401435, 0.412868, 0.425995,
2077  0.441563, 0.45052, 0.460463, 0.471717, 0.477974, 0.484665, 0.487438,
2078  0.490248, 0.493085, 0.49596, 0.498923, 0.502084, 0.505527,
2079  0.507222, 0.508526, 0.508875, 0.508627, 0.508251, 0.507926,
2080  0.507863, 0.507785, 0.50767, 0.507484, 0.507181, 0.506113, 0.504624,
2081  0.503839, 0.50306}, {0.114342, 0.113963, 0.115141, 0.114074,
2082  0.11486, 0.114789, 0.114485, 0.114338, 0.114452, 0.114665, 0.114512,
2083  0.114807, 0.11467, 0.114821, 0.114995, 0.115025, 0.115231,
2084  0.115438, 0.115661, 0.115846, 0.11605, 0.116249, 0.116452, 0.116951,
2085  0.117454, 0.118454, 0.11946, 0.120464, 0.122464, 0.124443,
2086  0.126383, 0.128266, 0.130073, 0.131781, 0.133368, 0.134813, 0.13609,
2087  0.137179, 0.138065, 0.138742, 0.139567, 0.139335, 0.138333,
2088  0.136834, 0.135064, 0.133208, 0.131418, 0.129826, 0.128564,
2089  0.127775, 0.127629, 0.128336, 0.130133, 0.133252, 0.137863,
2090  0.144021, 0.151672, 0.160684, 0.170902, 0.182186, 0.194429,
2091  0.207556, 0.221528, 0.236327, 0.251955, 0.268421, 0.285744, 0.30395,
2092  0.311492, 0.319195, 0.327076, 0.335168, 0.343522, 0.352232,
2093  0.361443, 0.371382, 0.382361, 0.394771, 0.409089, 0.426092,
2094  0.436065, 0.4474, 0.460415, 0.467675, 0.475563, 0.478922, 0.482402,
2095  0.485993, 0.489665, 0.493377, 0.497113, 0.500995, 0.503086,
2096  0.505273, 0.507186, 0.507677, 0.507628, 0.507177, 0.507077,
2097  0.506981, 0.506892, 0.506806, 0.506714, 0.506383, 0.505391,
2098  0.504576, 0.503665}, {0.0996362, 0.098809, 0.0988228, 0.0989612,
2099  0.0991812, 0.0993225, 0.0990912, 0.0989133, 0.0990066, 0.0992056,
2100  0.0990844, 0.0992013, 0.0993046, 0.0993698, 0.0994135, 0.0995406,
2101  0.0997102, 0.0999057, 0.100109, 0.100292, 0.100464, 0.100668,
2102  0.100843, 0.10132, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617,
2103  0.108576, 0.11054, 0.112492, 0.114417, 0.116296, 0.118106,
2104  0.119822, 0.121422, 0.122876, 0.12415, 0.125214, 0.12686, 0.127085,
2105  0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.10844,
2106  0.104598, 0.100602, 0.0966436, 0.0934548, 0.0928224, 0.0967608,
2107  0.105267, 0.116748, 0.129817, 0.143719, 0.158124, 0.17292, 0.188094,
2108  0.203673, 0.219697, 0.236201, 0.253208, 0.270727, 0.288784,
2109  0.296181, 0.303707, 0.311404, 0.319342, 0.327628, 0.336416,
2110  0.345907, 0.35633, 0.367923, 0.380968, 0.395965, 0.413866, 0.424377,
2111  0.436366, 0.450442, 0.458506, 0.467375, 0.471171, 0.475126,
2112  0.479254, 0.483568, 0.488052, 0.492639, 0.497232, 0.499557,
2113  0.501993, 0.504598, 0.505838, 0.506697, 0.506742, 0.506649,
2114  0.506536, 0.50641, 0.506281, 0.506156, 0.505924, 0.505541, 0.505047,
2115  0.504219}};
2116 
2117  const double imomegaqnm21[8][107] = {{0.0743116, 0.0772659, 0.0791824, 0.0812815, 0.0822652, 0.082556,
2118  0.0827684, 0.082926, 0.0830445, 0.0831347, 0.0833596, 0.0834304,
2119  0.0834555, 0.0834714, 0.0834806, 0.0834917, 0.0835195, 0.0835507,
2120  0.0835831, 0.0836156, 0.0836481, 0.0836804, 0.0837126, 0.083792,
2121  0.0838704, 0.0840241, 0.0841737, 0.0843193, 0.0845994, 0.084865,
2122  0.085117, 0.0853561, 0.0855831, 0.0857987, 0.0860035, 0.086198,
2123  0.0863828, 0.0865584, 0.0867253, 0.086884, 0.087247, 0.0875662,
2124  0.0878462, 0.0880906, 0.0883025, 0.088484, 0.088637, 0.0887628,
2125  0.0888621, 0.0889354, 0.0889828, 0.0890037, 0.0889973, 0.0889623,
2126  0.0888968, 0.0887983, 0.0886636, 0.0884885, 0.0882679, 0.0879952,
2127  0.0876618, 0.0872571, 0.086767, 0.086173, 0.0854501, 0.0845642,
2128  0.0834665, 0.0820852, 0.0814304, 0.0807035, 0.0798926, 0.0789827,
2129  0.077955, 0.0767847, 0.0754394, 0.0738744, 0.072027, 0.0698043,
2130  0.067061, 0.0635492, 0.0613721, 0.058791, 0.0556436, 0.0537759,
2131  0.0516427, 0.0506978, 0.0496908, 0.0486136, 0.0474565, 0.0462084,
2132  0.0448564, 0.0433879, 0.0426068, 0.0417939, 0.0409501, 0.0405173,
2133  0.0400777, 0.0396319, 0.039542, 0.0394519, 0.0393616, 0.039271,
2134  0.0391802, 0.0389974, 0.0388111, 0.038714, 0.0386091}, {0.258785,
2135  0.258526, 0.258215, 0.257703, 0.257385, 0.257284, 0.25721, 0.257158,
2136  0.257123, 0.257101, 0.257089, 0.257133, 0.257178, 0.257248,
2137  0.257304, 0.257357, 0.257465, 0.257574, 0.257683, 0.257791,
2138  0.257898, 0.258005, 0.258112, 0.258376, 0.258637, 0.259149,
2139  0.259649, 0.260137, 0.261076, 0.261967, 0.262812, 0.263613,
2140  0.264372, 0.265089, 0.265768, 0.26641, 0.267016, 0.267589, 0.26813,
2141  0.26864, 0.269792, 0.270782, 0.271629, 0.272346, 0.272945, 0.273434,
2142  0.273821, 0.274112, 0.274309, 0.274415, 0.27443, 0.274354,
2143  0.274183, 0.273915, 0.273543, 0.273058, 0.272452, 0.271711,
2144  0.270819, 0.269754, 0.268489, 0.266992, 0.265218, 0.263108,
2145  0.260587, 0.257547, 0.253838, 0.249238, 0.247078, 0.244692,
2146  0.242045, 0.239089, 0.235766, 0.231999, 0.227686, 0.222686, 0.2168,
2147  0.209731, 0.201006, 0.189803, 0.18282, 0.174484, 0.164205, 0.158029,
2148  0.150891, 0.1477, 0.14428, 0.140606, 0.136657, 0.132444, 0.128112,
2149  0.124511, 0.123925, 0.123321, 0.12167, 0.121162, 0.120732, 0.12014,
2150  0.120048, 0.119951, 0.119844, 0.119734, 0.119631, 0.119429,
2151  0.119227, 0.119127, 0.119027}, {0.451082, 0.450126, 0.449946,
2152  0.450393, 0.450836, 0.450954, 0.451016, 0.451037, 0.451032,
2153  0.451015, 0.450927, 0.450953, 0.451028, 0.451151, 0.451242,
2154  0.451336, 0.451538, 0.451736, 0.451932, 0.452129, 0.452326,
2155  0.452521, 0.452716, 0.453201, 0.453683, 0.454634, 0.45557, 0.456489,
2156  0.458275, 0.459989, 0.461626, 0.463185, 0.464665, 0.466067,
2157  0.46739, 0.468636, 0.469808, 0.470906, 0.471935, 0.472897, 0.475022,
2158  0.476783, 0.478216, 0.479352, 0.48022, 0.48084, 0.481231, 0.481407,
2159  0.481377, 0.481149, 0.480726, 0.480109, 0.479294, 0.478277,
2160  0.477047, 0.475592, 0.473893, 0.471929, 0.469669, 0.467076,
2161  0.464104, 0.460691, 0.456761, 0.45221, 0.446903, 0.440653, 0.433196,
2162  0.424144, 0.419951, 0.415358, 0.4103, 0.404693, 0.398434, 0.391383,
2163  0.383355, 0.374094, 0.363227, 0.350188, 0.334044, 0.313093,
2164  0.299808, 0.283583, 0.262719, 0.249472, 0.233119, 0.225306,
2165  0.216483, 0.206365, 0.194563, 0.180538, 0.16345, 0.141483, 0.12731,
2166  0.111596, 0.0954876, 0.0868316, 0.0774193, 0.066857, 0.0645541,
2167  0.0621712, 0.0596988, 0.057125, 0.0544355, 0.0486318, 0.0420655,
2168  0.0383765, 0.0343031}, {0.670736, 0.672092, 0.671812, 0.670663,
2169  0.670549, 0.67073, 0.670927, 0.671078, 0.671164, 0.671189, 0.671021,
2170  0.671075, 0.671219, 0.67131, 0.671427, 0.671572, 0.671807,
2171  0.672062, 0.672309, 0.672557, 0.672808, 0.673057, 0.673305,
2172  0.673929, 0.674552, 0.675799, 0.677043, 0.678283, 0.680743,
2173  0.683166, 0.685536, 0.68784, 0.690067, 0.692205, 0.694247, 0.696187,
2174  0.69802, 0.699744, 0.701359, 0.702865, 0.706165, 0.708833,
2175  0.710915, 0.71246, 0.71351, 0.714105, 0.714277, 0.714053, 0.713452,
2176  0.71249, 0.711176, 0.709516, 0.707509, 0.705148, 0.702423, 0.699317,
2177  0.695803, 0.691851, 0.687416, 0.682445, 0.676867, 0.670592,
2178  0.663504, 0.655451, 0.646227, 0.635554, 0.623036, 0.60809, 0.601244,
2179  0.593791, 0.58563, 0.576638, 0.566651, 0.555455, 0.54276, 0.528156,
2180  0.511038, 0.490465, 0.464847, 0.431189, 0.409563, 0.382936,
2181  0.348824, 0.32773, 0.302947, 0.291759, 0.279694, 0.26659, 0.252176,
2182  0.235931, 0.216835, 0.192946, 0.178198, 0.160681, 0.138951,
2183  0.125667, 0.110911, 0.095128, 0.0917732, 0.0883219, 0.0847576,
2184  0.0810612, 0.0772103, 0.0689279, 0.0595841, 0.0543422,
2185  0.048559}, {0.910592, 0.910063, 0.91138, 0.911832, 0.911012,
2186  0.911003, 0.911199, 0.911439, 0.911606, 0.91166, 0.911352, 0.911585,
2187  0.911648, 0.911704, 0.911854, 0.911933, 0.912192, 0.912425,
2188  0.912663, 0.912897, 0.913141, 0.913376, 0.913616, 0.91422, 0.91483,
2189  0.916061, 0.917309, 0.918574, 0.921148, 0.923769, 0.92642, 0.929083,
2190  0.931738, 0.934365, 0.936941, 0.939446, 0.941862, 0.944173,
2191  0.946367, 0.948436, 0.953025, 0.956761, 0.959656, 0.961747, 0.96308,
2192  0.963701, 0.963651, 0.962967, 0.96168, 0.959815, 0.957389,
2193  0.954417, 0.950902, 0.946845, 0.942236, 0.937057, 0.931283,
2194  0.924873, 0.917775, 0.909918, 0.901208, 0.891524, 0.880707,
2195  0.868545, 0.854753, 0.838939, 0.820547, 0.798756, 0.788822,
2196  0.778034, 0.76625, 0.75329, 0.738922, 0.722836, 0.704612, 0.683652,
2197  0.659084, 0.629562, 0.592913, 0.54542, 0.515651, 0.480063, 0.436051,
2198  0.409334, 0.377864, 0.363486, 0.347803, 0.330563, 0.311454,
2199  0.290066, 0.265802, 0.237412, 0.220683, 0.201065, 0.17693, 0.162373,
2200  0.145371, 0.124789, 0.120176, 0.115422, 0.110541, 0.105527,
2201  0.100358, 0.0893955, 0.0771778, 0.0703585, 0.0628494}, {1.16313,
2202  1.16205, 1.16102, 1.16236, 1.1618, 1.16155, 1.16165, 1.16191,
2203  1.16212, 1.16217, 1.16185, 1.16214, 1.162, 1.16222, 1.16228, 1.1624,
2204  1.16261, 1.16279, 1.163, 1.16321, 1.16342, 1.16362, 1.16384,
2205  1.16436, 1.16489, 1.16598, 1.1671, 1.16824, 1.1706, 1.17306,
2206  1.17562, 1.17826, 1.18098, 1.18376, 1.18658, 1.18941, 1.19222,
2207  1.19499, 1.19769, 1.20029, 1.20624, 1.21127, 1.21528, 1.21824,
2208  1.22017, 1.2211, 1.22105, 1.22006, 1.21814, 1.21533, 1.21164,
2209  1.20711, 1.20176, 1.19561, 1.18868, 1.18098, 1.17251, 1.16324,
2210  1.15314, 1.14213, 1.13009, 1.11686, 1.10224, 1.08592, 1.06753,
2211  1.04652, 1.02214, 0.993243, 0.980058, 0.965724, 0.950047, 0.932779,
2212  0.913601, 0.892095, 0.867699, 0.839644, 0.806856, 0.767797,
2213  0.720146, 0.659944, 0.622848, 0.578732, 0.524237, 0.491317,
2214  0.452927, 0.435542, 0.416661, 0.395943, 0.372912, 0.346898,
2215  0.316949, 0.28167, 0.261342, 0.238436, 0.211307, 0.195088, 0.176156,
2216  0.153337, 0.148132, 0.142654, 0.136869, 0.130747, 0.124273,
2217  0.110319, 0.0949385, 0.0864639, 0.0771851}, {1.41428, 1.41604,
2218  1.4156, 1.41536, 1.4156, 1.41524, 1.41519, 1.41543, 1.41565,
2219  1.41568, 1.41551, 1.41554, 1.41563, 1.41566, 1.41579, 1.41591,
2220  1.41608, 1.41624, 1.41643, 1.41663, 1.4168, 1.417, 1.41717, 1.41765,
2221  1.41813, 1.41911, 1.42011, 1.42114, 1.42328, 1.42554, 1.42792,
2222  1.43041, 1.43303, 1.43576, 1.4386, 1.44152, 1.44453, 1.44758,
2223  1.45065, 1.45369, 1.46099, 1.46752, 1.473, 1.47733, 1.48042,
2224  1.48226, 1.48282, 1.48207, 1.47997, 1.47646, 1.4715, 1.46505,
2225  1.45715, 1.44791, 1.43752, 1.42619, 1.41412, 1.4014, 1.38801,
2226  1.37384, 1.35872, 1.34237, 1.32445, 1.30456, 1.28213, 1.25643,
2227  1.22645, 1.19065, 1.17422, 1.15628, 1.13659, 1.11481, 1.09053,
2228  1.06323, 1.03225, 0.996712, 0.955487, 0.906959, 0.848541, 0.775494,
2229  0.730792, 0.678016, 0.613349, 0.574379, 0.528885, 0.508284,
2230  0.485946, 0.461517, 0.434493, 0.404108, 0.369135, 0.327547,
2231  0.303278, 0.275875, 0.244209, 0.225953, 0.204982, 0.179727,
2232  0.173965, 0.167908, 0.161519, 0.154752, 0.147552, 0.131555,
2233  0.113035, 0.102763, 0.09161}, {1.6695, 1.6684, 1.66944, 1.66866,
2234  1.66927, 1.66897, 1.66882, 1.66899, 1.6692, 1.66921, 1.66919,
2235  1.66906, 1.66925, 1.66933, 1.66938, 1.66941, 1.6696, 1.66977,
2236  1.66995, 1.67014, 1.67031, 1.67048, 1.67066, 1.6711, 1.67155,
2237  1.67246, 1.6734, 1.67436, 1.67635, 1.67846, 1.68069, 1.68303,
2238  1.68552, 1.68814, 1.69089, 1.69379, 1.69681, 1.69996, 1.70322,
2239  1.70655, 1.71494, 1.72293, 1.73008, 1.73612, 1.7409, 1.74437,
2240  1.74645, 1.74707, 1.74612, 1.74337, 1.73845, 1.73073, 1.71933,
2241  1.70384, 1.68568, 1.6674, 1.65022, 1.63402, 1.61822, 1.60219,
2242  1.58534, 1.56716, 1.54712, 1.52462, 1.49894, 1.46917, 1.43397,
2243  1.39142, 1.37171, 1.35009, 1.32623, 1.29974, 1.27014, 1.23683,
2244  1.19912, 1.15609, 1.10649, 1.04841, 0.97878, 0.892317, 0.839828,
2245  0.778168, 0.702974, 0.657884, 0.605411, 0.581667, 0.555906,
2246  0.527711, 0.496517, 0.46151, 0.421398, 0.373867, 0.346042, 0.314367,
2247  0.277467, 0.25637, 0.232725, 0.204918, 0.198597, 0.191947,
2248  0.184925, 0.177485, 0.169568, 0.151985, 0.131247, 0.119312,
2249  0.106197}};
2250 
2251  /* 2, 0 mode */
2252  const double reomegaqnm20[8][107] = {{0.4247721439, 0.4247863113, 0.4247985972, 0.4248325877,
2253  0.4248584259, 0.4248659433, 0.4248700764, 0.4248712306,
2254  0.4248698326, 0.4248662798, 0.4248267198, 0.4247676547,
2255  0.4247005042, 0.424557753, 0.4244119723, 0.4242658712, 0.4239745379,
2256  0.4236846241, 0.4233960302, 0.4231086991, 0.4228226189,
2257  0.4225377956, 0.4222542405, 0.4215509794, 0.420855887, 0.4194906865,
2258  0.4181592598, 0.4168617799, 0.4143677184, 0.4120044663,
2259  0.4097658509, 0.40764485, 0.4056343086, 0.4037273098, 0.4019173509,
2260  0.4001984114, 0.3985649653, 0.3970119631, 0.3955348022,
2261  0.3941292897, 0.3909047276, 0.3880539184, 0.3855360484, 0.383318276,
2262  0.3813740024, 0.3796815867, 0.3782233906, 0.3769850625,
2263  0.3759550001, 0.3751239445, 0.3744846758, 0.3740317881,
2264  0.3737615278, 0.3736716844, 0.3737615278, 0.3740317881,
2265  0.3744846758, 0.3751239445, 0.3759550001, 0.3769850625,
2266  0.3782233906, 0.3796815867, 0.3813740024, 0.383318276, 0.3855360484,
2267  0.3880539184, 0.3909047276, 0.3941292897, 0.3955348022,
2268  0.3970119631, 0.3985649653, 0.4001984114, 0.4019173509,
2269  0.4037273098, 0.4056343086, 0.40764485, 0.4097658509, 0.4120044663,
2270  0.4143677184, 0.4168617799, 0.4181592598, 0.4194906865, 0.420855887,
2271  0.4215509794, 0.4222542405, 0.4225377956, 0.4228226189,
2272  0.4231086991, 0.4233960302, 0.4236846241, 0.4239745379,
2273  0.4242658712, 0.4244119723, 0.424557753, 0.4247005042, 0.4247676547,
2274  0.4248267198, 0.4248662798, 0.4248698326, 0.4248712306,
2275  0.4248700764, 0.4248659433, 0.4248584259, 0.4248325877,
2276  0.4247985972, 0.4247863113, 0.4247721439}, {0.4022595044,
2277  0.4025176372, 0.4026385253, 0.402714655, 0.4027157267, 0.4027081834,
2278  0.4026990446, 0.4026895027, 0.4026801424, 0.4026712204,
2279  0.4026338048, 0.4026034279, 0.402574986, 0.4025177609, 0.4024587579,
2280  0.4023983315, 0.4022740572, 0.402145468, 0.4020126089,
2281  0.4018755539, 0.4017344007, 0.4015892521, 0.401440212, 0.4010512734,
2282  0.4006403236, 0.3997591492, 0.3988102405, 0.397806802,
2283  0.3956841928, 0.3934728792, 0.3912313515, 0.3889989525,
2284  0.3868012743, 0.3846545743, 0.3825688955, 0.3805501632,
2285  0.3786015741, 0.3767245157, 0.3749191785, 0.3731849675,
2286  0.3691526314, 0.3655335386, 0.3623007731, 0.3594283374,
2287  0.3568927266, 0.3546733772, 0.3527526583, 0.3511156895,
2288  0.3497501098, 0.348645853, 0.34779495, 0.3471913675, 0.3468308827,
2289  0.3467109969, 0.3468308827, 0.3471913675, 0.34779495, 0.348645853,
2290  0.3497501098, 0.3511156895, 0.3527526583, 0.3546733772,
2291  0.3568927266, 0.3594283374, 0.3623007731, 0.3655335386,
2292  0.3691526314, 0.3731849675, 0.3749191785, 0.3767245157,
2293  0.3786015741, 0.3805501632, 0.3825688955, 0.3846545743,
2294  0.3868012743, 0.3889989525, 0.3912313515, 0.3934728792,
2295  0.3956841928, 0.397806802, 0.3988102405, 0.3997591492, 0.4006403236,
2296  0.4010512734, 0.401440212, 0.4015892521, 0.4017344007,
2297  0.4018755539, 0.4020126089, 0.402145468, 0.4022740572, 0.4023983315,
2298  0.4024587579, 0.4025177609, 0.402574986, 0.4026034279,
2299  0.4026338048, 0.4026712204, 0.4026801424, 0.4026895027,
2300  0.4026990446, 0.4027081834, 0.4027157267, 0.402714655, 0.4026385253,
2301  0.4025176372, 0.4022595044}, {0.3587631202, 0.3586562755,
2302  0.3585571621, 0.3584767648, 0.3584871698, 0.3585031359, 0.358520196,
2303  0.3585364516, 0.3585511443, 0.3585641498, 0.3586123314,
2304  0.3586525789, 0.3586945293, 0.358781211, 0.3588663108, 0.3589493444,
2305  0.3591108827, 0.3592664061, 0.3594155854, 0.3595583252,
2306  0.3596945387, 0.3598241205, 0.3599469676, 0.3602240117,
2307  0.3604570682, 0.3607872733, 0.3609323176, 0.360891042, 0.3602774401,
2308  0.3590639204, 0.3574099949, 0.3554578534, 0.3533158689,
2309  0.3510620393, 0.3487514511, 0.3464228554, 0.3441035438,
2310  0.3418127732, 0.3395641339, 0.337367187, 0.332139771, 0.3273292258,
2311  0.3229529922, 0.3190100679, 0.3154913069, 0.3123844448,
2312  0.3096766084, 0.3073555756, 0.3054103975, 0.30383169, 0.3026117559,
2313  0.3017446212, 0.3012260348, 0.3010534545, 0.3012260348,
2314  0.3017446212, 0.3026117559, 0.30383169, 0.3054103975, 0.3073555756,
2315  0.3096766084, 0.3123844448, 0.3154913069, 0.3190100679,
2316  0.3229529922, 0.3273292258, 0.332139771, 0.337367187, 0.3395641339,
2317  0.3418127732, 0.3441035438, 0.3464228554, 0.3487514511,
2318  0.3510620393, 0.3533158689, 0.3554578534, 0.3574099949,
2319  0.3590639204, 0.3602774401, 0.360891042, 0.3609323176, 0.3607872733,
2320  0.3604570682, 0.3602240117, 0.3599469676, 0.3598241205,
2321  0.3596945387, 0.3595583252, 0.3594155854, 0.3592664061,
2322  0.3591108827, 0.3589493444, 0.3588663108, 0.358781211, 0.3586945293,
2323  0.3586525789, 0.3586123314, 0.3585641498, 0.3585511443,
2324  0.3585364516, 0.358520196, 0.3585031359, 0.3584871698, 0.3584767648,
2325  0.3585571621, 0.3586562755, 0.3587631202}, {0.2955931981,
2326  0.2956911763, 0.2959013663, 0.2960902804, 0.2960805341, 0.296070603,
2327  0.2960715835, 0.2960841755, 0.2961057593, 0.2961328408,
2328  0.2962715691, 0.2963767257, 0.2964791366, 0.2967001479,
2329  0.2969184558, 0.2971346512, 0.2975687544, 0.2980006488,
2330  0.2984308575, 0.2988593119, 0.2992856405, 0.2997097563,
2331  0.3001315265, 0.3011744976, 0.3021986114, 0.3041793062, 0.306042046,
2332  0.30776228, 0.3106733357, 0.3125253856, 0.3131974762, 0.3128916813,
2333  0.311865866, 0.3103333453, 0.3084523863, 0.306337079, 0.304069452,
2334  0.301708867, 0.2992986826, 0.2968708711, 0.2908660077, 0.2851210461,
2335  0.2797541132, 0.2748239607, 0.2703586352, 0.2663699371,
2336  0.2628610658, 0.2598308118, 0.2572759173, 0.25519243, 0.2535764879,
2337  0.2524247751, 0.2517347842, 0.2515049622, 0.2517347842,
2338  0.2524247751, 0.2535764879, 0.25519243, 0.2572759173, 0.2598308118,
2339  0.2628610658, 0.2663699371, 0.2703586352, 0.2748239607,
2340  0.2797541132, 0.2851210461, 0.2908660077, 0.2968708711,
2341  0.2992986826, 0.301708867, 0.304069452, 0.306337079, 0.3084523863,
2342  0.3103333453, 0.311865866, 0.3128916813, 0.3131974762, 0.3125253856,
2343  0.3106733357, 0.30776228, 0.306042046, 0.3041793062, 0.3021986114,
2344  0.3011744976, 0.3001315265, 0.2997097563, 0.2992856405,
2345  0.2988593119, 0.2984308575, 0.2980006488, 0.2975687544,
2346  0.2971346512, 0.2969184558, 0.2967001479, 0.2964791366,
2347  0.2963767257, 0.2962715691, 0.2961328408, 0.2961057593,
2348  0.2960841755, 0.2960715835, 0.296070603, 0.2960805341, 0.2960902804,
2349  0.2959013663, 0.2956911763, 0.2955931981}, {0.2265759655,
2350  0.2263134666, 0.2259201107, 0.226033261, 0.2263091114, 0.2263241376,
2351  0.2262966437, 0.2262653635, 0.2262534991, 0.2262677342,
2352  0.2264910301, 0.226604597, 0.2267226381, 0.2270204493, 0.2272816677,
2353  0.2275628966, 0.2281119757, 0.2286682789, 0.2292233708,
2354  0.2297821291, 0.2303431133, 0.2309055008, 0.2314706692, 0.232891702,
2355  0.2343288764, 0.2372425752, 0.2401516712, 0.2432064357,
2356  0.2490028794, 0.2551643774, 0.2609821536, 0.2649179918,
2357  0.2670263535, 0.2677578325, 0.2675054998, 0.2665561482,
2358  0.2651128405, 0.2633200598, 0.2612820783, 0.2590753625,
2359  0.2531607164, 0.2470884185, 0.2411635985, 0.2355561825,
2360  0.2303648137, 0.2256486007, 0.2214438733, 0.2177734415,
2361  0.2146518936, 0.2120886995, 0.2100900575, 0.2086599993,
2362  0.2078010452, 0.2075145798, 0.2078010452, 0.2086599993,
2363  0.2100900575, 0.2120886995, 0.2146518936, 0.2177734415,
2364  0.2214438733, 0.2256486007, 0.2303648137, 0.2355561825,
2365  0.2411635985, 0.2470884185, 0.2531607164, 0.2590753625,
2366  0.2612820783, 0.2633200598, 0.2651128405, 0.2665561482,
2367  0.2675054998, 0.2677578325, 0.2670263535, 0.2649179918,
2368  0.2609821536, 0.2551643774, 0.2490028794, 0.2432064357,
2369  0.2401516712, 0.2372425752, 0.2343288764, 0.232891702, 0.2314706692,
2370  0.2309055008, 0.2303431133, 0.2297821291, 0.2292233708,
2371  0.2286682789, 0.2281119757, 0.2275628966, 0.2272816677,
2372  0.2270204493, 0.2267226381, 0.226604597, 0.2264910301, 0.2262677342,
2373  0.2262534991, 0.2262653635, 0.2262966437, 0.2263241376,
2374  0.2263091114, 0.226033261, 0.2259201107, 0.2263134666,
2375  0.2265759655}, {0.162467714, 0.1634934248, 0.1638277421,
2376  0.1630968281, 0.1635010049, 0.1636759976, 0.1636803676,
2377  0.1635845741, 0.163488315, 0.1634553864, 0.1638050393, 0.163791891,
2378  0.1639844275, 0.1642094594, 0.1645146073, 0.1647460864, 0.165288291,
2379  0.1658098185, 0.1663401778, 0.1668757036, 0.1674133259,
2380  0.1679475306, 0.1685023684, 0.1698847398, 0.1712487246,
2381  0.1741108365, 0.1768267467, 0.1804631771, 0.18630515, 0.1935771765,
2382  0.1987452707, 0.2093226733, 0.2181547856, 0.2237317269,
2383  0.2269036596, 0.2284118203, 0.228756399, 0.2282723907, 0.2271898972,
2384  0.2256715181, 0.2206696442, 0.2147729564, 0.2085926425,
2385  0.2024747303, 0.1966287474, 0.1911890101, 0.1862461282,
2386  0.1818640842, 0.178089795, 0.1749585446, 0.1724970437, 0.1707251041,
2387  0.1696565048, 0.1692994034, 0.1696565048, 0.1707251041,
2388  0.1724970437, 0.1749585446, 0.178089795, 0.1818640842, 0.1862461282,
2389  0.1911890101, 0.1966287474, 0.2024747303, 0.2085926425,
2390  0.2147729564, 0.2206696442, 0.2256715181, 0.2271898972,
2391  0.2282723907, 0.228756399, 0.2284118203, 0.2269036596, 0.2237317269,
2392  0.2181547856, 0.2093226733, 0.1987452707, 0.1935771765, 0.18630515,
2393  0.1804631771, 0.1768267467, 0.1741108365, 0.1712487246,
2394  0.1698847398, 0.1685023684, 0.1679475306, 0.1674133259,
2395  0.1668757036, 0.1663401778, 0.1658098185, 0.165288291, 0.1647460864,
2396  0.1645146073, 0.1642094594, 0.1639844275, 0.163791891,
2397  0.1638050393, 0.1634553864, 0.163488315, 0.1635845741, 0.1636803676,
2398  0.1636759976, 0.1635010049, 0.1630968281, 0.1638277421,
2399  0.1634934248, 0.162467714}, {0.1150947175, 0.1136995811,
2400  0.1144317617, 0.1145108329, 0.1143223733, 0.1147075752,
2401  0.1148529865, 0.1147211083, 0.1145101899, 0.1144146127,
2402  0.1148757124, 0.1147623558, 0.1150527078, 0.1152162011,
2403  0.1153522163, 0.1156670599, 0.1160937605, 0.1165085059,
2404  0.1169521137, 0.1174121457, 0.1178333408, 0.1183089991,
2405  0.1188779907, 0.1199614936, 0.1212661221, 0.122907988, 0.1252696237,
2406  0.1300527498, 0.136371485, 0.1365743504, 0.1502937555,
2407  0.1499042247, 0.1576063359, 0.1737999474, 0.1840565193,
2408  0.1901954481, 0.1937178657, 0.1954878977, 0.1960322476,
2409  0.1956928755, 0.1923495252, 0.1869716004, 0.1806432357,
2410  0.1739650338, 0.167302038, 0.1608944901, 0.1549126532, 0.1494856455,
2411  0.1447169546, 0.1406923509, 0.1374833382, 0.1351476926,
2412  0.1337284518, 0.1332523443, 0.1337284518, 0.1351476926,
2413  0.1374833382, 0.1406923509, 0.1447169546, 0.1494856455,
2414  0.1549126532, 0.1608944901, 0.167302038, 0.1739650338, 0.1806432357,
2415  0.1869716004, 0.1923495252, 0.1956928755, 0.1960322476,
2416  0.1954878977, 0.1937178657, 0.1901954481, 0.1840565193,
2417  0.1737999474, 0.1576063359, 0.1499042247, 0.1502937555,
2418  0.1365743504, 0.136371485, 0.1300527498, 0.1252696237, 0.122907988,
2419  0.1212661221, 0.1199614936, 0.1188779907, 0.1183089991,
2420  0.1178333408, 0.1174121457, 0.1169521137, 0.1165085059,
2421  0.1160937605, 0.1156670599, 0.1153522163, 0.1152162011,
2422  0.1150527078, 0.1147623558, 0.1148757124, 0.1144146127,
2423  0.1145101899, 0.1147211083, 0.1148529865, 0.1147075752,
2424  0.1143223733, 0.1145108329, 0.1144317617, 0.1136995811,
2425  0.1150947175}, {0.07824594797, 0.07897765236, 0.07781656751,
2426  0.07894919224, 0.07811549687, 0.07852555182, 0.0788734926,
2427  0.07877853969, 0.0784682439, 0.07832233515, 0.0787241668,
2428  0.07887758159, 0.07876636539, 0.07904172864, 0.07931185989,
2429  0.07935962619, 0.07970963786, 0.08015321455, 0.08049831171,
2430  0.08098647273, 0.08113113975, 0.08171084479, 0.08245975407,
2431  0.08198058103, 0.08310489532, 0.08636947463, 0.08742026462,
2432  0.09301825285, 0.09708260702, 0.1044921151, 0.09410791221,
2433  0.1163296909, 0.1194610774, 0.1071758642, 0.131059966, 0.1479210288,
2434  0.1575029326, 0.1631326584, 0.1662931627, 0.1677797021,
2435  0.1669344646, 0.162339839, 0.1558069565, 0.1482827082, 0.1403267639,
2436  0.1323069592, 0.1244931384, 0.1171075385, 0.1103537661,
2437  0.1044314061, 0.09954024628, 0.0958728709, 0.09359533547,
2438  0.09282239791, 0.09359533547, 0.0958728709, 0.09954024628,
2439  0.1044314061, 0.1103537661, 0.1171075385, 0.1244931384,
2440  0.1323069592, 0.1403267639, 0.1482827082, 0.1558069565, 0.162339839,
2441  0.1669344646, 0.1677797021, 0.1662931627, 0.1631326584,
2442  0.1575029326, 0.1479210288, 0.131059966, 0.1071758642, 0.1194610774,
2443  0.1163296909, 0.09410791221, 0.1044921151, 0.09708260702,
2444  0.09301825285, 0.08742026462, 0.08636947463, 0.08310489532,
2445  0.08198058103, 0.08245975407, 0.08171084479, 0.08113113975,
2446  0.08098647273, 0.08049831171, 0.08015321455, 0.07970963786,
2447  0.07935962619, 0.07931185989, 0.07904172864, 0.07876636539,
2448  0.07887758159, 0.0787241668, 0.07832233515, 0.0784682439,
2449  0.07877853969, 0.0788734926, 0.07852555182, 0.07811549687,
2450  0.07894919224, 0.07781656751, 0.07897765236, 0.07824594797}};
2451  const double imomegaqnm20[8][107] = {{0.06956111286, 0.07057665227, 0.07109516199, 0.07156667263,
2452  0.07176004502, 0.0718151936, 0.07185564256, 0.071886392,
2453  0.07191058835, 0.07193027264, 0.07199608801, 0.07204342275,
2454  0.07208725348, 0.07217445117, 0.07226259362, 0.07235103048,
2455  0.07252698509, 0.07270070919, 0.07287193971, 0.07304067834,
2456  0.07320697034, 0.0733708643, 0.07353240627, 0.07392625431,
2457  0.07430631954, 0.07502754477, 0.07570073722, 0.076330175,
2458  0.07747297842, 0.07848269543, 0.07938083725, 0.08018464701,
2459  0.08090799941, 0.08156214052, 0.08215626528, 0.08269795953,
2460  0.08319353674, 0.08364829544, 0.08406671695, 0.08445261881,
2461  0.0852954969, 0.08599466937, 0.08657885062, 0.08706905134,
2462  0.0874809756, 0.08782655405, 0.08811495632, 0.08835327799,
2463  0.08854701612, 0.08870040374, 0.08881664656, 0.08889809023,
2464  0.08894633586, 0.08896231569, 0.08894633586, 0.08889809023,
2465  0.08881664656, 0.08870040374, 0.08854701612, 0.08835327799,
2466  0.08811495632, 0.08782655405, 0.0874809756, 0.08706905134,
2467  0.08657885062, 0.08599466937, 0.0852954969, 0.08445261881,
2468  0.08406671695, 0.08364829544, 0.08319353674, 0.08269795953,
2469  0.08215626528, 0.08156214052, 0.08090799941, 0.08018464701,
2470  0.07938083725, 0.07848269543, 0.07747297842, 0.076330175,
2471  0.07570073722, 0.07502754477, 0.07430631954, 0.07392625431,
2472  0.07353240627, 0.0733708643, 0.07320697034, 0.07304067834,
2473  0.07287193971, 0.07270070919, 0.07252698509, 0.07235103048,
2474  0.07226259362, 0.07217445117, 0.07208725348, 0.07204342275,
2475  0.07199608801, 0.07193027264, 0.07191058835, 0.071886392,
2476  0.07185564256, 0.0718151936, 0.07176004502, 0.07156667263,
2477  0.07109516199, 0.07057665227, 0.06956111286}, {0.2185411094,
2478  0.2185862168, 0.2185760597, 0.2185502469, 0.2185551556,
2479  0.2185670597, 0.2185832072, 0.2186023833, 0.2186236698,
2480  0.2186463949, 0.2187689601, 0.21889384, 0.219017296, 0.2192613118,
2481  0.2195038699, 0.219745778, 0.2202276534, 0.2207065981, 0.2211824488,
2482  0.2216551307, 0.2221245734, 0.2225907052, 0.2230534566,
2483  0.2241951244, 0.2253143564, 0.2274827082, 0.2295545126,
2484  0.2315282566, 0.2351860943, 0.2384795534, 0.2414444658,
2485  0.2441189781, 0.2465387707, 0.2487354182, 0.2507361819,
2486  0.2525643629, 0.2542398214, 0.2557795018, 0.2571979034,
2487  0.2585074823, 0.2613723978, 0.2637535915, 0.2657465547,
2488  0.2674214198, 0.2688307276, 0.2700144584, 0.2710033792,
2489  0.2718213228, 0.2724867699, 0.273013963, 0.2734136955, 0.2736938697,
2490  0.2738598819, 0.2739148753, 0.2738598819, 0.2736938697,
2491  0.2734136955, 0.273013963, 0.2724867699, 0.2718213228, 0.2710033792,
2492  0.2700144584, 0.2688307276, 0.2674214198, 0.2657465547,
2493  0.2637535915, 0.2613723978, 0.2585074823, 0.2571979034,
2494  0.2557795018, 0.2542398214, 0.2525643629, 0.2507361819,
2495  0.2487354182, 0.2465387707, 0.2441189781, 0.2414444658,
2496  0.2384795534, 0.2351860943, 0.2315282566, 0.2295545126,
2497  0.2274827082, 0.2253143564, 0.2241951244, 0.2230534566,
2498  0.2225907052, 0.2221245734, 0.2216551307, 0.2211824488,
2499  0.2207065981, 0.2202276534, 0.219745778, 0.2195038699, 0.2192613118,
2500  0.219017296, 0.21889384, 0.2187689601, 0.2186463949, 0.2186236698,
2501  0.2186023833, 0.2185832072, 0.2185670597, 0.2185551556,
2502  0.2185502469, 0.2185760597, 0.2185862168,
2503  0.2185411094}, {0.3746283234, 0.3744760286, 0.3744655082,
2504  0.3745713459, 0.3746804416, 0.3747239651, 0.3747616125,
2505  0.3747951976, 0.3748262688, 0.3748559959, 0.3750036033,
2506  0.3751595179, 0.3753190966, 0.3756378976, 0.3759558332,
2507  0.3762746082, 0.3769149521, 0.3775582079, 0.3782042318,
2508  0.3788529456, 0.3795041978, 0.3801578285, 0.3808136809,
2509  0.3824619707, 0.3841204813, 0.3874566765, 0.3907983942,
2510  0.3941199491, 0.4005962971, 0.4067113438, 0.4123795696,
2511  0.4175861754, 0.422352588, 0.426714443, 0.4307106786, 0.4343787455,
2512  0.4377527783, 0.4408631174, 0.4437364171, 0.4463959791,
2513  0.4522370945, 0.4571173234, 0.4612213527, 0.4646855141,
2514  0.4676122255, 0.4700795615, 0.47214769, 0.4738632779, 0.4752625561,
2515  0.4763734789, 0.4772172535, 0.4778094206, 0.4781606008,
2516  0.4782769831, 0.4781606008, 0.4778094206, 0.4772172535,
2517  0.4763734789, 0.4752625561, 0.4738632779, 0.47214769, 0.4700795615,
2518  0.4676122255, 0.4646855141, 0.4612213527, 0.4571173234,
2519  0.4522370945, 0.4463959791, 0.4437364171, 0.4408631174,
2520  0.4377527783, 0.4343787455, 0.4307106786, 0.426714443, 0.422352588,
2521  0.4175861754, 0.4123795696, 0.4067113438, 0.4005962971,
2522  0.3941199491, 0.3907983942, 0.3874566765, 0.3841204813,
2523  0.3824619707, 0.3808136809, 0.3801578285, 0.3795041978,
2524  0.3788529456, 0.3782042318, 0.3775582079, 0.3769149521,
2525  0.3762746082, 0.3759558332, 0.3756378976, 0.3753190966,
2526  0.3751595179, 0.3750036033, 0.3748559959, 0.3748262688,
2527  0.3747951976, 0.3747616125, 0.3747239651, 0.3746804416,
2528  0.3745713459, 0.3744655082, 0.3744760286,
2529  0.3746283234}, {0.5488977566, 0.5492725578, 0.5493796167,
2530  0.5493030521, 0.5492800515, 0.5493081779, 0.5493493533,
2531  0.5493946353, 0.549438419, 0.5494780738, 0.5496229054, 0.5497549686,
2532  0.5499025591, 0.5501989882, 0.5504901744, 0.5507853393,
2533  0.5513807914, 0.5519818189, 0.552589775, 0.5532041749, 0.5538251797,
2534  0.5544529382, 0.5550874672, 0.5567036937, 0.5583633611,
2535  0.5618146957, 0.5654450115, 0.5692386679, 0.5773386388,
2536  0.5859421423, 0.5945472028, 0.602787763, 0.6105064194, 0.6176644895,
2537  0.624277053, 0.6303804075, 0.6360171698, 0.641229749, 0.6460576806,
2538  0.6505367243, 0.6604082105, 0.6686938222, 0.6756913514,
2539  0.6816215439, 0.6866504101, 0.6909045159, 0.6944813958,
2540  0.6974567098, 0.6998892223, 0.7018243015, 0.7032963922,
2541  0.7043307557, 0.7049446682, 0.7051482024, 0.7049446682,
2542  0.7043307557, 0.7032963922, 0.7018243015, 0.6998892223,
2543  0.6974567098, 0.6944813958, 0.6909045159, 0.6866504101,
2544  0.6816215439, 0.6756913514, 0.6686938222, 0.6604082105,
2545  0.6505367243, 0.6460576806, 0.641229749, 0.6360171698, 0.6303804075,
2546  0.624277053, 0.6176644895, 0.6105064194, 0.602787763, 0.5945472028,
2547  0.5859421423, 0.5773386388, 0.5692386679, 0.5654450115,
2548  0.5618146957, 0.5583633611, 0.5567036937, 0.5550874672,
2549  0.5544529382, 0.5538251797, 0.5532041749, 0.552589775, 0.5519818189,
2550  0.5513807914, 0.5507853393, 0.5504901744, 0.5501989882,
2551  0.5499025591, 0.5497549686, 0.5496229054, 0.5494780738, 0.549438419,
2552  0.5493946353, 0.5493493533, 0.5493081779, 0.5492800515,
2553  0.5493030521, 0.5493796167, 0.5492725578,
2554  0.5488977566}, {0.7501379784, 0.7495636806, 0.749650308,
2555  0.7501258019, 0.7500613683, 0.7499927446, 0.7499667401, 0.749986257,
2556  0.7500353707, 0.7500943083, 0.7502378208, 0.7502955686,
2557  0.7504262429, 0.7506329733, 0.7508454096, 0.7510636293,
2558  0.7514901194, 0.7519267005, 0.7523658758, 0.75281185, 0.7532615237,
2559  0.7537170118, 0.7541777199, 0.7553533494, 0.7565672969,
2560  0.7591011388, 0.7618191441, 0.7646738706, 0.771240475, 0.7783465723,
2561  0.7875759366, 0.7980345082, 0.8085705185, 0.8186647248,
2562  0.8281387322, 0.8369567431, 0.8451396344, 0.8527290961,
2563  0.8597724928, 0.8663164947, 0.8807666598, 0.8929239587,
2564  0.9032139277, 0.9119531958, 0.9193796679, 0.9256743556,
2565  0.9309764881, 0.9353939337, 0.9390104311, 0.9418906437,
2566  0.9440837035, 0.9456256811, 0.946541273, 0.9468448909, 0.946541273,
2567  0.9456256811, 0.9440837035, 0.9418906437, 0.9390104311,
2568  0.9353939337, 0.9309764881, 0.9256743556, 0.9193796679,
2569  0.9119531958, 0.9032139277, 0.8929239587, 0.8807666598,
2570  0.8663164947, 0.8597724928, 0.8527290961, 0.8451396344,
2571  0.8369567431, 0.8281387322, 0.8186647248, 0.8085705185,
2572  0.7980345082, 0.7875759366, 0.7783465723, 0.771240475, 0.7646738706,
2573  0.7618191441, 0.7591011388, 0.7565672969, 0.7553533494,
2574  0.7541777199, 0.7537170118, 0.7532615237, 0.75281185, 0.7523658758,
2575  0.7519267005, 0.7514901194, 0.7510636293, 0.7508454096,
2576  0.7506329733, 0.7504262429, 0.7502955686, 0.7502378208,
2577  0.7500943083, 0.7500353707, 0.749986257, 0.7499667401, 0.7499927446,
2578  0.7500613683, 0.7501258019, 0.749650308, 0.7495636806,
2579  0.7501379784}, {0.9742529776, 0.9747874524, 0.9741123398,
2580  0.9741101898, 0.9745054107, 0.9743713094, 0.9742131924,
2581  0.9741459996, 0.9741878531, 0.9742927333, 0.9744241227,
2582  0.9744440584, 0.9745998745, 0.9746798313, 0.9748508069,
2583  0.9749764636, 0.9752738201, 0.9755817532, 0.9758699637,
2584  0.9761776339, 0.9764736452, 0.9767861418, 0.9770899129,
2585  0.9778706747, 0.9786413703, 0.9802309584, 0.982150519, 0.9839171716,
2586  0.987227465, 0.9938892699, 0.9973348177, 1.002960092, 1.013708296,
2587  1.025861928, 1.037903138, 1.049355648, 1.060088661, 1.07009284,
2588  1.079402597, 1.088066636, 1.107231852, 1.123387254, 1.137086935,
2589  1.148745393, 1.158673191, 1.167105446, 1.174222093, 1.180161946,
2590  1.185032451, 1.188916455, 1.191876898, 1.193960032, 1.195197574,
2591  1.195608054, 1.195197574, 1.193960032, 1.191876898, 1.188916455,
2592  1.185032451, 1.180161946, 1.174222093, 1.167105446, 1.158673191,
2593  1.148745393, 1.137086935, 1.123387254, 1.107231852, 1.088066636,
2594  1.079402597, 1.07009284, 1.060088661, 1.049355648, 1.037903138,
2595  1.025861928, 1.013708296, 1.002960092, 0.9973348177, 0.9938892699,
2596  0.987227465, 0.9839171716, 0.982150519, 0.9802309584, 0.9786413703,
2597  0.9778706747, 0.9770899129, 0.9767861418, 0.9764736452,
2598  0.9761776339, 0.9758699637, 0.9755817532, 0.9752738201,
2599  0.9749764636, 0.9748508069, 0.9746798313, 0.9745998745,
2600  0.9744440584, 0.9744241227, 0.9742927333, 0.9741878531,
2601  0.9741459996, 0.9742131924, 0.9743713094, 0.9745054107,
2602  0.9741101898, 0.9741123398, 0.9747874524,
2603  0.9742529776}, {1.211526857, 1.211922483, 1.212758151, 1.211726992,
2604  1.212482465, 1.212475394, 1.212205486, 1.212000716, 1.212018349,
2605  1.212199008, 1.212212997, 1.212444728, 1.212370608, 1.2125862,
2606  1.212619732, 1.212746897, 1.212984684, 1.213207534, 1.213402392,
2607  1.213636737, 1.213847925, 1.214157158, 1.214311053, 1.21508082,
2608  1.215773219, 1.216721426, 1.218690906, 1.219600693, 1.221394824,
2609  1.223150892, 1.228953387, 1.236823174, 1.230978076, 1.238359914,
2610  1.251235241, 1.264746546, 1.277799572, 1.290112987, 1.301635176,
2611  1.312389501, 1.33624286, 1.356406755, 1.373555087, 1.388197376,
2612  1.400713453, 1.411387828, 1.420435218, 1.428018603, 1.434261866,
2613  1.439258803, 1.443079447, 1.445774471, 1.447378225, 1.447910632,
2614  1.447378225, 1.445774471, 1.443079447, 1.439258803, 1.434261866,
2615  1.428018603, 1.420435218, 1.411387828, 1.400713453, 1.388197376,
2616  1.373555087, 1.356406755, 1.33624286, 1.312389501, 1.301635176,
2617  1.290112987, 1.277799572, 1.264746546, 1.251235241, 1.238359914,
2618  1.230978076, 1.236823174, 1.228953387, 1.223150892, 1.221394824,
2619  1.219600693, 1.218690906, 1.216721426, 1.215773219, 1.21508082,
2620  1.214311053, 1.214157158, 1.213847925, 1.213636737, 1.213402392,
2621  1.213207534, 1.212984684, 1.212746897, 1.212619732, 1.2125862,
2622  1.212370608, 1.212444728, 1.212212997, 1.212199008, 1.212018349,
2623  1.212000716, 1.212205486, 1.212475394, 1.212482465, 1.211726992,
2624  1.212758151, 1.211922483, 1.211526857}, {1.457166384, 1.455774437,
2625  1.45614065, 1.456163388, 1.456398915, 1.456702444, 1.456452029,
2626  1.456111048, 1.456084183, 1.456343126, 1.456203267, 1.456611834,
2627  1.456405008, 1.456495794, 1.456708475, 1.456856113, 1.45703245,
2628  1.457199255, 1.457216831, 1.457758397, 1.458078952, 1.458344132,
2629  1.458161964, 1.458541639, 1.4580717, 1.462140395, 1.464201092,
2630  1.463724506, 1.468574149, 1.46434673, 1.472722297, 1.467376603,
2631  1.483390561, 1.480075895, 1.470177613, 1.482565512, 1.497109984,
2632  1.511416992, 1.524995064, 1.537744972, 1.566154575, 1.590272672,
2633  1.610878824, 1.628579645, 1.643827476, 1.656957371, 1.668215944,
2634  1.677781064, 1.685775835, 1.692277814, 1.697328618, 1.700942134,
2635  1.7031156, 1.703841327, 1.7031156, 1.700942134, 1.697328618,
2636  1.692277814, 1.685775835, 1.677781064, 1.668215944, 1.656957371,
2637  1.643827476, 1.628579645, 1.610878824, 1.590272672, 1.566154575,
2638  1.537744972, 1.524995064, 1.511416992, 1.497109984, 1.482565512,
2639  1.470177613, 1.480075895, 1.483390561, 1.467376603, 1.472722297,
2640  1.46434673, 1.468574149, 1.463724506, 1.464201092, 1.462140395,
2641  1.4580717, 1.458541639, 1.458161964, 1.458344132, 1.458078952,
2642  1.457758397, 1.457216831, 1.457199255, 1.45703245, 1.456856113,
2643  1.456708475, 1.456495794, 1.456405008, 1.456611834, 1.456203267,
2644  1.456343126, 1.456084183, 1.456111048, 1.456452029, 1.456702444,
2645  1.456398915, 1.456163388, 1.45614065, 1.455774437, 1.457166384}};
2646 
2647  /* 3, 3 mode */
2648  const double reomegaqnm33[8][107] = {{0.445768, 0.452799, 0.456948, 0.460943, 0.462462, 0.462842,
2649  0.463095, 0.463269, 0.463394, 0.463488, 0.463746, 0.463886,
2650  0.463989, 0.464144, 0.464267, 0.464374, 0.464572, 0.464763,
2651  0.464952, 0.46514, 0.465329, 0.465518, 0.465707, 0.466182, 0.466657,
2652  0.467612, 0.468573, 0.46954, 0.471491, 0.473465, 0.475464,
2653  0.477487, 0.479535, 0.481609, 0.483709, 0.485837, 0.487991,
2654  0.490174, 0.492386, 0.494627, 0.500363, 0.5063, 0.512449, 0.518826,
2655  0.525445, 0.532323, 0.539479, 0.546934, 0.55471, 0.562834, 0.571335,
2656  0.580244, 0.5896, 0.599443, 0.609823, 0.620796, 0.632425, 0.644787,
2657  0.657972, 0.672086, 0.68726, 0.70365, 0.721455, 0.740921, 0.762369,
2658  0.786223, 0.813057, 0.843687, 0.857254, 0.871717, 0.887201,
2659  0.90386, 0.921885, 0.941521, 0.963088, 0.987016, 1.01391, 1.04464,
2660  1.08058, 1.1241, 1.14998, 1.17986, 1.21547, 1.23637, 1.26023,
2661  1.27086, 1.28227, 1.29462, 1.30812, 1.32308, 1.33999, 1.35965,
2662  1.37094, 1.38363, 1.39829, 1.40666, 1.41603, 1.42679, 1.42917,
2663  1.43164, 1.43422, 1.43692, 1.43975, 1.44591, 1.45295, 1.45695,
2664  1.46139}, {0.428357, 0.432238, 0.434351, 0.436362, 0.437184,
2665  0.437404, 0.437552, 0.437654, 0.437725, 0.437773, 0.437868,
2666  0.437898, 0.437929, 0.438015, 0.438115, 0.438217, 0.438421,
2667  0.438623, 0.438826, 0.43903, 0.439233, 0.439437, 0.439641, 0.440152,
2668  0.440665, 0.441694, 0.442729, 0.443771, 0.445872, 0.447999,
2669  0.45015, 0.452328, 0.454532, 0.456764, 0.459023, 0.461311, 0.463627,
2670  0.465974, 0.46835, 0.470758, 0.476918, 0.483289, 0.489884,
2671  0.496717, 0.503805, 0.511164, 0.518814, 0.526776, 0.535074,
2672  0.543734, 0.552785, 0.562261, 0.5722, 0.582644, 0.593642, 0.60525,
2673  0.617535, 0.630573, 0.644453, 0.659285, 0.675198, 0.692352,
2674  0.710943, 0.731221, 0.753507, 0.778225, 0.805952, 0.837504,
2675  0.851449, 0.866295, 0.882167, 0.89922, 0.917645, 0.937687, 0.959667,
2676  0.984015, 1.01133, 1.0425, 1.07889, 1.12285, 1.14897, 1.17907,
2677  1.21491, 1.23591, 1.25988, 1.27055, 1.28201, 1.2944, 1.30794,
2678  1.32294, 1.33989, 1.35958, 1.37089, 1.38359, 1.39826, 1.40664,
2679  1.41601, 1.42678, 1.42916, 1.43163, 1.43421, 1.43691, 1.43974,
2680  1.4459, 1.45295, 1.45695, 1.46139}, {0.390162, 0.390933, 0.390855,
2681  0.39013, 0.389593, 0.389452, 0.389377, 0.389349, 0.389352, 0.389374,
2682  0.389533, 0.389627, 0.38968, 0.38978, 0.389896, 0.390013, 0.390243,
2683  0.390473, 0.390704, 0.390935, 0.391167, 0.391398, 0.39163,
2684  0.392211, 0.392793, 0.393963, 0.395139, 0.396321, 0.398706,
2685  0.401118, 0.403557, 0.406025, 0.408522, 0.411048, 0.413604,
2686  0.416191, 0.41881, 0.42146, 0.424144, 0.426861, 0.433807, 0.44098,
2687  0.448397, 0.456071, 0.464019, 0.47226, 0.480815, 0.489704, 0.498954,
2688  0.50859, 0.518645, 0.529153, 0.540151, 0.551685, 0.563804,
2689  0.576567, 0.590041, 0.604302, 0.619445, 0.635578, 0.652833,
2690  0.671371, 0.691391, 0.713145, 0.736956, 0.763249, 0.792606,
2691  0.825846, 0.840483, 0.856032, 0.872619, 0.890397, 0.90956, 0.930355,
2692  0.953102, 0.978234, 1.00636, 1.03835, 1.07558, 1.12042, 1.14697,
2693  1.17752, 1.21379, 1.23502, 1.2592, 1.26995, 1.28149, 1.29396,
2694  1.30758, 1.32266, 1.33967, 1.35943, 1.37078, 1.38351, 1.3982,
2695  1.4066, 1.41598, 1.42676, 1.42914, 1.43162, 1.4342, 1.4369, 1.43973,
2696  1.44589, 1.45294, 1.45694, 1.46139}, {0.332321, 0.329612, 0.329447,
2697  0.330998, 0.331533, 0.331485, 0.331367, 0.331244, 0.331151,
2698  0.331101, 0.331226, 0.331354, 0.331387, 0.331504, 0.331643,
2699  0.331766, 0.332024, 0.33228, 0.332537, 0.332795, 0.333053, 0.333311,
2700  0.333569, 0.334216, 0.334865, 0.336168, 0.337478, 0.338796,
2701  0.341454, 0.344143, 0.346863, 0.349614, 0.352398, 0.355215,
2702  0.358066, 0.360951, 0.363872, 0.366829, 0.369823, 0.372855,
2703  0.380605, 0.388612, 0.39689, 0.405455, 0.414327, 0.423525, 0.43307,
2704  0.442986, 0.4533, 0.464039, 0.475237, 0.486928, 0.499155, 0.511962,
2705  0.525402, 0.539534, 0.554428, 0.570163, 0.586836, 0.604556, 0.62346,
2706  0.643711, 0.665511, 0.689115, 0.71485, 0.743145, 0.774586,
2707  0.809998, 0.82553, 0.841991, 0.859506, 0.878231, 0.898362, 0.920146,
2708  0.943908, 0.970086, 0.999286, 1.0324, 1.0708, 1.11686, 1.14404,
2709  1.17523, 1.21215, 1.23369, 1.25818, 1.26906, 1.28072, 1.2933,
2710  1.30704, 1.32223, 1.33936, 1.35922, 1.37061, 1.38339, 1.39812,
2711  1.40653, 1.41593, 1.42673, 1.42911, 1.43159, 1.43418, 1.43688,
2712  1.43971, 1.44588, 1.45294, 1.45694, 1.46138}, {0.279748, 0.281425,
2713  0.280003, 0.278496, 0.279479, 0.279701, 0.279679, 0.279534, 0.27938,
2714  0.279284, 0.279511, 0.279556, 0.279569, 0.279745, 0.279852,
2715  0.279994, 0.280246, 0.280507, 0.280766, 0.281026, 0.281285,
2716  0.281546, 0.281806, 0.282459, 0.283115, 0.284431, 0.285757,
2717  0.287091, 0.289787, 0.292519, 0.295288, 0.298095, 0.30094, 0.303825,
2718  0.306751, 0.309717, 0.312725, 0.315776, 0.318871, 0.322011,
2719  0.330062, 0.338415, 0.347087, 0.356096, 0.365463, 0.37521, 0.385359,
2720  0.395936, 0.406968, 0.418488, 0.430528, 0.443126, 0.456326,
2721  0.470174, 0.484725, 0.500042, 0.516195, 0.533269, 0.551359,
2722  0.570583, 0.591077, 0.61301, 0.636588, 0.662069, 0.689786, 0.720173,
2723  0.753822, 0.791564, 0.808064, 0.825515, 0.844044, 0.863808,
2724  0.885005, 0.907885, 0.932779, 0.960131, 0.990559, 1.02497, 1.06475,
2725  1.11229, 1.14026, 1.17226, 1.21, 1.23195, 1.25686, 1.26789, 1.2797,
2726  1.29245, 1.30633, 1.32167, 1.33893, 1.35893, 1.37038, 1.38322,
2727  1.39801, 1.40645, 1.41587, 1.42669, 1.42908, 1.43156, 1.43415,
2728  1.43685, 1.43969, 1.44587, 1.45293, 1.45693, 1.46137}, {0.239992,
2729  0.240995, 0.242946, 0.24156, 0.241854, 0.242213, 0.242269, 0.242117,
2730  0.241939, 0.241855, 0.242174, 0.24208, 0.242226, 0.242298,
2731  0.242438, 0.242546, 0.242783, 0.243024, 0.243261, 0.243498,
2732  0.243736, 0.243974, 0.244213, 0.244811, 0.245412, 0.246621, 0.24784,
2733  0.249069, 0.251558, 0.254089, 0.256662, 0.259279, 0.26194,
2734  0.264647, 0.2674, 0.2702, 0.273049, 0.275948, 0.278897, 0.281899,
2735  0.289636, 0.297725, 0.306186, 0.315041, 0.324312, 0.334027, 0.34421,
2736  0.354891, 0.366101, 0.377873, 0.390245, 0.403257, 0.416954,
2737  0.431386, 0.446612, 0.462696, 0.479713, 0.49775, 0.516906, 0.537303,
2738  0.559082, 0.582416, 0.607517, 0.634649, 0.66415, 0.696462,
2739  0.732182, 0.77215, 0.789586, 0.807999, 0.827516, 0.848298, 0.870543,
2740  0.894505, 0.920521, 0.949042, 0.980704, 1.01643, 1.05767, 1.10684,
2741  1.1357, 1.16864, 1.20737, 1.22983, 1.25522, 1.26646, 1.27846,
2742  1.29139, 1.30546, 1.32098, 1.33842, 1.35857, 1.3701, 1.38301,
2743  1.39787, 1.40634, 1.41579, 1.42664, 1.42903, 1.43152, 1.43411,
2744  1.43682, 1.43966, 1.44585, 1.45291, 1.45692, 1.46137}, {0.21884,
2745  0.216298, 0.216633, 0.217244, 0.216888, 0.217233, 0.217329,
2746  0.217189, 0.217034, 0.217006, 0.217217, 0.217255, 0.217293,
2747  0.217414, 0.217505, 0.217599, 0.217807, 0.218016, 0.218223,
2748  0.218427, 0.218635, 0.218841, 0.21905, 0.21957, 0.220094, 0.221148,
2749  0.222212, 0.223288, 0.22547, 0.227696, 0.229966, 0.232282, 0.234646,
2750  0.237057, 0.239517, 0.242028, 0.244591, 0.247207, 0.249877,
2751  0.252604, 0.259674, 0.267128, 0.274991, 0.283291, 0.292057,
2752  0.301319, 0.31111, 0.321465, 0.332419, 0.344012, 0.356285, 0.369284,
2753  0.383057, 0.39766, 0.413152, 0.429604, 0.447094, 0.465712,
2754  0.485563, 0.506772, 0.529486, 0.553883, 0.580183, 0.608655,
2755  0.639647, 0.673609, 0.711146, 0.753105, 0.771386, 0.790674,
2756  0.811095, 0.832808, 0.856013, 0.880965, 0.908002, 0.937583,
2757  0.970359, 1.00729, 1.04987, 1.10064, 1.13044, 1.16442, 1.20427,
2758  1.22731, 1.2533, 1.26476, 1.27699, 1.29015, 1.30444, 1.32016,
2759  1.3378, 1.35815, 1.36977, 1.38276, 1.3977, 1.40621, 1.4157, 1.42658,
2760  1.42898, 1.43147, 1.43407, 1.43678, 1.43963, 1.44582, 1.4529,
2761  1.45691, 1.46135}, {0.199814, 0.201353, 0.200132, 0.200956,
2762  0.200467, 0.200722, 0.200829, 0.200716, 0.200604, 0.200626,
2763  0.200705, 0.200826, 0.200822, 0.200914, 0.201004, 0.201103,
2764  0.201273, 0.201448, 0.201625, 0.2018, 0.201975, 0.202153, 0.202329,
2765  0.202773, 0.20322, 0.204121, 0.205032, 0.205953, 0.207826, 0.209742,
2766  0.211702, 0.213706, 0.215757, 0.217854, 0.220001, 0.222198,
2767  0.224447, 0.226749, 0.229105, 0.231518, 0.237809, 0.244492,
2768  0.251597, 0.25916, 0.267216, 0.275804, 0.284965, 0.294742, 0.305178,
2769  0.316322, 0.328221, 0.340928, 0.354499, 0.368992, 0.384475,
2770  0.401019, 0.418708, 0.437635, 0.45791, 0.479661, 0.50304, 0.528232,
2771  0.555461, 0.585008, 0.617226, 0.652577, 0.691676, 0.735379,
2772  0.754411, 0.774477, 0.795706, 0.818253, 0.842317, 0.868149,
2773  0.896082, 0.926573, 0.960272, 0.998162, 1.04182, 1.09394, 1.1246,
2774  1.15963, 1.20071, 1.22441, 1.25107, 1.2628, 1.2753, 1.28872,
2775  1.30326, 1.31923, 1.3371, 1.35766, 1.36938, 1.38248, 1.39751,
2776  1.40606, 1.41559, 1.4265, 1.42891, 1.43141, 1.43401, 1.43673,
2777  1.43959, 1.44579, 1.45288, 1.45689, 1.46134}};
2778 
2779  const double imomegaqnm33[8][107] = {{0.068612, 0.0735351, 0.0774984, 0.0829193, 0.0860369, 0.0870572,
2780  0.0878377, 0.0884398, 0.0889085, 0.0892767, 0.0902685, 0.0906386,
2781  0.0907974, 0.0909101, 0.0909414, 0.090952, 0.0909603, 0.0909664,
2782  0.0909729, 0.0909798, 0.090987, 0.0909942, 0.0910015, 0.0910197,
2783  0.0910378, 0.091074, 0.09111, 0.0911457, 0.0912166, 0.0912867,
2784  0.091356, 0.0914243, 0.0914917, 0.0915582, 0.0916236, 0.091688,
2785  0.0917514, 0.0918136, 0.0918746, 0.0919344, 0.0920784, 0.0922137,
2786  0.0923394, 0.0924547, 0.0925583, 0.0926492, 0.0927258, 0.0927867,
2787  0.0928302, 0.0928541, 0.0928562, 0.0928338, 0.092784, 0.092703,
2788  0.0925869, 0.0924305, 0.0922281, 0.0919726, 0.0916556, 0.0912666,
2789  0.0907928, 0.0902179, 0.0895213, 0.0886763, 0.087647, 0.0863849,
2790  0.0848213, 0.0828557, 0.0819248, 0.0808922, 0.0797413, 0.0784512,
2791  0.0769953, 0.075339, 0.0734361, 0.0712234, 0.0686106, 0.0654629,
2792  0.0615646, 0.056537, 0.0533881, 0.0496087, 0.0449046, 0.0420439,
2793  0.0386881, 0.0371631, 0.0355053, 0.0336873, 0.0316714, 0.0294027,
2794  0.0267968, 0.023711, 0.0219107, 0.0198652, 0.0174725, 0.0160908,
2795  0.014533, 0.0127266, 0.0123252, 0.011907, 0.0114701, 0.011012,
2796  0.0105299, 0.00947732, 0.00826624, 0.0075764,
2797  0.00680679}, {0.277496, 0.278402, 0.278809, 0.278955, 0.278824,
2798  0.278742, 0.278664, 0.278594, 0.278534, 0.278482, 0.278334,
2799  0.278289, 0.278281, 0.278294, 0.278307, 0.278318, 0.278336,
2800  0.278354, 0.278373, 0.278391, 0.278409, 0.278427, 0.278446,
2801  0.278491, 0.278537, 0.278627, 0.278716, 0.278805, 0.27898, 0.279153,
2802  0.279323, 0.279489, 0.279653, 0.279813, 0.27997, 0.280123,
2803  0.280273, 0.280419, 0.280561, 0.280699, 0.281026, 0.281324,
2804  0.281591, 0.281825, 0.28202, 0.282175, 0.282285, 0.282345, 0.28235,
2805  0.282293, 0.282168, 0.281967, 0.281681, 0.281298, 0.280807,
2806  0.280191, 0.279434, 0.278515, 0.277407, 0.27608, 0.274494, 0.272602,
2807  0.27034, 0.26763, 0.264363, 0.260394, 0.255518, 0.249435, 0.246568,
2808  0.243397, 0.239871, 0.235928, 0.231489, 0.226451, 0.220675,
2809  0.213971, 0.206071, 0.19657, 0.184822, 0.169692, 0.160224, 0.148867,
2810  0.134739, 0.12615, 0.116076, 0.111499, 0.106524, 0.101069,
2811  0.0950193, 0.088212, 0.0803933, 0.0711348, 0.0657335, 0.0595967,
2812  0.0524182, 0.0482728, 0.0435993, 0.03818, 0.0369756, 0.0357211,
2813  0.0344103, 0.0330362, 0.0315898, 0.028432, 0.0247987, 0.0227292,
2814  0.0204204}, {0.486993, 0.484741, 0.483427, 0.482389, 0.482301,
2815  0.482372, 0.48246, 0.482542, 0.482611, 0.482664, 0.482744, 0.482718,
2816  0.482702, 0.482709, 0.482722, 0.482729, 0.482743, 0.482759,
2817  0.482774, 0.482789, 0.482804, 0.482819, 0.482834, 0.482871,
2818  0.482907, 0.48298, 0.483051, 0.483121, 0.483256, 0.483386, 0.483511,
2819  0.48363, 0.483742, 0.483849, 0.483949, 0.484043, 0.48413, 0.48421,
2820  0.484283, 0.484348, 0.484477, 0.484555, 0.484575, 0.484535,
2821  0.484428, 0.484247, 0.483987, 0.483638, 0.483192, 0.48264, 0.481968,
2822  0.481164, 0.480211, 0.479093, 0.477786, 0.476267, 0.474506,
2823  0.472466, 0.470105, 0.467369, 0.464195, 0.4605, 0.456181, 0.451103,
2824  0.44509, 0.437899, 0.42919, 0.418467, 0.413455, 0.407937, 0.401829,
2825  0.39503, 0.387407, 0.37879, 0.36895, 0.357573, 0.344212, 0.328195,
2826  0.308447, 0.283082, 0.267235, 0.248247, 0.224647, 0.210309,
2827  0.193501, 0.185866, 0.177568, 0.168469, 0.158382, 0.147032,
2828  0.133998, 0.118564, 0.10956, 0.0993313, 0.0873659, 0.0804562,
2829  0.0726665, 0.0636339, 0.0616265, 0.0595355, 0.0573509, 0.0550606,
2830  0.0526499, 0.0473868, 0.0413313, 0.0378821, 0.034034}, {0.709974,
2831  0.711601, 0.713499, 0.714385, 0.713785, 0.713546, 0.713418,
2832  0.713383, 0.713411, 0.713468, 0.713655, 0.713595, 0.713563,
2833  0.713584, 0.713571, 0.713561, 0.71355, 0.713535, 0.713522, 0.713507,
2834  0.713493, 0.713479, 0.713465, 0.713428, 0.713392, 0.713317,
2835  0.713241, 0.713162, 0.712999, 0.712828, 0.712649, 0.712461,
2836  0.712264, 0.712058, 0.711843, 0.711618, 0.711383, 0.711138,
2837  0.710882, 0.710616, 0.709899, 0.709105, 0.708229, 0.707264,
2838  0.706201, 0.705033, 0.703748, 0.702336, 0.700785, 0.699079,
2839  0.697202, 0.695135, 0.692855, 0.690337, 0.68755, 0.684459, 0.68102,
2840  0.677183, 0.672887, 0.668056, 0.662599, 0.656401, 0.649315,
2841  0.641153, 0.631664, 0.620511, 0.607221, 0.591101, 0.583641,
2842  0.575473, 0.566484, 0.556529, 0.545428, 0.532943, 0.518759,
2843  0.502439, 0.48336, 0.460589, 0.432625, 0.396831, 0.37452, 0.347819,
2844  0.314676, 0.294558, 0.270986, 0.260282, 0.248651, 0.235902,
2845  0.221769, 0.20587, 0.187614, 0.166001, 0.153393, 0.13907, 0.122317,
2846  0.112642, 0.101735, 0.0890889, 0.0862783, 0.0833507, 0.080292,
2847  0.0770855, 0.0737103, 0.0663418, 0.057864, 0.053035,
2848  0.0476477}, {0.972477, 0.969229, 0.96766, 0.969029, 0.969442,
2849  0.969155, 0.968886, 0.968746, 0.968738, 0.968815, 0.969029,
2850  0.968878, 0.968919, 0.968877, 0.968857, 0.968828, 0.968768,
2851  0.968706, 0.968649, 0.968589, 0.968529, 0.96847, 0.96841, 0.96826,
2852  0.96811, 0.967806, 0.9675, 0.96719, 0.966561, 0.96592, 0.965265,
2853  0.964597, 0.963916, 0.96322, 0.962509, 0.961784, 0.961043, 0.960287,
2854  0.959514, 0.958725, 0.956678, 0.954518, 0.952237, 0.949827,
2855  0.947277, 0.944577, 0.941715, 0.938677, 0.935446, 0.932005,
2856  0.928331, 0.924401, 0.920185, 0.915649, 0.910755, 0.905456,
2857  0.899695, 0.893406, 0.88651, 0.878908, 0.870479, 0.861073, 0.850501,
2858  0.838516, 0.824795, 0.808901, 0.790225, 0.767883, 0.757639,
2859  0.746483, 0.73427, 0.720819, 0.7059, 0.689212, 0.670355, 0.648776,
2860  0.623682, 0.593881, 0.557455, 0.511016, 0.482143, 0.44764, 0.404868,
2861  0.378929, 0.348555, 0.334768, 0.319791, 0.303378, 0.285189,
2862  0.264731, 0.241246, 0.213447, 0.197233, 0.178815, 0.157271,
2863  0.144831, 0.130807, 0.114545, 0.110932, 0.107167, 0.103234,
2864  0.0991113, 0.0947715, 0.0852972, 0.0743968, 0.068188,
2865  0.0612614}, {1.23488, 1.2385, 1.23757, 1.23638, 1.23735, 1.23719,
2866  1.23689, 1.23671, 1.23672, 1.23684, 1.23689, 1.23686, 1.23687,
2867  1.23681, 1.23674, 1.23671, 1.2366, 1.23651, 1.23641, 1.23631,
2868  1.23622, 1.23612, 1.23602, 1.23578, 1.23553, 1.23504, 1.23454,
2869  1.23403, 1.23301, 1.23196, 1.23088, 1.22979, 1.22867, 1.22753,
2870  1.22637, 1.22518, 1.22396, 1.22272, 1.22145, 1.22016, 1.21681,
2871  1.21328, 1.20956, 1.20564, 1.20152, 1.19717, 1.19258, 1.18775,
2872  1.18264, 1.17724, 1.17153, 1.16546, 1.15902, 1.15215, 1.14481,
2873  1.13695, 1.12848, 1.11934, 1.10942, 1.09859, 1.08672, 1.07361,
2874  1.05902, 1.04265, 1.02409, 1.00282, 0.978074, 0.948772, 0.935434,
2875  0.920971, 0.905209, 0.887929, 0.868853, 0.847622, 0.823753,
2876  0.796583, 0.765161, 0.728048, 0.682917, 0.625639, 0.590118,
2877  0.547732, 0.49525, 0.463448, 0.42623, 0.409344, 0.391005, 0.370913,
2878  0.348652, 0.323623, 0.294897, 0.260904, 0.241081, 0.218564,
2879  0.192229, 0.177023, 0.159881, 0.140004, 0.135587, 0.130985,
2880  0.126178, 0.121138, 0.115834, 0.104253, 0.09093, 0.0833412,
2881  0.0748751}, {1.50812, 1.50714, 1.50886, 1.50765, 1.50833, 1.50831,
2882  1.50805, 1.5079, 1.50794, 1.50808, 1.50796, 1.50805, 1.50794,
2883  1.50791, 1.50787, 1.50779, 1.50768, 1.50756, 1.50745, 1.50733,
2884  1.50721, 1.50709, 1.50697, 1.50667, 1.50637, 1.50577, 1.50515,
2885  1.50453, 1.50326, 1.50195, 1.50061, 1.49924, 1.49784, 1.49639,
2886  1.49491, 1.4934, 1.49185, 1.49025, 1.48862, 1.48695, 1.4826,
2887  1.47798, 1.47308, 1.46789, 1.46239, 1.45657, 1.45042, 1.44391,
2888  1.43702, 1.42973, 1.42201, 1.41383, 1.40515, 1.39591, 1.38607,
2889  1.37555, 1.36428, 1.35215, 1.33904, 1.32481, 1.30928, 1.29221,
2890  1.27333, 1.25226, 1.22852, 1.20145, 1.17016, 1.13335, 1.11668,
2891  1.09865, 1.07906, 1.05766, 1.03413, 1.00803, 0.978819, 0.945725,
2892  0.907651, 0.862934, 0.808869, 0.7406, 0.698384, 0.648072, 0.585828,
2893  0.54813, 0.50403, 0.484027, 0.462309, 0.43852, 0.412171, 0.382553,
2894  0.348572, 0.308374, 0.284937, 0.258319, 0.227191, 0.209218,
2895  0.188957, 0.165464, 0.160243, 0.154805, 0.149123, 0.143167,
2896  0.136898, 0.123211, 0.107464, 0.0984948, 0.102103}, {1.77947,
2897  1.77829, 1.77828, 1.77845, 1.7786, 1.77868, 1.7785, 1.77838,
2898  1.77844, 1.77854, 1.77842, 1.77841, 1.77841, 1.77834, 1.77827,
2899  1.7782, 1.77808, 1.77795, 1.77783, 1.7777, 1.77757, 1.77744,
2900  1.77732, 1.77699, 1.77667, 1.77601, 1.77534, 1.77466, 1.77327,
2901  1.77183, 1.77035, 1.76883, 1.76726, 1.76564, 1.76398, 1.76226,
2902  1.7605, 1.75868, 1.75682, 1.75489, 1.74985, 1.74445, 1.73867,
2903  1.73249, 1.72589, 1.71886, 1.71137, 1.7034, 1.69493, 1.68592,
2904  1.67635, 1.66618, 1.65536, 1.64384, 1.63157, 1.61846, 1.60441,
2905  1.58931, 1.57303, 1.55539, 1.53617, 1.5151, 1.49185, 1.46597,
2906  1.43689, 1.40384, 1.36575, 1.32111, 1.30093, 1.27916, 1.25555,
2907  1.22981, 1.20156, 1.17032, 1.13545, 1.09609, 1.05101, 0.998352,
2908  0.935078, 0.85569, 0.806777, 0.748562, 0.676569, 0.632966, 0.58196,
2909  0.558828, 0.533715, 0.506213, 0.475757, 0.441533, 0.40228, 0.355861,
2910  0.328804, 0.29808, 0.262156, 0.241415, 0.218035, 0.190926,
2911  0.184902, 0.178626, 0.17207, 0.165197, 0.157962, 0.142169, 0.123998,
2912  0.113649, 0.115718}};
2913 
2914 
2915  /* 4, 4 mode */
2916  const double reomegaqnm44[8][107] = {{0.603485, 0.613847, 0.619636, 0.623952, 0.624219, 0.623894,
2917  0.623504, 0.623122, 0.62278, 0.622487, 0.621648, 0.621375, 0.621309,
2918  0.621365, 0.621483, 0.621613, 0.621877, 0.622141, 0.622404,
2919  0.622667, 0.62293, 0.623194, 0.623458, 0.624119, 0.624781, 0.626113,
2920  0.627452, 0.628799, 0.631518, 0.634269, 0.637054, 0.639872,
2921  0.642726, 0.645615, 0.648541, 0.651503, 0.654504, 0.657544,
2922  0.660623, 0.663743, 0.671728, 0.679989, 0.688543, 0.697411,
2923  0.706611, 0.716168, 0.726107, 0.736455, 0.747243, 0.758508,
2924  0.770286, 0.782624, 0.795569, 0.809178, 0.823517, 0.83866, 0.854693,
2925  0.871718, 0.889853, 0.909242, 0.930054, 0.9525, 0.976839, 1.0034,
2926  1.03259, 1.06498, 1.10131, 1.14265, 1.16092, 1.18036, 1.20114,
2927  1.22345, 1.24755, 1.27374, 1.30245, 1.33422, 1.36984, 1.41042,
2928  1.45773, 1.51478, 1.54862, 1.58759, 1.6339, 1.66102, 1.69194,
2929  1.7057, 1.72045, 1.73641, 1.75384, 1.77314, 1.79492, 1.82022,
2930  1.83474, 1.85104, 1.86985, 1.8806, 1.8926, 1.9064, 1.90945, 1.91261,
2931  1.91592, 1.91937, 1.92299, 1.93088, 1.93989, 1.945,
2932  1.95068}, {0.59231, 0.596523, 0.598412, 0.599977, 0.600617,
2933  0.600806, 0.600947, 0.601053, 0.601136, 0.601202, 0.601389,
2934  0.601485, 0.601558, 0.601693, 0.601828, 0.601964, 0.602238,
2935  0.602511, 0.602785, 0.60306, 0.603334, 0.603609, 0.603884, 0.604574,
2936  0.605265, 0.606653, 0.60805, 0.609455, 0.61229, 0.615158, 0.618061,
2937  0.620998, 0.623972, 0.626982, 0.630029, 0.633115, 0.63624,
2938  0.639405, 0.64261, 0.645858, 0.654166, 0.662758, 0.671651, 0.680865,
2939  0.69042, 0.700341, 0.710653, 0.721383, 0.732565, 0.744232,
2940  0.756425, 0.769188, 0.782571, 0.796632, 0.811434, 0.827055,
2941  0.843581, 0.861114, 0.879773, 0.899703, 0.921074, 0.944098,
2942  0.969034, 0.996209, 1.02604, 1.05909, 1.09611, 1.13816, 1.15671,
2943  1.17644, 1.19752, 1.22013, 1.24453, 1.27103, 1.30005, 1.33214,
2944  1.36806, 1.40896, 1.45658, 1.51396, 1.54795, 1.58707, 1.63353,
2945  1.66073, 1.69172, 1.7055, 1.72028, 1.73626, 1.75372, 1.77304,
2946  1.79485, 1.82017, 1.8347, 1.85101, 1.86983, 1.88058, 1.89259,
2947  1.90639, 1.90944, 1.91261, 1.91591, 1.91936, 1.92299, 1.93087,
2948  1.93989, 1.945, 1.95068}, {0.559386, 0.561881, 0.562985, 0.563673,
2949  0.563747, 0.563732, 0.563712, 0.563695, 0.563683, 0.563678,
2950  0.563718, 0.563794, 0.563872, 0.564021, 0.564168, 0.564316,
2951  0.564612, 0.564908, 0.565204, 0.565501, 0.565798, 0.566096,
2952  0.566394, 0.567139, 0.567887, 0.56939, 0.570901, 0.57242, 0.575484,
2953  0.578584, 0.58172, 0.584892, 0.588102, 0.59135, 0.594637, 0.597965,
2954  0.601333, 0.604743, 0.608195, 0.611692, 0.62063, 0.629865, 0.639415,
2955  0.649299, 0.65954, 0.670161, 0.681189, 0.692653, 0.704586,
2956  0.717023, 0.730006, 0.743579, 0.757794, 0.77271, 0.788392, 0.804918,
2957  0.822375, 0.840868, 0.860518, 0.88147, 0.903897, 0.928012,
2958  0.954076, 0.982419, 1.01346, 1.04777, 1.08608, 1.12947, 1.14857,
2959  1.16887, 1.19051, 1.21369, 1.23867, 1.26576, 1.29538, 1.32806,
2960  1.36459, 1.4061, 1.45434, 1.51232, 1.54662, 1.58604, 1.6328,
2961  1.66014, 1.69127, 1.70511, 1.71994, 1.73598, 1.75348, 1.77286,
2962  1.79471, 1.82008, 1.83463, 1.85096, 1.8698, 1.88055, 1.89257,
2963  1.90638, 1.90943, 1.9126, 1.9159, 1.91935, 1.92298, 1.93087,
2964  1.93989, 1.945, 1.95068}, {0.514416, 0.513669, 0.512866, 0.5122,
2965  0.512256, 0.512336, 0.512404, 0.512455, 0.512488, 0.51251, 0.512565,
2966  0.51264, 0.512726, 0.512889, 0.513051, 0.513214, 0.51354, 0.513866,
2967  0.514193, 0.51452, 0.514848, 0.515175, 0.515503, 0.516325,
2968  0.517149, 0.518804, 0.520467, 0.522139, 0.525511, 0.52892, 0.532367,
2969  0.535852, 0.539377, 0.542943, 0.546549, 0.550198, 0.553889,
2970  0.557625, 0.561406, 0.565233, 0.575009, 0.585097, 0.595517,
2971  0.606289, 0.617438, 0.628986, 0.640963, 0.653399, 0.666327,
2972  0.679785, 0.693815, 0.708464, 0.723784, 0.739837, 0.75669, 0.774421,
2973  0.793122, 0.812899, 0.833875, 0.856197, 0.880043, 0.905628,
2974  0.933216, 0.96314, 0.995828, 1.03184, 1.07193, 1.11717, 1.13703,
2975  1.1581, 1.18052, 1.20451, 1.2303, 1.25821, 1.28866, 1.32219,
2976  1.35958, 1.40195, 1.45106, 1.50993, 1.54467, 1.58453, 1.63172,
2977  1.65927, 1.69061, 1.70453, 1.71944, 1.73555, 1.75313, 1.77258,
2978  1.79451, 1.81994, 1.83452, 1.85088, 1.86975, 1.88051, 1.89254,
2979  1.90636, 1.90941, 1.91258, 1.91589, 1.91934, 1.92297, 1.93086,
2980  1.93988, 1.94499, 1.95068}, {0.454601, 0.454746, 0.455842, 0.456343,
2981  0.456046, 0.455998, 0.456018, 0.456071, 0.456127, 0.456171,
2982  0.456246, 0.456327, 0.456423, 0.456596, 0.456773, 0.456949,
2983  0.457302, 0.457655, 0.458009, 0.458363, 0.458717, 0.459072,
2984  0.459427, 0.460317, 0.461208, 0.462999, 0.464799, 0.466609,
2985  0.470257, 0.473946, 0.477675, 0.481446, 0.485259, 0.489115,
2986  0.493016, 0.496962, 0.500954, 0.504993, 0.509081, 0.513219,
2987  0.523786, 0.534689, 0.545948, 0.557585, 0.569625, 0.582093, 0.59502,
2988  0.608436, 0.622378, 0.636885, 0.652, 0.667772, 0.684256, 0.701516,
2989  0.71962, 0.738651, 0.758702, 0.779882, 0.802317, 0.82616, 0.851591,
2990  0.878829, 0.908143, 0.939873, 0.974449, 1.01244, 1.05461, 1.10202,
2991  1.12279, 1.14477, 1.16814, 1.19308, 1.21984, 1.24875, 1.28021,
2992  1.31477, 1.35322, 1.39666, 1.44687, 1.50684, 1.54214, 1.58256,
2993  1.63031, 1.65813, 1.68974, 1.70376, 1.71878, 1.73499, 1.75267,
2994  1.77222, 1.79424, 1.81975, 1.83438, 1.85077, 1.86967, 1.88046,
2995  1.8925, 1.90633, 1.90939, 1.91256, 1.91587, 1.91932, 1.92296,
2996  1.93085, 1.93987, 1.94499, 1.95067}, {0.405546, 0.404573, 0.403366,
2997  0.404025, 0.404115, 0.403989, 0.40394, 0.403971, 0.404037, 0.404098,
2998  0.40416, 0.404265, 0.404355, 0.404535, 0.404715, 0.404897, 0.40526,
2999  0.405624, 0.405988, 0.406353, 0.406718, 0.407083, 0.407449,
3000  0.408365, 0.409284, 0.411129, 0.412986, 0.414853, 0.418619, 0.42243,
3001  0.426286, 0.430188, 0.434137, 0.438134, 0.44218, 0.446277,
3002  0.450425, 0.454625, 0.458878, 0.463187, 0.474206, 0.485594,
3003  0.497376, 0.509573, 0.522212, 0.535321, 0.54893, 0.563075, 0.577791,
3004  0.593121, 0.609109, 0.625808, 0.643274, 0.661572, 0.680777,
3005  0.700971, 0.722252, 0.744732, 0.768542, 0.793839, 0.820807,
3006  0.849672, 0.880708, 0.914263, 0.950774, 0.990817, 1.03516, 1.0849,
3007  1.10664, 1.12961, 1.15399, 1.17998, 1.20782, 1.23782, 1.27041,
3008  1.30613, 1.34576, 1.39042, 1.44188, 1.50314, 1.53909, 1.58017,
3009  1.62858, 1.65673, 1.68866, 1.70281, 1.71796, 1.7343, 1.7521,
3010  1.77176, 1.7939, 1.81952, 1.83419, 1.85064, 1.86958, 1.88039,
3011  1.89245, 1.9063, 1.90936, 1.91253, 1.91584, 1.9193, 1.92294,
3012  1.93083, 1.93986, 1.94498, 1.95067}, {0.35976, 0.362048, 0.362088,
3013  0.361405, 0.361838, 0.361724, 0.361635, 0.361653, 0.361731,
3014  0.361798, 0.361829, 0.361951, 0.362022, 0.362204, 0.362384,
3015  0.362559, 0.362914, 0.363269, 0.363624, 0.36398, 0.364336, 0.364693,
3016  0.36505, 0.365945, 0.366843, 0.368648, 0.370465, 0.372293,
3017  0.375986, 0.379729, 0.383522, 0.387367, 0.391264, 0.395214, 0.39922,
3018  0.403281, 0.4074, 0.411576, 0.415813, 0.42011, 0.431129, 0.44256,
3019  0.454427, 0.466756, 0.479575, 0.492914, 0.506807, 0.521289,
3020  0.536401, 0.552185, 0.568691, 0.585972, 0.604089, 0.623109,
3021  0.643109, 0.664176, 0.686412, 0.709933, 0.734875, 0.761399,
3022  0.789696, 0.819999, 0.85259, 0.887824, 0.92615, 0.968153, 1.01462,
3023  1.06665, 1.08936, 1.11334, 1.13875, 1.16581, 1.19475, 1.22589,
3024  1.25966, 1.29659, 1.33748, 1.38345, 1.43625, 1.49892, 1.53559,
3025  1.57741, 1.62657, 1.6551, 1.6874, 1.7017, 1.717, 1.73348, 1.75142,
3026  1.77123, 1.79349, 1.81924, 1.83398, 1.85048, 1.86948, 1.8803,
3027  1.89239, 1.90626, 1.90932, 1.9125, 1.91581, 1.91928, 1.92291,
3028  1.93082, 1.93985, 1.94497, 1.95066},
3029 {0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72}};
3030 
3031  const double imomegaqnm44[8][107] = {{0.0472887, 0.0570846, 0.0652857, 0.0769202, 0.0835313, 0.0855743,
3032  0.0870596, 0.0881437, 0.0889418, 0.0895359, 0.0909619, 0.0914196,
3033  0.0916056, 0.091741, 0.0917845, 0.0918026, 0.0918186, 0.0918281,
3034  0.0918366, 0.0918448, 0.0918531, 0.0918614, 0.0918696, 0.0918903,
3035  0.0919109, 0.0919521, 0.0919931, 0.092034, 0.0921151, 0.0921956,
3036  0.0922753, 0.0923543, 0.0924324, 0.0925097, 0.0925861, 0.0926616,
3037  0.0927361, 0.0928096, 0.0928821, 0.0929535, 0.0931268, 0.093292,
3038  0.0934484, 0.0935949, 0.0937302, 0.0938532, 0.0939623, 0.0940559,
3039  0.0941321, 0.0941887, 0.0942233, 0.094233, 0.0942145, 0.094164,
3040  0.0940768, 0.0939478, 0.0937705, 0.0935374, 0.0932393, 0.092865,
3041  0.0924006, 0.0918287, 0.0911274, 0.0902679, 0.0892124, 0.0879094,
3042  0.086287, 0.0842401, 0.0832692, 0.0821917, 0.0809905, 0.0796442,
3043  0.0781255, 0.0763992, 0.0744185, 0.0721192, 0.0694103, 0.066156,
3044  0.0621396, 0.056982, 0.0537633, 0.0499111, 0.0451315, 0.0422323,
3045  0.0388376, 0.037297, 0.0356236, 0.0337901, 0.0317587, 0.0294747,
3046  0.0268536, 0.0237529, 0.0219453, 0.0198926, 0.0174928, 0.0161075,
3047  0.0145463, 0.0127365, 0.0123344, 0.0119155, 0.0114779, 0.0110192,
3048  0.0105364, 0.00948248, 0.00827008, 0.00757959,
3049  0.00680933}, {0.267496, 0.27243, 0.275117, 0.277412, 0.278166,
3050  0.278332, 0.278431, 0.278489, 0.278523, 0.278542, 0.278554,
3051  0.278543, 0.278539, 0.278544, 0.278555, 0.278567, 0.27859, 0.278613,
3052  0.278636, 0.278659, 0.278682, 0.278704, 0.278727, 0.278784,
3053  0.278841, 0.278955, 0.279068, 0.27918, 0.279403, 0.279623, 0.279841,
3054  0.280057, 0.28027, 0.28048, 0.280687, 0.280892, 0.281093, 0.281291,
3055  0.281485, 0.281676, 0.282137, 0.282572, 0.282979, 0.283355,
3056  0.283696, 0.283998, 0.284257, 0.284467, 0.284624, 0.284721,
3057  0.284749, 0.284701, 0.284567, 0.284334, 0.28399, 0.283519, 0.282901,
3058  0.282113, 0.281129, 0.279913, 0.278426, 0.276614, 0.274412,
3059  0.271733, 0.268465, 0.264452, 0.25948, 0.253233, 0.250278, 0.247003,
3060  0.243357, 0.239276, 0.234678, 0.229458, 0.223476, 0.216539,
3061  0.208375, 0.198576, 0.186494, 0.170992, 0.161324, 0.149756,
3062  0.135408, 0.126707, 0.116519, 0.111896, 0.106875, 0.101374,
3063  0.0952787, 0.0884259, 0.0805622, 0.0712595, 0.0658364, 0.0596782,
3064  0.0524786, 0.0483228, 0.043639, 0.0382095, 0.0370031, 0.0357465,
3065  0.0344338, 0.0330576, 0.0316092, 0.0284475, 0.0248103, 0.0227388,
3066  0.020428}, {0.476992, 0.476552, 0.476059, 0.475354, 0.475023,
3067  0.474945, 0.474902, 0.47488, 0.474873, 0.474873, 0.474904, 0.474923,
3068  0.474932, 0.474945, 0.47496, 0.474975, 0.475006, 0.475036,
3069  0.475066, 0.475097, 0.475127, 0.475157, 0.475187, 0.475263,
3070  0.475338, 0.475487, 0.475635, 0.475782, 0.476073, 0.476359,
3071  0.476641, 0.476918, 0.47719, 0.477456, 0.477718, 0.477973, 0.478223,
3072  0.478467, 0.478704, 0.478936, 0.479483, 0.479984, 0.480434,
3073  0.480828, 0.48116, 0.481423, 0.48161, 0.481712, 0.481721, 0.481624,
3074  0.48141, 0.481064, 0.48057, 0.479908, 0.479056, 0.477986, 0.476666,
3075  0.47506, 0.47312, 0.470791, 0.468003, 0.464669, 0.460679, 0.45589,
3076  0.450113, 0.44309, 0.434465, 0.423712, 0.41865, 0.413055, 0.406842,
3077  0.399905, 0.392108, 0.383276, 0.373175, 0.361487, 0.347759,
3078  0.331313, 0.311071, 0.28514, 0.268985, 0.249669, 0.225726, 0.21121,
3079  0.194221, 0.186512, 0.17814, 0.168968, 0.158807, 0.147383, 0.134275,
3080  0.118768, 0.109729, 0.099465, 0.0874652, 0.0805385, 0.072732,
3081  0.0636828, 0.0616721, 0.0595777, 0.0573898, 0.0550962, 0.0526822,
3082  0.0474125, 0.0413505, 0.037898, 0.0340467}, {0.688887, 0.687276,
3083  0.68687, 0.687194, 0.687484, 0.687529, 0.687535, 0.687523, 0.687504,
3084  0.687487, 0.687464, 0.68748, 0.687488, 0.687497, 0.687509,
3085  0.687521, 0.687544, 0.687567, 0.68759, 0.687613, 0.687636, 0.687658,
3086  0.687681, 0.687738, 0.687794, 0.687905, 0.688015, 0.688122,
3087  0.688333, 0.688537, 0.688734, 0.688923, 0.689105, 0.689278,
3088  0.689444, 0.689601, 0.689749, 0.689889, 0.690018, 0.690138,
3089  0.690394, 0.690579, 0.69069, 0.690717, 0.690652, 0.690487, 0.690211,
3090  0.689812, 0.689276, 0.688589, 0.687732, 0.686685, 0.685425,
3091  0.683924, 0.682151, 0.680068, 0.677629, 0.674782, 0.671462,
3092  0.667589, 0.663066, 0.657772, 0.651551, 0.644203, 0.635463,
3093  0.624972, 0.612229, 0.596503, 0.589146, 0.581044, 0.572077,
3094  0.562097, 0.550915, 0.538287, 0.523888, 0.507273, 0.48781, 0.464555,
3095  0.436002, 0.399509, 0.376808, 0.349693, 0.316109, 0.295761,
3096  0.271954, 0.261154, 0.249426, 0.236578, 0.222347, 0.206349,
3097  0.187993, 0.166281, 0.153625, 0.139254, 0.122453, 0.112755,
3098  0.101826, 0.0891563, 0.0863413, 0.0834091, 0.080346, 0.0771349,
3099  0.0737552, 0.0663776, 0.0578907, 0.0530572, 0.0476654}, {0.918235,
3100  0.920515, 0.920895, 0.920137, 0.920012, 0.920094, 0.920167,
3101  0.920207, 0.920214, 0.920202, 0.920149, 0.920166, 0.920164, 0.92016,
3102  0.920158, 0.920156, 0.920152, 0.920148, 0.920144, 0.92014,
3103  0.920136, 0.920132, 0.920127, 0.920116, 0.920104, 0.920079,
3104  0.920051, 0.920022, 0.919956, 0.919881, 0.919796, 0.919702,
3105  0.919597, 0.919482, 0.919356, 0.919218, 0.919069, 0.918908,
3106  0.918734, 0.918547, 0.91802, 0.917401, 0.916681, 0.915851, 0.9149,
3107  0.913815, 0.912584, 0.91119, 0.909617, 0.907843, 0.905847, 0.903603,
3108  0.901078, 0.898239, 0.895043, 0.891442, 0.887378, 0.88278,
3109  0.877566, 0.871633, 0.864855, 0.857075, 0.848091, 0.837647, 0.8254,
3110  0.81089, 0.79347, 0.772205, 0.762324, 0.751485, 0.739534, 0.72628,
3111  0.711484, 0.694831, 0.675907, 0.654142, 0.628729, 0.598457, 0.5614,
3112  0.514171, 0.484847, 0.449863, 0.406581, 0.380377, 0.349729,
3113  0.335831, 0.32074, 0.304211, 0.285904, 0.265327, 0.24172, 0.213799,
3114  0.197524, 0.179045, 0.157442, 0.144973, 0.13092, 0.11463, 0.111011,
3115  0.107241, 0.103302, 0.0991739, 0.0948285, 0.0853429, 0.0744311,
3116  0.0682165, 0.0612841}, {1.17243, 1.17025, 1.17072, 1.17153, 1.17109,
3117  1.17107, 1.17115, 1.17122, 1.17125, 1.17124, 1.17116, 1.17118,
3118  1.17115, 1.17114, 1.17112, 1.17109, 1.17105, 1.171, 1.17096,
3119  1.17092, 1.17087, 1.17083, 1.17078, 1.17067, 1.17055, 1.17033,
3120  1.17009, 1.16986, 1.16938, 1.16889, 1.16838, 1.16786, 1.16733,
3121  1.16679, 1.16622, 1.16565, 1.16506, 1.16445, 1.16382, 1.16318,
3122  1.1615, 1.15969, 1.15776, 1.15567, 1.15344, 1.15103, 1.14843,
3123  1.14562, 1.14259, 1.1393, 1.13573, 1.13184, 1.12761, 1.12298,
3124  1.1179, 1.11232, 1.10615, 1.09933, 1.09174, 1.08325, 1.07371,
3125  1.06294, 1.05067, 1.0366, 1.0203, 1.00121, 0.97854, 0.951144,
3126  0.9385, 0.92468, 0.909499, 0.892724, 0.874063, 0.853135, 0.829435,
3127  0.802272, 0.770663, 0.733138, 0.687353, 0.629184, 0.593147,
3128  0.550213, 0.497162, 0.465071, 0.427558, 0.410551, 0.392089,
3129  0.371872, 0.349482, 0.32432, 0.295457, 0.261323, 0.241428, 0.218839,
3130  0.192433, 0.177192, 0.160015, 0.140105, 0.135681, 0.131073,
3131  0.126259, 0.121213, 0.115902, 0.104308, 0.0909715, 0.0833759,
3132  0.0749029}, {1.43411, 1.43505, 1.43374, 1.43433, 1.43411, 1.43401,
3133  1.43406, 1.43415, 1.43418, 1.43415, 1.4341, 1.43407, 1.43405,
3134  1.43401, 1.43397, 1.43393, 1.43384, 1.43376, 1.43367, 1.43359,
3135  1.4335, 1.43342, 1.43333, 1.43312, 1.4329, 1.43247, 1.43203,
3136  1.43159, 1.43069, 1.42978, 1.42884, 1.42789, 1.42691, 1.42592,
3137  1.4249, 1.42387, 1.42281, 1.42173, 1.42062, 1.41949, 1.41656,
3138  1.41345, 1.41017, 1.4067, 1.40302, 1.39911, 1.39496, 1.39054,
3139  1.38582, 1.38079, 1.3754, 1.36961, 1.36339, 1.35669, 1.34943,
3140  1.34155, 1.33296, 1.32356, 1.31324, 1.30183, 1.28915, 1.27497,
3141  1.259, 1.24085, 1.22004, 1.19589, 1.16745, 1.13339, 1.11775,
3142  1.10072, 1.08207, 1.06154, 1.03877, 1.01331, 0.984584, 0.951766,
3143  0.913705, 0.868675, 0.81392, 0.744589, 0.701738, 0.650764, 0.587868,
3144  0.549856, 0.505448, 0.485323, 0.46348, 0.439564, 0.413085,
3145  0.383331, 0.349205, 0.308853, 0.285337, 0.258637, 0.227427,
3146  0.209413, 0.189112, 0.16558, 0.160352, 0.154906, 0.149217, 0.143253,
3147  0.136976, 0.123274, 0.107512, 0.0985354, 0.0885218},
3148 {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
3149 
3150  /* 5, 5 mode */
3151  const double reomegaqnm55[8][107] = {{0.752532, 0.769133, 0.779179, 0.78709, 0.786149, 0.784329, 0.782338,
3152  0.780485, 0.778903, 0.777615, 0.774286, 0.773282, 0.772966,
3153  0.77289, 0.772999, 0.773149, 0.773476, 0.77381, 0.774145, 0.77448,
3154  0.774816, 0.775152, 0.775488, 0.776331, 0.777176, 0.778874,
3155  0.780582, 0.782299, 0.785766, 0.789274, 0.792825, 0.79642, 0.800059,
3156  0.803743, 0.807474, 0.811253, 0.81508, 0.818956, 0.822883,
3157  0.826863, 0.837046, 0.847582, 0.858493, 0.869802, 0.881536,
3158  0.893724, 0.906398, 0.919594, 0.93335, 0.947712, 0.962728, 0.978454,
3159  0.994953, 1.0123, 1.03056, 1.04985, 1.07027, 1.09194, 1.11502,
3160  1.13968, 1.16614, 1.19467, 1.22558, 1.25928, 1.29631, 1.33734,
3161  1.38332, 1.43555, 1.45861, 1.48313, 1.50932, 1.53742, 1.56774,
3162  1.60067, 1.63671, 1.67655, 1.72115, 1.77188, 1.83092, 1.90197,
3163  1.94403, 1.99239, 2.04977, 2.08333, 2.12154, 2.13852, 2.15673,
3164  2.17641, 2.1979, 2.22168, 2.24849, 2.27961, 2.29746, 2.31749,
3165  2.34058, 2.35377, 2.3685, 2.38542, 2.38915, 2.39303, 2.39708,
3166  2.40131, 2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.753001,
3167  0.757208, 0.757533, 0.756804, 0.756468, 0.756414, 0.756397,
3168  0.756401, 0.756417, 0.756438, 0.756561, 0.756667, 0.756761,
3169  0.756937, 0.757109, 0.75728, 0.757623, 0.757967, 0.758311, 0.758656,
3170  0.759001, 0.759346, 0.759692, 0.760558, 0.761427, 0.763172,
3171  0.764927, 0.766693, 0.770255, 0.77386, 0.777508, 0.7812, 0.784938,
3172  0.788722, 0.792553, 0.796433, 0.800362, 0.804341, 0.808372,
3173  0.812456, 0.822904, 0.833711, 0.844898, 0.85649, 0.868513, 0.880997,
3174  0.893974, 0.90748, 0.921555, 0.936243, 0.951594, 0.967664,
3175  0.984515, 1.00222, 1.02086, 1.04054, 1.06135, 1.08343, 1.10693,
3176  1.13203, 1.15894, 1.18793, 1.21932, 1.25352, 1.29105, 1.33262,
3177  1.37915, 1.43196, 1.45525, 1.48001, 1.50644, 1.53478, 1.56534,
3178  1.59852, 1.63481, 1.67491, 1.71976, 1.77074, 1.83004, 1.90134,
3179  1.94352, 1.992, 2.0495, 2.08311, 2.12137, 2.13838, 2.15661, 2.17631,
3180  2.19781, 2.22161, 2.24844, 2.27957, 2.29743, 2.31747, 2.34057,
3181  2.35376, 2.36849, 2.38541, 2.38915, 2.39303, 2.39708, 2.40131,
3182  2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.7196, 0.722567,
3183  0.723924, 0.725024, 0.725386, 0.725467, 0.725518, 0.725552,
3184  0.725576, 0.725595, 0.725675, 0.72576, 0.725849, 0.72603, 0.726211,
3185  0.726392, 0.726754, 0.727117, 0.72748, 0.727843, 0.728207, 0.728571,
3186  0.728936, 0.729849, 0.730765, 0.732605, 0.734456, 0.736316,
3187  0.740071, 0.743868, 0.747711, 0.751599, 0.755534, 0.759516,
3188  0.763547, 0.767627, 0.771759, 0.775942, 0.780178, 0.784469,
3189  0.795442, 0.806783, 0.818514, 0.830662, 0.843253, 0.856316,
3190  0.869886, 0.883998, 0.898692, 0.914015, 0.930016, 0.946752,
3191  0.964288, 0.982696, 1.00206, 1.02247, 1.04405, 1.06692, 1.09123,
3192  1.11716, 1.14494, 1.17482, 1.20713, 1.24229, 1.28082, 1.32342,
3193  1.37101, 1.42493, 1.44867, 1.47389, 1.50078, 1.5296, 1.56064,
3194  1.5943, 1.63108, 1.67167, 1.71702, 1.7685, 1.82829, 1.90008, 1.9425,
3195  1.99122, 2.04895, 2.08267, 2.12104, 2.13809, 2.15636, 2.1761,
3196  2.19764, 2.22147, 2.24834, 2.27951, 2.29738, 2.31743, 2.34054,
3197  2.35374, 2.36848, 2.3854, 2.38914, 2.39302, 2.39707, 2.4013,
3198  2.40575, 2.41541, 2.42645, 2.43271, 2.43966}, {0.680361, 0.681655,
3199  0.681927, 0.681788, 0.681669, 0.681657, 0.681664, 0.681682,
3200  0.681705, 0.681729, 0.681838, 0.681934, 0.682031, 0.682225, 0.68242,
3201  0.682614, 0.683004, 0.683394, 0.683784, 0.684175, 0.684566,
3202  0.684957, 0.685349, 0.686331, 0.687316, 0.689293, 0.69128, 0.693279,
3203  0.69731, 0.701387, 0.705509, 0.709679, 0.713897, 0.718164,
3204  0.722481, 0.72685, 0.731271, 0.735746, 0.740276, 0.744863, 0.756582,
3205  0.768683, 0.781187, 0.794122, 0.807514, 0.821395, 0.835799,
3206  0.850762, 0.866327, 0.88254, 0.899452, 0.917122, 0.935614, 0.955004,
3207  0.975376, 0.996827, 1.01947, 1.04344, 1.06888, 1.09599, 1.12497,
3208  1.1561, 1.18971, 1.22621, 1.26614, 1.31018, 1.35928, 1.41476,
3209  1.43915, 1.46502, 1.49258, 1.52208, 1.5538, 1.58816, 1.62564,
3210  1.66694, 1.713, 1.76521, 1.82572, 1.89823, 1.941, 1.99007, 2.04813,
3211  2.08202, 2.12055, 2.13766, 2.15599, 2.17578, 2.19738, 2.22127,
3212  2.24819, 2.2794, 2.2973, 2.31737, 2.34051, 2.35371, 2.36846,
3213  2.38539, 2.38913, 2.39301, 2.39706, 2.40129, 2.40574, 2.4154,
3214  2.42645, 2.43271, 2.43966}, {0.630475, 0.629154, 0.628652, 0.628812,
3215  0.628995, 0.62902, 0.629028, 0.629035, 0.629045, 0.629061,
3216  0.629172, 0.629277, 0.629381, 0.629592, 0.629802, 0.630012,
3217  0.630433, 0.630855, 0.631277, 0.631699, 0.632122, 0.632545,
3218  0.632968, 0.634029, 0.635093, 0.637229, 0.639376, 0.641534,
3219  0.645886, 0.650284, 0.65473, 0.659225, 0.66377, 0.668366, 0.673014,
3220  0.677716, 0.682472, 0.687284, 0.692153, 0.69708, 0.709663, 0.722641,
3221  0.73604, 0.749885, 0.764206, 0.779035, 0.794407, 0.81036, 0.826938,
3222  0.844188, 0.862164, 0.880925, 0.900539, 0.921082, 0.94264,
3223  0.965314, 0.989218, 1.01449, 1.04128, 1.06978, 1.1002, 1.13284,
3224  1.168, 1.20613, 1.24774, 1.29355, 1.34449, 1.4019, 1.42708, 1.45377,
3225  1.48215, 1.51248, 1.54506, 1.58029, 1.61866, 1.66085, 1.70782,
3226  1.76095, 1.82238, 1.89581, 1.93904, 1.98856, 2.04706, 2.08116,
3227  2.1199, 2.13709, 2.1555, 2.17537, 2.19704, 2.221, 2.24799, 2.27927,
3228  2.29719, 2.31729, 2.34045, 2.35367, 2.36843, 2.38537, 2.38911,
3229  2.39299, 2.39704, 2.40128, 2.40573, 2.41539, 2.42644, 2.4327,
3230  2.43966}, {0.571708, 0.573132, 0.573635, 0.573297, 0.573329,
3231  0.573398, 0.573443, 0.573465, 0.573477, 0.573488, 0.5736, 0.573712,
3232  0.573823, 0.574048, 0.574272, 0.574496, 0.574944, 0.575393,
3233  0.575843, 0.576292, 0.576743, 0.577194, 0.577645, 0.578775,
3234  0.579908, 0.582183, 0.58447, 0.586768, 0.591402, 0.596085, 0.600818,
3235  0.605603, 0.61044, 0.61533, 0.620276, 0.625278, 0.630337, 0.635455,
3236  0.640632, 0.645871, 0.659247, 0.673038, 0.687272, 0.701975,
3237  0.717178, 0.732914, 0.74922, 0.766136, 0.783707, 0.801983, 0.821018,
3238  0.840873, 0.86162, 0.883336, 0.90611, 0.930046, 0.955261, 0.981893,
3239  1.0101, 1.04008, 1.07205, 1.10629, 1.14315, 1.18304, 1.22651,
3240  1.27427, 1.32727, 1.38685, 1.41293, 1.44053, 1.46986, 1.50115,
3241  1.53471, 1.57094, 1.61033, 1.65357, 1.70161, 1.75581, 1.81834,
3242  1.89287, 1.93665, 1.98671, 2.04575, 2.08011, 2.1191, 2.13638,
3243  2.15489, 2.17486, 2.19662, 2.22067, 2.24774, 2.2791, 2.29706,
3244  2.31719, 2.34039, 2.35362, 2.36839, 2.38534, 2.38909, 2.39297,
3245  2.39703, 2.40126, 2.40571, 2.41538, 2.42643, 2.4327,
3246  2.43966}, {0.522196, 0.520579, 0.52057, 0.521087, 0.52093, 0.520981,
3247  0.521047, 0.521087, 0.521102, 0.52111, 0.521228, 0.521338,
3248  0.521456, 0.521686, 0.521918, 0.522149, 0.522613, 0.523077,
3249  0.523541, 0.524006, 0.524471, 0.524937, 0.525404, 0.526572,
3250  0.527743, 0.530095, 0.53246, 0.534837, 0.539631, 0.544478, 0.549379,
3251  0.554335, 0.559348, 0.564418, 0.569547, 0.574737, 0.579987,
3252  0.585301, 0.590679, 0.596123, 0.61003, 0.624382, 0.639206, 0.654532,
3253  0.670391, 0.686819, 0.703853, 0.721535, 0.739912, 0.759036,
3254  0.778963, 0.799758, 0.821493, 0.844248, 0.868117, 0.893205,
3255  0.919633, 0.947544, 0.977101, 1.0085, 1.04198, 1.07781, 1.11634,
3256  1.15802, 1.20338, 1.25315, 1.30829, 1.37015, 1.39719, 1.42578,
3257  1.45611, 1.48844, 1.52307, 1.56039, 1.6009, 1.64529, 1.69451,
3258  1.74992, 1.81368, 1.88946, 1.93386, 1.98455, 2.0442, 2.07886,
3259  2.11815, 2.13555, 2.15417, 2.17425, 2.19612, 2.22028, 2.24745,
3260  2.2789, 2.29691, 2.31708, 2.34031, 2.35356, 2.36835, 2.38531,
3261  2.38906, 2.39295, 2.39701, 2.40125, 2.4057, 2.41537, 2.42643,
3262  2.43269, 2.43965},
3263 {0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9}};
3264 
3265  const double imomegaqnm55[8][107] = {{0.0151971, 0.02987, 0.0432352, 0.064849, 0.0789971, 0.0834521,
3266  0.0865117, 0.0885261, 0.0898184, 0.090638, 0.0919286, 0.0920896,
3267  0.0921222, 0.0921485, 0.0921652, 0.0921765, 0.092191, 0.0922013,
3268  0.0922106, 0.0922195, 0.0922283, 0.0922371, 0.0922459, 0.0922679,
3269  0.0922898, 0.0923335, 0.092377, 0.0924205, 0.0925068, 0.0925926,
3270  0.0926777, 0.092762, 0.0928457, 0.0929286, 0.0930106, 0.0930918,
3271  0.0931722, 0.0932516, 0.09333, 0.0934074, 0.0935961, 0.0937773,
3272  0.09395, 0.0941133, 0.094266, 0.0944066, 0.0945339, 0.094646,
3273  0.0947411, 0.0948169, 0.0948709, 0.0949002, 0.0949014, 0.0948705,
3274  0.094803, 0.0946932, 0.0945348, 0.0943198, 0.0940389, 0.0936804,
3275  0.0932301, 0.09267, 0.0919774, 0.0911228, 0.0900671, 0.0887575,
3276  0.0871199, 0.0850466, 0.0840612, 0.0829665, 0.0817451, 0.0803751,
3277  0.0788289, 0.0770706, 0.0750526, 0.0727103, 0.0699513, 0.0666388,
3278  0.0625545, 0.0573174, 0.054054, 0.0501531, 0.0453206, 0.0423931,
3279  0.038969, 0.0374162, 0.0357305, 0.0338844, 0.0318402, 0.0295431,
3280  0.0269089, 0.0237947, 0.0219803, 0.0199207, 0.017514, 0.0161252,
3281  0.0145605, 0.0127472, 0.0123443, 0.0119247, 0.0114865, 0.011027,
3282  0.0105435, 0.00948819, 0.00827437, 0.00758316,
3283  0.00681219}, {0.25166, 0.264251, 0.270831, 0.275931, 0.277491,
3284  0.277846, 0.278073, 0.278222, 0.278323, 0.278391, 0.278527,
3285  0.278556, 0.278565, 0.278576, 0.278588, 0.2786, 0.278625, 0.27865,
3286  0.278676, 0.278701, 0.278726, 0.278751, 0.278776, 0.278839,
3287  0.278901, 0.279026, 0.27915, 0.279273, 0.279519, 0.279763, 0.280005,
3288  0.280244, 0.280481, 0.280716, 0.280948, 0.281177, 0.281404,
3289  0.281627, 0.281847, 0.282065, 0.282593, 0.283097, 0.283575,
3290  0.284023, 0.284438, 0.284817, 0.285154, 0.285444, 0.285682,
3291  0.285862, 0.285974, 0.286011, 0.285963, 0.285817, 0.28556, 0.285175,
3292  0.284643, 0.28394, 0.283038, 0.281902, 0.280489, 0.278746,
3293  0.276603, 0.273974, 0.27074, 0.266744, 0.261763, 0.255474, 0.252491,
3294  0.249179, 0.245488, 0.24135, 0.236685, 0.231383, 0.225304,
3295  0.218251, 0.20995, 0.199989, 0.187715, 0.171984, 0.162185, 0.150475,
3296  0.135971, 0.127186, 0.116912, 0.112252, 0.107194, 0.101656,
3297  0.0955223, 0.0886307, 0.0807275, 0.0713845, 0.0659411, 0.0597624,
3298  0.0525421, 0.0483758, 0.0436815, 0.0382415, 0.037033, 0.0357743,
3299  0.0344594, 0.0330811, 0.0316306, 0.0284646, 0.0248231, 0.0227495,
3300  0.0204366}, {0.467579, 0.470028, 0.470942, 0.471348, 0.471322,
3301  0.47129, 0.471261, 0.471239, 0.471223, 0.471213, 0.471201, 0.47121,
3302  0.471221, 0.47124, 0.471258, 0.471277, 0.471314, 0.471351, 0.471388,
3303  0.471425, 0.471462, 0.471499, 0.471536, 0.471628, 0.47172,
3304  0.471904, 0.472086, 0.472268, 0.472628, 0.472984, 0.473336,
3305  0.473684, 0.474028, 0.474367, 0.474701, 0.475031, 0.475355,
3306  0.475674, 0.475987, 0.476294, 0.477036, 0.477735, 0.478387,
3307  0.478987, 0.479529, 0.480006, 0.480411, 0.480735, 0.480968,
3308  0.481101, 0.481119, 0.481008, 0.480751, 0.480328, 0.479717,
3309  0.478889, 0.477812, 0.476446, 0.474745, 0.472651, 0.470091,
3310  0.466978, 0.463197, 0.4586, 0.452993, 0.446112, 0.437588, 0.426883,
3311  0.421821, 0.416213, 0.409971, 0.402987, 0.395124, 0.386201,
3312  0.375984, 0.364147, 0.350231, 0.333554, 0.313026, 0.286746,
3313  0.270386, 0.250845, 0.226651, 0.212, 0.194868, 0.1871, 0.178668,
3314  0.169434, 0.15921, 0.147722, 0.134549, 0.118976, 0.109903,
3315  0.0996047, 0.0875705, 0.0806266, 0.0728027, 0.063736, 0.0617217,
3316  0.0596238, 0.0574324, 0.0551353, 0.0527177, 0.047441, 0.0413719,
3317  0.0379158, 0.034061}, {0.676801, 0.675633, 0.67493, 0.67443, 0.6744,
3318  0.674422, 0.674445, 0.674462, 0.674474, 0.674481, 0.67449,
3319  0.674497, 0.674508, 0.674528, 0.674548, 0.674568, 0.674609,
3320  0.674649, 0.674689, 0.674729, 0.674769, 0.674809, 0.674849,
3321  0.674948, 0.675048, 0.675245, 0.675441, 0.675635, 0.67602, 0.676399,
3322  0.676771, 0.677137, 0.677496, 0.677847, 0.678192, 0.678529,
3323  0.678858, 0.679179, 0.679492, 0.679795, 0.680514, 0.681168,
3324  0.681753, 0.68226, 0.682681, 0.683008, 0.683228, 0.683332, 0.683303,
3325  0.683128, 0.682788, 0.682263, 0.681529, 0.680557, 0.679315,
3326  0.677766, 0.675862, 0.673549, 0.67076, 0.667416, 0.663415, 0.658633,
3327  0.65291, 0.64604, 0.637751, 0.627674, 0.615292, 0.599856, 0.592588,
3328  0.584557, 0.575639, 0.565684, 0.554498, 0.541831, 0.527355,
3329  0.510615, 0.490971, 0.467468, 0.438585, 0.401662, 0.378702,
3330  0.351292, 0.317377, 0.296847, 0.272846, 0.261966, 0.250155,
3331  0.237224, 0.222906, 0.20682, 0.188374, 0.16657, 0.153867, 0.139448,
3332  0.1226, 0.112878, 0.101924, 0.0892306, 0.0864106, 0.0834736,
3333  0.0804055, 0.0771896, 0.0738049, 0.0664175, 0.0579207, 0.0530822,
3334  0.0476854}, {0.891895, 0.89147, 0.891863, 0.892311, 0.89227,
3335  0.892236, 0.892217, 0.892213, 0.892217, 0.892223, 0.892242,
3336  0.892246, 0.892254, 0.892269, 0.892283, 0.892298, 0.892327,
3337  0.892357, 0.892386, 0.892415, 0.892444, 0.892473, 0.892502,
3338  0.892574, 0.892646, 0.892788, 0.892927, 0.893065, 0.893335,
3339  0.893597, 0.89385, 0.894094, 0.894329, 0.894554, 0.89477, 0.894975,
3340  0.89517, 0.895353, 0.895526, 0.895686, 0.896031, 0.896291, 0.896458,
3341  0.896521, 0.89647, 0.896292, 0.895974, 0.895501, 0.894855,
3342  0.894014, 0.892957, 0.891657, 0.890083, 0.888198, 0.88596, 0.88332,
3343  0.880219, 0.876586, 0.872336, 0.867364, 0.86154, 0.854705, 0.846653,
3344  0.83712, 0.825754, 0.812083, 0.795442, 0.774871, 0.765236,
3345  0.754619, 0.742864, 0.729775, 0.715106, 0.698537, 0.679644,
3346  0.657847, 0.632324, 0.601851, 0.564477, 0.516789, 0.487173,
3347  0.451846, 0.408167, 0.381741, 0.350856, 0.336857, 0.321664, 0.30503,
3348  0.286614, 0.265926, 0.242205, 0.214167, 0.197833, 0.179293,
3349  0.15763, 0.14513, 0.131046, 0.114725, 0.1111, 0.107324, 0.103379,
3350  0.099244, 0.0948923, 0.085394, 0.0744695, 0.0682486,
3351  0.0613098}, {1.12614, 1.12697, 1.12642, 1.12612, 1.12629, 1.12629,
3352  1.12627, 1.12625, 1.12624, 1.12624, 1.12626, 1.12625, 1.12626,
3353  1.12626, 1.12626, 1.12626, 1.12626, 1.12626, 1.12627, 1.12627,
3354  1.12627, 1.12627, 1.12628, 1.12628, 1.12628, 1.12629, 1.12629,
3355  1.1263, 1.12629, 1.12628, 1.12625, 1.12622, 1.12617, 1.12611,
3356  1.12604, 1.12595, 1.12586, 1.12574, 1.12562, 1.12548, 1.12505,
3357  1.12453, 1.12388, 1.1231, 1.12219, 1.12111, 1.11986, 1.11841,
3358  1.11675, 1.11485, 1.11267, 1.1102, 1.10738, 1.10418, 1.10054,
3359  1.09641, 1.0917, 1.08634, 1.08021, 1.07319, 1.06513, 1.05582,
3360  1.04501, 1.03238, 1.0175, 0.999787, 0.978439, 0.952276, 0.940091,
3361  0.926705, 0.911928, 0.895521, 0.877184, 0.856528, 0.833035, 0.806,
3362  0.774421, 0.736806, 0.690779, 0.632177, 0.595837, 0.552533,
3363  0.499038, 0.466693, 0.428905, 0.411781, 0.393199, 0.372856,
3364  0.350338, 0.325043, 0.296043, 0.261768, 0.241802, 0.219141,
3365  0.192661, 0.177383, 0.160169, 0.140221, 0.135789, 0.131174,
3366  0.126352, 0.121299, 0.11598, 0.104371, 0.0910184, 0.083415,
3367  0.0749342}, {1.3749, 1.37446, 1.37529, 1.37504, 1.37506, 1.37511,
3368  1.37511, 1.37508, 1.37506, 1.37506, 1.37507, 1.37505, 1.37505,
3369  1.37503, 1.37501, 1.37499, 1.37496, 1.37492, 1.37488, 1.37485,
3370  1.37481, 1.37478, 1.37474, 1.37465, 1.37456, 1.37437, 1.37418,
3371  1.37399, 1.37359, 1.37319, 1.37277, 1.37233, 1.37188, 1.37142,
3372  1.37094, 1.37045, 1.36993, 1.36941, 1.36886, 1.36829, 1.3668,
3373  1.36517, 1.36339, 1.36145, 1.35934, 1.35704, 1.35452, 1.35177,
3374  1.34875, 1.34544, 1.3418, 1.33779, 1.33338, 1.3285, 1.32309,
3375  1.31709, 1.3104, 1.30292, 1.29452, 1.28507, 1.27436, 1.26216,
3376  1.24818, 1.23202, 1.2132, 1.19101, 1.1645, 1.13228, 1.11735,
3377  1.10101, 1.08301, 1.06309, 1.04089, 1.01595, 0.987663, 0.955194,
3378  0.917365, 0.872418, 0.817554, 0.747869, 0.704729, 0.653377,
3379  0.590005, 0.551715, 0.507, 0.486743, 0.464764, 0.440707, 0.41408,
3380  0.384173, 0.34989, 0.309375, 0.285775, 0.25899, 0.227694, 0.209637,
3381  0.189292, 0.165716, 0.160479, 0.155024, 0.149326, 0.143353,
3382  0.137067, 0.123347, 0.107567, 0.0985815, 0.0885587},
3383 {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
3384 
3385  /* To actually calculate the ringdown, we will use the following pointers to point to the correct mode */
3386  const double (*reomegaqnm)[107] = NULL;
3387  const double (*imomegaqnm)[107] = NULL;
3388  REAL8 totalMass;
3389 
3390  /* Stuff for interpolating the data */
3391  gsl_spline *spline = NULL;
3392  gsl_interp_accel *acc = NULL;
3393 
3394  UINT4 i;
3395  REAL8 signm = m < 0 ? -1.0 : 1.0;
3396 
3397  /* Check we do not require more overtones than we have */
3398  if ( nmodes > 8 )
3399  {
3400  XLALPrintError( "Requesting more overtones than we have data to generate!\n");
3401  XLAL_ERROR( XLAL_EINVAL );
3402  }
3403 
3404  /* Choose the appropriate data bases on the user requested l an m */
3405  switch ( l )
3406  {
3407  case 2:
3408  if ( abs(m) == 2 )
3409  {
3410  reomegaqnm = reomegaqnm22;
3411  imomegaqnm = imomegaqnm22;
3412  }
3413  else if ( abs(m) == 1 )
3414  {
3415  reomegaqnm = reomegaqnm21;
3416  imomegaqnm = imomegaqnm21;
3417  }
3418  else if ( abs(m) == 0 )
3419  {
3420  reomegaqnm = reomegaqnm20;
3421  imomegaqnm = imomegaqnm20;
3422  }
3423  else
3424  {
3425  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
3426  XLAL_ERROR( XLAL_EINVAL );
3427  }
3428  break;
3429  case 3:
3430  if ( abs(m) == 3 )
3431  {
3432  reomegaqnm = reomegaqnm33;
3433  imomegaqnm = imomegaqnm33;
3434  }
3435  else
3436  {
3437  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
3438  XLAL_ERROR( XLAL_EINVAL );
3439  }
3440  break;
3441  case 4:
3442  if ( abs(m) == 4 )
3443  {
3444  reomegaqnm = reomegaqnm44;
3445  imomegaqnm = imomegaqnm44;
3446  }
3447  else
3448  {
3449  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
3450  XLAL_ERROR( XLAL_EINVAL );
3451  }
3452  break;
3453  case 5:
3454  if ( abs(m) == 5 )
3455  {
3456  reomegaqnm = reomegaqnm55;
3457  imomegaqnm = imomegaqnm55;
3458  }
3459  else
3460  {
3461  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
3462  XLAL_ERROR( XLAL_EINVAL );
3463  }
3464  break;
3465  default:
3466  XLALPrintError( "Unsupported combination of l, m (%d, %d)\n", l, m );
3467  XLAL_ERROR( XLAL_EINVAL );
3468  break;
3469  }
3470 
3471  spline = gsl_spline_alloc( gsl_interp_cspline, 107 );
3472  acc = gsl_interp_accel_alloc();
3473 
3474  totalMass = mass1 + mass2;
3475  if ( finalSpin < -0.9996 ) finalSpin = -0.9996;
3476  if ( finalSpin > 0.9996 ) finalSpin = 0.9996;
3477 
3478  /* Now get the QNM frequencies from interpolating the above data */
3479  for ( i = 0; i < nmodes; i++ )
3480  {
3481  gsl_spline_init( spline, afinallist, reomegaqnm[i], 107 );
3482  gsl_interp_accel_reset( acc );
3483 
3484  modefreqs->data[i] = signm*gsl_spline_eval( spline, signm*finalSpin, acc );
3485 
3486  gsl_spline_init( spline, afinallist, imomegaqnm[i], 107 );
3487  gsl_interp_accel_reset( acc );
3488 
3489  modefreqs->data[i] += I*gsl_spline_eval( spline, signm*finalSpin, acc );
3490 
3491  /* Scale by the appropriate mass factors */
3492  modefreqs->data[i] *= 1./ finalMass / (totalMass * LAL_MTSUN_SI);
3493  }
3494  /* Free memory and exit */
3495  gsl_spline_free( spline );
3496  gsl_interp_accel_free( acc );
3497 
3498  return XLAL_SUCCESS;
3499 }
k11
static const REAL8 k11
Definition: LALSimBlackHoleRingdown.h:98
k12
static const REAL8 k12
Definition: LALSimBlackHoleRingdown.h:99
k04
static const REAL8 k04
Definition: LALSimBlackHoleRingdown.h:96
k01
static const REAL8 k01
Definition: LALSimBlackHoleRingdown.h:93
k24
static const REAL8 k24
Definition: LALSimBlackHoleRingdown.h:106
k30
static const REAL8 k30
Definition: LALSimBlackHoleRingdown.h:107
k02
static const REAL8 k02
Definition: LALSimBlackHoleRingdown.h:94
k31
static const REAL8 k31
Definition: LALSimBlackHoleRingdown.h:108
k32
static const REAL8 k32
Definition: LALSimBlackHoleRingdown.h:109
k13
static const REAL8 k13
Definition: LALSimBlackHoleRingdown.h:100
k14
static const REAL8 k14
Definition: LALSimBlackHoleRingdown.h:101
k34
static const REAL8 k34
Definition: LALSimBlackHoleRingdown.h:111
k33
static const REAL8 k33
Definition: LALSimBlackHoleRingdown.h:110
k23
static const REAL8 k23
Definition: LALSimBlackHoleRingdown.h:105
k20
static const REAL8 k20
Definition: LALSimBlackHoleRingdown.h:102
k00
static const REAL8 k00
Definition: LALSimBlackHoleRingdown.h:92
k22
static const REAL8 k22
Definition: LALSimBlackHoleRingdown.h:104
k21
static const REAL8 k21
Definition: LALSimBlackHoleRingdown.h:103
k03
static const REAL8 k03
Definition: LALSimBlackHoleRingdown.h:95
k10
static const REAL8 k10
Definition: LALSimBlackHoleRingdown.h:97
XLALSimIMREOBFinalMassSpinPrec
INT4 XLALSimIMREOBFinalMassSpinPrec(REAL8 *finalMass, REAL8 *finalSpin, const REAL8 mass1, const REAL8 mass2, const REAL8 spin1[3], const REAL8 spin2[3], Approximant approximant)
Computes the final mass and spin of the black hole resulting from merger.
Definition: LALSimBlackHoleRingdownPrec.c:39
XLALSimIMREOBGenerateQNMFreqV2FromFinalPrec
INT4 XLALSimIMREOBGenerateQNMFreqV2FromFinalPrec(COMPLEX16Vector *modefreqs, const REAL8 mass1, const REAL8 mass2, const REAL8 finalMass, REAL8 finalSpin, UINT4 l, INT4 m, UINT4 nmodes)
This function generates the quasinormal mode frequencies for a black hole ringdown.
Definition: LALSimBlackHoleRingdownPrec.c:1926
XLALSimIMREOBGenerateQNMFreqV2Prec
INT4 XLALSimIMREOBGenerateQNMFreqV2Prec(COMPLEX16Vector *modefreqs, const REAL8 mass1, const REAL8 mass2, const REAL8 spin1[3], const REAL8 spin2[3], UINT4 l, INT4 m, UINT4 nmodes, Approximant approximant)
This function generates the quasinormal mode frequencies for a black hole ringdown.
Definition: LALSimBlackHoleRingdownPrec.c:329
beta
static double beta(const double a, const double b, const sysq *system)
Internal function that computes the spin-orbit couplings.
Definition: LALSimInspiralFDPrecAngles_internals.c:798
q2
static REAL8 UNUSED q2(REAL8 e0, REAL8 f0, REAL8 inc, REAL8 bet, REAL8 FPlus, REAL8 FCross)
Definition: LALSimInspiralOptimizedCoefficientsEccentricityFD.c:1175
z1
static REAL8 UNUSED z1(REAL8 e0, REAL8 f0, REAL8 inc, REAL8 bet, REAL8 FPlus, REAL8 FCross)
Definition: LALSimInspiralOptimizedCoefficientsEccentricityFD.c:505
z2
static REAL8 UNUSED z2(REAL8 e0, REAL8 f0, REAL8 inc, REAL8 bet, REAL8 FPlus, REAL8 FCross)
Definition: LALSimInspiralOptimizedCoefficientsEccentricityFD.c:527
l
int l
Definition: bh_qnmode.c:135
i
double i
Definition: bh_ringdown.c:118
e
double e
Definition: bh_ringdown.c:117
a2
const double a2
Definition: exact_derivatives-HrealHeader.c:33
csi
const double csi
Definition: exact_derivatives-HrealHeader.c:125
LAL_MTSUN_SI
#define LAL_MTSUN_SI
REAL8
double REAL8
UINT4
uint32_t UINT4
INT4
int32_t INT4
XLALSimEnergyKerrISCO
REAL8 XLALSimEnergyKerrISCO(REAL8 rISCO)
Definition: LALSimBlackHoleRingdown.c:691
XLALSimAngMomKerrISCO
REAL8 XLALSimAngMomKerrISCO(REAL8 rISCO)
Definition: LALSimBlackHoleRingdown.c:699
XLALSimRadiusKerrISCO
REAL8 XLALSimRadiusKerrISCO(REAL8 a)
Definition: LALSimBlackHoleRingdown.c:676
Approximant
Approximant
Enum that specifies the PN approximant to be used in computing the waveform.
Definition: LALSimInspiral.h:229
EOBNRv2HM
@ EOBNRv2HM
UNDOCUMENTED.
Definition: LALSimInspiral.h:316
SEOBNRv2
@ SEOBNRv2
Spin-aligned EOBNR model v2.
Definition: LALSimInspiral.h:326
SEOBNRv1
@ SEOBNRv1
Spin-aligned EOBNR model.
Definition: LALSimInspiral.h:324
SEOBNRv3
@ SEOBNRv3
Spin precessing EOBNR model v3.
Definition: LALSimInspiral.h:330
EOBNRv2
@ EOBNRv2
UNDOCUMENTED.
Definition: LALSimInspiral.h:314
SEOBNRv4P
@ SEOBNRv4P
Spin precessing EOBNR model based on SEOBNRv4.
Definition: LALSimInspiral.h:342
EOBNR
@ EOBNR
UNDOCUMENTED.
Definition: LALSimInspiral.h:312
SEOBNRv4PHM
@ SEOBNRv4PHM
Spin precessing EOBNR model based on SEOBNRv4HM.
Definition: LALSimInspiral.h:344
SEOBNRv3_opt
@ SEOBNRv3_opt
Optimized Spin precessing EOBNR model v3.
Definition: LALSimInspiral.h:334
m
static const INT4 m
q
static const INT4 q
XLAL_ERROR
#define XLAL_ERROR(...)
XLAL_PRINT_WARNING
#define XLAL_PRINT_WARNING(...)
XLALPrintError
int XLALPrintError(const char *fmt,...) _LAL_GCC_PRINTF_FORMAT_(1
XLAL_SUCCESS
XLAL_SUCCESS
XLAL_EFUNC
XLAL_EFUNC
XLAL_EINVAL
XLAL_EINVAL
XLAL_FAILURE
XLAL_FAILURE
alpha
double alpha
Definition: sgwb.c:106
COMPLEX16Vector::data
COMPLEX16 * data