LALSimulation  5.4.0.1-fe68b98
LALSimBlackHoleRingdown.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 <lal/LALSimBlackHoleRingdown.h>
13 
14 #include <lal/LALSimIMR.h>
15 
16 /* note: use double-precision variables, but demand single-precision accuracy */
17 #define EPS LAL_REAL4_EPS
18 #define TINY LAL_REAL4_MIN
19 #define MAXITER 16384
20 
21 #ifdef __GNUC__
22 #define UNUSED __attribute__ ((unused))
23 #else
24 #define UNUSED
25 #endif
26 
27 struct LALSimBlackHoleRingdownModeLeaver {
28  double a;
29  int l;
30  int m;
31  int s;
32  COMPLEX16 A;
33  COMPLEX16 omega;
34 };
35 
36 /* Expansion coefficients for Schwarzschild modes. */
37 /* Equation 8 of Leaver (1985). */
38 static int XLALSimBlackHoleRingdownModeSphericalCoefficientsLeaver(COMPLEX16 * alp, COMPLEX16 * bet, COMPLEX16 * gam, double UNUSED a, int l, int UNUSED m, int n, int s, COMPLEX16 UNUSED A, COMPLEX16 omega)
39 {
40  COMPLEX16 rho = -I * omega;
41  int epsilon = s * s - 1;
42  *alp = n * n + (2.0 * rho + 2.0) * n + 2.0 * rho + 1.0;
43  *bet = -(2.0 * n * n + (8.0 * rho + 2.0) * n + 8.0 * rho * rho + 4.0 * rho + l * (l + 1.0) - epsilon);
44  *gam = n * n + 4.0 * rho * n + 4.0 * rho * rho - epsilon - 1.0;
45  return 0;
46 }
47 
48 /* Angular expansion coefficients for Kerr modes. */
49 /* Equation 20 of Leaver (1985). */
50 static int XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver(COMPLEX16 * alp, COMPLEX16 * bet, COMPLEX16 * gam, double a, int UNUSED l, int m, int n, int s, COMPLEX16 A, COMPLEX16 omega)
51 {
52  double k1 = 0.5 * abs(m - s);
53  double k2 = 0.5 * abs(m + s);
54  *alp = -2.0 * (n + 1.0) * (n + 2.0 * k1 + 1.0);
55  *bet = n * (n - 1.0) + 2.0 * n * (k1 + k2 + 1.0 - 2.0 * a * omega);
56  *bet -= 2.0 * a * omega * (2.0 * k1 + s + 1.0) - (k1 + k2) * (k1 + k2 + 1.0);
57  *bet -= a * a * omega * omega + s * (s + 1.0) + A;
58  *gam = 2.0 * a * omega * (n + k1 + k2 + s);
59  return 0;
60 }
61 
62 /* Radial expansion coefficients for Kerr modes. */
63 /* Equations 25 and 26 of Leaver (1985). */
64 static int XLALSimBlackHoleRingdownModeRadialCoefficientsLeaver(COMPLEX16 * alp, COMPLEX16 * bet, COMPLEX16 * gam, double a, int UNUSED l, int m, int n, int s, COMPLEX16 A, COMPLEX16 omega)
65 {
66  COMPLEX16 c0, c1, c2, c3, c4;
67  double b = sqrt(1.0 - 4.0 * a * a);
68  c0 = 1.0 - s - I * omega - 2.0 * I * (0.5 * omega - a * m) / b;
69  c1 = -4.0 + 2.0 * I * omega * (2.0 + b) + 4.0 * I * (0.5 * omega - a * m) / b;
70  c2 = s + 3.0 - 3.0 * I * omega - 2.0 * I * (0.5 * omega - a * m) / b;
71  c3 = omega * omega * (4.0 + 2.0 * b - a * a) - 2.0 * a * m * omega - s - 1.0 + (2.0 + b) * I * omega - A + (4.0 * omega + 2.0 * I) * (0.5 * omega - a * m) / b;
72  c4 = s + 1.0 - 2.0 * omega * omega - (2.0 * s + 3.0) * I * omega - (4.0 * omega + 2.0 * I) * (0.5 * omega - a * m) / b;
73  *alp = n * n + (c0 + 1.0) * n + c0;
74  *bet = -2.0 * n * n + (c1 + 2.0) * n + c3;
75  *gam = n * n + (c2 - 3.0) * n + c4 - c2 + 2.0;
76  return 0;
77 }
78 
79 /* Evaluates the continued fractions in */
80 /* Equations (13), (21), or (27) of Leaver (1985). */
81 /* TODO: if we ever want overtones, we will need */
82 /* generalize this so that it can solve inversions */
83 /* such as Equation (14) of Leaver (1985).... */
84 /* Uses the modified Lentz's method (see Numerical */
85 /* Recipes). */
86 static COMPLEX16 XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver(double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega, int (*coef) (COMPLEX16 *, COMPLEX16 *, COMPLEX16 *, double, int, int, int, int, COMPLEX16, COMPLEX16))
87 {
88  int n = 0;
89  COMPLEX16 alp, alpsv, bet, gam;
90  COMPLEX16 afac, bfac;
91  COMPLEX16 f, fsv, C, D, Delta;
92 
93  alpsv = 0;
94  coef(&alp, &bet, &gam, a, l, m, n, s, A, omega);
95  afac = -alpsv * gam;
96  alpsv = alp;
97  bfac = bet;
98  f = bfac;
99  if (cabs(f) < TINY)
100  f = TINY;
101  C = f;
102  D = 0;
103 
104  while (n++ < MAXITER) {
105  coef(&alp, &bet, &gam, a, l, m, n, s, A, omega);
106  afac = -alpsv * gam;
107  alpsv = alp;
108  bfac = bet;
109  D = bfac + afac * D;
110  if (cabs(D) < TINY)
111  D = TINY;
112  C = bfac + afac / C;
113  if (cabs(C) < TINY)
114  C = TINY;
115  D = 1.0 / D;
116  Delta = C * D;
117  fsv = f;
118  f *= Delta;
119  if (cabs(f - fsv) < EPS)
120  return f;
121  }
122 
123  /* only get here if MAXITER is exceeded */
124  XLAL_ERROR(XLAL_EMAXITER);
125 }
126 
127 /* Residual function for solving the continued fraction equation */
128 /* Equation (13) of Leaver (1985). */
129 static int XLALSimBlackHoleRingdownModeSchwarzschildEigenvalueSolveResid(const gsl_vector * x, void *params, gsl_vector * f)
130 {
131  struct LALSimBlackHoleRingdownModeLeaver *p = params;
132  COMPLEX16 A = 0.0, omega;
133  COMPLEX16 cf;
134  int errnum;
135  omega = gsl_vector_get(x, 0) + I * gsl_vector_get(x, 1);
136  XLAL_TRY(cf = XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver(p->a, p->l, p->m, p->s, A, omega, XLALSimBlackHoleRingdownModeSphericalCoefficientsLeaver), errnum);
137  if (errnum)
138  XLAL_ERROR(XLAL_EFUNC);
139 
140  gsl_vector_set(f, 0, creal(cf));
141  gsl_vector_set(f, 1, cimag(cf));
142  return 0;
143 }
144 
145 /* Residual function for solving the continued fraction equations */
146 /* Equation (21) and (27) of Leaver (1985). */
147 /* Note: simultaneously solves both of these equations together. */
148 static int XLALSimBlackHoleRingdownModeKerrEigenvalueSolveResid(const gsl_vector * x, void *params, gsl_vector * f)
149 {
150  struct LALSimBlackHoleRingdownModeLeaver *p = params;
151  COMPLEX16 A, omega;
152  COMPLEX16 cf1, cf2;
153  int errnum;
154  A = gsl_vector_get(x, 0) + I * gsl_vector_get(x, 1);
155  omega = gsl_vector_get(x, 2) + I * gsl_vector_get(x, 3);
156  XLAL_TRY(cf1 = XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver(p->a, p->l, p->m, p->s, A, omega, XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver), errnum);
157  if (errnum)
158  XLAL_ERROR(XLAL_EFUNC);
159  XLAL_TRY(cf2 = XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver(p->a, p->l, p->m, p->s, A, omega, XLALSimBlackHoleRingdownModeRadialCoefficientsLeaver), errnum);
160  if (errnum)
161  XLAL_ERROR(XLAL_EFUNC);
162  gsl_vector_set(f, 0, creal(cf1));
163  gsl_vector_set(f, 1, cimag(cf1));
164  gsl_vector_set(f, 2, creal(cf2));
165  gsl_vector_set(f, 3, cimag(cf2));
166  return 0;
167 }
168 
169 /* Solves the continued fraction equation, */
170 /* Equation (13) of Leaver (1985), */
171 /* for the eigenfrequency omega of the */
172 /* quasinormal mode for Schwarzschild. */
173 static int XLALSimBlackHoleRingdownModeEigenvalueSolveSchwarzschild(COMPLEX16 * omega, int l, int m, int s)
174 {
175  enum { ndim = 2 };
176  const gsl_multiroot_fsolver_type *T;
177  gsl_multiroot_fsolver *solver;
178  int status;
179  size_t iter = 0;
180  int errnum;
181  struct LALSimBlackHoleRingdownModeLeaver p;
182  gsl_multiroot_function f = { &XLALSimBlackHoleRingdownModeSchwarzschildEigenvalueSolveResid, ndim, &p };
183  gsl_vector *x = gsl_vector_alloc(ndim);
184 
185  if (!x)
186  XLAL_ERROR(XLAL_ENOMEM);
187 
188  gsl_vector_set(x, 0, creal(*omega));
189  gsl_vector_set(x, 1, cimag(*omega));
190  p.a = 0.0;
191  p.l = l;
192  p.m = m;
193  p.s = s;
194 
195  T = gsl_multiroot_fsolver_hybrids;
196  solver = gsl_multiroot_fsolver_alloc(T, ndim);
197  if (!solver) {
198  gsl_vector_free(x);
199  XLAL_ERROR(XLAL_ENOMEM);
200  }
201  gsl_multiroot_fsolver_set(solver, &f, x);
202 
203  do {
204  ++iter;
205  XLAL_TRY(status = gsl_multiroot_fsolver_iterate(solver), errnum);
206  if (errnum) {
207  gsl_multiroot_fsolver_free(solver);
208  gsl_vector_free(x);
209  XLAL_ERROR(XLAL_EFUNC);
210  }
211  if (status)
212  break;
213  XLAL_TRY(status = gsl_multiroot_test_residual(solver->f, EPS), errnum);
214  if (errnum) {
215  gsl_multiroot_fsolver_free(solver);
216  gsl_vector_free(x);
217  XLAL_ERROR(XLAL_EFUNC);
218  }
219  } while (status == GSL_CONTINUE && iter < MAXITER);
220  if (iter >= MAXITER) {
221  gsl_multiroot_fsolver_free(solver);
222  gsl_vector_free(x);
223  XLAL_ERROR(XLAL_EMAXITER);
224  }
225 
226  *omega = gsl_vector_get(solver->x, 0) + I * gsl_vector_get(solver->x, 1);
227 
228  gsl_multiroot_fsolver_free(solver);
229  gsl_vector_free(x);
230  return 0;
231 }
232 
233 /* Solves the continued fraction equation, */
234 /* Equations (21) and (27) of Leaver (1985), */
235 /* for the eigenfrequency omega and angular */
236 /* separation constant A of the */
237 /* quasinormal mode for Kerr. */
238 static int XLALSimBlackHoleRingdownModeEigenvalueSolveKerr(COMPLEX16 * A, COMPLEX16 * omega, double a, int l, int m, int s)
239 {
240  enum { ndim = 4 };
241  const gsl_multiroot_fsolver_type *T;
242  gsl_multiroot_fsolver *solver;
243  int status;
244  size_t iter = 0;
245  struct LALSimBlackHoleRingdownModeLeaver p;
246  int errnum;
247  gsl_multiroot_function f = { &XLALSimBlackHoleRingdownModeKerrEigenvalueSolveResid, ndim, &p };
248  gsl_vector *x = gsl_vector_alloc(ndim);
249 
250  if (!x)
251  XLAL_ERROR(XLAL_ENOMEM);
252 
253  gsl_vector_set(x, 0, creal(*A));
254  gsl_vector_set(x, 1, cimag(*A));
255  gsl_vector_set(x, 2, creal(*omega));
256  gsl_vector_set(x, 3, cimag(*omega));
257  p.a = a;
258  p.l = l;
259  p.m = m;
260  p.s = s;
261 
262  T = gsl_multiroot_fsolver_hybrids;
263  solver = gsl_multiroot_fsolver_alloc(T, ndim);
264  if (!solver) {
265  gsl_vector_free(x);
266  XLAL_ERROR(XLAL_ENOMEM);
267  }
268  gsl_multiroot_fsolver_set(solver, &f, x);
269 
270  do {
271  ++iter;
272  XLAL_TRY(status = gsl_multiroot_fsolver_iterate(solver), errnum);
273  if (errnum) {
274  gsl_multiroot_fsolver_free(solver);
275  gsl_vector_free(x);
276  XLAL_ERROR(XLAL_EFUNC);
277  }
278  if (status)
279  break;
280  XLAL_TRY(status = gsl_multiroot_test_residual(solver->f, EPS), errnum);
281  if (errnum) {
282  gsl_multiroot_fsolver_free(solver);
283  gsl_vector_free(x);
284  XLAL_ERROR(XLAL_EFUNC);
285  }
286  } while (status == GSL_CONTINUE && iter < MAXITER);
287  if (iter >= MAXITER) {
288  gsl_multiroot_fsolver_free(solver);
289  gsl_vector_free(x);
290  XLAL_ERROR(XLAL_EMAXITER);
291  }
292 
293  *A = gsl_vector_get(solver->x, 0) + I * gsl_vector_get(solver->x, 1);
294  *omega = gsl_vector_get(solver->x, 2) + I * gsl_vector_get(solver->x, 3);
295 
296  /* problems occur if imaginary part of A is tiny but not zero */
297  if (fabs(cimag(*A)) < EPS)
298  *A = creal(*A);
299 
300  gsl_multiroot_fsolver_free(solver);
301  gsl_vector_free(x);
302  return 0;
303 }
304 
305 /* Equations 18 and 19 of Leaver (1985) */
306 static COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(double mu, double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega)
307 {
308  COMPLEX16 alp, bet, gam;
309  double mup1 = mu + 1;
310  double mum1 = mu - 1;
311  COMPLEX16 prod = 1;
312  COMPLEX16 sum;
313  COMPLEX16 delta;
314  COMPLEX16 a_n;
315  COMPLEX16 a_nm1;
316  COMPLEX16 a_np1;
317  int n = 0;
318 
319  XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver(&alp, &bet, &gam, a, l, m, n, s, A, omega);
320  sum = 1.0;
321  a_n = 1.0;
322  a_np1 = -bet * a_n / alp; /* Eq. 19, first line */
323  while (n++ < MAXITER) {
324  a_nm1 = a_n;
325  a_n = a_np1;
326  prod *= mup1;
327  delta = a_n * prod;
328  sum += delta;
329  if (cabs(delta) * cabs(delta) < /* FIXME EPS */ 1e-4)
330  break;
331  XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver(&alp, &bet, &gam, a, l, m, n, s, A, omega);
332  a_np1 = -(bet * a_n + gam * a_nm1) / alp; /* Eq. 19, second line */
333  }
334  if (n >= MAXITER)
335  XLAL_ERROR(XLAL_EMAXITER);
336  sum *= pow(mup1, 0.5 * abs(m - s));
337  sum *= pow(-mum1, 0.5 * abs(m + s));
338  sum *= cexp(a * omega * mu);
339  return sum;
340 }
341 
342 /* Integrand function for gsl integrator used to compute
343  * normalization factor for spheroidal wave functions. */
344 static double XLALSimBlackHoleRingdownSpheriodalWaveFunctionNormIntegrand(double mu, void *params)
345 {
346  struct LALSimBlackHoleRingdownModeLeaver *p = params;
347  COMPLEX16 sphwf;
348  double r;
349  int errnum;
350 
351  XLAL_TRY(sphwf = XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(mu, p->a, p->l, p->m, p->s, p->A, p->omega), errnum);
352  if (errnum)
353  XLAL_ERROR_REAL8(XLAL_EFUNC);
354  r = cabs(sphwf);
355 
356  return r * r;
357 }
358 
359 /* Computes the normalization factor for spheroidal wave functions. */
360 static COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver(double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega)
361 {
362  struct LALSimBlackHoleRingdownModeLeaver p;
363  enum { WORKSPACESIZE = 1000 };
364  gsl_integration_workspace *w = gsl_integration_workspace_alloc(WORKSPACESIZE);
365  double integral, error;
366  COMPLEX16 sphwf;
367  COMPLEX16 norm;
368  int signneg;
369  gsl_function f;
370  int errnum;
371  int status;
372 
373  p.a = a;
374  p.l = l;
375  p.m = m;
376  p.s = s;
377  p.A = A;
378  p.omega = omega;
379  f.function = XLALSimBlackHoleRingdownSpheriodalWaveFunctionNormIntegrand;
380  f.params = &p;
381  XLAL_TRY(status = gsl_integration_qags(&f, -1.0, 1.0, 0.0, 1e-6, WORKSPACESIZE, w, &integral, &error), errnum);
382  gsl_integration_workspace_free(w);
383  if (status || errnum) /* there was an error during integration */
384  XLAL_ERROR_REAL8(XLAL_EFUNC);
385 
386  /* get complex part so that sphwf is real at mu=0 */
387  XLAL_TRY(sphwf = XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(0.0, a, l, m, s, A, omega), errnum);
388  if (errnum)
389  XLAL_ERROR_REAL8(XLAL_EFUNC);
390  norm = cabs(sphwf) / sphwf;
391 
392  XLAL_TRY(sphwf = XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(-1.0 + EPS, a, l, m, s, A, omega), errnum);
393  if (errnum)
394  XLAL_ERROR_REAL8(XLAL_EFUNC);
395  sphwf *= norm;
396  signneg = signbit(creal(sphwf));
397  signneg = (l - (m > s ? m : s)) % 2 ? !signneg : signneg;
398 
399  norm /= sqrt(integral);
400  if (signneg)
401  norm *= -1;
402 
403  return norm;
404 }
405 
406 /**
407  * @addtogroup LALSimBlackHoleRingdown_h
408  * @{
409  */
410 
411 /**
412  * @name Low-Level Routines
413  * @attention The variables are represented in Leaver's conventions
414  * in which G = c = 2M = 1. In particular this means, |a| < 0.5.
415  * @{
416  */
417 
418 /**
419  * Low-level routine that computes the black hole quasinormal mode
420  * eigenefrequency, omega, and angular separation constant A for a given
421  * (l,m) mode and spin-weight s (s=-2 for gravitational perturbations).
422  *
423  * Implements Leaver's method by simultaneously
424  * solving the continued fraction equations Eq. (21) and Eq. (27)
425  * of Leaver (1985):
426  * E. W. Leaver "An analyitic representation for the quasi-normal
427  * modes of Kerr black holes", Proc. R. Soc. Lond. A 402 285-298 (1985).
428  *
429  * \attention The variables are represented in Leaver's conventions
430  * in which G = c = 2M = 1. In particular this means, |a| < 0.5.
431  *
432  * \todo Extend so that overtones can be computed too.
433  */
434 int XLALSimBlackHoleRingdownModeEigenvaluesLeaver(COMPLEX16 * A,
435  /**< angular separation constant [returned] */
436  COMPLEX16 * omega, /**< eigenfrequency [returned] */
437  double a, /**< spin parameter (note: |a| < 0.5) */
438  int l, /**< mode value l */
439  int m, /**< mode value m */
440  int s /**< spin weight (s = -2 for gravitational perturbations) */
441  )
442 {
443  double fac = 1.0 / sqrt(27.0);
444  double atry;
445  int aneg = 0;
446 
447  /* negative values of a can be obtained from positive values by an identity */
448  if (signbit(a)) {
449  aneg = 1;
450  a = fabs(a);
451  m = -m;
452  }
453 
454  if (a >= 0.5 || l < abs(s) || abs(m) > l || s > 0 || s < -2)
455  XLAL_ERROR(XLAL_EINVAL);
456 
457  /* start at Schwarzschild values */
458  *A = l * (l + 1) - s * (s + 1);
459  *omega = fac * (2 * l + 1 - I); /* asymptotic value for large l */
460  if (XLALSimBlackHoleRingdownModeEigenvalueSolveSchwarzschild(omega, l, m, s) < 0)
461  XLAL_ERROR(XLAL_EFUNC);
462 
463  if (a < 1e-2) /* we have the Schwarzschild solution */
464  return 0;
465 
466  /* step towards requested value of a */
467  for (atry = 1e-2; atry < a; atry += 0.1 * (0.5 - atry))
468  if (XLALSimBlackHoleRingdownModeEigenvalueSolveKerr(A, omega, atry, l, m, s) < 0)
469  XLAL_ERROR(XLAL_EFUNC);
470 
471  /* now use the current guess to get value at requested a */
472  if (XLALSimBlackHoleRingdownModeEigenvalueSolveKerr(A, omega, a, l, m, s) < 0)
473  XLAL_ERROR(XLAL_EFUNC);
474 
475  /* if a was negative, apply the identity */
476  if (aneg) {
477  *A = conj(*A);
478  *omega = I * conj(-I * (*omega));
479  }
480 
481  return 0;
482 }
483 
484 /**
485  * Low-level routine that evaluates the spheroidal wave function at a
486  * specified value of mu = cos(theta) for a given (l,m) mode and
487  * spin-weight s (s=-2 for gravitational perturbations).
488  * Also requires the angular separation constant A and eigenvalue
489  * omega for that mode, which are calculated by the routine
490  * XLALSimBlackHoleRingdownModeEigenvaluesLeaver().
491  *
492  * Implements Leaver's method by simultaneously
493  * solving the continued fraction equations Eq. (21) and Eq. (27)
494  * of Leaver (1985):
495  * E. W. Leaver "An analyitic representation for the quasi-normal
496  * modes of Kerr black holes", Proc. R. Soc. Lond. A 402 285-298 (1985).
497  *
498  * \attention The variables are represented in Leaver's conventions
499  * in which G = c = 2M = 1. In particular this means, |a| < 0.5.
500  *
501  * \todo Extend so that overtones can be computed too.
502  */
503 COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver(double mu,
504  /**< cosine of polar angle */
505  double a, /**< spin parameter (note: |a| < 0.5) */
506  int l, /**< mode value l */
507  int m, /**< mode value m */
508  int s, /**< spin weight (s = -2 for gravitational perturbations) */
509  COMPLEX16 A, /**< angular separation constant */
510  COMPLEX16 omega /**< eigenfrequency */
511  )
512 {
513  COMPLEX16 norm;
514  COMPLEX16 sphwf;
515  int errnum;
516 
517  if (fabs(mu) > 1.0 || fabs(a) >= 0.5 || l < abs(s) || abs(m) > l || s > 0 || s < -2)
518  XLAL_ERROR(XLAL_EINVAL);
519 
520  XLAL_TRY(norm = XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver(a, l, m, s, A, omega), errnum);
521  if (errnum)
522  XLAL_ERROR_REAL8(XLAL_EFUNC);
523  XLAL_TRY(sphwf = XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(mu, a, l, m, s, A, omega), errnum);
524  if (errnum)
525  XLAL_ERROR_REAL8(XLAL_EFUNC);
526  sphwf *= norm;
527 
528  return sphwf;
529 }
530 
531 /** @} */
532 
533 /**
534  * @name High-Level Routines
535  * @{
536  */
537 
538 /**
539  * Computes the frequency and quality factor of a specified quasinormal
540  * mode (l,m) of spin weight s perturbations (s=-2 for gravitational
541  * perturbations) of a black hole of a specified mass and spin.
542  *
543  * Uses the method of Leaver (1985):
544  * E. W. Leaver "An analyitic representation for the quasi-normal
545  * modes of Kerr black holes", Proc. R. Soc. Lond. A 402 285-298 (1985).
546  *
547  * \note The dimensionless spin assumes values between -1 and 1.
548  *
549  * \todo Extend so that overtones can be computed too.
550  */
551 int XLALSimBlackHoleRingdownMode(double *frequency,
552  /**< mode frequency (Hz) [returned] */
553  double *quality, /**< mode quality factor [returned] */
554  double mass, /**< black hole mass (kg) */
555  double dimensionless_spin, /**< black hole dimensionless spin parameter (-1,+1) */
556  int l, /**< polar mode number */
557  int m, /**< azimuthal mode number */
558  int s /**< spin weight (s=-2 for gravitational radiation) */
559  )
560 {
561  double a = 0.5 * dimensionless_spin; /* convert to Leaver's convention 2M = 1 */
562  COMPLEX16 A, omega;
563  if (XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s) < 0)
564  XLAL_ERROR_REAL8(XLAL_EFUNC);
565  omega *= 0.5; /* convert from Leaver's convention 2M = 1 */
566  *frequency = fabs(creal(omega)) / (LAL_TWOPI * mass);
567  *quality = fabs(creal(omega)) / (-2.0 * cimag(omega));
568  return 0;
569 }
570 
571 /**
572  * Evaluates the value of spheroidal wave function at a given
573  * polar angle theta for a specified mode (l,m) and spin weight s
574  * (s=-2 for gravitational perturbations) and
575  * dimensionless spin parameter.
576  *
577  * Uses the method of Leaver (1985):
578  * E. W. Leaver "An analyitic representation for the quasi-normal
579  * modes of Kerr black holes", Proc. R. Soc. Lond. A 402 285-298 (1985).
580  *
581  * \note The dimensionless spin assumes values between -1 and 1.
582  *
583  * \todo Extend so that overtones can be computed too.
584  */
585 COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunction(double theta,
586  /**< polar angle (radians) */
587  double dimensionless_spin, /**< black hole dimensionless spin parameter */
588  int l, /**< polar mode number */
589  int m, /**< azimuthal mode number */
590  int s /**< spin weight (s=-2 for gravitational radiation) */
591  )
592 {
593  double a = 0.5 * dimensionless_spin; /* convert to Leaver conventions 2M = 1 */
594  double mu = cos(theta);
595  COMPLEX16 A, omega;
596  COMPLEX16 sphwf;
597 
598  if (XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s) < 0)
599  XLAL_ERROR_REAL8(XLAL_EFUNC);
600  sphwf = XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver(mu, a, l, m, s, A, omega);
601  return sphwf;
602 }
603 
604 /**
605  * Computes the waveform for the ringdown of a black hole
606  * quasinormal mode (l,m).
607  *
608  * \note The dimensionless spin assumes values between -1 and 1.
609  *
610  * \todo Extend so that overtones can be computed too.
611  */
612 int XLALSimBlackHoleRingdown(REAL8TimeSeries ** hplus,
613  /**< plus-polarization waveform [returned] */
614  REAL8TimeSeries ** hcross, /**< cross-polarization waveform [returned] */
615  const LIGOTimeGPS * t0, /**< start time of ringdown */
616  double phi0, /**< initial phase of ringdown (rad) */
617  double deltaT, /**< sampling interval (s) */
618  double mass, /**< black hole mass (kg) */
619  double dimensionless_spin, /**< black hole dimensionless spin parameter */
620  double fractional_mass_loss, /**< fraction of mass radiated in this mode */
621  double distance, /**< distance to source (m) */
622  double inclination, /**< inclination of source's spin axis (rad) */
623  int l, /**< polar mode number */
624  int m /**< azimuthal mode number */
625  )
626 {
627  const int s = -2; /* spin weight for gravitational radiation */
628  double mu = cos(inclination);
629  double a = 0.5 * dimensionless_spin; /* convert to Leaver conventions 2M = 1 */
630  COMPLEX16 A, omega;
631  COMPLEX16 sphwf1, sphwf2;
632  COMPLEX16 A1, A2;
633  COMPLEX16 omega_dt;
634  size_t length;
635  size_t j;
636  int errnum;
637 
638  if (XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s) < 0)
639  XLAL_ERROR(XLAL_EFUNC);
640  XLAL_TRY(sphwf1 = XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver(mu, a, l, m, s, A, omega), errnum);
641  XLAL_TRY(sphwf2 = XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver(-mu, a, l, m, s, A, omega), errnum);
642  if (errnum)
643  XLAL_ERROR(XLAL_EFUNC);
644  omega *= 0.5; /* convert from Leaver's convention 2M = 1 */
645 
646  /* compute length of waveform to compute */
647  length = ceil(log(LAL_REAL8_EPS) * LAL_G_SI * mass / (pow(LAL_C_SI, 3.0) * cimag(omega) * deltaT));
648  if (length < 1)
649  XLAL_ERROR(XLAL_EBADLEN);
650 
651  /* compute the amplitude factors for the +m and -m modes */
652  A1 = A2 = -4.0 * (LAL_G_SI * mass / (pow(LAL_C_SI, 2.0) * distance))
653  * sqrt(-0.5 * cimag(omega) * fractional_mass_loss) / cabs(omega)
654  * cexp(I * m * phi0);
655  A1 *= sphwf1;
656  A2 = conj(A2 * sphwf2);
657 
658  omega_dt = pow(LAL_C_SI, 3.0) * omega * deltaT / (LAL_G_SI * mass);
659 
660  *hplus = XLALCreateREAL8TimeSeries("H_PLUS", t0, 0.0, deltaT, &lalStrainUnit, length);
661  *hcross = XLALCreateREAL8TimeSeries("H_CROSS", t0, 0.0, deltaT, &lalStrainUnit, length);
662  if (hplus == NULL || hcross == NULL)
663  XLAL_ERROR(XLAL_EFUNC);
664 
665  /* compute the waveforms */
666  for (j = 0; j < length; ++j) {
667  COMPLEX16 h;
668  h = A1 * cexp(-I * omega_dt * j) + A2 * cexp(I * conj(omega_dt) * j);
669  (*hplus)->data->data[j] = creal(h);
670  (*hcross)->data->data[j] = -cimag(h);
671  }
672 
673  return 0;
674 }
675 
676 REAL8 XLALSimRadiusKerrISCO ( REAL8 a ) {
677  REAL8 z1, z2;
678  if ( 1. - a * a < 0. || 1. + a < 0. || 1. - a < 0. ) {
679  XLALPrintError("XLAL Error %s - Arguments of pow and sqrt functions should be nonnegative!\n", __func__);
680  XLAL_ERROR(XLAL_EINVAL);
681  }
682  z1 = 1. + pow(1. - a * a, 1. / 3.) * (pow(1. + a, 1. / 3.) + pow(1. - a, 1. / 3.));
683  z2 = sqrt(3. * a * a + z1 * z1);
684  if ( (3. - z1) * (3. + z1 + 2. * z2) < 0. ) {
685  XLALPrintError("XLAL Error %s - Arguments of pow and sqrt functions should be nonnegative!\n", __func__);
686  XLAL_ERROR(XLAL_EINVAL);
687  }
688  return 3. + z2 - (a < 0. ? -1. : 1.) * sqrt((3. - z1) * (3. + z1 + 2. * z2));
689 }
690 
691 REAL8 XLALSimEnergyKerrISCO ( REAL8 rISCO ) {
692  if ( 1. - 2. / (3. * rISCO) < 0. ) {
693  XLALPrintError("XLAL Error %s - Arguments of pow and sqrt functions should be nonnegative!\n", __func__);
694  XLAL_ERROR(XLAL_EINVAL);
695  }
696  return sqrt(1. - 2. / (3. * rISCO));
697 }
698 
699 REAL8 XLALSimAngMomKerrISCO ( REAL8 rISCO ) {
700  if ( 3. * rISCO - 2. < 0. ) {
701  XLALPrintError("XLAL Error %s - Arguments of pow and sqrt functions should be nonnegative!\n", __func__);
702  XLAL_ERROR(XLAL_EINVAL);
703  }
704  return 2. / (3. * sqrt(3.)) * (1. + 2. * sqrt(3. * rISCO - 2.));
705 }
706 
707 /**
708  * Computes the final mass and spin of the black hole resulting from merger.
709  * They are given by fittings of NR simulations results. Specifically,
710  * for EOBNR, Table I of Buonanno et al. PRD76, 104049;
711  * for EOBNRv2 and EOBNRv2HM, Eqs. 29a and 29b of Pan et al. PRD84, 124052;
712  * for SEOBNRv1 Eq. 8 of Tichy and Marronetti PRD78, 081501 and
713  * Eqs. 1 and 3 of Barausse and Rezzolla ApJ704, L40;
714  * for SEOBNRv2 the formulas in Barausse and Rezzolla ApJ704, L40 were refitted
715  * to the set of NR wfs used in the calibration of SEOBNRv2;
716  * for SEOBNRv4 same mass formula as for SEOBNRv2 and final spin
717  * formula from Astrophys.J. 825 (2016) no.2, L19
718  * for SEOBNRv5_ROM final mass formula from Jimenez Forteza et al. https://arxiv.org/abs/1611.00332
719  * and same final spin formula as SEOBNRv4
720  */
721 INT4 XLALSimIMREOBFinalMassSpin(REAL8 * finalMass,
722  /**<< OUTPUT, the final mass (scaled by original total mass) */
723  REAL8 * finalSpin, /**<< OUTPUT, the final spin (scaled by final mass) */
724  const REAL8 mass1, /**<< The mass of the 1st component of the system */
725  const REAL8 mass2, /**<< The mass of the 2nd component of the system */
726  const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
727  const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
728  Approximant approximant /**<< The waveform approximant being used */
729  ) {
730  if ( mass1 <= 0. || mass2 <= 0. ) {
731  XLALPrintError("XLAL Error %s - Masses should be positive numbers!\n", __func__);
732  XLAL_ERROR(XLAL_EINVAL);
733  }
734  static const INT4 Z_COORDINATE = 2;
735  static const REAL8 root9ovr8minus1 = -0.057190958417936644;
736  static const REAL8 root12 = 3.4641016151377544;
737 
738  REAL8 totalMass;
739  REAL8 eta, eta2, eta3;
740  REAL8 a1, a2, chiS, q;
741  REAL8 rISCO, eISCO, LISCO, atl, tmpVar, csi, S1, S2, Seff, atot, aeff, physpart, fitpart;
742 
743  /* get a local copy of the intrinsic parameters */
744  totalMass = mass1 + mass2;
745  eta = mass1 * mass2 / (totalMass * totalMass);
746  eta2 = eta * eta;
747  eta3 = eta2 * eta;
748 //printf("Approximant: %d\n",approximant);
749 
750  /* Coefficients entering the final mass formulas are defined in LALSimBlackHoleRingdown.h */
751  switch (approximant) {
752  case EOBNRv2:
753  case EOBNRv2HM:
754  eta3 = eta2 * eta;
755  /* Final mass and spin given by Eqs. 29a and 29b of Pan et al. PRD84, 124052 */
756  *finalMass = 1. + root9ovr8minus1 * eta - 0.4333 * eta2 - 0.4392 * eta3;
757  *finalSpin = root12 * eta - 3.871 * eta2 + 4.028 * eta3;
758  break;
759  case EOBNR:
760  /* Final mass and spin given by Table I of Buonanno et al. PRD76, 104049 */
761  *finalMass = 1 - 0.057191 * eta - 0.498 * eta2;
762  *finalSpin = 3.464102 * eta - 2.9 * eta2;
763  break;
764  case SEOBNRv2:
765  case SEOBNRv4:
766  case SEOBNRv5_ROM:
767  a1 = spin1[Z_COORDINATE];
768  a2 = spin2[Z_COORDINATE];
769  q = mass1 / mass2;
770  REAL8 InvQ = 1./q;
771  REAL8 OnePlusInvQ = 1. + InvQ;
772  REAL8 InvQ2 = InvQ * InvQ;
773 
774  atl = (a1 + a2 * InvQ2) / (OnePlusInvQ * OnePlusInvQ);
775  tmpVar = (a1 + a2 * InvQ2) / (1. + InvQ2);
776  rISCO = XLALSimRadiusKerrISCO( atl );
777  eISCO = XLALSimEnergyKerrISCO( rISCO );
778  if ( approximant == SEOBNRv5_ROM ) {
779  /* Final mass formula from Jimenez Forteza et al. https://arxiv.org/abs/1611.00332 */
780  /* Rescaled by the total mass to be consitent with SEOBNRv4 */
781 
782  *finalMass = XLALbbh_final_mass_non_precessing_UIB2016(mass1, mass2, a1, a2) / (mass1 + mass2);
783  }
784  else {
785  /* See page 3 of the dcc document T1400476-v3, quantity MFinal, for expression below. */
786 
787  *finalMass = 1. - ((1. - eISCO) * eta + 16. * eta * eta * (0.00258 - 0.0773 / (1. / ((1. + InvQ2) / (OnePlusInvQ * OnePlusInvQ)) * atl - 1.6939) - 0.25 * (1. - eISCO)));
788  }
789  if ( approximant == SEOBNRv2 ) {
790  /* See page 3 of the dcc document T1400476-v3, quantity aFinal, for expression below. */
791  *finalSpin = tmpVar + tmpVar * eta * (s9coeff * eta * tmpVar * tmpVar + s8coeff * eta * eta * tmpVar + s7coeff * eta * tmpVar + s6coeff * tmpVar * tmpVar + s4v2coeff * tmpVar + s5v2coeff * eta + t0v2coeff)
792  + eta * (2. * sqrt(3.) + t2v2coeff * eta + t3v2coeff * eta * eta);
793  }
794  else {
795  /* Final spin formula from Barausse+16 http://arxiv.org/pdf/1605.01938.pdf */
796  csi = 0.474046;
797  S1 = mass1 * mass1 * a1;
798  S2 = mass2 * mass2 * a2;
799  Seff = (1. + csi * InvQ) * S1 + (1. + csi * q) * S2;
800  aeff = Seff / (totalMass * totalMass);
801  atot = (S1 + S2) / (totalMass * totalMass);
802  rISCO = XLALSimRadiusKerrISCO( aeff );
803  eISCO = XLALSimEnergyKerrISCO( rISCO );
804  LISCO = XLALSimAngMomKerrISCO( rISCO );
805  physpart = atot + eta * (LISCO - 2. * atot * (eISCO - 1.));
806 
807  /* The k00, k01, ... coefficients are defined in LALSimBlackHoleRingdown.h */
808  REAL8 eta4 = eta * eta3;
809  REAL8 eta5 = eta * eta4;
810  if (fabs(aeff) > 0.) {
811  REAL8 aeff2 = aeff * aeff;
812  REAL8 aeff3 = aeff * aeff2;
813  REAL8 aeff4 = aeff * aeff3;
814  fitpart = k00 * eta2 + k01 * aeff * eta2 + k02 * aeff2 * eta2 + k03 * aeff3 * eta2 + k04 * aeff4 * eta2 +
815  k10 * eta3 + k11 * aeff * eta3 + k12 * aeff2 * eta3 + k13 * aeff3 * eta3 + k14 * aeff4 * eta3 +
816  k20 * eta4 + k21 * aeff * eta4 + k22 * aeff2 * eta4 + k23 * aeff3 * eta4 + k24 * aeff4 * eta4 +
817  k30 * eta5 + k31 * aeff * eta5 + k32 * aeff2 * eta5 + k33 * aeff3 * eta5 + k34 * aeff4 * eta5;
818  } else {
819  fitpart = k00 * eta2 + k10 * eta3 + k20 * eta4 + k30 * eta5;
820  }
821  *finalSpin = physpart + fitpart;
822 // printf("aeff = %.16e, LISCO = %.16e, eISCO = %.16e, rISCO = %.16e\n",aeff,LISCO,eISCO,rISCO);
823 // printf("af = %.16e\n",*finalSpin);
824  }
825  break;
826  case SEOBNRv1:
827  /* Final mass/spin comes from Eq. 8 of Tichy and Marronetti PRD78, 081501
828  * and from Eqs. 1 and 3 of Barausse and Rezzolla ApJ704, L40 */
829  a1 = spin1[Z_COORDINATE];
830  a2 = spin2[Z_COORDINATE];
831 
832  chiS = 0.5 * (a1 + a2);
833  q = mass1 / mass2;
834  *finalMass = 1. - p0coeff + 2. * p1coeff * chiS + 4. * p2coeff * chiS * chiS;
835  *finalMass = 1. + (0.9515 - 1.0) * 4. * eta - 0.013 * 16. * eta2 * (a1 + a2);
836  tmpVar = (a1 + a2 / q / q) / (1. + 1 / q / q);
837  *finalSpin = tmpVar + tmpVar * eta * (s4coeff * tmpVar + s5coeff * eta + t0coeff) + eta * (2. * sqrt(3.) + t2coeff * eta + t3coeff * eta * eta);
838  break;
839  default:
840  XLALPrintError("XLAL Error %s - Unsupported approximant.\n", __func__);
841  XLAL_ERROR(XLAL_EINVAL);
842  }
843 
844 // printf( "Final mass = %.16e, Final spin = %.16e\n", *finalMass, *finalSpin );
845  return XLAL_SUCCESS;
846 }
847 
848 /**
849  * These functions generate the quasinormal mode frequencies for a black
850  * hole ringdown. At present, this function works for the 22, 21, 33, 44
851  * and 55 modes, and includes 8 overtones. The final frequencies are
852  * computed by interpolating the data found on the webpage of
853  * Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
854  * In this page, frequecy data are given for positive final spins only.
855  * For a negative final spin chi<0 case, the (l,m) mode frequency is given by
856  * the (l,-m) mode frequency of the positive final spin -chi case.
857  */
858 INT4 XLALSimIMREOBGenerateQNMFreqV2(COMPLEX16Vector * modefreqs,
859  /**<< OUTPUT, complex freqs of overtones in unit of Hz */
860  const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
861  const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
862  const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
863  const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
864  UINT4 l, /**<< The l value of the mode in question */
865  INT4 m, /**<< The m value of the mode in question */
866  UINT4 nmodes, /**<< The number of overtones that should be included (max 8) */
867  Approximant approximant /**<< The waveform approximant being used */
868  ) {
869 
870  REAL8 totalMass, finalMass, finalSpin;
871 
872  /* Call XLALSimIMREOBFinalMassSpin() to get mass and spin of the final black hole */
873  if (XLALSimIMREOBFinalMassSpin(&finalMass, &finalSpin, mass1, mass2, spin1, spin2, approximant) == XLAL_FAILURE) {
874  XLAL_ERROR(XLAL_EFUNC);
875  }
876 
877  /* finalSpin interpolation is available only between -0.9996 and 0.9996 */
878  /* Set finalSpin to +/- 0.9996 if it is out of this range */
879  if (finalSpin < -0.9996)
880  finalSpin = -0.9996;
881  if (finalSpin > 0.9996)
882  finalSpin = 0.9996;
883  /* The final mass is scaled by the original total mass */
884  totalMass = mass1 + mass2;
885  finalMass *= totalMass;
886 
887  if (XLALSimIMREOBGenerateQNMFreqV2fromFinal(modefreqs, finalMass, finalSpin, l, m, nmodes) == XLAL_FAILURE) {
888  XLAL_ERROR(XLAL_EFUNC);
889  }
890 
891  return XLAL_SUCCESS;
892 
893 }
894 
895 INT4 XLALSimIMREOBGenerateQNMFreqV2fromFinal(COMPLEX16Vector * modefreqs,
896  /**<< OUTPUT, complex freqs of overtones in unit of Hz */
897  const REAL8 finalMass, /**<< The mass of the final black hole (in Solar masses) */
898  const REAL8 finalSpin, /**<< The spin of the final object; only needed for spin waveforms */
899  UINT4 l, /**<< The l value of the mode in question */
900  INT4 m, /**<< The m value of the mode in question */
901  UINT4 nmodes /**<< The number of overtones that should be included (max 8) */
902  ) {
903 
904  /* Data for interpolating the quasinormal mode frequencies is taken from
905  * The webpage of Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
906  * In the spin range of (-0.995, 0.999),
907  * interpolation error within 5e-5 for the first 3 overtones of the 22 mode
908  * interpolation error within 0.005 for the first 8 overtones of the 22 mode
909  * On the data points, interpolation error is within 1e-5, except for the
910  * highest overtone of the (4,4) and (5,5) modes.
911  */
912 
913  static const double afinallist[107] = { -0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
914  -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
915  -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,
916  -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,
917  -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,
918  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,
919  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,
920  0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996
921  };
922 
923  /* 2, 2 mode */
924 
925  const double reomegaqnm22[8][107] =
926  { {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,
927  0.955854, 0.960358, 0.965514, 0.968438, 0.97169},
928  {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,
929  0.955847, 0.960353, 0.96551, 0.968435, 0.971688},
930  {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,
931  0.955833, 0.960343, 0.965503, 0.96843, 0.971683},
932  {0.127766, 0.134925, 0.137314, 0.135026, 0.132545, 0.132613, 0.133213, 0.133927, 0.134502, 0.134846, 0.134197,
933  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},
934  {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,
935  0.955773, 0.960306, 0.965484, 0.968417, 0.971675},
936  {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,
937  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},
938  {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,
939  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},
940  {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,
941  0.947755, 0.949602, 0.951525, 0.953535, 0.955643, 0.960217, 0.965434, 0.968355, 0.971639}
942  };
943 
944  const double imomegaqnm22[8][107] =
945  { {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,
946  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},
947  {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,
948  0.0330384, 0.0315916, 0.0284334, 0.0247999, 0.0227304, 0.0204216},
949  {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,
950  0.0526555, 0.0473899, 0.0413327, 0.037883, 0.0340348},
951  {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,
952  0.0737264, 0.0663517, 0.0578682, 0.053037, 0.0476481},
953  {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},
954  {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},
955  {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},
956  {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}
957  };
958 
959  /* 2, 1 mode */
960 
961  const double reomegaqnm21[8][107] = { {0.336609, 0.339386, 0.340852, 0.342219, 0.342818, 0.343002,
962  0.343143, 0.343254, 0.343344, 0.343417, 0.343641, 0.343748,
963  0.343804, 0.343853, 0.343871, 0.343879, 0.343886, 0.343891,
964  0.343896, 0.343902, 0.343909, 0.343915, 0.343922, 0.343941, 0.34396,
965  0.344002, 0.344049, 0.344101, 0.34422, 0.344359, 0.344517,
966  0.344696, 0.344896, 0.345115, 0.345356, 0.345617, 0.345899,
967  0.346201, 0.346525, 0.34687, 0.347824, 0.348911, 0.350132, 0.351491,
968  0.35299, 0.354633, 0.356423, 0.358366, 0.360469, 0.362738,
969  0.365183, 0.367812, 0.370637, 0.373672, 0.376931, 0.380432,
970  0.384197, 0.388248, 0.392615, 0.39733, 0.402436, 0.407979, 0.41402,
971  0.420632, 0.427909, 0.435968, 0.444968, 0.455121, 0.459569,
972  0.464271, 0.469259, 0.474564, 0.480231, 0.486308, 0.492859,
973  0.499965, 0.507729, 0.516291, 0.525845, 0.536673, 0.542693,
974  0.549213, 0.556329, 0.560146, 0.564155, 0.565814, 0.567505,
975  0.569227, 0.570976, 0.572749, 0.574535, 0.576322, 0.577208,
976  0.578084, 0.578948, 0.579374, 0.579795, 0.580212, 0.580295,
977  0.580377, 0.58046, 0.580541, 0.580623, 0.580784, 0.580942, 0.581018,
978  0.581093}, {0.313486, 0.314984, 0.315748, 0.31636, 0.316504,
979  0.316512, 0.316502, 0.316483, 0.31646, 0.316436, 0.316347, 0.316311,
980  0.316305, 0.316315, 0.316325, 0.31633, 0.316338, 0.316345,
981  0.316352, 0.31636, 0.316368, 0.316375, 0.316383, 0.316401, 0.316419,
982  0.316455, 0.316491, 0.316527, 0.316602, 0.316682, 0.316772,
983  0.316874, 0.316989, 0.317122, 0.317273, 0.317444, 0.317636,
984  0.317851, 0.31809, 0.318353, 0.319124, 0.320064, 0.321179, 0.322476,
985  0.32396, 0.325636, 0.327508, 0.329582, 0.331865, 0.334364,
986  0.337088, 0.340045, 0.343249, 0.346711, 0.350448, 0.354478,
987  0.358823, 0.363506, 0.368558, 0.374014, 0.379916, 0.386313,
988  0.393268, 0.400856, 0.409172, 0.418337, 0.428509, 0.439897,
989  0.444855, 0.450076, 0.455587, 0.46142, 0.467612, 0.474208, 0.481261,
990  0.488834, 0.497004, 0.505862, 0.515506, 0.526011, 0.531572,
991  0.537263, 0.542874, 0.545479, 0.547723, 0.548438, 0.548984, 0.54929,
992  0.549241, 0.548642, 0.54714, 0.544185, 0.542606, 0.542325,
993  0.541626, 0.540962, 0.540617, 0.540156, 0.540066, 0.539986,
994  0.539906, 0.539818, 0.539726, 0.539553, 0.539377, 0.539288,
995  0.539198}, {0.270281, 0.269419, 0.268655, 0.267935, 0.267923,
996  0.268009, 0.268102, 0.268185, 0.268251, 0.268297, 0.268334,
997  0.268285, 0.268273, 0.268312, 0.268342, 0.268359, 0.268398,
998  0.268442, 0.268483, 0.268523, 0.268562, 0.268601, 0.26864, 0.268733,
999  0.268822, 0.268989, 0.269141, 0.26928, 0.26952, 0.269718, 0.269881,
1000  0.270016, 0.270132, 0.270235, 0.270333, 0.270431, 0.270536,
1001  0.270653, 0.270785, 0.270937, 0.271426, 0.2721, 0.272992, 0.274121,
1002  0.275504, 0.277153, 0.279078, 0.281288, 0.283792, 0.286598,
1003  0.289716, 0.293156, 0.296931, 0.301053, 0.30554, 0.31041, 0.315684,
1004  0.321389, 0.327554, 0.334218, 0.341421, 0.349217, 0.357668,
1005  0.366852, 0.376864, 0.387825, 0.39989, 0.413261, 0.419032, 0.425075,
1006  0.431414, 0.438075, 0.445088, 0.452488, 0.46031, 0.468593,
1007  0.477369, 0.48665, 0.49639, 0.506348, 0.511184, 0.515607, 0.51903,
1008  0.519992, 0.5201, 0.51983, 0.519361, 0.51871, 0.517943, 0.517204,
1009  0.516728, 0.516696, 0.516098, 0.513376, 0.509813, 0.508083,
1010  0.506412, 0.504789, 0.504468, 0.504148, 0.50383, 0.503511, 0.503194,
1011  0.502559, 0.501923, 0.501605, 0.501286}, {0.21269, 0.214089,
1012  0.215208, 0.215364, 0.21474, 0.214584, 0.21456, 0.214625, 0.21473,
1013  0.214837, 0.214992, 0.214885, 0.214922, 0.215045, 0.215071,
1014  0.215139, 0.215267, 0.215383, 0.215507, 0.215624, 0.215741,
1015  0.215858, 0.215974, 0.216256, 0.216533, 0.217064, 0.217566, 0.21804,
1016  0.218903, 0.219653, 0.220295, 0.220836, 0.221285, 0.22165,
1017  0.221945, 0.22218, 0.222368, 0.22252, 0.222647, 0.222759, 0.223032,
1018  0.223383, 0.2239, 0.224647, 0.225672, 0.22701, 0.228689, 0.23073,
1019  0.233151, 0.235969, 0.239199, 0.242854, 0.246951, 0.251505,
1020  0.256534, 0.262058, 0.268101, 0.274689, 0.281852, 0.289628,
1021  0.298059, 0.307197, 0.317104, 0.327855, 0.339542, 0.352278,
1022  0.366207, 0.38151, 0.388065, 0.394895, 0.402017, 0.409454, 0.417227,
1023  0.425361, 0.433878, 0.442797, 0.452127, 0.461855, 0.471918,
1024  0.482195, 0.48739, 0.49271, 0.498495, 0.501813, 0.5056, 0.507251,
1025  0.508939, 0.510585, 0.512031, 0.513028, 0.513289, 0.512758,
1026  0.512367, 0.512091, 0.511921, 0.51135, 0.5096, 0.50715, 0.50665,
1027  0.506154, 0.505662, 0.505175, 0.504694, 0.503744, 0.502809,
1028  0.502344, 0.50188}, {0.171239, 0.169224, 0.168634, 0.170053,
1029  0.169938, 0.169613, 0.169418, 0.169408, 0.169531, 0.169696,
1030  0.169825, 0.169724, 0.16992, 0.169916, 0.170075, 0.17014, 0.170344,
1031  0.170511, 0.17071, 0.170886, 0.171073, 0.171258, 0.171437, 0.171892,
1032  0.172337, 0.173213, 0.174064, 0.174889, 0.176453, 0.177895,
1033  0.179203, 0.180372, 0.181395, 0.182273, 0.183007, 0.183606,
1034  0.184081, 0.184444, 0.18471, 0.184896, 0.185105, 0.18512, 0.185113,
1035  0.185222, 0.18555, 0.186176, 0.187164, 0.188562, 0.190413, 0.192751,
1036  0.195604, 0.199, 0.202962, 0.207515, 0.212679, 0.21848, 0.224939,
1037  0.232083, 0.23994, 0.248543, 0.257928, 0.268139, 0.279228, 0.291258,
1038  0.304303, 0.318456, 0.33383, 0.350563, 0.357675, 0.365045,
1039  0.372687, 0.380617, 0.388855, 0.397422, 0.406346, 0.41567, 0.425462,
1040  0.435857, 0.447149, 0.45999, 0.467349, 0.475546, 0.484594,
1041  0.489367, 0.494295, 0.496339, 0.498459, 0.500692, 0.50308, 0.505635,
1042  0.508214, 0.510197, 0.510572, 0.510387, 0.509864, 0.509635,
1043  0.509456, 0.50879, 0.508443, 0.507999, 0.50747, 0.506881, 0.506257,
1044  0.504974, 0.503704, 0.503082, 0.502466}, {0.136159, 0.137914,
1045  0.137016, 0.136626, 0.137329, 0.137055, 0.136755, 0.136667,
1046  0.136793, 0.136997, 0.136954, 0.137117, 0.137154, 0.137279, 0.1373,
1047  0.13747, 0.137649, 0.137842, 0.138069, 0.138258, 0.138476, 0.138671,
1048  0.138881, 0.139389, 0.139898, 0.14091, 0.14191, 0.142898, 0.144829,
1049  0.146684, 0.148447, 0.150099, 0.151622, 0.153001, 0.154221,
1050  0.15527, 0.156142, 0.156839, 0.157368, 0.15774, 0.158094, 0.157845,
1051  0.15725, 0.156526, 0.155847, 0.155354, 0.155162, 0.155369, 0.156061,
1052  0.157316, 0.159206, 0.161795, 0.165143, 0.169299, 0.174306,
1053  0.180192, 0.186977, 0.194671, 0.203282, 0.212811, 0.223263,
1054  0.234649, 0.246985, 0.260297, 0.274622, 0.290009, 0.306518,
1055  0.324226, 0.331666, 0.339322, 0.347205, 0.355332, 0.363727,
1056  0.372432, 0.381518, 0.391111, 0.401435, 0.412868, 0.425995,
1057  0.441563, 0.45052, 0.460463, 0.471717, 0.477974, 0.484665, 0.487438,
1058  0.490248, 0.493085, 0.49596, 0.498923, 0.502084, 0.505527,
1059  0.507222, 0.508526, 0.508875, 0.508627, 0.508251, 0.507926,
1060  0.507863, 0.507785, 0.50767, 0.507484, 0.507181, 0.506113, 0.504624,
1061  0.503839, 0.50306}, {0.114342, 0.113963, 0.115141, 0.114074,
1062  0.11486, 0.114789, 0.114485, 0.114338, 0.114452, 0.114665, 0.114512,
1063  0.114807, 0.11467, 0.114821, 0.114995, 0.115025, 0.115231,
1064  0.115438, 0.115661, 0.115846, 0.11605, 0.116249, 0.116452, 0.116951,
1065  0.117454, 0.118454, 0.11946, 0.120464, 0.122464, 0.124443,
1066  0.126383, 0.128266, 0.130073, 0.131781, 0.133368, 0.134813, 0.13609,
1067  0.137179, 0.138065, 0.138742, 0.139567, 0.139335, 0.138333,
1068  0.136834, 0.135064, 0.133208, 0.131418, 0.129826, 0.128564,
1069  0.127775, 0.127629, 0.128336, 0.130133, 0.133252, 0.137863,
1070  0.144021, 0.151672, 0.160684, 0.170902, 0.182186, 0.194429,
1071  0.207556, 0.221528, 0.236327, 0.251955, 0.268421, 0.285744, 0.30395,
1072  0.311492, 0.319195, 0.327076, 0.335168, 0.343522, 0.352232,
1073  0.361443, 0.371382, 0.382361, 0.394771, 0.409089, 0.426092,
1074  0.436065, 0.4474, 0.460415, 0.467675, 0.475563, 0.478922, 0.482402,
1075  0.485993, 0.489665, 0.493377, 0.497113, 0.500995, 0.503086,
1076  0.505273, 0.507186, 0.507677, 0.507628, 0.507177, 0.507077,
1077  0.506981, 0.506892, 0.506806, 0.506714, 0.506383, 0.505391,
1078  0.504576, 0.503665}, {0.0996362, 0.098809, 0.0988228, 0.0989612,
1079  0.0991812, 0.0993225, 0.0990912, 0.0989133, 0.0990066, 0.0992056,
1080  0.0990844, 0.0992013, 0.0993046, 0.0993698, 0.0994135, 0.0995406,
1081  0.0997102, 0.0999057, 0.100109, 0.100292, 0.100464, 0.100668,
1082  0.100843, 0.10132, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617,
1083  0.108576, 0.11054, 0.112492, 0.114417, 0.116296, 0.118106,
1084  0.119822, 0.121422, 0.122876, 0.12415, 0.125214, 0.12686, 0.127085,
1085  0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.10844,
1086  0.104598, 0.100602, 0.0966436, 0.0934548, 0.0928224, 0.0967608,
1087  0.105267, 0.116748, 0.129817, 0.143719, 0.158124, 0.17292, 0.188094,
1088  0.203673, 0.219697, 0.236201, 0.253208, 0.270727, 0.288784,
1089  0.296181, 0.303707, 0.311404, 0.319342, 0.327628, 0.336416,
1090  0.345907, 0.35633, 0.367923, 0.380968, 0.395965, 0.413866, 0.424377,
1091  0.436366, 0.450442, 0.458506, 0.467375, 0.471171, 0.475126,
1092  0.479254, 0.483568, 0.488052, 0.492639, 0.497232, 0.499557,
1093  0.501993, 0.504598, 0.505838, 0.506697, 0.506742, 0.506649,
1094  0.506536, 0.50641, 0.506281, 0.506156, 0.505924, 0.505541, 0.505047,
1095  0.504219}
1096  };
1097 
1098  const double imomegaqnm21[8][107] = { {0.0743116, 0.0772659, 0.0791824, 0.0812815, 0.0822652, 0.082556,
1099  0.0827684, 0.082926, 0.0830445, 0.0831347, 0.0833596, 0.0834304,
1100  0.0834555, 0.0834714, 0.0834806, 0.0834917, 0.0835195, 0.0835507,
1101  0.0835831, 0.0836156, 0.0836481, 0.0836804, 0.0837126, 0.083792,
1102  0.0838704, 0.0840241, 0.0841737, 0.0843193, 0.0845994, 0.084865,
1103  0.085117, 0.0853561, 0.0855831, 0.0857987, 0.0860035, 0.086198,
1104  0.0863828, 0.0865584, 0.0867253, 0.086884, 0.087247, 0.0875662,
1105  0.0878462, 0.0880906, 0.0883025, 0.088484, 0.088637, 0.0887628,
1106  0.0888621, 0.0889354, 0.0889828, 0.0890037, 0.0889973, 0.0889623,
1107  0.0888968, 0.0887983, 0.0886636, 0.0884885, 0.0882679, 0.0879952,
1108  0.0876618, 0.0872571, 0.086767, 0.086173, 0.0854501, 0.0845642,
1109  0.0834665, 0.0820852, 0.0814304, 0.0807035, 0.0798926, 0.0789827,
1110  0.077955, 0.0767847, 0.0754394, 0.0738744, 0.072027, 0.0698043,
1111  0.067061, 0.0635492, 0.0613721, 0.058791, 0.0556436, 0.0537759,
1112  0.0516427, 0.0506978, 0.0496908, 0.0486136, 0.0474565, 0.0462084,
1113  0.0448564, 0.0433879, 0.0426068, 0.0417939, 0.0409501, 0.0405173,
1114  0.0400777, 0.0396319, 0.039542, 0.0394519, 0.0393616, 0.039271,
1115  0.0391802, 0.0389974, 0.0388111, 0.038714, 0.0386091}, {0.258785,
1116  0.258526, 0.258215, 0.257703, 0.257385, 0.257284, 0.25721, 0.257158,
1117  0.257123, 0.257101, 0.257089, 0.257133, 0.257178, 0.257248,
1118  0.257304, 0.257357, 0.257465, 0.257574, 0.257683, 0.257791,
1119  0.257898, 0.258005, 0.258112, 0.258376, 0.258637, 0.259149,
1120  0.259649, 0.260137, 0.261076, 0.261967, 0.262812, 0.263613,
1121  0.264372, 0.265089, 0.265768, 0.26641, 0.267016, 0.267589, 0.26813,
1122  0.26864, 0.269792, 0.270782, 0.271629, 0.272346, 0.272945, 0.273434,
1123  0.273821, 0.274112, 0.274309, 0.274415, 0.27443, 0.274354,
1124  0.274183, 0.273915, 0.273543, 0.273058, 0.272452, 0.271711,
1125  0.270819, 0.269754, 0.268489, 0.266992, 0.265218, 0.263108,
1126  0.260587, 0.257547, 0.253838, 0.249238, 0.247078, 0.244692,
1127  0.242045, 0.239089, 0.235766, 0.231999, 0.227686, 0.222686, 0.2168,
1128  0.209731, 0.201006, 0.189803, 0.18282, 0.174484, 0.164205, 0.158029,
1129  0.150891, 0.1477, 0.14428, 0.140606, 0.136657, 0.132444, 0.128112,
1130  0.124511, 0.123925, 0.123321, 0.12167, 0.121162, 0.120732, 0.12014,
1131  0.120048, 0.119951, 0.119844, 0.119734, 0.119631, 0.119429,
1132  0.119227, 0.119127, 0.119027}, {0.451082, 0.450126, 0.449946,
1133  0.450393, 0.450836, 0.450954, 0.451016, 0.451037, 0.451032,
1134  0.451015, 0.450927, 0.450953, 0.451028, 0.451151, 0.451242,
1135  0.451336, 0.451538, 0.451736, 0.451932, 0.452129, 0.452326,
1136  0.452521, 0.452716, 0.453201, 0.453683, 0.454634, 0.45557, 0.456489,
1137  0.458275, 0.459989, 0.461626, 0.463185, 0.464665, 0.466067,
1138  0.46739, 0.468636, 0.469808, 0.470906, 0.471935, 0.472897, 0.475022,
1139  0.476783, 0.478216, 0.479352, 0.48022, 0.48084, 0.481231, 0.481407,
1140  0.481377, 0.481149, 0.480726, 0.480109, 0.479294, 0.478277,
1141  0.477047, 0.475592, 0.473893, 0.471929, 0.469669, 0.467076,
1142  0.464104, 0.460691, 0.456761, 0.45221, 0.446903, 0.440653, 0.433196,
1143  0.424144, 0.419951, 0.415358, 0.4103, 0.404693, 0.398434, 0.391383,
1144  0.383355, 0.374094, 0.363227, 0.350188, 0.334044, 0.313093,
1145  0.299808, 0.283583, 0.262719, 0.249472, 0.233119, 0.225306,
1146  0.216483, 0.206365, 0.194563, 0.180538, 0.16345, 0.141483, 0.12731,
1147  0.111596, 0.0954876, 0.0868316, 0.0774193, 0.066857, 0.0645541,
1148  0.0621712, 0.0596988, 0.057125, 0.0544355, 0.0486318, 0.0420655,
1149  0.0383765, 0.0343031}, {0.670736, 0.672092, 0.671812, 0.670663,
1150  0.670549, 0.67073, 0.670927, 0.671078, 0.671164, 0.671189, 0.671021,
1151  0.671075, 0.671219, 0.67131, 0.671427, 0.671572, 0.671807,
1152  0.672062, 0.672309, 0.672557, 0.672808, 0.673057, 0.673305,
1153  0.673929, 0.674552, 0.675799, 0.677043, 0.678283, 0.680743,
1154  0.683166, 0.685536, 0.68784, 0.690067, 0.692205, 0.694247, 0.696187,
1155  0.69802, 0.699744, 0.701359, 0.702865, 0.706165, 0.708833,
1156  0.710915, 0.71246, 0.71351, 0.714105, 0.714277, 0.714053, 0.713452,
1157  0.71249, 0.711176, 0.709516, 0.707509, 0.705148, 0.702423, 0.699317,
1158  0.695803, 0.691851, 0.687416, 0.682445, 0.676867, 0.670592,
1159  0.663504, 0.655451, 0.646227, 0.635554, 0.623036, 0.60809, 0.601244,
1160  0.593791, 0.58563, 0.576638, 0.566651, 0.555455, 0.54276, 0.528156,
1161  0.511038, 0.490465, 0.464847, 0.431189, 0.409563, 0.382936,
1162  0.348824, 0.32773, 0.302947, 0.291759, 0.279694, 0.26659, 0.252176,
1163  0.235931, 0.216835, 0.192946, 0.178198, 0.160681, 0.138951,
1164  0.125667, 0.110911, 0.095128, 0.0917732, 0.0883219, 0.0847576,
1165  0.0810612, 0.0772103, 0.0689279, 0.0595841, 0.0543422,
1166  0.048559}, {0.910592, 0.910063, 0.91138, 0.911832, 0.911012,
1167  0.911003, 0.911199, 0.911439, 0.911606, 0.91166, 0.911352, 0.911585,
1168  0.911648, 0.911704, 0.911854, 0.911933, 0.912192, 0.912425,
1169  0.912663, 0.912897, 0.913141, 0.913376, 0.913616, 0.91422, 0.91483,
1170  0.916061, 0.917309, 0.918574, 0.921148, 0.923769, 0.92642, 0.929083,
1171  0.931738, 0.934365, 0.936941, 0.939446, 0.941862, 0.944173,
1172  0.946367, 0.948436, 0.953025, 0.956761, 0.959656, 0.961747, 0.96308,
1173  0.963701, 0.963651, 0.962967, 0.96168, 0.959815, 0.957389,
1174  0.954417, 0.950902, 0.946845, 0.942236, 0.937057, 0.931283,
1175  0.924873, 0.917775, 0.909918, 0.901208, 0.891524, 0.880707,
1176  0.868545, 0.854753, 0.838939, 0.820547, 0.798756, 0.788822,
1177  0.778034, 0.76625, 0.75329, 0.738922, 0.722836, 0.704612, 0.683652,
1178  0.659084, 0.629562, 0.592913, 0.54542, 0.515651, 0.480063, 0.436051,
1179  0.409334, 0.377864, 0.363486, 0.347803, 0.330563, 0.311454,
1180  0.290066, 0.265802, 0.237412, 0.220683, 0.201065, 0.17693, 0.162373,
1181  0.145371, 0.124789, 0.120176, 0.115422, 0.110541, 0.105527,
1182  0.100358, 0.0893955, 0.0771778, 0.0703585, 0.0628494}, {1.16313,
1183  1.16205, 1.16102, 1.16236, 1.1618, 1.16155, 1.16165, 1.16191,
1184  1.16212, 1.16217, 1.16185, 1.16214, 1.162, 1.16222, 1.16228, 1.1624,
1185  1.16261, 1.16279, 1.163, 1.16321, 1.16342, 1.16362, 1.16384,
1186  1.16436, 1.16489, 1.16598, 1.1671, 1.16824, 1.1706, 1.17306,
1187  1.17562, 1.17826, 1.18098, 1.18376, 1.18658, 1.18941, 1.19222,
1188  1.19499, 1.19769, 1.20029, 1.20624, 1.21127, 1.21528, 1.21824,
1189  1.22017, 1.2211, 1.22105, 1.22006, 1.21814, 1.21533, 1.21164,
1190  1.20711, 1.20176, 1.19561, 1.18868, 1.18098, 1.17251, 1.16324,
1191  1.15314, 1.14213, 1.13009, 1.11686, 1.10224, 1.08592, 1.06753,
1192  1.04652, 1.02214, 0.993243, 0.980058, 0.965724, 0.950047, 0.932779,
1193  0.913601, 0.892095, 0.867699, 0.839644, 0.806856, 0.767797,
1194  0.720146, 0.659944, 0.622848, 0.578732, 0.524237, 0.491317,
1195  0.452927, 0.435542, 0.416661, 0.395943, 0.372912, 0.346898,
1196  0.316949, 0.28167, 0.261342, 0.238436, 0.211307, 0.195088, 0.176156,
1197  0.153337, 0.148132, 0.142654, 0.136869, 0.130747, 0.124273,
1198  0.110319, 0.0949385, 0.0864639, 0.0771851}, {1.41428, 1.41604,
1199  1.4156, 1.41536, 1.4156, 1.41524, 1.41519, 1.41543, 1.41565,
1200  1.41568, 1.41551, 1.41554, 1.41563, 1.41566, 1.41579, 1.41591,
1201  1.41608, 1.41624, 1.41643, 1.41663, 1.4168, 1.417, 1.41717, 1.41765,
1202  1.41813, 1.41911, 1.42011, 1.42114, 1.42328, 1.42554, 1.42792,
1203  1.43041, 1.43303, 1.43576, 1.4386, 1.44152, 1.44453, 1.44758,
1204  1.45065, 1.45369, 1.46099, 1.46752, 1.473, 1.47733, 1.48042,
1205  1.48226, 1.48282, 1.48207, 1.47997, 1.47646, 1.4715, 1.46505,
1206  1.45715, 1.44791, 1.43752, 1.42619, 1.41412, 1.4014, 1.38801,
1207  1.37384, 1.35872, 1.34237, 1.32445, 1.30456, 1.28213, 1.25643,
1208  1.22645, 1.19065, 1.17422, 1.15628, 1.13659, 1.11481, 1.09053,
1209  1.06323, 1.03225, 0.996712, 0.955487, 0.906959, 0.848541, 0.775494,
1210  0.730792, 0.678016, 0.613349, 0.574379, 0.528885, 0.508284,
1211  0.485946, 0.461517, 0.434493, 0.404108, 0.369135, 0.327547,
1212  0.303278, 0.275875, 0.244209, 0.225953, 0.204982, 0.179727,
1213  0.173965, 0.167908, 0.161519, 0.154752, 0.147552, 0.131555,
1214  0.113035, 0.102763, 0.09161}, {1.6695, 1.6684, 1.66944, 1.66866,
1215  1.66927, 1.66897, 1.66882, 1.66899, 1.6692, 1.66921, 1.66919,
1216  1.66906, 1.66925, 1.66933, 1.66938, 1.66941, 1.6696, 1.66977,
1217  1.66995, 1.67014, 1.67031, 1.67048, 1.67066, 1.6711, 1.67155,
1218  1.67246, 1.6734, 1.67436, 1.67635, 1.67846, 1.68069, 1.68303,
1219  1.68552, 1.68814, 1.69089, 1.69379, 1.69681, 1.69996, 1.70322,
1220  1.70655, 1.71494, 1.72293, 1.73008, 1.73612, 1.7409, 1.74437,
1221  1.74645, 1.74707, 1.74612, 1.74337, 1.73845, 1.73073, 1.71933,
1222  1.70384, 1.68568, 1.6674, 1.65022, 1.63402, 1.61822, 1.60219,
1223  1.58534, 1.56716, 1.54712, 1.52462, 1.49894, 1.46917, 1.43397,
1224  1.39142, 1.37171, 1.35009, 1.32623, 1.29974, 1.27014, 1.23683,
1225  1.19912, 1.15609, 1.10649, 1.04841, 0.97878, 0.892317, 0.839828,
1226  0.778168, 0.702974, 0.657884, 0.605411, 0.581667, 0.555906,
1227  0.527711, 0.496517, 0.46151, 0.421398, 0.373867, 0.346042, 0.314367,
1228  0.277467, 0.25637, 0.232725, 0.204918, 0.198597, 0.191947,
1229  0.184925, 0.177485, 0.169568, 0.151985, 0.131247, 0.119312,
1230  0.106197}
1231  };
1232 
1233  /* 2, 0 mode */
1234  const double reomegaqnm20[8][107] = { {0.4247721439, 0.4247863113, 0.4247985972, 0.4248325877,
1235  0.4248584259, 0.4248659433, 0.4248700764, 0.4248712306,
1236  0.4248698326, 0.4248662798, 0.4248267198, 0.4247676547,
1237  0.4247005042, 0.424557753, 0.4244119723, 0.4242658712, 0.4239745379,
1238  0.4236846241, 0.4233960302, 0.4231086991, 0.4228226189,
1239  0.4225377956, 0.4222542405, 0.4215509794, 0.420855887, 0.4194906865,
1240  0.4181592598, 0.4168617799, 0.4143677184, 0.4120044663,
1241  0.4097658509, 0.40764485, 0.4056343086, 0.4037273098, 0.4019173509,
1242  0.4001984114, 0.3985649653, 0.3970119631, 0.3955348022,
1243  0.3941292897, 0.3909047276, 0.3880539184, 0.3855360484, 0.383318276,
1244  0.3813740024, 0.3796815867, 0.3782233906, 0.3769850625,
1245  0.3759550001, 0.3751239445, 0.3744846758, 0.3740317881,
1246  0.3737615278, 0.3736716844, 0.3737615278, 0.3740317881,
1247  0.3744846758, 0.3751239445, 0.3759550001, 0.3769850625,
1248  0.3782233906, 0.3796815867, 0.3813740024, 0.383318276, 0.3855360484,
1249  0.3880539184, 0.3909047276, 0.3941292897, 0.3955348022,
1250  0.3970119631, 0.3985649653, 0.4001984114, 0.4019173509,
1251  0.4037273098, 0.4056343086, 0.40764485, 0.4097658509, 0.4120044663,
1252  0.4143677184, 0.4168617799, 0.4181592598, 0.4194906865, 0.420855887,
1253  0.4215509794, 0.4222542405, 0.4225377956, 0.4228226189,
1254  0.4231086991, 0.4233960302, 0.4236846241, 0.4239745379,
1255  0.4242658712, 0.4244119723, 0.424557753, 0.4247005042, 0.4247676547,
1256  0.4248267198, 0.4248662798, 0.4248698326, 0.4248712306,
1257  0.4248700764, 0.4248659433, 0.4248584259, 0.4248325877,
1258  0.4247985972, 0.4247863113, 0.4247721439}, {0.4022595044,
1259  0.4025176372, 0.4026385253, 0.402714655, 0.4027157267, 0.4027081834,
1260  0.4026990446, 0.4026895027, 0.4026801424, 0.4026712204,
1261  0.4026338048, 0.4026034279, 0.402574986, 0.4025177609, 0.4024587579,
1262  0.4023983315, 0.4022740572, 0.402145468, 0.4020126089,
1263  0.4018755539, 0.4017344007, 0.4015892521, 0.401440212, 0.4010512734,
1264  0.4006403236, 0.3997591492, 0.3988102405, 0.397806802,
1265  0.3956841928, 0.3934728792, 0.3912313515, 0.3889989525,
1266  0.3868012743, 0.3846545743, 0.3825688955, 0.3805501632,
1267  0.3786015741, 0.3767245157, 0.3749191785, 0.3731849675,
1268  0.3691526314, 0.3655335386, 0.3623007731, 0.3594283374,
1269  0.3568927266, 0.3546733772, 0.3527526583, 0.3511156895,
1270  0.3497501098, 0.348645853, 0.34779495, 0.3471913675, 0.3468308827,
1271  0.3467109969, 0.3468308827, 0.3471913675, 0.34779495, 0.348645853,
1272  0.3497501098, 0.3511156895, 0.3527526583, 0.3546733772,
1273  0.3568927266, 0.3594283374, 0.3623007731, 0.3655335386,
1274  0.3691526314, 0.3731849675, 0.3749191785, 0.3767245157,
1275  0.3786015741, 0.3805501632, 0.3825688955, 0.3846545743,
1276  0.3868012743, 0.3889989525, 0.3912313515, 0.3934728792,
1277  0.3956841928, 0.397806802, 0.3988102405, 0.3997591492, 0.4006403236,
1278  0.4010512734, 0.401440212, 0.4015892521, 0.4017344007,
1279  0.4018755539, 0.4020126089, 0.402145468, 0.4022740572, 0.4023983315,
1280  0.4024587579, 0.4025177609, 0.402574986, 0.4026034279,
1281  0.4026338048, 0.4026712204, 0.4026801424, 0.4026895027,
1282  0.4026990446, 0.4027081834, 0.4027157267, 0.402714655, 0.4026385253,
1283  0.4025176372, 0.4022595044}, {0.3587631202, 0.3586562755,
1284  0.3585571621, 0.3584767648, 0.3584871698, 0.3585031359, 0.358520196,
1285  0.3585364516, 0.3585511443, 0.3585641498, 0.3586123314,
1286  0.3586525789, 0.3586945293, 0.358781211, 0.3588663108, 0.3589493444,
1287  0.3591108827, 0.3592664061, 0.3594155854, 0.3595583252,
1288  0.3596945387, 0.3598241205, 0.3599469676, 0.3602240117,
1289  0.3604570682, 0.3607872733, 0.3609323176, 0.360891042, 0.3602774401,
1290  0.3590639204, 0.3574099949, 0.3554578534, 0.3533158689,
1291  0.3510620393, 0.3487514511, 0.3464228554, 0.3441035438,
1292  0.3418127732, 0.3395641339, 0.337367187, 0.332139771, 0.3273292258,
1293  0.3229529922, 0.3190100679, 0.3154913069, 0.3123844448,
1294  0.3096766084, 0.3073555756, 0.3054103975, 0.30383169, 0.3026117559,
1295  0.3017446212, 0.3012260348, 0.3010534545, 0.3012260348,
1296  0.3017446212, 0.3026117559, 0.30383169, 0.3054103975, 0.3073555756,
1297  0.3096766084, 0.3123844448, 0.3154913069, 0.3190100679,
1298  0.3229529922, 0.3273292258, 0.332139771, 0.337367187, 0.3395641339,
1299  0.3418127732, 0.3441035438, 0.3464228554, 0.3487514511,
1300  0.3510620393, 0.3533158689, 0.3554578534, 0.3574099949,
1301  0.3590639204, 0.3602774401, 0.360891042, 0.3609323176, 0.3607872733,
1302  0.3604570682, 0.3602240117, 0.3599469676, 0.3598241205,
1303  0.3596945387, 0.3595583252, 0.3594155854, 0.3592664061,
1304  0.3591108827, 0.3589493444, 0.3588663108, 0.358781211, 0.3586945293,
1305  0.3586525789, 0.3586123314, 0.3585641498, 0.3585511443,
1306  0.3585364516, 0.358520196, 0.3585031359, 0.3584871698, 0.3584767648,
1307  0.3585571621, 0.3586562755, 0.3587631202}, {0.2955931981,
1308  0.2956911763, 0.2959013663, 0.2960902804, 0.2960805341, 0.296070603,
1309  0.2960715835, 0.2960841755, 0.2961057593, 0.2961328408,
1310  0.2962715691, 0.2963767257, 0.2964791366, 0.2967001479,
1311  0.2969184558, 0.2971346512, 0.2975687544, 0.2980006488,
1312  0.2984308575, 0.2988593119, 0.2992856405, 0.2997097563,
1313  0.3001315265, 0.3011744976, 0.3021986114, 0.3041793062, 0.306042046,
1314  0.30776228, 0.3106733357, 0.3125253856, 0.3131974762, 0.3128916813,
1315  0.311865866, 0.3103333453, 0.3084523863, 0.306337079, 0.304069452,
1316  0.301708867, 0.2992986826, 0.2968708711, 0.2908660077, 0.2851210461,
1317  0.2797541132, 0.2748239607, 0.2703586352, 0.2663699371,
1318  0.2628610658, 0.2598308118, 0.2572759173, 0.25519243, 0.2535764879,
1319  0.2524247751, 0.2517347842, 0.2515049622, 0.2517347842,
1320  0.2524247751, 0.2535764879, 0.25519243, 0.2572759173, 0.2598308118,
1321  0.2628610658, 0.2663699371, 0.2703586352, 0.2748239607,
1322  0.2797541132, 0.2851210461, 0.2908660077, 0.2968708711,
1323  0.2992986826, 0.301708867, 0.304069452, 0.306337079, 0.3084523863,
1324  0.3103333453, 0.311865866, 0.3128916813, 0.3131974762, 0.3125253856,
1325  0.3106733357, 0.30776228, 0.306042046, 0.3041793062, 0.3021986114,
1326  0.3011744976, 0.3001315265, 0.2997097563, 0.2992856405,
1327  0.2988593119, 0.2984308575, 0.2980006488, 0.2975687544,
1328  0.2971346512, 0.2969184558, 0.2967001479, 0.2964791366,
1329  0.2963767257, 0.2962715691, 0.2961328408, 0.2961057593,
1330  0.2960841755, 0.2960715835, 0.296070603, 0.2960805341, 0.2960902804,
1331  0.2959013663, 0.2956911763, 0.2955931981}, {0.2265759655,
1332  0.2263134666, 0.2259201107, 0.226033261, 0.2263091114, 0.2263241376,
1333  0.2262966437, 0.2262653635, 0.2262534991, 0.2262677342,
1334  0.2264910301, 0.226604597, 0.2267226381, 0.2270204493, 0.2272816677,
1335  0.2275628966, 0.2281119757, 0.2286682789, 0.2292233708,
1336  0.2297821291, 0.2303431133, 0.2309055008, 0.2314706692, 0.232891702,
1337  0.2343288764, 0.2372425752, 0.2401516712, 0.2432064357,
1338  0.2490028794, 0.2551643774, 0.2609821536, 0.2649179918,
1339  0.2670263535, 0.2677578325, 0.2675054998, 0.2665561482,
1340  0.2651128405, 0.2633200598, 0.2612820783, 0.2590753625,
1341  0.2531607164, 0.2470884185, 0.2411635985, 0.2355561825,
1342  0.2303648137, 0.2256486007, 0.2214438733, 0.2177734415,
1343  0.2146518936, 0.2120886995, 0.2100900575, 0.2086599993,
1344  0.2078010452, 0.2075145798, 0.2078010452, 0.2086599993,
1345  0.2100900575, 0.2120886995, 0.2146518936, 0.2177734415,
1346  0.2214438733, 0.2256486007, 0.2303648137, 0.2355561825,
1347  0.2411635985, 0.2470884185, 0.2531607164, 0.2590753625,
1348  0.2612820783, 0.2633200598, 0.2651128405, 0.2665561482,
1349  0.2675054998, 0.2677578325, 0.2670263535, 0.2649179918,
1350  0.2609821536, 0.2551643774, 0.2490028794, 0.2432064357,
1351  0.2401516712, 0.2372425752, 0.2343288764, 0.232891702, 0.2314706692,
1352  0.2309055008, 0.2303431133, 0.2297821291, 0.2292233708,
1353  0.2286682789, 0.2281119757, 0.2275628966, 0.2272816677,
1354  0.2270204493, 0.2267226381, 0.226604597, 0.2264910301, 0.2262677342,
1355  0.2262534991, 0.2262653635, 0.2262966437, 0.2263241376,
1356  0.2263091114, 0.226033261, 0.2259201107, 0.2263134666,
1357  0.2265759655}, {0.162467714, 0.1634934248, 0.1638277421,
1358  0.1630968281, 0.1635010049, 0.1636759976, 0.1636803676,
1359  0.1635845741, 0.163488315, 0.1634553864, 0.1638050393, 0.163791891,
1360  0.1639844275, 0.1642094594, 0.1645146073, 0.1647460864, 0.165288291,
1361  0.1658098185, 0.1663401778, 0.1668757036, 0.1674133259,
1362  0.1679475306, 0.1685023684, 0.1698847398, 0.1712487246,
1363  0.1741108365, 0.1768267467, 0.1804631771, 0.18630515, 0.1935771765,
1364  0.1987452707, 0.2093226733, 0.2181547856, 0.2237317269,
1365  0.2269036596, 0.2284118203, 0.228756399, 0.2282723907, 0.2271898972,
1366  0.2256715181, 0.2206696442, 0.2147729564, 0.2085926425,
1367  0.2024747303, 0.1966287474, 0.1911890101, 0.1862461282,
1368  0.1818640842, 0.178089795, 0.1749585446, 0.1724970437, 0.1707251041,
1369  0.1696565048, 0.1692994034, 0.1696565048, 0.1707251041,
1370  0.1724970437, 0.1749585446, 0.178089795, 0.1818640842, 0.1862461282,
1371  0.1911890101, 0.1966287474, 0.2024747303, 0.2085926425,
1372  0.2147729564, 0.2206696442, 0.2256715181, 0.2271898972,
1373  0.2282723907, 0.228756399, 0.2284118203, 0.2269036596, 0.2237317269,
1374  0.2181547856, 0.2093226733, 0.1987452707, 0.1935771765, 0.18630515,
1375  0.1804631771, 0.1768267467, 0.1741108365, 0.1712487246,
1376  0.1698847398, 0.1685023684, 0.1679475306, 0.1674133259,
1377  0.1668757036, 0.1663401778, 0.1658098185, 0.165288291, 0.1647460864,
1378  0.1645146073, 0.1642094594, 0.1639844275, 0.163791891,
1379  0.1638050393, 0.1634553864, 0.163488315, 0.1635845741, 0.1636803676,
1380  0.1636759976, 0.1635010049, 0.1630968281, 0.1638277421,
1381  0.1634934248, 0.162467714}, {0.1150947175, 0.1136995811,
1382  0.1144317617, 0.1145108329, 0.1143223733, 0.1147075752,
1383  0.1148529865, 0.1147211083, 0.1145101899, 0.1144146127,
1384  0.1148757124, 0.1147623558, 0.1150527078, 0.1152162011,
1385  0.1153522163, 0.1156670599, 0.1160937605, 0.1165085059,
1386  0.1169521137, 0.1174121457, 0.1178333408, 0.1183089991,
1387  0.1188779907, 0.1199614936, 0.1212661221, 0.122907988, 0.1252696237,
1388  0.1300527498, 0.136371485, 0.1365743504, 0.1502937555,
1389  0.1499042247, 0.1576063359, 0.1737999474, 0.1840565193,
1390  0.1901954481, 0.1937178657, 0.1954878977, 0.1960322476,
1391  0.1956928755, 0.1923495252, 0.1869716004, 0.1806432357,
1392  0.1739650338, 0.167302038, 0.1608944901, 0.1549126532, 0.1494856455,
1393  0.1447169546, 0.1406923509, 0.1374833382, 0.1351476926,
1394  0.1337284518, 0.1332523443, 0.1337284518, 0.1351476926,
1395  0.1374833382, 0.1406923509, 0.1447169546, 0.1494856455,
1396  0.1549126532, 0.1608944901, 0.167302038, 0.1739650338, 0.1806432357,
1397  0.1869716004, 0.1923495252, 0.1956928755, 0.1960322476,
1398  0.1954878977, 0.1937178657, 0.1901954481, 0.1840565193,
1399  0.1737999474, 0.1576063359, 0.1499042247, 0.1502937555,
1400  0.1365743504, 0.136371485, 0.1300527498, 0.1252696237, 0.122907988,
1401  0.1212661221, 0.1199614936, 0.1188779907, 0.1183089991,
1402  0.1178333408, 0.1174121457, 0.1169521137, 0.1165085059,
1403  0.1160937605, 0.1156670599, 0.1153522163, 0.1152162011,
1404  0.1150527078, 0.1147623558, 0.1148757124, 0.1144146127,
1405  0.1145101899, 0.1147211083, 0.1148529865, 0.1147075752,
1406  0.1143223733, 0.1145108329, 0.1144317617, 0.1136995811,
1407  0.1150947175}, {0.07824594797, 0.07897765236, 0.07781656751,
1408  0.07894919224, 0.07811549687, 0.07852555182, 0.0788734926,
1409  0.07877853969, 0.0784682439, 0.07832233515, 0.0787241668,
1410  0.07887758159, 0.07876636539, 0.07904172864, 0.07931185989,
1411  0.07935962619, 0.07970963786, 0.08015321455, 0.08049831171,
1412  0.08098647273, 0.08113113975, 0.08171084479, 0.08245975407,
1413  0.08198058103, 0.08310489532, 0.08636947463, 0.08742026462,
1414  0.09301825285, 0.09708260702, 0.1044921151, 0.09410791221,
1415  0.1163296909, 0.1194610774, 0.1071758642, 0.131059966, 0.1479210288,
1416  0.1575029326, 0.1631326584, 0.1662931627, 0.1677797021,
1417  0.1669344646, 0.162339839, 0.1558069565, 0.1482827082, 0.1403267639,
1418  0.1323069592, 0.1244931384, 0.1171075385, 0.1103537661,
1419  0.1044314061, 0.09954024628, 0.0958728709, 0.09359533547,
1420  0.09282239791, 0.09359533547, 0.0958728709, 0.09954024628,
1421  0.1044314061, 0.1103537661, 0.1171075385, 0.1244931384,
1422  0.1323069592, 0.1403267639, 0.1482827082, 0.1558069565, 0.162339839,
1423  0.1669344646, 0.1677797021, 0.1662931627, 0.1631326584,
1424  0.1575029326, 0.1479210288, 0.131059966, 0.1071758642, 0.1194610774,
1425  0.1163296909, 0.09410791221, 0.1044921151, 0.09708260702,
1426  0.09301825285, 0.08742026462, 0.08636947463, 0.08310489532,
1427  0.08198058103, 0.08245975407, 0.08171084479, 0.08113113975,
1428  0.08098647273, 0.08049831171, 0.08015321455, 0.07970963786,
1429  0.07935962619, 0.07931185989, 0.07904172864, 0.07876636539,
1430  0.07887758159, 0.0787241668, 0.07832233515, 0.0784682439,
1431  0.07877853969, 0.0788734926, 0.07852555182, 0.07811549687,
1432  0.07894919224, 0.07781656751, 0.07897765236, 0.07824594797}
1433  };
1434  const double imomegaqnm20[8][107] = { {0.06956111286, 0.07057665227, 0.07109516199, 0.07156667263,
1435  0.07176004502, 0.0718151936, 0.07185564256, 0.071886392,
1436  0.07191058835, 0.07193027264, 0.07199608801, 0.07204342275,
1437  0.07208725348, 0.07217445117, 0.07226259362, 0.07235103048,
1438  0.07252698509, 0.07270070919, 0.07287193971, 0.07304067834,
1439  0.07320697034, 0.0733708643, 0.07353240627, 0.07392625431,
1440  0.07430631954, 0.07502754477, 0.07570073722, 0.076330175,
1441  0.07747297842, 0.07848269543, 0.07938083725, 0.08018464701,
1442  0.08090799941, 0.08156214052, 0.08215626528, 0.08269795953,
1443  0.08319353674, 0.08364829544, 0.08406671695, 0.08445261881,
1444  0.0852954969, 0.08599466937, 0.08657885062, 0.08706905134,
1445  0.0874809756, 0.08782655405, 0.08811495632, 0.08835327799,
1446  0.08854701612, 0.08870040374, 0.08881664656, 0.08889809023,
1447  0.08894633586, 0.08896231569, 0.08894633586, 0.08889809023,
1448  0.08881664656, 0.08870040374, 0.08854701612, 0.08835327799,
1449  0.08811495632, 0.08782655405, 0.0874809756, 0.08706905134,
1450  0.08657885062, 0.08599466937, 0.0852954969, 0.08445261881,
1451  0.08406671695, 0.08364829544, 0.08319353674, 0.08269795953,
1452  0.08215626528, 0.08156214052, 0.08090799941, 0.08018464701,
1453  0.07938083725, 0.07848269543, 0.07747297842, 0.076330175,
1454  0.07570073722, 0.07502754477, 0.07430631954, 0.07392625431,
1455  0.07353240627, 0.0733708643, 0.07320697034, 0.07304067834,
1456  0.07287193971, 0.07270070919, 0.07252698509, 0.07235103048,
1457  0.07226259362, 0.07217445117, 0.07208725348, 0.07204342275,
1458  0.07199608801, 0.07193027264, 0.07191058835, 0.071886392,
1459  0.07185564256, 0.0718151936, 0.07176004502, 0.07156667263,
1460  0.07109516199, 0.07057665227, 0.06956111286}, {0.2185411094,
1461  0.2185862168, 0.2185760597, 0.2185502469, 0.2185551556,
1462  0.2185670597, 0.2185832072, 0.2186023833, 0.2186236698,
1463  0.2186463949, 0.2187689601, 0.21889384, 0.219017296, 0.2192613118,
1464  0.2195038699, 0.219745778, 0.2202276534, 0.2207065981, 0.2211824488,
1465  0.2216551307, 0.2221245734, 0.2225907052, 0.2230534566,
1466  0.2241951244, 0.2253143564, 0.2274827082, 0.2295545126,
1467  0.2315282566, 0.2351860943, 0.2384795534, 0.2414444658,
1468  0.2441189781, 0.2465387707, 0.2487354182, 0.2507361819,
1469  0.2525643629, 0.2542398214, 0.2557795018, 0.2571979034,
1470  0.2585074823, 0.2613723978, 0.2637535915, 0.2657465547,
1471  0.2674214198, 0.2688307276, 0.2700144584, 0.2710033792,
1472  0.2718213228, 0.2724867699, 0.273013963, 0.2734136955, 0.2736938697,
1473  0.2738598819, 0.2739148753, 0.2738598819, 0.2736938697,
1474  0.2734136955, 0.273013963, 0.2724867699, 0.2718213228, 0.2710033792,
1475  0.2700144584, 0.2688307276, 0.2674214198, 0.2657465547,
1476  0.2637535915, 0.2613723978, 0.2585074823, 0.2571979034,
1477  0.2557795018, 0.2542398214, 0.2525643629, 0.2507361819,
1478  0.2487354182, 0.2465387707, 0.2441189781, 0.2414444658,
1479  0.2384795534, 0.2351860943, 0.2315282566, 0.2295545126,
1480  0.2274827082, 0.2253143564, 0.2241951244, 0.2230534566,
1481  0.2225907052, 0.2221245734, 0.2216551307, 0.2211824488,
1482  0.2207065981, 0.2202276534, 0.219745778, 0.2195038699, 0.2192613118,
1483  0.219017296, 0.21889384, 0.2187689601, 0.2186463949, 0.2186236698,
1484  0.2186023833, 0.2185832072, 0.2185670597, 0.2185551556,
1485  0.2185502469, 0.2185760597, 0.2185862168,
1486  0.2185411094}, {0.3746283234, 0.3744760286, 0.3744655082,
1487  0.3745713459, 0.3746804416, 0.3747239651, 0.3747616125,
1488  0.3747951976, 0.3748262688, 0.3748559959, 0.3750036033,
1489  0.3751595179, 0.3753190966, 0.3756378976, 0.3759558332,
1490  0.3762746082, 0.3769149521, 0.3775582079, 0.3782042318,
1491  0.3788529456, 0.3795041978, 0.3801578285, 0.3808136809,
1492  0.3824619707, 0.3841204813, 0.3874566765, 0.3907983942,
1493  0.3941199491, 0.4005962971, 0.4067113438, 0.4123795696,
1494  0.4175861754, 0.422352588, 0.426714443, 0.4307106786, 0.4343787455,
1495  0.4377527783, 0.4408631174, 0.4437364171, 0.4463959791,
1496  0.4522370945, 0.4571173234, 0.4612213527, 0.4646855141,
1497  0.4676122255, 0.4700795615, 0.47214769, 0.4738632779, 0.4752625561,
1498  0.4763734789, 0.4772172535, 0.4778094206, 0.4781606008,
1499  0.4782769831, 0.4781606008, 0.4778094206, 0.4772172535,
1500  0.4763734789, 0.4752625561, 0.4738632779, 0.47214769, 0.4700795615,
1501  0.4676122255, 0.4646855141, 0.4612213527, 0.4571173234,
1502  0.4522370945, 0.4463959791, 0.4437364171, 0.4408631174,
1503  0.4377527783, 0.4343787455, 0.4307106786, 0.426714443, 0.422352588,
1504  0.4175861754, 0.4123795696, 0.4067113438, 0.4005962971,
1505  0.3941199491, 0.3907983942, 0.3874566765, 0.3841204813,
1506  0.3824619707, 0.3808136809, 0.3801578285, 0.3795041978,
1507  0.3788529456, 0.3782042318, 0.3775582079, 0.3769149521,
1508  0.3762746082, 0.3759558332, 0.3756378976, 0.3753190966,
1509  0.3751595179, 0.3750036033, 0.3748559959, 0.3748262688,
1510  0.3747951976, 0.3747616125, 0.3747239651, 0.3746804416,
1511  0.3745713459, 0.3744655082, 0.3744760286,
1512  0.3746283234}, {0.5488977566, 0.5492725578, 0.5493796167,
1513  0.5493030521, 0.5492800515, 0.5493081779, 0.5493493533,
1514  0.5493946353, 0.549438419, 0.5494780738, 0.5496229054, 0.5497549686,
1515  0.5499025591, 0.5501989882, 0.5504901744, 0.5507853393,
1516  0.5513807914, 0.5519818189, 0.552589775, 0.5532041749, 0.5538251797,
1517  0.5544529382, 0.5550874672, 0.5567036937, 0.5583633611,
1518  0.5618146957, 0.5654450115, 0.5692386679, 0.5773386388,
1519  0.5859421423, 0.5945472028, 0.602787763, 0.6105064194, 0.6176644895,
1520  0.624277053, 0.6303804075, 0.6360171698, 0.641229749, 0.6460576806,
1521  0.6505367243, 0.6604082105, 0.6686938222, 0.6756913514,
1522  0.6816215439, 0.6866504101, 0.6909045159, 0.6944813958,
1523  0.6974567098, 0.6998892223, 0.7018243015, 0.7032963922,
1524  0.7043307557, 0.7049446682, 0.7051482024, 0.7049446682,
1525  0.7043307557, 0.7032963922, 0.7018243015, 0.6998892223,
1526  0.6974567098, 0.6944813958, 0.6909045159, 0.6866504101,
1527  0.6816215439, 0.6756913514, 0.6686938222, 0.6604082105,
1528  0.6505367243, 0.6460576806, 0.641229749, 0.6360171698, 0.6303804075,
1529  0.624277053, 0.6176644895, 0.6105064194, 0.602787763, 0.5945472028,
1530  0.5859421423, 0.5773386388, 0.5692386679, 0.5654450115,
1531  0.5618146957, 0.5583633611, 0.5567036937, 0.5550874672,
1532  0.5544529382, 0.5538251797, 0.5532041749, 0.552589775, 0.5519818189,
1533  0.5513807914, 0.5507853393, 0.5504901744, 0.5501989882,
1534  0.5499025591, 0.5497549686, 0.5496229054, 0.5494780738, 0.549438419,
1535  0.5493946353, 0.5493493533, 0.5493081779, 0.5492800515,
1536  0.5493030521, 0.5493796167, 0.5492725578,
1537  0.5488977566}, {0.7501379784, 0.7495636806, 0.749650308,
1538  0.7501258019, 0.7500613683, 0.7499927446, 0.7499667401, 0.749986257,
1539  0.7500353707, 0.7500943083, 0.7502378208, 0.7502955686,
1540  0.7504262429, 0.7506329733, 0.7508454096, 0.7510636293,
1541  0.7514901194, 0.7519267005, 0.7523658758, 0.75281185, 0.7532615237,
1542  0.7537170118, 0.7541777199, 0.7553533494, 0.7565672969,
1543  0.7591011388, 0.7618191441, 0.7646738706, 0.771240475, 0.7783465723,
1544  0.7875759366, 0.7980345082, 0.8085705185, 0.8186647248,
1545  0.8281387322, 0.8369567431, 0.8451396344, 0.8527290961,
1546  0.8597724928, 0.8663164947, 0.8807666598, 0.8929239587,
1547  0.9032139277, 0.9119531958, 0.9193796679, 0.9256743556,
1548  0.9309764881, 0.9353939337, 0.9390104311, 0.9418906437,
1549  0.9440837035, 0.9456256811, 0.946541273, 0.9468448909, 0.946541273,
1550  0.9456256811, 0.9440837035, 0.9418906437, 0.9390104311,
1551  0.9353939337, 0.9309764881, 0.9256743556, 0.9193796679,
1552  0.9119531958, 0.9032139277, 0.8929239587, 0.8807666598,
1553  0.8663164947, 0.8597724928, 0.8527290961, 0.8451396344,
1554  0.8369567431, 0.8281387322, 0.8186647248, 0.8085705185,
1555  0.7980345082, 0.7875759366, 0.7783465723, 0.771240475, 0.7646738706,
1556  0.7618191441, 0.7591011388, 0.7565672969, 0.7553533494,
1557  0.7541777199, 0.7537170118, 0.7532615237, 0.75281185, 0.7523658758,
1558  0.7519267005, 0.7514901194, 0.7510636293, 0.7508454096,
1559  0.7506329733, 0.7504262429, 0.7502955686, 0.7502378208,
1560  0.7500943083, 0.7500353707, 0.749986257, 0.7499667401, 0.7499927446,
1561  0.7500613683, 0.7501258019, 0.749650308, 0.7495636806,
1562  0.7501379784}, {0.9742529776, 0.9747874524, 0.9741123398,
1563  0.9741101898, 0.9745054107, 0.9743713094, 0.9742131924,
1564  0.9741459996, 0.9741878531, 0.9742927333, 0.9744241227,
1565  0.9744440584, 0.9745998745, 0.9746798313, 0.9748508069,
1566  0.9749764636, 0.9752738201, 0.9755817532, 0.9758699637,
1567  0.9761776339, 0.9764736452, 0.9767861418, 0.9770899129,
1568  0.9778706747, 0.9786413703, 0.9802309584, 0.982150519, 0.9839171716,
1569  0.987227465, 0.9938892699, 0.9973348177, 1.002960092, 1.013708296,
1570  1.025861928, 1.037903138, 1.049355648, 1.060088661, 1.07009284,
1571  1.079402597, 1.088066636, 1.107231852, 1.123387254, 1.137086935,
1572  1.148745393, 1.158673191, 1.167105446, 1.174222093, 1.180161946,
1573  1.185032451, 1.188916455, 1.191876898, 1.193960032, 1.195197574,
1574  1.195608054, 1.195197574, 1.193960032, 1.191876898, 1.188916455,
1575  1.185032451, 1.180161946, 1.174222093, 1.167105446, 1.158673191,
1576  1.148745393, 1.137086935, 1.123387254, 1.107231852, 1.088066636,
1577  1.079402597, 1.07009284, 1.060088661, 1.049355648, 1.037903138,
1578  1.025861928, 1.013708296, 1.002960092, 0.9973348177, 0.9938892699,
1579  0.987227465, 0.9839171716, 0.982150519, 0.9802309584, 0.9786413703,
1580  0.9778706747, 0.9770899129, 0.9767861418, 0.9764736452,
1581  0.9761776339, 0.9758699637, 0.9755817532, 0.9752738201,
1582  0.9749764636, 0.9748508069, 0.9746798313, 0.9745998745,
1583  0.9744440584, 0.9744241227, 0.9742927333, 0.9741878531,
1584  0.9741459996, 0.9742131924, 0.9743713094, 0.9745054107,
1585  0.9741101898, 0.9741123398, 0.9747874524,
1586  0.9742529776}, {1.211526857, 1.211922483, 1.212758151, 1.211726992,
1587  1.212482465, 1.212475394, 1.212205486, 1.212000716, 1.212018349,
1588  1.212199008, 1.212212997, 1.212444728, 1.212370608, 1.2125862,
1589  1.212619732, 1.212746897, 1.212984684, 1.213207534, 1.213402392,
1590  1.213636737, 1.213847925, 1.214157158, 1.214311053, 1.21508082,
1591  1.215773219, 1.216721426, 1.218690906, 1.219600693, 1.221394824,
1592  1.223150892, 1.228953387, 1.236823174, 1.230978076, 1.238359914,
1593  1.251235241, 1.264746546, 1.277799572, 1.290112987, 1.301635176,
1594  1.312389501, 1.33624286, 1.356406755, 1.373555087, 1.388197376,
1595  1.400713453, 1.411387828, 1.420435218, 1.428018603, 1.434261866,
1596  1.439258803, 1.443079447, 1.445774471, 1.447378225, 1.447910632,
1597  1.447378225, 1.445774471, 1.443079447, 1.439258803, 1.434261866,
1598  1.428018603, 1.420435218, 1.411387828, 1.400713453, 1.388197376,
1599  1.373555087, 1.356406755, 1.33624286, 1.312389501, 1.301635176,
1600  1.290112987, 1.277799572, 1.264746546, 1.251235241, 1.238359914,
1601  1.230978076, 1.236823174, 1.228953387, 1.223150892, 1.221394824,
1602  1.219600693, 1.218690906, 1.216721426, 1.215773219, 1.21508082,
1603  1.214311053, 1.214157158, 1.213847925, 1.213636737, 1.213402392,
1604  1.213207534, 1.212984684, 1.212746897, 1.212619732, 1.2125862,
1605  1.212370608, 1.212444728, 1.212212997, 1.212199008, 1.212018349,
1606  1.212000716, 1.212205486, 1.212475394, 1.212482465, 1.211726992,
1607  1.212758151, 1.211922483, 1.211526857}, {1.457166384, 1.455774437,
1608  1.45614065, 1.456163388, 1.456398915, 1.456702444, 1.456452029,
1609  1.456111048, 1.456084183, 1.456343126, 1.456203267, 1.456611834,
1610  1.456405008, 1.456495794, 1.456708475, 1.456856113, 1.45703245,
1611  1.457199255, 1.457216831, 1.457758397, 1.458078952, 1.458344132,
1612  1.458161964, 1.458541639, 1.4580717, 1.462140395, 1.464201092,
1613  1.463724506, 1.468574149, 1.46434673, 1.472722297, 1.467376603,
1614  1.483390561, 1.480075895, 1.470177613, 1.482565512, 1.497109984,
1615  1.511416992, 1.524995064, 1.537744972, 1.566154575, 1.590272672,
1616  1.610878824, 1.628579645, 1.643827476, 1.656957371, 1.668215944,
1617  1.677781064, 1.685775835, 1.692277814, 1.697328618, 1.700942134,
1618  1.7031156, 1.703841327, 1.7031156, 1.700942134, 1.697328618,
1619  1.692277814, 1.685775835, 1.677781064, 1.668215944, 1.656957371,
1620  1.643827476, 1.628579645, 1.610878824, 1.590272672, 1.566154575,
1621  1.537744972, 1.524995064, 1.511416992, 1.497109984, 1.482565512,
1622  1.470177613, 1.480075895, 1.483390561, 1.467376603, 1.472722297,
1623  1.46434673, 1.468574149, 1.463724506, 1.464201092, 1.462140395,
1624  1.4580717, 1.458541639, 1.458161964, 1.458344132, 1.458078952,
1625  1.457758397, 1.457216831, 1.457199255, 1.45703245, 1.456856113,
1626  1.456708475, 1.456495794, 1.456405008, 1.456611834, 1.456203267,
1627  1.456343126, 1.456084183, 1.456111048, 1.456452029, 1.456702444,
1628  1.456398915, 1.456163388, 1.45614065, 1.455774437, 1.457166384}
1629  };
1630 
1631  /* 3, 3 mode */
1632  const double reomegaqnm33[8][107] = { {0.445768, 0.452799, 0.456948, 0.460943, 0.462462, 0.462842,
1633  0.463095, 0.463269, 0.463394, 0.463488, 0.463746, 0.463886,
1634  0.463989, 0.464144, 0.464267, 0.464374, 0.464572, 0.464763,
1635  0.464952, 0.46514, 0.465329, 0.465518, 0.465707, 0.466182, 0.466657,
1636  0.467612, 0.468573, 0.46954, 0.471491, 0.473465, 0.475464,
1637  0.477487, 0.479535, 0.481609, 0.483709, 0.485837, 0.487991,
1638  0.490174, 0.492386, 0.494627, 0.500363, 0.5063, 0.512449, 0.518826,
1639  0.525445, 0.532323, 0.539479, 0.546934, 0.55471, 0.562834, 0.571335,
1640  0.580244, 0.5896, 0.599443, 0.609823, 0.620796, 0.632425, 0.644787,
1641  0.657972, 0.672086, 0.68726, 0.70365, 0.721455, 0.740921, 0.762369,
1642  0.786223, 0.813057, 0.843687, 0.857254, 0.871717, 0.887201,
1643  0.90386, 0.921885, 0.941521, 0.963088, 0.987016, 1.01391, 1.04464,
1644  1.08058, 1.1241, 1.14998, 1.17986, 1.21547, 1.23637, 1.26023,
1645  1.27086, 1.28227, 1.29462, 1.30812, 1.32308, 1.33999, 1.35965,
1646  1.37094, 1.38363, 1.39829, 1.40666, 1.41603, 1.42679, 1.42917,
1647  1.43164, 1.43422, 1.43692, 1.43975, 1.44591, 1.45295, 1.45695,
1648  1.46139}, {0.428357, 0.432238, 0.434351, 0.436362, 0.437184,
1649  0.437404, 0.437552, 0.437654, 0.437725, 0.437773, 0.437868,
1650  0.437898, 0.437929, 0.438015, 0.438115, 0.438217, 0.438421,
1651  0.438623, 0.438826, 0.43903, 0.439233, 0.439437, 0.439641, 0.440152,
1652  0.440665, 0.441694, 0.442729, 0.443771, 0.445872, 0.447999,
1653  0.45015, 0.452328, 0.454532, 0.456764, 0.459023, 0.461311, 0.463627,
1654  0.465974, 0.46835, 0.470758, 0.476918, 0.483289, 0.489884,
1655  0.496717, 0.503805, 0.511164, 0.518814, 0.526776, 0.535074,
1656  0.543734, 0.552785, 0.562261, 0.5722, 0.582644, 0.593642, 0.60525,
1657  0.617535, 0.630573, 0.644453, 0.659285, 0.675198, 0.692352,
1658  0.710943, 0.731221, 0.753507, 0.778225, 0.805952, 0.837504,
1659  0.851449, 0.866295, 0.882167, 0.89922, 0.917645, 0.937687, 0.959667,
1660  0.984015, 1.01133, 1.0425, 1.07889, 1.12285, 1.14897, 1.17907,
1661  1.21491, 1.23591, 1.25988, 1.27055, 1.28201, 1.2944, 1.30794,
1662  1.32294, 1.33989, 1.35958, 1.37089, 1.38359, 1.39826, 1.40664,
1663  1.41601, 1.42678, 1.42916, 1.43163, 1.43421, 1.43691, 1.43974,
1664  1.4459, 1.45295, 1.45695, 1.46139}, {0.390162, 0.390933, 0.390855,
1665  0.39013, 0.389593, 0.389452, 0.389377, 0.389349, 0.389352, 0.389374,
1666  0.389533, 0.389627, 0.38968, 0.38978, 0.389896, 0.390013, 0.390243,
1667  0.390473, 0.390704, 0.390935, 0.391167, 0.391398, 0.39163,
1668  0.392211, 0.392793, 0.393963, 0.395139, 0.396321, 0.398706,
1669  0.401118, 0.403557, 0.406025, 0.408522, 0.411048, 0.413604,
1670  0.416191, 0.41881, 0.42146, 0.424144, 0.426861, 0.433807, 0.44098,
1671  0.448397, 0.456071, 0.464019, 0.47226, 0.480815, 0.489704, 0.498954,
1672  0.50859, 0.518645, 0.529153, 0.540151, 0.551685, 0.563804,
1673  0.576567, 0.590041, 0.604302, 0.619445, 0.635578, 0.652833,
1674  0.671371, 0.691391, 0.713145, 0.736956, 0.763249, 0.792606,
1675  0.825846, 0.840483, 0.856032, 0.872619, 0.890397, 0.90956, 0.930355,
1676  0.953102, 0.978234, 1.00636, 1.03835, 1.07558, 1.12042, 1.14697,
1677  1.17752, 1.21379, 1.23502, 1.2592, 1.26995, 1.28149, 1.29396,
1678  1.30758, 1.32266, 1.33967, 1.35943, 1.37078, 1.38351, 1.3982,
1679  1.4066, 1.41598, 1.42676, 1.42914, 1.43162, 1.4342, 1.4369, 1.43973,
1680  1.44589, 1.45294, 1.45694, 1.46139}, {0.332321, 0.329612, 0.329447,
1681  0.330998, 0.331533, 0.331485, 0.331367, 0.331244, 0.331151,
1682  0.331101, 0.331226, 0.331354, 0.331387, 0.331504, 0.331643,
1683  0.331766, 0.332024, 0.33228, 0.332537, 0.332795, 0.333053, 0.333311,
1684  0.333569, 0.334216, 0.334865, 0.336168, 0.337478, 0.338796,
1685  0.341454, 0.344143, 0.346863, 0.349614, 0.352398, 0.355215,
1686  0.358066, 0.360951, 0.363872, 0.366829, 0.369823, 0.372855,
1687  0.380605, 0.388612, 0.39689, 0.405455, 0.414327, 0.423525, 0.43307,
1688  0.442986, 0.4533, 0.464039, 0.475237, 0.486928, 0.499155, 0.511962,
1689  0.525402, 0.539534, 0.554428, 0.570163, 0.586836, 0.604556, 0.62346,
1690  0.643711, 0.665511, 0.689115, 0.71485, 0.743145, 0.774586,
1691  0.809998, 0.82553, 0.841991, 0.859506, 0.878231, 0.898362, 0.920146,
1692  0.943908, 0.970086, 0.999286, 1.0324, 1.0708, 1.11686, 1.14404,
1693  1.17523, 1.21215, 1.23369, 1.25818, 1.26906, 1.28072, 1.2933,
1694  1.30704, 1.32223, 1.33936, 1.35922, 1.37061, 1.38339, 1.39812,
1695  1.40653, 1.41593, 1.42673, 1.42911, 1.43159, 1.43418, 1.43688,
1696  1.43971, 1.44588, 1.45294, 1.45694, 1.46138}, {0.279748, 0.281425,
1697  0.280003, 0.278496, 0.279479, 0.279701, 0.279679, 0.279534, 0.27938,
1698  0.279284, 0.279511, 0.279556, 0.279569, 0.279745, 0.279852,
1699  0.279994, 0.280246, 0.280507, 0.280766, 0.281026, 0.281285,
1700  0.281546, 0.281806, 0.282459, 0.283115, 0.284431, 0.285757,
1701  0.287091, 0.289787, 0.292519, 0.295288, 0.298095, 0.30094, 0.303825,
1702  0.306751, 0.309717, 0.312725, 0.315776, 0.318871, 0.322011,
1703  0.330062, 0.338415, 0.347087, 0.356096, 0.365463, 0.37521, 0.385359,
1704  0.395936, 0.406968, 0.418488, 0.430528, 0.443126, 0.456326,
1705  0.470174, 0.484725, 0.500042, 0.516195, 0.533269, 0.551359,
1706  0.570583, 0.591077, 0.61301, 0.636588, 0.662069, 0.689786, 0.720173,
1707  0.753822, 0.791564, 0.808064, 0.825515, 0.844044, 0.863808,
1708  0.885005, 0.907885, 0.932779, 0.960131, 0.990559, 1.02497, 1.06475,
1709  1.11229, 1.14026, 1.17226, 1.21, 1.23195, 1.25686, 1.26789, 1.2797,
1710  1.29245, 1.30633, 1.32167, 1.33893, 1.35893, 1.37038, 1.38322,
1711  1.39801, 1.40645, 1.41587, 1.42669, 1.42908, 1.43156, 1.43415,
1712  1.43685, 1.43969, 1.44587, 1.45293, 1.45693, 1.46137}, {0.239992,
1713  0.240995, 0.242946, 0.24156, 0.241854, 0.242213, 0.242269, 0.242117,
1714  0.241939, 0.241855, 0.242174, 0.24208, 0.242226, 0.242298,
1715  0.242438, 0.242546, 0.242783, 0.243024, 0.243261, 0.243498,
1716  0.243736, 0.243974, 0.244213, 0.244811, 0.245412, 0.246621, 0.24784,
1717  0.249069, 0.251558, 0.254089, 0.256662, 0.259279, 0.26194,
1718  0.264647, 0.2674, 0.2702, 0.273049, 0.275948, 0.278897, 0.281899,
1719  0.289636, 0.297725, 0.306186, 0.315041, 0.324312, 0.334027, 0.34421,
1720  0.354891, 0.366101, 0.377873, 0.390245, 0.403257, 0.416954,
1721  0.431386, 0.446612, 0.462696, 0.479713, 0.49775, 0.516906, 0.537303,
1722  0.559082, 0.582416, 0.607517, 0.634649, 0.66415, 0.696462,
1723  0.732182, 0.77215, 0.789586, 0.807999, 0.827516, 0.848298, 0.870543,
1724  0.894505, 0.920521, 0.949042, 0.980704, 1.01643, 1.05767, 1.10684,
1725  1.1357, 1.16864, 1.20737, 1.22983, 1.25522, 1.26646, 1.27846,
1726  1.29139, 1.30546, 1.32098, 1.33842, 1.35857, 1.3701, 1.38301,
1727  1.39787, 1.40634, 1.41579, 1.42664, 1.42903, 1.43152, 1.43411,
1728  1.43682, 1.43966, 1.44585, 1.45291, 1.45692, 1.46137}, {0.21884,
1729  0.216298, 0.216633, 0.217244, 0.216888, 0.217233, 0.217329,
1730  0.217189, 0.217034, 0.217006, 0.217217, 0.217255, 0.217293,
1731  0.217414, 0.217505, 0.217599, 0.217807, 0.218016, 0.218223,
1732  0.218427, 0.218635, 0.218841, 0.21905, 0.21957, 0.220094, 0.221148,
1733  0.222212, 0.223288, 0.22547, 0.227696, 0.229966, 0.232282, 0.234646,
1734  0.237057, 0.239517, 0.242028, 0.244591, 0.247207, 0.249877,
1735  0.252604, 0.259674, 0.267128, 0.274991, 0.283291, 0.292057,
1736  0.301319, 0.31111, 0.321465, 0.332419, 0.344012, 0.356285, 0.369284,
1737  0.383057, 0.39766, 0.413152, 0.429604, 0.447094, 0.465712,
1738  0.485563, 0.506772, 0.529486, 0.553883, 0.580183, 0.608655,
1739  0.639647, 0.673609, 0.711146, 0.753105, 0.771386, 0.790674,
1740  0.811095, 0.832808, 0.856013, 0.880965, 0.908002, 0.937583,
1741  0.970359, 1.00729, 1.04987, 1.10064, 1.13044, 1.16442, 1.20427,
1742  1.22731, 1.2533, 1.26476, 1.27699, 1.29015, 1.30444, 1.32016,
1743  1.3378, 1.35815, 1.36977, 1.38276, 1.3977, 1.40621, 1.4157, 1.42658,
1744  1.42898, 1.43147, 1.43407, 1.43678, 1.43963, 1.44582, 1.4529,
1745  1.45691, 1.46135}, {0.199814, 0.201353, 0.200132, 0.200956,
1746  0.200467, 0.200722, 0.200829, 0.200716, 0.200604, 0.200626,
1747  0.200705, 0.200826, 0.200822, 0.200914, 0.201004, 0.201103,
1748  0.201273, 0.201448, 0.201625, 0.2018, 0.201975, 0.202153, 0.202329,
1749  0.202773, 0.20322, 0.204121, 0.205032, 0.205953, 0.207826, 0.209742,
1750  0.211702, 0.213706, 0.215757, 0.217854, 0.220001, 0.222198,
1751  0.224447, 0.226749, 0.229105, 0.231518, 0.237809, 0.244492,
1752  0.251597, 0.25916, 0.267216, 0.275804, 0.284965, 0.294742, 0.305178,
1753  0.316322, 0.328221, 0.340928, 0.354499, 0.368992, 0.384475,
1754  0.401019, 0.418708, 0.437635, 0.45791, 0.479661, 0.50304, 0.528232,
1755  0.555461, 0.585008, 0.617226, 0.652577, 0.691676, 0.735379,
1756  0.754411, 0.774477, 0.795706, 0.818253, 0.842317, 0.868149,
1757  0.896082, 0.926573, 0.960272, 0.998162, 1.04182, 1.09394, 1.1246,
1758  1.15963, 1.20071, 1.22441, 1.25107, 1.2628, 1.2753, 1.28872,
1759  1.30326, 1.31923, 1.3371, 1.35766, 1.36938, 1.38248, 1.39751,
1760  1.40606, 1.41559, 1.4265, 1.42891, 1.43141, 1.43401, 1.43673,
1761  1.43959, 1.44579, 1.45288, 1.45689, 1.46134}
1762  };
1763 
1764  const double imomegaqnm33[8][107] = { {0.068612, 0.0735351, 0.0774984, 0.0829193, 0.0860369, 0.0870572,
1765  0.0878377, 0.0884398, 0.0889085, 0.0892767, 0.0902685, 0.0906386,
1766  0.0907974, 0.0909101, 0.0909414, 0.090952, 0.0909603, 0.0909664,
1767  0.0909729, 0.0909798, 0.090987, 0.0909942, 0.0910015, 0.0910197,
1768  0.0910378, 0.091074, 0.09111, 0.0911457, 0.0912166, 0.0912867,
1769  0.091356, 0.0914243, 0.0914917, 0.0915582, 0.0916236, 0.091688,
1770  0.0917514, 0.0918136, 0.0918746, 0.0919344, 0.0920784, 0.0922137,
1771  0.0923394, 0.0924547, 0.0925583, 0.0926492, 0.0927258, 0.0927867,
1772  0.0928302, 0.0928541, 0.0928562, 0.0928338, 0.092784, 0.092703,
1773  0.0925869, 0.0924305, 0.0922281, 0.0919726, 0.0916556, 0.0912666,
1774  0.0907928, 0.0902179, 0.0895213, 0.0886763, 0.087647, 0.0863849,
1775  0.0848213, 0.0828557, 0.0819248, 0.0808922, 0.0797413, 0.0784512,
1776  0.0769953, 0.075339, 0.0734361, 0.0712234, 0.0686106, 0.0654629,
1777  0.0615646, 0.056537, 0.0533881, 0.0496087, 0.0449046, 0.0420439,
1778  0.0386881, 0.0371631, 0.0355053, 0.0336873, 0.0316714, 0.0294027,
1779  0.0267968, 0.023711, 0.0219107, 0.0198652, 0.0174725, 0.0160908,
1780  0.014533, 0.0127266, 0.0123252, 0.011907, 0.0114701, 0.011012,
1781  0.0105299, 0.00947732, 0.00826624, 0.0075764,
1782  0.00680679}, {0.277496, 0.278402, 0.278809, 0.278955, 0.278824,
1783  0.278742, 0.278664, 0.278594, 0.278534, 0.278482, 0.278334,
1784  0.278289, 0.278281, 0.278294, 0.278307, 0.278318, 0.278336,
1785  0.278354, 0.278373, 0.278391, 0.278409, 0.278427, 0.278446,
1786  0.278491, 0.278537, 0.278627, 0.278716, 0.278805, 0.27898, 0.279153,
1787  0.279323, 0.279489, 0.279653, 0.279813, 0.27997, 0.280123,
1788  0.280273, 0.280419, 0.280561, 0.280699, 0.281026, 0.281324,
1789  0.281591, 0.281825, 0.28202, 0.282175, 0.282285, 0.282345, 0.28235,
1790  0.282293, 0.282168, 0.281967, 0.281681, 0.281298, 0.280807,
1791  0.280191, 0.279434, 0.278515, 0.277407, 0.27608, 0.274494, 0.272602,
1792  0.27034, 0.26763, 0.264363, 0.260394, 0.255518, 0.249435, 0.246568,
1793  0.243397, 0.239871, 0.235928, 0.231489, 0.226451, 0.220675,
1794  0.213971, 0.206071, 0.19657, 0.184822, 0.169692, 0.160224, 0.148867,
1795  0.134739, 0.12615, 0.116076, 0.111499, 0.106524, 0.101069,
1796  0.0950193, 0.088212, 0.0803933, 0.0711348, 0.0657335, 0.0595967,
1797  0.0524182, 0.0482728, 0.0435993, 0.03818, 0.0369756, 0.0357211,
1798  0.0344103, 0.0330362, 0.0315898, 0.028432, 0.0247987, 0.0227292,
1799  0.0204204}, {0.486993, 0.484741, 0.483427, 0.482389, 0.482301,
1800  0.482372, 0.48246, 0.482542, 0.482611, 0.482664, 0.482744, 0.482718,
1801  0.482702, 0.482709, 0.482722, 0.482729, 0.482743, 0.482759,
1802  0.482774, 0.482789, 0.482804, 0.482819, 0.482834, 0.482871,
1803  0.482907, 0.48298, 0.483051, 0.483121, 0.483256, 0.483386, 0.483511,
1804  0.48363, 0.483742, 0.483849, 0.483949, 0.484043, 0.48413, 0.48421,
1805  0.484283, 0.484348, 0.484477, 0.484555, 0.484575, 0.484535,
1806  0.484428, 0.484247, 0.483987, 0.483638, 0.483192, 0.48264, 0.481968,
1807  0.481164, 0.480211, 0.479093, 0.477786, 0.476267, 0.474506,
1808  0.472466, 0.470105, 0.467369, 0.464195, 0.4605, 0.456181, 0.451103,
1809  0.44509, 0.437899, 0.42919, 0.418467, 0.413455, 0.407937, 0.401829,
1810  0.39503, 0.387407, 0.37879, 0.36895, 0.357573, 0.344212, 0.328195,
1811  0.308447, 0.283082, 0.267235, 0.248247, 0.224647, 0.210309,
1812  0.193501, 0.185866, 0.177568, 0.168469, 0.158382, 0.147032,
1813  0.133998, 0.118564, 0.10956, 0.0993313, 0.0873659, 0.0804562,
1814  0.0726665, 0.0636339, 0.0616265, 0.0595355, 0.0573509, 0.0550606,
1815  0.0526499, 0.0473868, 0.0413313, 0.0378821, 0.034034}, {0.709974,
1816  0.711601, 0.713499, 0.714385, 0.713785, 0.713546, 0.713418,
1817  0.713383, 0.713411, 0.713468, 0.713655, 0.713595, 0.713563,
1818  0.713584, 0.713571, 0.713561, 0.71355, 0.713535, 0.713522, 0.713507,
1819  0.713493, 0.713479, 0.713465, 0.713428, 0.713392, 0.713317,
1820  0.713241, 0.713162, 0.712999, 0.712828, 0.712649, 0.712461,
1821  0.712264, 0.712058, 0.711843, 0.711618, 0.711383, 0.711138,
1822  0.710882, 0.710616, 0.709899, 0.709105, 0.708229, 0.707264,
1823  0.706201, 0.705033, 0.703748, 0.702336, 0.700785, 0.699079,
1824  0.697202, 0.695135, 0.692855, 0.690337, 0.68755, 0.684459, 0.68102,
1825  0.677183, 0.672887, 0.668056, 0.662599, 0.656401, 0.649315,
1826  0.641153, 0.631664, 0.620511, 0.607221, 0.591101, 0.583641,
1827  0.575473, 0.566484, 0.556529, 0.545428, 0.532943, 0.518759,
1828  0.502439, 0.48336, 0.460589, 0.432625, 0.396831, 0.37452, 0.347819,
1829  0.314676, 0.294558, 0.270986, 0.260282, 0.248651, 0.235902,
1830  0.221769, 0.20587, 0.187614, 0.166001, 0.153393, 0.13907, 0.122317,
1831  0.112642, 0.101735, 0.0890889, 0.0862783, 0.0833507, 0.080292,
1832  0.0770855, 0.0737103, 0.0663418, 0.057864, 0.053035,
1833  0.0476477}, {0.972477, 0.969229, 0.96766, 0.969029, 0.969442,
1834  0.969155, 0.968886, 0.968746, 0.968738, 0.968815, 0.969029,
1835  0.968878, 0.968919, 0.968877, 0.968857, 0.968828, 0.968768,
1836  0.968706, 0.968649, 0.968589, 0.968529, 0.96847, 0.96841, 0.96826,
1837  0.96811, 0.967806, 0.9675, 0.96719, 0.966561, 0.96592, 0.965265,
1838  0.964597, 0.963916, 0.96322, 0.962509, 0.961784, 0.961043, 0.960287,
1839  0.959514, 0.958725, 0.956678, 0.954518, 0.952237, 0.949827,
1840  0.947277, 0.944577, 0.941715, 0.938677, 0.935446, 0.932005,
1841  0.928331, 0.924401, 0.920185, 0.915649, 0.910755, 0.905456,
1842  0.899695, 0.893406, 0.88651, 0.878908, 0.870479, 0.861073, 0.850501,
1843  0.838516, 0.824795, 0.808901, 0.790225, 0.767883, 0.757639,
1844  0.746483, 0.73427, 0.720819, 0.7059, 0.689212, 0.670355, 0.648776,
1845  0.623682, 0.593881, 0.557455, 0.511016, 0.482143, 0.44764, 0.404868,
1846  0.378929, 0.348555, 0.334768, 0.319791, 0.303378, 0.285189,
1847  0.264731, 0.241246, 0.213447, 0.197233, 0.178815, 0.157271,
1848  0.144831, 0.130807, 0.114545, 0.110932, 0.107167, 0.103234,
1849  0.0991113, 0.0947715, 0.0852972, 0.0743968, 0.068188,
1850  0.0612614}, {1.23488, 1.2385, 1.23757, 1.23638, 1.23735, 1.23719,
1851  1.23689, 1.23671, 1.23672, 1.23684, 1.23689, 1.23686, 1.23687,
1852  1.23681, 1.23674, 1.23671, 1.2366, 1.23651, 1.23641, 1.23631,
1853  1.23622, 1.23612, 1.23602, 1.23578, 1.23553, 1.23504, 1.23454,
1854  1.23403, 1.23301, 1.23196, 1.23088, 1.22979, 1.22867, 1.22753,
1855  1.22637, 1.22518, 1.22396, 1.22272, 1.22145, 1.22016, 1.21681,
1856  1.21328, 1.20956, 1.20564, 1.20152, 1.19717, 1.19258, 1.18775,
1857  1.18264, 1.17724, 1.17153, 1.16546, 1.15902, 1.15215, 1.14481,
1858  1.13695, 1.12848, 1.11934, 1.10942, 1.09859, 1.08672, 1.07361,
1859  1.05902, 1.04265, 1.02409, 1.00282, 0.978074, 0.948772, 0.935434,
1860  0.920971, 0.905209, 0.887929, 0.868853, 0.847622, 0.823753,
1861  0.796583, 0.765161, 0.728048, 0.682917, 0.625639, 0.590118,
1862  0.547732, 0.49525, 0.463448, 0.42623, 0.409344, 0.391005, 0.370913,
1863  0.348652, 0.323623, 0.294897, 0.260904, 0.241081, 0.218564,
1864  0.192229, 0.177023, 0.159881, 0.140004, 0.135587, 0.130985,
1865  0.126178, 0.121138, 0.115834, 0.104253, 0.09093, 0.0833412,
1866  0.0748751}, {1.50812, 1.50714, 1.50886, 1.50765, 1.50833, 1.50831,
1867  1.50805, 1.5079, 1.50794, 1.50808, 1.50796, 1.50805, 1.50794,
1868  1.50791, 1.50787, 1.50779, 1.50768, 1.50756, 1.50745, 1.50733,
1869  1.50721, 1.50709, 1.50697, 1.50667, 1.50637, 1.50577, 1.50515,
1870  1.50453, 1.50326, 1.50195, 1.50061, 1.49924, 1.49784, 1.49639,
1871  1.49491, 1.4934, 1.49185, 1.49025, 1.48862, 1.48695, 1.4826,
1872  1.47798, 1.47308, 1.46789, 1.46239, 1.45657, 1.45042, 1.44391,
1873  1.43702, 1.42973, 1.42201, 1.41383, 1.40515, 1.39591, 1.38607,
1874  1.37555, 1.36428, 1.35215, 1.33904, 1.32481, 1.30928, 1.29221,
1875  1.27333, 1.25226, 1.22852, 1.20145, 1.17016, 1.13335, 1.11668,
1876  1.09865, 1.07906, 1.05766, 1.03413, 1.00803, 0.978819, 0.945725,
1877  0.907651, 0.862934, 0.808869, 0.7406, 0.698384, 0.648072, 0.585828,
1878  0.54813, 0.50403, 0.484027, 0.462309, 0.43852, 0.412171, 0.382553,
1879  0.348572, 0.308374, 0.284937, 0.258319, 0.227191, 0.209218,
1880  0.188957, 0.165464, 0.160243, 0.154805, 0.149123, 0.143167,
1881  0.136898, 0.123211, 0.107464, 0.0984948, 0.102103}, {1.77947,
1882  1.77829, 1.77828, 1.77845, 1.7786, 1.77868, 1.7785, 1.77838,
1883  1.77844, 1.77854, 1.77842, 1.77841, 1.77841, 1.77834, 1.77827,
1884  1.7782, 1.77808, 1.77795, 1.77783, 1.7777, 1.77757, 1.77744,
1885  1.77732, 1.77699, 1.77667, 1.77601, 1.77534, 1.77466, 1.77327,
1886  1.77183, 1.77035, 1.76883, 1.76726, 1.76564, 1.76398, 1.76226,
1887  1.7605, 1.75868, 1.75682, 1.75489, 1.74985, 1.74445, 1.73867,
1888  1.73249, 1.72589, 1.71886, 1.71137, 1.7034, 1.69493, 1.68592,
1889  1.67635, 1.66618, 1.65536, 1.64384, 1.63157, 1.61846, 1.60441,
1890  1.58931, 1.57303, 1.55539, 1.53617, 1.5151, 1.49185, 1.46597,
1891  1.43689, 1.40384, 1.36575, 1.32111, 1.30093, 1.27916, 1.25555,
1892  1.22981, 1.20156, 1.17032, 1.13545, 1.09609, 1.05101, 0.998352,
1893  0.935078, 0.85569, 0.806777, 0.748562, 0.676569, 0.632966, 0.58196,
1894  0.558828, 0.533715, 0.506213, 0.475757, 0.441533, 0.40228, 0.355861,
1895  0.328804, 0.29808, 0.262156, 0.241415, 0.218035, 0.190926,
1896  0.184902, 0.178626, 0.17207, 0.165197, 0.157962, 0.142169, 0.123998,
1897  0.113649, 0.115718}
1898  };
1899 
1900  /* 4, 4 mode */
1901  const double reomegaqnm44[8][107] = { {0.603485, 0.613847, 0.619636, 0.623952, 0.624219, 0.623894,
1902  0.623504, 0.623122, 0.62278, 0.622487, 0.621648, 0.621375, 0.621309,
1903  0.621365, 0.621483, 0.621613, 0.621877, 0.622141, 0.622404,
1904  0.622667, 0.62293, 0.623194, 0.623458, 0.624119, 0.624781, 0.626113,
1905  0.627452, 0.628799, 0.631518, 0.634269, 0.637054, 0.639872,
1906  0.642726, 0.645615, 0.648541, 0.651503, 0.654504, 0.657544,
1907  0.660623, 0.663743, 0.671728, 0.679989, 0.688543, 0.697411,
1908  0.706611, 0.716168, 0.726107, 0.736455, 0.747243, 0.758508,
1909  0.770286, 0.782624, 0.795569, 0.809178, 0.823517, 0.83866, 0.854693,
1910  0.871718, 0.889853, 0.909242, 0.930054, 0.9525, 0.976839, 1.0034,
1911  1.03259, 1.06498, 1.10131, 1.14265, 1.16092, 1.18036, 1.20114,
1912  1.22345, 1.24755, 1.27374, 1.30245, 1.33422, 1.36984, 1.41042,
1913  1.45773, 1.51478, 1.54862, 1.58759, 1.6339, 1.66102, 1.69194,
1914  1.7057, 1.72045, 1.73641, 1.75384, 1.77314, 1.79492, 1.82022,
1915  1.83474, 1.85104, 1.86985, 1.8806, 1.8926, 1.9064, 1.90945, 1.91261,
1916  1.91592, 1.91937, 1.92299, 1.93088, 1.93989, 1.945,
1917  1.95068}, {0.59231, 0.596523, 0.598412, 0.599977, 0.600617,
1918  0.600806, 0.600947, 0.601053, 0.601136, 0.601202, 0.601389,
1919  0.601485, 0.601558, 0.601693, 0.601828, 0.601964, 0.602238,
1920  0.602511, 0.602785, 0.60306, 0.603334, 0.603609, 0.603884, 0.604574,
1921  0.605265, 0.606653, 0.60805, 0.609455, 0.61229, 0.615158, 0.618061,
1922  0.620998, 0.623972, 0.626982, 0.630029, 0.633115, 0.63624,
1923  0.639405, 0.64261, 0.645858, 0.654166, 0.662758, 0.671651, 0.680865,
1924  0.69042, 0.700341, 0.710653, 0.721383, 0.732565, 0.744232,
1925  0.756425, 0.769188, 0.782571, 0.796632, 0.811434, 0.827055,
1926  0.843581, 0.861114, 0.879773, 0.899703, 0.921074, 0.944098,
1927  0.969034, 0.996209, 1.02604, 1.05909, 1.09611, 1.13816, 1.15671,
1928  1.17644, 1.19752, 1.22013, 1.24453, 1.27103, 1.30005, 1.33214,
1929  1.36806, 1.40896, 1.45658, 1.51396, 1.54795, 1.58707, 1.63353,
1930  1.66073, 1.69172, 1.7055, 1.72028, 1.73626, 1.75372, 1.77304,
1931  1.79485, 1.82017, 1.8347, 1.85101, 1.86983, 1.88058, 1.89259,
1932  1.90639, 1.90944, 1.91261, 1.91591, 1.91936, 1.92299, 1.93087,
1933  1.93989, 1.945, 1.95068}, {0.559386, 0.561881, 0.562985, 0.563673,
1934  0.563747, 0.563732, 0.563712, 0.563695, 0.563683, 0.563678,
1935  0.563718, 0.563794, 0.563872, 0.564021, 0.564168, 0.564316,
1936  0.564612, 0.564908, 0.565204, 0.565501, 0.565798, 0.566096,
1937  0.566394, 0.567139, 0.567887, 0.56939, 0.570901, 0.57242, 0.575484,
1938  0.578584, 0.58172, 0.584892, 0.588102, 0.59135, 0.594637, 0.597965,
1939  0.601333, 0.604743, 0.608195, 0.611692, 0.62063, 0.629865, 0.639415,
1940  0.649299, 0.65954, 0.670161, 0.681189, 0.692653, 0.704586,
1941  0.717023, 0.730006, 0.743579, 0.757794, 0.77271, 0.788392, 0.804918,
1942  0.822375, 0.840868, 0.860518, 0.88147, 0.903897, 0.928012,
1943  0.954076, 0.982419, 1.01346, 1.04777, 1.08608, 1.12947, 1.14857,
1944  1.16887, 1.19051, 1.21369, 1.23867, 1.26576, 1.29538, 1.32806,
1945  1.36459, 1.4061, 1.45434, 1.51232, 1.54662, 1.58604, 1.6328,
1946  1.66014, 1.69127, 1.70511, 1.71994, 1.73598, 1.75348, 1.77286,
1947  1.79471, 1.82008, 1.83463, 1.85096, 1.8698, 1.88055, 1.89257,
1948  1.90638, 1.90943, 1.9126, 1.9159, 1.91935, 1.92298, 1.93087,
1949  1.93989, 1.945, 1.95068}, {0.514416, 0.513669, 0.512866, 0.5122,
1950  0.512256, 0.512336, 0.512404, 0.512455, 0.512488, 0.51251, 0.512565,
1951  0.51264, 0.512726, 0.512889, 0.513051, 0.513214, 0.51354, 0.513866,
1952  0.514193, 0.51452, 0.514848, 0.515175, 0.515503, 0.516325,
1953  0.517149, 0.518804, 0.520467, 0.522139, 0.525511, 0.52892, 0.532367,
1954  0.535852, 0.539377, 0.542943, 0.546549, 0.550198, 0.553889,
1955  0.557625, 0.561406, 0.565233, 0.575009, 0.585097, 0.595517,
1956  0.606289, 0.617438, 0.628986, 0.640963, 0.653399, 0.666327,
1957  0.679785, 0.693815, 0.708464, 0.723784, 0.739837, 0.75669, 0.774421,
1958  0.793122, 0.812899, 0.833875, 0.856197, 0.880043, 0.905628,
1959  0.933216, 0.96314, 0.995828, 1.03184, 1.07193, 1.11717, 1.13703,
1960  1.1581, 1.18052, 1.20451, 1.2303, 1.25821, 1.28866, 1.32219,
1961  1.35958, 1.40195, 1.45106, 1.50993, 1.54467, 1.58453, 1.63172,
1962  1.65927, 1.69061, 1.70453, 1.71944, 1.73555, 1.75313, 1.77258,
1963  1.79451, 1.81994, 1.83452, 1.85088, 1.86975, 1.88051, 1.89254,
1964  1.90636, 1.90941, 1.91258, 1.91589, 1.91934, 1.92297, 1.93086,
1965  1.93988, 1.94499, 1.95068}, {0.454601, 0.454746, 0.455842, 0.456343,
1966  0.456046, 0.455998, 0.456018, 0.456071, 0.456127, 0.456171,
1967  0.456246, 0.456327, 0.456423, 0.456596, 0.456773, 0.456949,
1968  0.457302, 0.457655, 0.458009, 0.458363, 0.458717, 0.459072,
1969  0.459427, 0.460317, 0.461208, 0.462999, 0.464799, 0.466609,
1970  0.470257, 0.473946, 0.477675, 0.481446, 0.485259, 0.489115,
1971  0.493016, 0.496962, 0.500954, 0.504993, 0.509081, 0.513219,
1972  0.523786, 0.534689, 0.545948, 0.557585, 0.569625, 0.582093, 0.59502,
1973  0.608436, 0.622378, 0.636885, 0.652, 0.667772, 0.684256, 0.701516,
1974  0.71962, 0.738651, 0.758702, 0.779882, 0.802317, 0.82616, 0.851591,
1975  0.878829, 0.908143, 0.939873, 0.974449, 1.01244, 1.05461, 1.10202,
1976  1.12279, 1.14477, 1.16814, 1.19308, 1.21984, 1.24875, 1.28021,
1977  1.31477, 1.35322, 1.39666, 1.44687, 1.50684, 1.54214, 1.58256,
1978  1.63031, 1.65813, 1.68974, 1.70376, 1.71878, 1.73499, 1.75267,
1979  1.77222, 1.79424, 1.81975, 1.83438, 1.85077, 1.86967, 1.88046,
1980  1.8925, 1.90633, 1.90939, 1.91256, 1.91587, 1.91932, 1.92296,
1981  1.93085, 1.93987, 1.94499, 1.95067}, {0.405546, 0.404573, 0.403366,
1982  0.404025, 0.404115, 0.403989, 0.40394, 0.403971, 0.404037, 0.404098,
1983  0.40416, 0.404265, 0.404355, 0.404535, 0.404715, 0.404897, 0.40526,
1984  0.405624, 0.405988, 0.406353, 0.406718, 0.407083, 0.407449,
1985  0.408365, 0.409284, 0.411129, 0.412986, 0.414853, 0.418619, 0.42243,
1986  0.426286, 0.430188, 0.434137, 0.438134, 0.44218, 0.446277,
1987  0.450425, 0.454625, 0.458878, 0.463187, 0.474206, 0.485594,
1988  0.497376, 0.509573, 0.522212, 0.535321, 0.54893, 0.563075, 0.577791,
1989  0.593121, 0.609109, 0.625808, 0.643274, 0.661572, 0.680777,
1990  0.700971, 0.722252, 0.744732, 0.768542, 0.793839, 0.820807,
1991  0.849672, 0.880708, 0.914263, 0.950774, 0.990817, 1.03516, 1.0849,
1992  1.10664, 1.12961, 1.15399, 1.17998, 1.20782, 1.23782, 1.27041,
1993  1.30613, 1.34576, 1.39042, 1.44188, 1.50314, 1.53909, 1.58017,
1994  1.62858, 1.65673, 1.68866, 1.70281, 1.71796, 1.7343, 1.7521,
1995  1.77176, 1.7939, 1.81952, 1.83419, 1.85064, 1.86958, 1.88039,
1996  1.89245, 1.9063, 1.90936, 1.91253, 1.91584, 1.9193, 1.92294,
1997  1.93083, 1.93986, 1.94498, 1.95067}, {0.35976, 0.362048, 0.362088,
1998  0.361405, 0.361838, 0.361724, 0.361635, 0.361653, 0.361731,
1999  0.361798, 0.361829, 0.361951, 0.362022, 0.362204, 0.362384,
2000  0.362559, 0.362914, 0.363269, 0.363624, 0.36398, 0.364336, 0.364693,
2001  0.36505, 0.365945, 0.366843, 0.368648, 0.370465, 0.372293,
2002  0.375986, 0.379729, 0.383522, 0.387367, 0.391264, 0.395214, 0.39922,
2003  0.403281, 0.4074, 0.411576, 0.415813, 0.42011, 0.431129, 0.44256,
2004  0.454427, 0.466756, 0.479575, 0.492914, 0.506807, 0.521289,
2005  0.536401, 0.552185, 0.568691, 0.585972, 0.604089, 0.623109,
2006  0.643109, 0.664176, 0.686412, 0.709933, 0.734875, 0.761399,
2007  0.789696, 0.819999, 0.85259, 0.887824, 0.92615, 0.968153, 1.01462,
2008  1.06665, 1.08936, 1.11334, 1.13875, 1.16581, 1.19475, 1.22589,
2009  1.25966, 1.29659, 1.33748, 1.38345, 1.43625, 1.49892, 1.53559,
2010  1.57741, 1.62657, 1.6551, 1.6874, 1.7017, 1.717, 1.73348, 1.75142,
2011  1.77123, 1.79349, 1.81924, 1.83398, 1.85048, 1.86948, 1.8803,
2012  1.89239, 1.90626, 1.90932, 1.9125, 1.91581, 1.91928, 1.92291,
2013  1.93082, 1.93985, 1.94497, 1.95066},
2014  {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}
2015  };
2016 
2017  const double imomegaqnm44[8][107] = { {0.0472887, 0.0570846, 0.0652857, 0.0769202, 0.0835313, 0.0855743,
2018  0.0870596, 0.0881437, 0.0889418, 0.0895359, 0.0909619, 0.0914196,
2019  0.0916056, 0.091741, 0.0917845, 0.0918026, 0.0918186, 0.0918281,
2020  0.0918366, 0.0918448, 0.0918531, 0.0918614, 0.0918696, 0.0918903,
2021  0.0919109, 0.0919521, 0.0919931, 0.092034, 0.0921151, 0.0921956,
2022  0.0922753, 0.0923543, 0.0924324, 0.0925097, 0.0925861, 0.0926616,
2023  0.0927361, 0.0928096, 0.0928821, 0.0929535, 0.0931268, 0.093292,
2024  0.0934484, 0.0935949, 0.0937302, 0.0938532, 0.0939623, 0.0940559,
2025  0.0941321, 0.0941887, 0.0942233, 0.094233, 0.0942145, 0.094164,
2026  0.0940768, 0.0939478, 0.0937705, 0.0935374, 0.0932393, 0.092865,
2027  0.0924006, 0.0918287, 0.0911274, 0.0902679, 0.0892124, 0.0879094,
2028  0.086287, 0.0842401, 0.0832692, 0.0821917, 0.0809905, 0.0796442,
2029  0.0781255, 0.0763992, 0.0744185, 0.0721192, 0.0694103, 0.066156,
2030  0.0621396, 0.056982, 0.0537633, 0.0499111, 0.0451315, 0.0422323,
2031  0.0388376, 0.037297, 0.0356236, 0.0337901, 0.0317587, 0.0294747,
2032  0.0268536, 0.0237529, 0.0219453, 0.0198926, 0.0174928, 0.0161075,
2033  0.0145463, 0.0127365, 0.0123344, 0.0119155, 0.0114779, 0.0110192,
2034  0.0105364, 0.00948248, 0.00827008, 0.00757959,
2035  0.00680933}, {0.267496, 0.27243, 0.275117, 0.277412, 0.278166,
2036  0.278332, 0.278431, 0.278489, 0.278523, 0.278542, 0.278554,
2037  0.278543, 0.278539, 0.278544, 0.278555, 0.278567, 0.27859, 0.278613,
2038  0.278636, 0.278659, 0.278682, 0.278704, 0.278727, 0.278784,
2039  0.278841, 0.278955, 0.279068, 0.27918, 0.279403, 0.279623, 0.279841,
2040  0.280057, 0.28027, 0.28048, 0.280687, 0.280892, 0.281093, 0.281291,
2041  0.281485, 0.281676, 0.282137, 0.282572, 0.282979, 0.283355,
2042  0.283696, 0.283998, 0.284257, 0.284467, 0.284624, 0.284721,
2043  0.284749, 0.284701, 0.284567, 0.284334, 0.28399, 0.283519, 0.282901,
2044  0.282113, 0.281129, 0.279913, 0.278426, 0.276614, 0.274412,
2045  0.271733, 0.268465, 0.264452, 0.25948, 0.253233, 0.250278, 0.247003,
2046  0.243357, 0.239276, 0.234678, 0.229458, 0.223476, 0.216539,
2047  0.208375, 0.198576, 0.186494, 0.170992, 0.161324, 0.149756,
2048  0.135408, 0.126707, 0.116519, 0.111896, 0.106875, 0.101374,
2049  0.0952787, 0.0884259, 0.0805622, 0.0712595, 0.0658364, 0.0596782,
2050  0.0524786, 0.0483228, 0.043639, 0.0382095, 0.0370031, 0.0357465,
2051  0.0344338, 0.0330576, 0.0316092, 0.0284475, 0.0248103, 0.0227388,
2052  0.020428}, {0.476992, 0.476552, 0.476059, 0.475354, 0.475023,
2053  0.474945, 0.474902, 0.47488, 0.474873, 0.474873, 0.474904, 0.474923,
2054  0.474932, 0.474945, 0.47496, 0.474975, 0.475006, 0.475036,
2055  0.475066, 0.475097, 0.475127, 0.475157, 0.475187, 0.475263,
2056  0.475338, 0.475487, 0.475635, 0.475782, 0.476073, 0.476359,
2057  0.476641, 0.476918, 0.47719, 0.477456, 0.477718, 0.477973, 0.478223,
2058  0.478467, 0.478704, 0.478936, 0.479483, 0.479984, 0.480434,
2059  0.480828, 0.48116, 0.481423, 0.48161, 0.481712, 0.481721, 0.481624,
2060  0.48141, 0.481064, 0.48057, 0.479908, 0.479056, 0.477986, 0.476666,
2061  0.47506, 0.47312, 0.470791, 0.468003, 0.464669, 0.460679, 0.45589,
2062  0.450113, 0.44309, 0.434465, 0.423712, 0.41865, 0.413055, 0.406842,
2063  0.399905, 0.392108, 0.383276, 0.373175, 0.361487, 0.347759,
2064  0.331313, 0.311071, 0.28514, 0.268985, 0.249669, 0.225726, 0.21121,
2065  0.194221, 0.186512, 0.17814, 0.168968, 0.158807, 0.147383, 0.134275,
2066  0.118768, 0.109729, 0.099465, 0.0874652, 0.0805385, 0.072732,
2067  0.0636828, 0.0616721, 0.0595777, 0.0573898, 0.0550962, 0.0526822,
2068  0.0474125, 0.0413505, 0.037898, 0.0340467}, {0.688887, 0.687276,
2069  0.68687, 0.687194, 0.687484, 0.687529, 0.687535, 0.687523, 0.687504,
2070  0.687487, 0.687464, 0.68748, 0.687488, 0.687497, 0.687509,
2071  0.687521, 0.687544, 0.687567, 0.68759, 0.687613, 0.687636, 0.687658,
2072  0.687681, 0.687738, 0.687794, 0.687905, 0.688015, 0.688122,
2073  0.688333, 0.688537, 0.688734, 0.688923, 0.689105, 0.689278,
2074  0.689444, 0.689601, 0.689749, 0.689889, 0.690018, 0.690138,
2075  0.690394, 0.690579, 0.69069, 0.690717, 0.690652, 0.690487, 0.690211,
2076  0.689812, 0.689276, 0.688589, 0.687732, 0.686685, 0.685425,
2077  0.683924, 0.682151, 0.680068, 0.677629, 0.674782, 0.671462,
2078  0.667589, 0.663066, 0.657772, 0.651551, 0.644203, 0.635463,
2079  0.624972, 0.612229, 0.596503, 0.589146, 0.581044, 0.572077,
2080  0.562097, 0.550915, 0.538287, 0.523888, 0.507273, 0.48781, 0.464555,
2081  0.436002, 0.399509, 0.376808, 0.349693, 0.316109, 0.295761,
2082  0.271954, 0.261154, 0.249426, 0.236578, 0.222347, 0.206349,
2083  0.187993, 0.166281, 0.153625, 0.139254, 0.122453, 0.112755,
2084  0.101826, 0.0891563, 0.0863413, 0.0834091, 0.080346, 0.0771349,
2085  0.0737552, 0.0663776, 0.0578907, 0.0530572, 0.0476654}, {0.918235,
2086  0.920515, 0.920895, 0.920137, 0.920012, 0.920094, 0.920167,
2087  0.920207, 0.920214, 0.920202, 0.920149, 0.920166, 0.920164, 0.92016,
2088  0.920158, 0.920156, 0.920152, 0.920148, 0.920144, 0.92014,
2089  0.920136, 0.920132, 0.920127, 0.920116, 0.920104, 0.920079,
2090  0.920051, 0.920022, 0.919956, 0.919881, 0.919796, 0.919702,
2091  0.919597, 0.919482, 0.919356, 0.919218, 0.919069, 0.918908,
2092  0.918734, 0.918547, 0.91802, 0.917401, 0.916681, 0.915851, 0.9149,
2093  0.913815, 0.912584, 0.91119, 0.909617, 0.907843, 0.905847, 0.903603,
2094  0.901078, 0.898239, 0.895043, 0.891442, 0.887378, 0.88278,
2095  0.877566, 0.871633, 0.864855, 0.857075, 0.848091, 0.837647, 0.8254,
2096  0.81089, 0.79347, 0.772205, 0.762324, 0.751485, 0.739534, 0.72628,
2097  0.711484, 0.694831, 0.675907, 0.654142, 0.628729, 0.598457, 0.5614,
2098  0.514171, 0.484847, 0.449863, 0.406581, 0.380377, 0.349729,
2099  0.335831, 0.32074, 0.304211, 0.285904, 0.265327, 0.24172, 0.213799,
2100  0.197524, 0.179045, 0.157442, 0.144973, 0.13092, 0.11463, 0.111011,
2101  0.107241, 0.103302, 0.0991739, 0.0948285, 0.0853429, 0.0744311,
2102  0.0682165, 0.0612841}, {1.17243, 1.17025, 1.17072, 1.17153, 1.17109,
2103  1.17107, 1.17115, 1.17122, 1.17125, 1.17124, 1.17116, 1.17118,
2104  1.17115, 1.17114, 1.17112, 1.17109, 1.17105, 1.171, 1.17096,
2105  1.17092, 1.17087, 1.17083, 1.17078, 1.17067, 1.17055, 1.17033,
2106  1.17009, 1.16986, 1.16938, 1.16889, 1.16838, 1.16786, 1.16733,
2107  1.16679, 1.16622, 1.16565, 1.16506, 1.16445, 1.16382, 1.16318,
2108  1.1615, 1.15969, 1.15776, 1.15567, 1.15344, 1.15103, 1.14843,
2109  1.14562, 1.14259, 1.1393, 1.13573, 1.13184, 1.12761, 1.12298,
2110  1.1179, 1.11232, 1.10615, 1.09933, 1.09174, 1.08325, 1.07371,
2111  1.06294, 1.05067, 1.0366, 1.0203, 1.00121, 0.97854, 0.951144,
2112  0.9385, 0.92468, 0.909499, 0.892724, 0.874063, 0.853135, 0.829435,
2113  0.802272, 0.770663, 0.733138, 0.687353, 0.629184, 0.593147,
2114  0.550213, 0.497162, 0.465071, 0.427558, 0.410551, 0.392089,
2115  0.371872, 0.349482, 0.32432, 0.295457, 0.261323, 0.241428, 0.218839,
2116  0.192433, 0.177192, 0.160015, 0.140105, 0.135681, 0.131073,
2117  0.126259, 0.121213, 0.115902, 0.104308, 0.0909715, 0.0833759,
2118  0.0749029}, {1.43411, 1.43505, 1.43374, 1.43433, 1.43411, 1.43401,
2119  1.43406, 1.43415, 1.43418, 1.43415, 1.4341, 1.43407, 1.43405,
2120  1.43401, 1.43397, 1.43393, 1.43384, 1.43376, 1.43367, 1.43359,
2121  1.4335, 1.43342, 1.43333, 1.43312, 1.4329, 1.43247, 1.43203,
2122  1.43159, 1.43069, 1.42978, 1.42884, 1.42789, 1.42691, 1.42592,
2123  1.4249, 1.42387, 1.42281, 1.42173, 1.42062, 1.41949, 1.41656,
2124  1.41345, 1.41017, 1.4067, 1.40302, 1.39911, 1.39496, 1.39054,
2125  1.38582, 1.38079, 1.3754, 1.36961, 1.36339, 1.35669, 1.34943,
2126  1.34155, 1.33296, 1.32356, 1.31324, 1.30183, 1.28915, 1.27497,
2127  1.259, 1.24085, 1.22004, 1.19589, 1.16745, 1.13339, 1.11775,
2128  1.10072, 1.08207, 1.06154, 1.03877, 1.01331, 0.984584, 0.951766,
2129  0.913705, 0.868675, 0.81392, 0.744589, 0.701738, 0.650764, 0.587868,
2130  0.549856, 0.505448, 0.485323, 0.46348, 0.439564, 0.413085,
2131  0.383331, 0.349205, 0.308853, 0.285337, 0.258637, 0.227427,
2132  0.209413, 0.189112, 0.16558, 0.160352, 0.154906, 0.149217, 0.143253,
2133  0.136976, 0.123274, 0.107512, 0.0985354, 0.0885218},
2134  {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}
2135  };
2136 
2137  /* 5, 5 mode */
2138  const double reomegaqnm55[8][107] = { {0.752532, 0.769133, 0.779179, 0.78709, 0.786149, 0.784329, 0.782338,
2139  0.780485, 0.778903, 0.777615, 0.774286, 0.773282, 0.772966,
2140  0.77289, 0.772999, 0.773149, 0.773476, 0.77381, 0.774145, 0.77448,
2141  0.774816, 0.775152, 0.775488, 0.776331, 0.777176, 0.778874,
2142  0.780582, 0.782299, 0.785766, 0.789274, 0.792825, 0.79642, 0.800059,
2143  0.803743, 0.807474, 0.811253, 0.81508, 0.818956, 0.822883,
2144  0.826863, 0.837046, 0.847582, 0.858493, 0.869802, 0.881536,
2145  0.893724, 0.906398, 0.919594, 0.93335, 0.947712, 0.962728, 0.978454,
2146  0.994953, 1.0123, 1.03056, 1.04985, 1.07027, 1.09194, 1.11502,
2147  1.13968, 1.16614, 1.19467, 1.22558, 1.25928, 1.29631, 1.33734,
2148  1.38332, 1.43555, 1.45861, 1.48313, 1.50932, 1.53742, 1.56774,
2149  1.60067, 1.63671, 1.67655, 1.72115, 1.77188, 1.83092, 1.90197,
2150  1.94403, 1.99239, 2.04977, 2.08333, 2.12154, 2.13852, 2.15673,
2151  2.17641, 2.1979, 2.22168, 2.24849, 2.27961, 2.29746, 2.31749,
2152  2.34058, 2.35377, 2.3685, 2.38542, 2.38915, 2.39303, 2.39708,
2153  2.40131, 2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.753001,
2154  0.757208, 0.757533, 0.756804, 0.756468, 0.756414, 0.756397,
2155  0.756401, 0.756417, 0.756438, 0.756561, 0.756667, 0.756761,
2156  0.756937, 0.757109, 0.75728, 0.757623, 0.757967, 0.758311, 0.758656,
2157  0.759001, 0.759346, 0.759692, 0.760558, 0.761427, 0.763172,
2158  0.764927, 0.766693, 0.770255, 0.77386, 0.777508, 0.7812, 0.784938,
2159  0.788722, 0.792553, 0.796433, 0.800362, 0.804341, 0.808372,
2160  0.812456, 0.822904, 0.833711, 0.844898, 0.85649, 0.868513, 0.880997,
2161  0.893974, 0.90748, 0.921555, 0.936243, 0.951594, 0.967664,
2162  0.984515, 1.00222, 1.02086, 1.04054, 1.06135, 1.08343, 1.10693,
2163  1.13203, 1.15894, 1.18793, 1.21932, 1.25352, 1.29105, 1.33262,
2164  1.37915, 1.43196, 1.45525, 1.48001, 1.50644, 1.53478, 1.56534,
2165  1.59852, 1.63481, 1.67491, 1.71976, 1.77074, 1.83004, 1.90134,
2166  1.94352, 1.992, 2.0495, 2.08311, 2.12137, 2.13838, 2.15661, 2.17631,
2167  2.19781, 2.22161, 2.24844, 2.27957, 2.29743, 2.31747, 2.34057,
2168  2.35376, 2.36849, 2.38541, 2.38915, 2.39303, 2.39708, 2.40131,
2169  2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.7196, 0.722567,
2170  0.723924, 0.725024, 0.725386, 0.725467, 0.725518, 0.725552,
2171  0.725576, 0.725595, 0.725675, 0.72576, 0.725849, 0.72603, 0.726211,
2172  0.726392, 0.726754, 0.727117, 0.72748, 0.727843, 0.728207, 0.728571,
2173  0.728936, 0.729849, 0.730765, 0.732605, 0.734456, 0.736316,
2174  0.740071, 0.743868, 0.747711, 0.751599, 0.755534, 0.759516,
2175  0.763547, 0.767627, 0.771759, 0.775942, 0.780178, 0.784469,
2176  0.795442, 0.806783, 0.818514, 0.830662, 0.843253, 0.856316,
2177  0.869886, 0.883998, 0.898692, 0.914015, 0.930016, 0.946752,
2178  0.964288, 0.982696, 1.00206, 1.02247, 1.04405, 1.06692, 1.09123,
2179  1.11716, 1.14494, 1.17482, 1.20713, 1.24229, 1.28082, 1.32342,
2180  1.37101, 1.42493, 1.44867, 1.47389, 1.50078, 1.5296, 1.56064,
2181  1.5943, 1.63108, 1.67167, 1.71702, 1.7685, 1.82829, 1.90008, 1.9425,
2182  1.99122, 2.04895, 2.08267, 2.12104, 2.13809, 2.15636, 2.1761,
2183  2.19764, 2.22147, 2.24834, 2.27951, 2.29738, 2.31743, 2.34054,
2184  2.35374, 2.36848, 2.3854, 2.38914, 2.39302, 2.39707, 2.4013,
2185  2.40575, 2.41541, 2.42645, 2.43271, 2.43966}, {0.680361, 0.681655,
2186  0.681927, 0.681788, 0.681669, 0.681657, 0.681664, 0.681682,
2187  0.681705, 0.681729, 0.681838, 0.681934, 0.682031, 0.682225, 0.68242,
2188  0.682614, 0.683004, 0.683394, 0.683784, 0.684175, 0.684566,
2189  0.684957, 0.685349, 0.686331, 0.687316, 0.689293, 0.69128, 0.693279,
2190  0.69731, 0.701387, 0.705509, 0.709679, 0.713897, 0.718164,
2191  0.722481, 0.72685, 0.731271, 0.735746, 0.740276, 0.744863, 0.756582,
2192  0.768683, 0.781187, 0.794122, 0.807514, 0.821395, 0.835799,
2193  0.850762, 0.866327, 0.88254, 0.899452, 0.917122, 0.935614, 0.955004,
2194  0.975376, 0.996827, 1.01947, 1.04344, 1.06888, 1.09599, 1.12497,
2195  1.1561, 1.18971, 1.22621, 1.26614, 1.31018, 1.35928, 1.41476,
2196  1.43915, 1.46502, 1.49258, 1.52208, 1.5538, 1.58816, 1.62564,
2197  1.66694, 1.713, 1.76521, 1.82572, 1.89823, 1.941, 1.99007, 2.04813,
2198  2.08202, 2.12055, 2.13766, 2.15599, 2.17578, 2.19738, 2.22127,
2199  2.24819, 2.2794, 2.2973, 2.31737, 2.34051, 2.35371, 2.36846,
2200  2.38539, 2.38913, 2.39301, 2.39706, 2.40129, 2.40574, 2.4154,
2201  2.42645, 2.43271, 2.43966}, {0.630475, 0.629154, 0.628652, 0.628812,
2202  0.628995, 0.62902, 0.629028, 0.629035, 0.629045, 0.629061,
2203  0.629172, 0.629277, 0.629381, 0.629592, 0.629802, 0.630012,
2204  0.630433, 0.630855, 0.631277, 0.631699, 0.632122, 0.632545,
2205  0.632968, 0.634029, 0.635093, 0.637229, 0.639376, 0.641534,
2206  0.645886, 0.650284, 0.65473, 0.659225, 0.66377, 0.668366, 0.673014,
2207  0.677716, 0.682472, 0.687284, 0.692153, 0.69708, 0.709663, 0.722641,
2208  0.73604, 0.749885, 0.764206, 0.779035, 0.794407, 0.81036, 0.826938,
2209  0.844188, 0.862164, 0.880925, 0.900539, 0.921082, 0.94264,
2210  0.965314, 0.989218, 1.01449, 1.04128, 1.06978, 1.1002, 1.13284,
2211  1.168, 1.20613, 1.24774, 1.29355, 1.34449, 1.4019, 1.42708, 1.45377,
2212  1.48215, 1.51248, 1.54506, 1.58029, 1.61866, 1.66085, 1.70782,
2213  1.76095, 1.82238, 1.89581, 1.93904, 1.98856, 2.04706, 2.08116,
2214  2.1199, 2.13709, 2.1555, 2.17537, 2.19704, 2.221, 2.24799, 2.27927,
2215  2.29719, 2.31729, 2.34045, 2.35367, 2.36843, 2.38537, 2.38911,
2216  2.39299, 2.39704, 2.40128, 2.40573, 2.41539, 2.42644, 2.4327,
2217  2.43966}, {0.571708, 0.573132, 0.573635, 0.573297, 0.573329,
2218  0.573398, 0.573443, 0.573465, 0.573477, 0.573488, 0.5736, 0.573712,
2219  0.573823, 0.574048, 0.574272, 0.574496, 0.574944, 0.575393,
2220  0.575843, 0.576292, 0.576743, 0.577194, 0.577645, 0.578775,
2221  0.579908, 0.582183, 0.58447, 0.586768, 0.591402, 0.596085, 0.600818,
2222  0.605603, 0.61044, 0.61533, 0.620276, 0.625278, 0.630337, 0.635455,
2223  0.640632, 0.645871, 0.659247, 0.673038, 0.687272, 0.701975,
2224  0.717178, 0.732914, 0.74922, 0.766136, 0.783707, 0.801983, 0.821018,
2225  0.840873, 0.86162, 0.883336, 0.90611, 0.930046, 0.955261, 0.981893,
2226  1.0101, 1.04008, 1.07205, 1.10629, 1.14315, 1.18304, 1.22651,
2227  1.27427, 1.32727, 1.38685, 1.41293, 1.44053, 1.46986, 1.50115,
2228  1.53471, 1.57094, 1.61033, 1.65357, 1.70161, 1.75581, 1.81834,
2229  1.89287, 1.93665, 1.98671, 2.04575, 2.08011, 2.1191, 2.13638,
2230  2.15489, 2.17486, 2.19662, 2.22067, 2.24774, 2.2791, 2.29706,
2231  2.31719, 2.34039, 2.35362, 2.36839, 2.38534, 2.38909, 2.39297,
2232  2.39703, 2.40126, 2.40571, 2.41538, 2.42643, 2.4327,
2233  2.43966}, {0.522196, 0.520579, 0.52057, 0.521087, 0.52093, 0.520981,
2234  0.521047, 0.521087, 0.521102, 0.52111, 0.521228, 0.521338,
2235  0.521456, 0.521686, 0.521918, 0.522149, 0.522613, 0.523077,
2236  0.523541, 0.524006, 0.524471, 0.524937, 0.525404, 0.526572,
2237  0.527743, 0.530095, 0.53246, 0.534837, 0.539631, 0.544478, 0.549379,
2238  0.554335, 0.559348, 0.564418, 0.569547, 0.574737, 0.579987,
2239  0.585301, 0.590679, 0.596123, 0.61003, 0.624382, 0.639206, 0.654532,
2240  0.670391, 0.686819, 0.703853, 0.721535, 0.739912, 0.759036,
2241  0.778963, 0.799758, 0.821493, 0.844248, 0.868117, 0.893205,
2242  0.919633, 0.947544, 0.977101, 1.0085, 1.04198, 1.07781, 1.11634,
2243  1.15802, 1.20338, 1.25315, 1.30829, 1.37015, 1.39719, 1.42578,
2244  1.45611, 1.48844, 1.52307, 1.56039, 1.6009, 1.64529, 1.69451,
2245  1.74992, 1.81368, 1.88946, 1.93386, 1.98455, 2.0442, 2.07886,
2246  2.11815, 2.13555, 2.15417, 2.17425, 2.19612, 2.22028, 2.24745,
2247  2.2789, 2.29691, 2.31708, 2.34031, 2.35356, 2.36835, 2.38531,
2248  2.38906, 2.39295, 2.39701, 2.40125, 2.4057, 2.41537, 2.42643,
2249  2.43269, 2.43965},
2250  {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}
2251  };
2252 
2253  const double imomegaqnm55[8][107] = { {0.0151971, 0.02987, 0.0432352, 0.064849, 0.0789971, 0.0834521,
2254  0.0865117, 0.0885261, 0.0898184, 0.090638, 0.0919286, 0.0920896,
2255  0.0921222, 0.0921485, 0.0921652, 0.0921765, 0.092191, 0.0922013,
2256  0.0922106, 0.0922195, 0.0922283, 0.0922371, 0.0922459, 0.0922679,
2257  0.0922898, 0.0923335, 0.092377, 0.0924205, 0.0925068, 0.0925926,
2258  0.0926777, 0.092762, 0.0928457, 0.0929286, 0.0930106, 0.0930918,
2259  0.0931722, 0.0932516, 0.09333, 0.0934074, 0.0935961, 0.0937773,
2260  0.09395, 0.0941133, 0.094266, 0.0944066, 0.0945339, 0.094646,
2261  0.0947411, 0.0948169, 0.0948709, 0.0949002, 0.0949014, 0.0948705,
2262  0.094803, 0.0946932, 0.0945348, 0.0943198, 0.0940389, 0.0936804,
2263  0.0932301, 0.09267, 0.0919774, 0.0911228, 0.0900671, 0.0887575,
2264  0.0871199, 0.0850466, 0.0840612, 0.0829665, 0.0817451, 0.0803751,
2265  0.0788289, 0.0770706, 0.0750526, 0.0727103, 0.0699513, 0.0666388,
2266  0.0625545, 0.0573174, 0.054054, 0.0501531, 0.0453206, 0.0423931,
2267  0.038969, 0.0374162, 0.0357305, 0.0338844, 0.0318402, 0.0295431,
2268  0.0269089, 0.0237947, 0.0219803, 0.0199207, 0.017514, 0.0161252,
2269  0.0145605, 0.0127472, 0.0123443, 0.0119247, 0.0114865, 0.011027,
2270  0.0105435, 0.00948819, 0.00827437, 0.00758316,
2271  0.00681219}, {0.25166, 0.264251, 0.270831, 0.275931, 0.277491,
2272  0.277846, 0.278073, 0.278222, 0.278323, 0.278391, 0.278527,
2273  0.278556, 0.278565, 0.278576, 0.278588, 0.2786, 0.278625, 0.27865,
2274  0.278676, 0.278701, 0.278726, 0.278751, 0.278776, 0.278839,
2275  0.278901, 0.279026, 0.27915, 0.279273, 0.279519, 0.279763, 0.280005,
2276  0.280244, 0.280481, 0.280716, 0.280948, 0.281177, 0.281404,
2277  0.281627, 0.281847, 0.282065, 0.282593, 0.283097, 0.283575,
2278  0.284023, 0.284438, 0.284817, 0.285154, 0.285444, 0.285682,
2279  0.285862, 0.285974, 0.286011, 0.285963, 0.285817, 0.28556, 0.285175,
2280  0.284643, 0.28394, 0.283038, 0.281902, 0.280489, 0.278746,
2281  0.276603, 0.273974, 0.27074, 0.266744, 0.261763, 0.255474, 0.252491,
2282  0.249179, 0.245488, 0.24135, 0.236685, 0.231383, 0.225304,
2283  0.218251, 0.20995, 0.199989, 0.187715, 0.171984, 0.162185, 0.150475,
2284  0.135971, 0.127186, 0.116912, 0.112252, 0.107194, 0.101656,
2285  0.0955223, 0.0886307, 0.0807275, 0.0713845, 0.0659411, 0.0597624,
2286  0.0525421, 0.0483758, 0.0436815, 0.0382415, 0.037033, 0.0357743,
2287  0.0344594, 0.0330811, 0.0316306, 0.0284646, 0.0248231, 0.0227495,
2288  0.0204366}, {0.467579, 0.470028, 0.470942, 0.471348, 0.471322,
2289  0.47129, 0.471261, 0.471239, 0.471223, 0.471213, 0.471201, 0.47121,
2290  0.471221, 0.47124, 0.471258, 0.471277, 0.471314, 0.471351, 0.471388,
2291  0.471425, 0.471462, 0.471499, 0.471536, 0.471628, 0.47172,
2292  0.471904, 0.472086, 0.472268, 0.472628, 0.472984, 0.473336,
2293  0.473684, 0.474028, 0.474367, 0.474701, 0.475031, 0.475355,
2294  0.475674, 0.475987, 0.476294, 0.477036, 0.477735, 0.478387,
2295  0.478987, 0.479529, 0.480006, 0.480411, 0.480735, 0.480968,
2296  0.481101, 0.481119, 0.481008, 0.480751, 0.480328, 0.479717,
2297  0.478889, 0.477812, 0.476446, 0.474745, 0.472651, 0.470091,
2298  0.466978, 0.463197, 0.4586, 0.452993, 0.446112, 0.437588, 0.426883,
2299  0.421821, 0.416213, 0.409971, 0.402987, 0.395124, 0.386201,
2300  0.375984, 0.364147, 0.350231, 0.333554, 0.313026, 0.286746,
2301  0.270386, 0.250845, 0.226651, 0.212, 0.194868, 0.1871, 0.178668,
2302  0.169434, 0.15921, 0.147722, 0.134549, 0.118976, 0.109903,
2303  0.0996047, 0.0875705, 0.0806266, 0.0728027, 0.063736, 0.0617217,
2304  0.0596238, 0.0574324, 0.0551353, 0.0527177, 0.047441, 0.0413719,
2305  0.0379158, 0.034061}, {0.676801, 0.675633, 0.67493, 0.67443, 0.6744,
2306  0.674422, 0.674445, 0.674462, 0.674474, 0.674481, 0.67449,
2307  0.674497, 0.674508, 0.674528, 0.674548, 0.674568, 0.674609,
2308  0.674649, 0.674689, 0.674729, 0.674769, 0.674809, 0.674849,
2309  0.674948, 0.675048, 0.675245, 0.675441, 0.675635, 0.67602, 0.676399,
2310  0.676771, 0.677137, 0.677496, 0.677847, 0.678192, 0.678529,
2311  0.678858, 0.679179, 0.679492, 0.679795, 0.680514, 0.681168,
2312  0.681753, 0.68226, 0.682681, 0.683008, 0.683228, 0.683332, 0.683303,
2313  0.683128, 0.682788, 0.682263, 0.681529, 0.680557, 0.679315,
2314  0.677766, 0.675862, 0.673549, 0.67076, 0.667416, 0.663415, 0.658633,
2315  0.65291, 0.64604, 0.637751, 0.627674, 0.615292, 0.599856, 0.592588,
2316  0.584557, 0.575639, 0.565684, 0.554498, 0.541831, 0.527355,
2317  0.510615, 0.490971, 0.467468, 0.438585, 0.401662, 0.378702,
2318  0.351292, 0.317377, 0.296847, 0.272846, 0.261966, 0.250155,
2319  0.237224, 0.222906, 0.20682, 0.188374, 0.16657, 0.153867, 0.139448,
2320  0.1226, 0.112878, 0.101924, 0.0892306, 0.0864106, 0.0834736,
2321  0.0804055, 0.0771896, 0.0738049, 0.0664175, 0.0579207, 0.0530822,
2322  0.0476854}, {0.891895, 0.89147, 0.891863, 0.892311, 0.89227,
2323  0.892236, 0.892217, 0.892213, 0.892217, 0.892223, 0.892242,
2324  0.892246, 0.892254, 0.892269, 0.892283, 0.892298, 0.892327,
2325  0.892357, 0.892386, 0.892415, 0.892444, 0.892473, 0.892502,
2326  0.892574, 0.892646, 0.892788, 0.892927, 0.893065, 0.893335,
2327  0.893597, 0.89385, 0.894094, 0.894329, 0.894554, 0.89477, 0.894975,
2328  0.89517, 0.895353, 0.895526, 0.895686, 0.896031, 0.896291, 0.896458,
2329  0.896521, 0.89647, 0.896292, 0.895974, 0.895501, 0.894855,
2330  0.894014, 0.892957, 0.891657, 0.890083, 0.888198, 0.88596, 0.88332,
2331  0.880219, 0.876586, 0.872336, 0.867364, 0.86154, 0.854705, 0.846653,
2332  0.83712, 0.825754, 0.812083, 0.795442, 0.774871, 0.765236,
2333  0.754619, 0.742864, 0.729775, 0.715106, 0.698537, 0.679644,
2334  0.657847, 0.632324, 0.601851, 0.564477, 0.516789, 0.487173,
2335  0.451846, 0.408167, 0.381741, 0.350856, 0.336857, 0.321664, 0.30503,
2336  0.286614, 0.265926, 0.242205, 0.214167, 0.197833, 0.179293,
2337  0.15763, 0.14513, 0.131046, 0.114725, 0.1111, 0.107324, 0.103379,
2338  0.099244, 0.0948923, 0.085394, 0.0744695, 0.0682486,
2339  0.0613098}, {1.12614, 1.12697, 1.12642, 1.12612, 1.12629, 1.12629,
2340  1.12627, 1.12625, 1.12624, 1.12624, 1.12626, 1.12625, 1.12626,
2341  1.12626, 1.12626, 1.12626, 1.12626, 1.12626, 1.12627, 1.12627,
2342  1.12627, 1.12627, 1.12628, 1.12628, 1.12628, 1.12629, 1.12629,
2343  1.1263, 1.12629, 1.12628, 1.12625, 1.12622, 1.12617, 1.12611,
2344  1.12604, 1.12595, 1.12586, 1.12574, 1.12562, 1.12548, 1.12505,
2345  1.12453, 1.12388, 1.1231, 1.12219, 1.12111, 1.11986, 1.11841,
2346  1.11675, 1.11485, 1.11267, 1.1102, 1.10738, 1.10418, 1.10054,
2347  1.09641, 1.0917, 1.08634, 1.08021, 1.07319, 1.06513, 1.05582,
2348  1.04501, 1.03238, 1.0175, 0.999787, 0.978439, 0.952276, 0.940091,
2349  0.926705, 0.911928, 0.895521, 0.877184, 0.856528, 0.833035, 0.806,
2350  0.774421, 0.736806, 0.690779, 0.632177, 0.595837, 0.552533,
2351  0.499038, 0.466693, 0.428905, 0.411781, 0.393199, 0.372856,
2352  0.350338, 0.325043, 0.296043, 0.261768, 0.241802, 0.219141,
2353  0.192661, 0.177383, 0.160169, 0.140221, 0.135789, 0.131174,
2354  0.126352, 0.121299, 0.11598, 0.104371, 0.0910184, 0.083415,
2355  0.0749342}, {1.3749, 1.37446, 1.37529, 1.37504, 1.37506, 1.37511,
2356  1.37511, 1.37508, 1.37506, 1.37506, 1.37507, 1.37505, 1.37505,
2357  1.37503, 1.37501, 1.37499, 1.37496, 1.37492, 1.37488, 1.37485,
2358  1.37481, 1.37478, 1.37474, 1.37465, 1.37456, 1.37437, 1.37418,
2359  1.37399, 1.37359, 1.37319, 1.37277, 1.37233, 1.37188, 1.37142,
2360  1.37094, 1.37045, 1.36993, 1.36941, 1.36886, 1.36829, 1.3668,
2361  1.36517, 1.36339, 1.36145, 1.35934, 1.35704, 1.35452, 1.35177,
2362  1.34875, 1.34544, 1.3418, 1.33779, 1.33338, 1.3285, 1.32309,
2363  1.31709, 1.3104, 1.30292, 1.29452, 1.28507, 1.27436, 1.26216,
2364  1.24818, 1.23202, 1.2132, 1.19101, 1.1645, 1.13228, 1.11735,
2365  1.10101, 1.08301, 1.06309, 1.04089, 1.01595, 0.987663, 0.955194,
2366  0.917365, 0.872418, 0.817554, 0.747869, 0.704729, 0.653377,
2367  0.590005, 0.551715, 0.507, 0.486743, 0.464764, 0.440707, 0.41408,
2368  0.384173, 0.34989, 0.309375, 0.285775, 0.25899, 0.227694, 0.209637,
2369  0.189292, 0.165716, 0.160479, 0.155024, 0.149326, 0.143353,
2370  0.137067, 0.123347, 0.107567, 0.0985815, 0.0885587},
2371  {0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}
2372  };
2373 
2374  /* To actually calculate the ringdown, we will use the following pointers to point to the correct mode */
2375  const double (*reomegaqnm)[107] = NULL;
2376  const double (*imomegaqnm)[107] = NULL;
2377 
2378  /* Stuff for interpolating the data */
2379  gsl_spline *spline = NULL;
2380  gsl_interp_accel *acc = NULL;
2381 
2382  UINT4 i;
2383  REAL8 signm = m < 0 ? -1.0 : 1.0;
2384 
2385  /* Check we do not require more overtones than we have */
2386  if (nmodes > 8) {
2387  XLALPrintError("Requesting more overtones than we have data to generate!\n");
2388  XLAL_ERROR(XLAL_EINVAL);
2389  }
2390 
2391  /* Choose the appropriate data bases on the user requested l and m */
2392  switch (l) {
2393  case 2:
2394  if (abs(m) == 2) {
2395  reomegaqnm = reomegaqnm22;
2396  imomegaqnm = imomegaqnm22;
2397  } else if (abs(m) == 1) {
2398  reomegaqnm = reomegaqnm21;
2399  imomegaqnm = imomegaqnm21;
2400  } else if (abs(m) == 0) {
2401  reomegaqnm = reomegaqnm20;
2402  imomegaqnm = imomegaqnm20;
2403  } else {
2404  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2405  XLAL_ERROR(XLAL_EINVAL);
2406  }
2407  break;
2408  case 3:
2409  if (abs(m) == 3) {
2410  reomegaqnm = reomegaqnm33;
2411  imomegaqnm = imomegaqnm33;
2412  } else {
2413  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2414  XLAL_ERROR(XLAL_EINVAL);
2415  }
2416  break;
2417  case 4:
2418  if (abs(m) == 4) {
2419  reomegaqnm = reomegaqnm44;
2420  imomegaqnm = imomegaqnm44;
2421  } else {
2422  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2423  XLAL_ERROR(XLAL_EINVAL);
2424  }
2425  break;
2426  case 5:
2427  if (abs(m) == 5) {
2428  reomegaqnm = reomegaqnm55;
2429  imomegaqnm = imomegaqnm55;
2430  } else {
2431  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2432  XLAL_ERROR(XLAL_EINVAL);
2433  }
2434  break;
2435  default:
2436  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2437  XLAL_ERROR(XLAL_EINVAL);
2438  break;
2439  }
2440 
2441  spline = gsl_spline_alloc(gsl_interp_cspline, 107);
2442  acc = gsl_interp_accel_alloc();
2443 
2444  /* finalSpin interpolation is available only between -0.9996 and 0.9996 */
2445  /* Set finalSpin to +/- 0.9996 if it is out of this range */
2446  if (finalSpin < -0.9996 || finalSpin > 0.9996) {
2447  XLALPrintError("Final spin must be between -0.9996 and 0.9996");
2448  XLAL_ERROR(XLAL_EINVAL);
2449  }
2450  /* Now get the QNM frequencies from interpolating the above data */
2451  for (i = 0; i < nmodes; i++) {
2452  gsl_spline_init(spline, afinallist, reomegaqnm[i], 107);
2453  gsl_interp_accel_reset(acc);
2454 
2455  modefreqs->data[i] = signm * gsl_spline_eval(spline, signm * finalSpin, acc);
2456 
2457  gsl_spline_init(spline, afinallist, imomegaqnm[i], 107);
2458  gsl_interp_accel_reset(acc);
2459 
2460  modefreqs->data[i] += I * gsl_spline_eval(spline, signm * finalSpin, acc);
2461 
2462  /* Scale by the appropriate mass factors */
2463  modefreqs->data[i] *= 1. / (finalMass * LAL_MTSUN_SI);
2464  }
2465  /* Free memory and exit */
2466  gsl_spline_free(spline);
2467  gsl_interp_accel_free(acc);
2468 
2469  return XLAL_SUCCESS;
2470 }
2471 
2472 /** @} */
2473 
2474 /** @} */
2475 
2476 /* TEST CODE */
2477 
2478 #if 0 /* TEST CODE */
2479 
2480 #include <stdio.h>
2481 int ringdown_waveform(void)
2482 {
2483  static LIGOTimeGPS epoch;
2484  const double M = 10.0 * LAL_MSUN_SI;
2485  const double a = 0.98;
2486  const double r = 1e6 * LAL_PC_SI;
2487  const double i = LAL_PI / 6;
2488  const double dt = 1.0 / 16384.0;
2489  const double eps = 0.01;
2490  const int l = 2;
2491  const int m = 2;
2492  const char *fname = "ringdown_waveform.dat";
2493  REAL8TimeSeries *hplus = NULL;
2494  REAL8TimeSeries *hcross = NULL;
2495  size_t j;
2496  FILE *fp;
2497 
2498  fp = fopen(fname, "w");
2499  XLALSimBlackHoleRingdown(&hplus, &hcross, &epoch, 0.0, dt, M, a, eps, r, i, l, m);
2500  for (j = 0; j < hplus->data->length; ++j)
2501  fprintf(fp, "%f\t%e\t%e\n", j * dt, hplus->data->data[j], hcross->data->data[j]);
2502  fclose(fp);
2503 
2504  XLALDestroyREAL8TimeSeries(hcross);
2505  XLALDestroyREAL8TimeSeries(hplus);
2506 
2507  return 0;
2508 }
2509 
2510 int grasp_spherical_table(void)
2511 {
2512  const double a = 0.0;
2513  const int l = 2;
2514  const int m = 2;
2515  const int s = -2;
2516  const char *fname = "grasp_spherical_table.txt";
2517  FILE *fp;
2518  COMPLEX16 A, omega;
2519  COMPLEX16 norm;
2520  COMPLEX16 sphwf;
2521  double fac = 1.0 / sqrt(2.0 * M_PI);
2522  double exactfac = sqrt(5.0 / (64.0 * M_PI));
2523  double muvec[] = { -0.99, -0.95, -0.75, -0.55, -0.35, -0.15, 0.15, 0.35, 0.55, 0.75, 0.95, 0.99 };
2524  size_t i;
2525 
2526  fp = fopen(fname, "w");
2527  /* note: multiply a by 0.5 for Leaver conventions */
2528  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, 0.5 * a, l, m, s);
2529  norm = XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver(0.5 * a, l, m, s, A, omega);
2530  for (i = 0; i < XLAL_NUM_ELEM(muvec); ++i) {
2531  double mu = muvec[i];
2532  sphwf = norm * XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(mu, a, l, m, s, A, omega);
2533  fprintf(fp, "%+e\t%e\t%e\n", mu, fac * creal(sphwf), exactfac * pow(1.0 + mu, 2));
2534  }
2535  fclose(fp);
2536 
2537  return 0;
2538 }
2539 
2540 int grasp_spheroid_figure(void)
2541 {
2542  const double a = 0.98;
2543  const int l = 2;
2544  const int m = 2;
2545  const int s = -2;
2546  const char *fname = "grasp_spheroid_figure.dat";
2547  FILE *fp;
2548  COMPLEX16 A, omega;
2549  COMPLEX16 norm;
2550  COMPLEX16 sphwf;
2551  double mu;
2552 
2553  fp = fopen(fname, "w");
2554  /* note: multiply a by 0.5 for Leaver conventions */
2555  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, 0.5 * a, l, m, s);
2556  norm = XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver(0.5 * a, l, m, s, A, omega);
2557  for (mu = -1.0; mu <= 1.0; mu += 0.01) {
2558  sphwf = norm * XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(mu, 0.5 * a, l, m, s, A, omega);
2559  fprintf(fp, "%e\t%e\t%e\n", mu, creal(sphwf), cimag(sphwf));
2560  }
2561  fclose(fp);
2562 
2563  return 0;
2564 }
2565 
2566 int leaver_table_2(void)
2567 {
2568  const int l = 2;
2569  const int m = 0;
2570  const int s = -2;
2571  const char *fname = "leaver_table_2.txt";
2572  FILE *fp;
2573  COMPLEX16 A, omega;
2574  double avec[] = { 0.0, 0.1, 0.2, 0.3, 0.4, 0.45, 0.49, 0.4999 };
2575  size_t i;
2576 
2577  fp = fopen(fname, "w");
2578 
2579  /* positive values of a */
2580  for (i = 0; i < XLAL_NUM_ELEM(avec); ++i) {
2581  double a = avec[i];
2582  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s);
2583  fprintf(fp, "%+.4f \t(%.5f,%+.5f)\t(%+.6f,%.6f)\n", a, creal(A), cimag(A), creal(omega), cimag(omega));
2584  }
2585 
2586  fprintf(fp, "\n");
2587 
2588  /* negative values of a */
2589  for (i = 0; i < XLAL_NUM_ELEM(avec); ++i) {
2590  double a = -avec[i];
2591  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s);
2592  fprintf(fp, "%+.4f \t(%.5f,%+.5f)\t(%+.6f,%.6f)\n", a, creal(A), cimag(A), creal(omega), cimag(omega));
2593  }
2594 
2595  fclose(fp);
2596  return 0;
2597 }
2598 
2599 int leaver_table_3(void)
2600 {
2601  const int l = 2;
2602  const int m = 1;
2603  const int s = -2;
2604  const char *fname = "leaver_table_3.txt";
2605  FILE *fp;
2606  COMPLEX16 A, omega;
2607  double avec[] = { 0.0, 0.1, 0.2, 0.3, 0.4, 0.45, 0.49, 0.4999 };
2608  size_t i;
2609 
2610  fp = fopen(fname, "w");
2611 
2612  /* positive values of a */
2613  for (i = 0; i < XLAL_NUM_ELEM(avec); ++i) {
2614  double a = avec[i];
2615  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s);
2616  fprintf(fp, "%+.4f \t(%.5f,%+.5f)\t(%+.6f,%.6f)\n", a, creal(A), cimag(A), creal(omega), cimag(omega));
2617  }
2618 
2619  fprintf(fp, "\n");
2620 
2621  /* negative values of a */
2622  for (i = 0; i < XLAL_NUM_ELEM(avec); ++i) {
2623  double a = -avec[i];
2624  XLALSimBlackHoleRingdownModeEigenvaluesLeaver(&A, &omega, a, l, m, s);
2625  fprintf(fp, "%+.4f \t(%.5f,%+.5f)\t(%+.6f,%.6f)\n", a, creal(A), cimag(A), creal(omega), cimag(omega));
2626  }
2627 
2628  fclose(fp);
2629  return 0;
2630 }
2631 
2632 int main(void)
2633 {
2634  XLALSetErrorHandler(XLALAbortErrorHandler);
2635  leaver_table_2();
2636  leaver_table_3();
2637  grasp_spherical_table();
2638  grasp_spheroid_figure();
2639  ringdown_waveform();
2640  return 0;
2641 }
2642 
2643 #endif /* TEST CODE */
2644 
2645 /**
2646  * These functions generate the quasinormal mode frequencies for a black
2647  * hole ringdown, as implemented in the SEOBNRv5HM model.
2648  *
2649  * At present, this function works for the 22, 21, 33, 44, 55, 32
2650  * and 43 modes, and includes only the n=0 overtone.
2651  * The final frequencies are computed using the qnm python
2652  * package https://arxiv.org/abs/1908.10377, as also done in SEOBNRv5HM.
2653  */
2654 INT4 XLALSimIMREOBGenerateQNMFreqV5(COMPLEX16Vector * modefreqs,
2655  /**<< OUTPUT, complex freqs of overtones in unit of Hz */
2656  const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
2657  const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
2658  const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
2659  const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
2660  UINT4 l, /**<< The l value of the mode in question */
2661  INT4 m, /**<< The m value of the mode in question */
2662  UINT4 nmodes, /**<< The number of overtones that should be included (max 8) */
2663  Approximant approximant /**<< The waveform approximant being used */
2664  ) {
2665 
2666  REAL8 totalMass, finalMass, finalSpin;
2667 
2668  /* Call XLALSimIMREOBFinalMassSpin() to get mass and spin of the final black hole */
2669  if (XLALSimIMREOBFinalMassSpin(&finalMass, &finalSpin, mass1, mass2, spin1, spin2, approximant) == XLAL_FAILURE) {
2670  XLAL_ERROR(XLAL_EFUNC);
2671  }
2672 
2673  /* finalSpin interpolation is available only between -0.9996 and 0.9996 */
2674  /* Set finalSpin to +/- 0.9996 if it is out of this range */
2675  if (finalSpin < -0.9996)
2676  finalSpin = -0.9996;
2677  if (finalSpin > 0.9996)
2678  finalSpin = 0.9996;
2679  /* The final mass is scaled by the original total mass */
2680  totalMass = mass1 + mass2;
2681  finalMass *= totalMass;
2682 
2683  if (XLALSimIMREOBGenerateQNMFreqV5fromFinal(modefreqs, finalMass, finalSpin, l, m, nmodes) == XLAL_FAILURE) {
2684  XLAL_ERROR(XLAL_EFUNC);
2685  }
2686 
2687  return XLAL_SUCCESS;
2688 
2689 }
2690 
2691 INT4 XLALSimIMREOBGenerateQNMFreqV5fromFinal(COMPLEX16Vector * modefreqs,
2692  /**<< OUTPUT, complex freqs of overtones in unit of Hz */
2693  const REAL8 finalMass, /**<< The mass of the final black hole (in Solar masses) */
2694  const REAL8 finalSpin, /**<< The spin of the final object; only needed for spin waveforms */
2695  UINT4 l, /**<< The l value of the mode in question */
2696  INT4 m, /**<< The m value of the mode in question */
2697  UINT4 nmodes /**<< The number of overtones that should be included (max 8) */
2698  ) {
2699 
2700  /* Data for interpolating the quasinormal mode frequencies computed using the qnm python package */
2701 
2702  static const double afinallist[107] = { -0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
2703  -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
2704  -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,
2705  -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,
2706  -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,
2707  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,
2708  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,
2709  0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996
2710  };
2711 
2712 
2713  /* 2, 2 mode */
2714 
2715  const double reomegaqnm22[1][107] =
2716  { { 0.2915755,0.291581,0.2915866,0.2915976,0.2916086,0.2916142,0.2916197,0.2916252,0.2916307,0.2916362,0.2916638,0.2916915,0.2917191,0.2917744,0.2918297,0.291885,0.2919958,0.2921067,0.2922178,0.2923289,0.2924403,0.2925517,0.2926633,0.292943,0.2932235,0.2937871,0.2943542,0.2949249,0.2960772,0.2972442,0.2984264,0.299624,0.3008375,0.3020672,0.3033134,0.3045767,0.3058573,0.3071558,0.3084726,0.3098081,0.3132321,0.316784,0.3204726,0.3243073,0.3282986,0.3324579,0.336798,0.3413329,0.3460786,0.3510526,0.3562748,0.3617677,0.3675569,0.3736717,0.3801456,0.3870175,0.394333,0.4021453,0.4105179,0.4195267,0.4292637,0.4398419,0.4514022,0.464123,0.4782352,0.4940448,0.5119692,0.5326002,0.5417937,0.5516303,0.5622007,0.5736164,0.586017,0.5995803,0.6145391,0.631206,0.6500179,0.6716143,0.6969947,0.7278753,0.74632,0.7676741,0.7932082,0.8082349,0.8254294,0.8331,0.8413426,0.8502722,0.8600456,0.8708927,0.8830905,0.8969183,0.9045305,0.912655,0.9213264,0.9258781,0.9305797,0.9354355,0.9364255,0.937422,0.9384248,0.9394341,0.9404498,0.9425009,0.9445784,0.9456271,0.9466825 } };
2717 
2718  const double imomegaqnm22[1][107] =
2719  { { 0.0880269,0.0880272,0.0880274,0.088028,0.0880285,0.0880288,0.088029,0.0880293,0.0880296,0.0880298,0.0880311,0.0880325,0.0880338,0.0880364,0.0880391,0.0880417,0.088047,0.0880523,0.0880575,0.0880628,0.088068,0.0880733,0.0880785,0.0880915,0.0881045,0.0881304,0.088156,0.0881813,0.0882315,0.0882807,0.0883289,0.0883763,0.0884226,0.0884679,0.0885122,0.0885555,0.0885976,0.0886386,0.0886785,0.0887172,0.0888085,0.0888917,0.0889663,0.0890315,0.0890868,0.0891313,0.0891643,0.0891846,0.0891911,0.0891825,0.0891574,0.0891138,0.0890496,0.0889623,0.0888489,0.0887057,0.0885283,0.0883112,0.0880477,0.0877293,0.0873453,0.086882,0.0863212,0.0856388,0.0848021,0.0837652,0.0824618,0.0807929,0.0799908,0.0790927,0.0780817,0.0769364,0.0756296,0.0741258,0.072378,0.0703215,0.0678642,0.0648692,0.0611186,0.0562313,0.053149,0.0494336,0.0447904,0.0419586,0.0386302,0.0371155,0.0354677,0.033659,0.0316517,0.0293904,0.0268082,0.0238377,0.0221857,0.0204114,0.0185063,0.0175021,0.016462,0.015385,0.0151651,0.0149437,0.0147207,0.0144962,0.0142701,0.0138132,0.0133501,0.0131161,0.0128806 } };
2720 
2721  /* 2, 1 mode */
2722 
2723  const double reomegaqnm21[1][107] =
2724  { { 0.3438626,0.3438628,0.3438631,0.3438636,0.3438641,0.3438644,0.3438647,0.3438649,0.3438652,0.3438655,0.3438668,0.3438681,0.3438695,0.3438722,0.343875,0.3438778,0.3438837,0.3438896,0.3438958,0.3439022,0.3439087,0.3439155,0.3439224,0.3439406,0.3439599,0.3440022,0.3440494,0.3441014,0.3442201,0.3443587,0.3445174,0.3446963,0.3448956,0.3451154,0.3453558,0.3456169,0.3458988,0.3462015,0.3465251,0.3468698,0.3478237,0.3489107,0.3501325,0.3514914,0.3529902,0.3546326,0.3564229,0.3583663,0.3604691,0.3627384,0.3651827,0.3678118,0.3706371,0.3736717,0.3769308,0.3804323,0.3841965,0.3882478,0.3926145,0.3973304,0.4024357,0.4079791,0.4140201,0.4206324,0.4279088,0.4359685,0.4449684,0.4551215,0.4595687,0.4642715,0.4692586,0.4745645,0.4802307,0.486308,0.4928595,0.4999652,0.5077294,0.5162914,0.5258452,0.5366734,0.542693,0.5492125,0.5563286,0.5601461,0.564155,0.5658144,0.5675056,0.5692268,0.5709753,0.5727486,0.5745442,0.5763596,0.5772738,0.5781921,0.5791141,0.5795763,0.5800393,0.5805031,0.580596,0.5806889,0.5807818,0.5808747,0.5809677,0.5811537,0.5813398,0.5814329,0.581526 } };
2725 
2726  const double imomegaqnm21[1][107] =
2727  { { 0.0833908,0.0833925,0.0833942,0.0833976,0.0834009,0.0834026,0.0834043,0.083406,0.0834077,0.0834094,0.0834177,0.0834261,0.0834345,0.0834512,0.0834679,0.0834845,0.0835176,0.0835506,0.0835833,0.0836159,0.0836483,0.0836806,0.0837126,0.0837921,0.0838704,0.0840241,0.0841737,0.0843193,0.0845994,0.084865,0.085117,0.0853561,0.0855831,0.0857987,0.0860035,0.086198,0.0863828,0.0865584,0.0867253,0.086884,0.087247,0.0875662,0.0878462,0.0880906,0.0883025,0.088484,0.088637,0.0887628,0.0888621,0.0889354,0.0889828,0.0890037,0.0889973,0.0889623,0.0888968,0.0887983,0.0886636,0.0884885,0.0882679,0.0879952,0.0876618,0.0872571,0.086767,0.086173,0.0854501,0.0845642,0.0834665,0.0820852,0.0814304,0.0807035,0.0798926,0.0789827,0.077955,0.0767847,0.0754394,0.0738744,0.072027,0.0698043,0.067061,0.0635492,0.0613721,0.058791,0.0556436,0.053776,0.0516427,0.0506978,0.0496911,0.0486136,0.0474559,0.0462084,0.0448616,0.0434061,0.0426347,0.0418324,0.0409982,0.0405688,0.0401309,0.0396845,0.0395942,0.0395035,0.0394124,0.0393211,0.0392293,0.0390448,0.0388588,0.0387653,0.0386714 } };
2728 
2729  /* 2, 0 mode */
2730 
2731  const double reomegaqnm20[1][107] =
2732  { { 0.4250863,0.4250715,0.4250568,0.4250273,0.4249979,0.4249832,0.4249684,0.4249537,0.424939,0.4249243,0.4248508,0.4247773,0.424704,0.4245575,0.4244112,0.4242653,0.4239744,0.4236846,0.423396,0.4231087,0.4228226,0.4225378,0.4222542,0.421551,0.4208559,0.4194907,0.4181593,0.4168618,0.4143677,0.4120045,0.4097659,0.4076449,0.4056343,0.4037273,0.4019174,0.4001984,0.398565,0.397012,0.3955348,0.3941293,0.3909047,0.3880539,0.385536,0.3833183,0.381374,0.3796816,0.3782234,0.3769851,0.375955,0.3751239,0.3744847,0.3740318,0.3737615,0.3736717,0.3737615,0.3740318,0.3744847,0.3751239,0.375955,0.3769851,0.3782234,0.3796816,0.381374,0.3833183,0.385536,0.3880539,0.3909047,0.3941293,0.3955348,0.397012,0.398565,0.4001984,0.4019174,0.4037273,0.4056343,0.4076449,0.4097659,0.4120045,0.4143677,0.4168618,0.4181593,0.4194907,0.4208559,0.421551,0.4222542,0.4225378,0.4228226,0.4231087,0.423396,0.4236846,0.4239744,0.4242653,0.4244112,0.4245575,0.424704,0.4247773,0.4248508,0.4249243,0.424939,0.4249537,0.4249684,0.4249832,0.4249979,0.4250273,0.4250568,0.4250715,0.4250863 } };
2733 
2734  const double imomegaqnm20[1][107] =
2735  { { 0.0718433,0.0718525,0.0718618,0.0718802,0.0718987,0.0719079,0.0719171,0.0719263,0.0719355,0.0719446,0.0719904,0.0720361,0.0720815,0.0721719,0.0722617,0.0723508,0.0725271,0.0727008,0.072872,0.0730407,0.073207,0.0733709,0.0735324,0.0739263,0.0743063,0.0750275,0.0757007,0.0763302,0.077473,0.0784827,0.0793808,0.0801846,0.080908,0.0815621,0.0821563,0.082698,0.0831935,0.0836483,0.0840667,0.0844526,0.0852955,0.0859947,0.0865789,0.0870691,0.087481,0.0878266,0.088115,0.0883533,0.088547,0.0887004,0.0888166,0.0888981,0.0889463,0.0889623,0.0889463,0.0888981,0.0888166,0.0887004,0.088547,0.0883533,0.088115,0.0878266,0.087481,0.0870691,0.0865789,0.0859947,0.0852955,0.0844526,0.0840667,0.0836483,0.0831935,0.082698,0.0821563,0.0815621,0.080908,0.0801846,0.0793808,0.0784827,0.077473,0.0763302,0.0757007,0.0750275,0.0743063,0.0739263,0.0735324,0.0733709,0.073207,0.0730407,0.072872,0.0727008,0.0725271,0.0723508,0.0722617,0.0721719,0.0720815,0.0720361,0.0719904,0.0719446,0.0719355,0.0719263,0.0719171,0.0719079,0.0718987,0.0718802,0.0718618,0.0718525,0.0718433 } };
2736 
2737  /* 3, 3 mode */
2738 
2739  const double reomegaqnm33[1][107] =
2740  { { 0.463862,0.4638713,0.4638807,0.4638994,0.4639182,0.4639275,0.4639369,0.4639463,0.4639556,0.463965,0.4640118,0.4640587,0.4641056,0.4641994,0.4642932,0.4643871,0.4645751,0.4647632,0.4649516,0.4651403,0.4653291,0.4655181,0.4657074,0.4661816,0.4666572,0.4676125,0.4685735,0.4695402,0.471491,0.4734653,0.4754638,0.4774869,0.4795352,0.4816091,0.4837094,0.4858366,0.4879912,0.490174,0.4923856,0.4946267,0.500363,0.5062995,0.5124492,0.5188258,0.5254448,0.532323,0.5394792,0.546934,0.5547105,0.5628344,0.5713348,0.5802442,0.5895997,0.5994433,0.6098233,0.6207956,0.6324249,0.644787,0.6579717,0.6720861,0.6872595,0.7036503,0.7214547,0.7409211,0.7623694,0.7862227,0.8130569,0.8436869,0.8572538,0.8717171,0.8872013,0.9038599,0.9218848,0.9415207,0.9630876,0.9870158,1.0139059,1.0446371,1.0805826,1.1240969,1.1499829,1.1798616,1.2154694,1.2363667,1.2602289,1.2708575,1.2822677,1.2946158,1.3081174,1.3230831,1.3399448,1.359167,1.3698085,1.3812143,1.3934425,1.3998831,1.4065511,1.4134538,1.4148631,1.4162821,1.417711,1.4191497,1.4205983,1.4235255,1.426493,1.427992,1.4295013 } };
2741 
2742  const double imomegaqnm33[1][107] =
2743  { { 0.0909297,0.0909301,0.0909305,0.0909312,0.0909319,0.0909323,0.0909327,0.090933,0.0909334,0.0909338,0.0909356,0.0909375,0.0909393,0.090943,0.0909466,0.0909503,0.0909576,0.090965,0.0909723,0.0909796,0.0909869,0.0909942,0.0910015,0.0910197,0.0910378,0.091074,0.09111,0.0911457,0.0912166,0.0912867,0.091356,0.0914243,0.0914917,0.0915582,0.0916236,0.091688,0.0917514,0.0918136,0.0918746,0.0919344,0.0920784,0.0922137,0.0923394,0.0924547,0.0925583,0.0926492,0.0927258,0.0927867,0.0928302,0.0928541,0.0928562,0.0928338,0.092784,0.092703,0.0925869,0.0924305,0.0922281,0.0919726,0.0916556,0.0912666,0.0907928,0.0902179,0.0895213,0.0886763,0.087647,0.0863849,0.0848213,0.0828557,0.0819248,0.0808922,0.0797413,0.0784512,0.0769953,0.075339,0.0734361,0.0712234,0.0686106,0.0654629,0.0615646,0.0565371,0.0533881,0.0496087,0.0449046,0.0420439,0.0386881,0.0371631,0.0355053,0.0336873,0.0316714,0.0294027,0.026805,0.0237965,0.0221125,0.020295,0.0183338,0.0172961,0.0162186,0.0151,0.0148713,0.0146409,0.0144087,0.0141748,0.0139392,0.0134627,0.0129791,0.0127347,0.0124884 } };
2744 
2745  /* 3, 2 mode */
2746 
2747  const double reomegaqnm32[1][107] =
2748  { { 0.5136068,0.513612,0.5136172,0.5136277,0.5136381,0.5136433,0.5136486,0.5136538,0.513659,0.5136642,0.5136904,0.5137165,0.5137426,0.513795,0.5138473,0.5138998,0.5140048,0.51411,0.5142154,0.514321,0.5144268,0.5145327,0.5146389,0.5149053,0.5151728,0.5157118,0.5162557,0.5168047,0.5179181,0.5190523,0.5202076,0.5213842,0.5225826,0.5238031,0.525046,0.5263118,0.5276007,0.5289131,0.5302496,0.5316104,0.5351221,0.5387961,0.5426403,0.5466633,0.5508747,0.5552848,0.5599054,0.5647494,0.5698311,0.5751666,0.5807739,0.5866734,0.5928879,0.5994433,0.6063693,0.6137,0.6214745,0.6297385,0.6385453,0.6479581,0.6580522,0.6689185,0.6806685,0.6934404,0.7074094,0.722802,0.7399192,0.7591747,0.7676002,0.7765087,0.7859588,0.7960213,0.8067828,0.8183509,0.8308625,0.844496,0.859491,0.8761828,0.8950661,0.9169285,0.9293747,0.9431793,0.9587794,0.9674661,0.9769241,0.9809677,0.985185,0.9896014,0.9942441,0.9991404,1.0043175,1.0098027,1.0126693,1.0156233,1.0186679,1.0202252,1.0218065,1.0234122,1.0237363,1.0240613,1.0243874,1.0247145,1.0250426,1.0257018,1.0263651,1.0266983,1.0270325 } };
2749 
2750  const double imomegaqnm32[1][107] =
2751  { { 0.0892015,0.0892023,0.0892031,0.0892048,0.0892064,0.0892072,0.089208,0.0892089,0.0892097,0.0892105,0.0892146,0.0892186,0.0892227,0.0892308,0.089239,0.0892471,0.0892632,0.0892794,0.0892954,0.0893115,0.0893275,0.0893434,0.0893593,0.0893988,0.089438,0.0895156,0.0895921,0.0896674,0.0898147,0.0899577,0.0900965,0.0902312,0.0903618,0.0904885,0.0906114,0.0907305,0.090846,0.0909578,0.0910661,0.0911709,0.0914181,0.0916444,0.0918505,0.0920366,0.0922029,0.0923491,0.092475,0.0925799,0.0926631,0.0927235,0.0927597,0.0927698,0.0927518,0.092703,0.0926202,0.0924995,0.0923361,0.0921243,0.0918568,0.0915248,0.0911173,0.0906203,0.0900158,0.0892804,0.0883827,0.08728,0.0859118,0.0841896,0.0833733,0.0824675,0.0814574,0.0803247,0.0790459,0.0775905,0.0759179,0.0739724,0.0716744,0.0689047,0.0654729,0.0610437,0.0582675,0.0549333,0.0507808,0.0482551,0.0452927,0.0439479,0.0424887,0.0408868,0.0391109,0.0371298,0.0349121,0.0324265,0.0310735,0.0296418,0.0281275,0.0273382,0.0265267,0.0256927,0.0255231,0.0253526,0.0251812,0.0250088,0.0248355,0.0244861,0.0241328,0.0239548,0.0237758 } };
2752 
2753  /* 4, 4 mode */
2754 
2755  const double reomegaqnm44[1][107] =
2756  { { 0.6208855,0.6208986,0.6209116,0.6209377,0.6209638,0.6209769,0.6209899,0.621003,0.6210161,0.6210291,0.6210944,0.6211597,0.6212251,0.6213558,0.6214866,0.6216175,0.6218794,0.6221417,0.6224043,0.6226672,0.6229304,0.6231939,0.6234577,0.6241186,0.6247814,0.6261129,0.6274522,0.6287994,0.6315179,0.6342691,0.6370537,0.6398724,0.6427259,0.6456151,0.6485406,0.6515033,0.654504,0.6575436,0.660623,0.6637431,0.6717278,0.6799888,0.6885434,0.6974107,0.7066113,0.7161682,0.7261067,0.7364547,0.7472435,0.7585077,0.7702864,0.7826235,0.7955686,0.8091784,0.8235174,0.8386602,0.8546934,0.871718,0.8898534,0.9092417,0.9300542,0.9525002,0.9768386,1.003396,1.0325924,1.0649814,1.101315,1.1426539,1.1609185,1.180359,1.2011367,1.2234501,1.247547,1.2737433,1.3024512,1.3342248,1.3698366,1.4104161,1.4577259,1.5147847,1.5486233,1.5875889,1.6339032,1.6610247,1.6919428,1.7056971,1.7204515,1.7364057,1.753835,1.7731363,1.7948438,1.819517,1.8331405,1.8477153,1.8633113,1.871514,1.8799983,1.8887728,1.8905633,1.8923658,1.8941804,1.8960072,1.8978463,1.9015614,1.9053262,1.9072275,1.9091415 } };
2757 
2758  const double imomegaqnm44[1][107] =
2759  { { 0.0917882,0.0917886,0.091789,0.0917898,0.0917907,0.0917911,0.0917915,0.0917919,0.0917923,0.0917928,0.0917948,0.0917969,0.091799,0.0918032,0.0918073,0.0918115,0.0918198,0.0918281,0.0918364,0.0918447,0.091853,0.0918613,0.0918696,0.0918903,0.0919109,0.0919521,0.0919931,0.092034,0.0921151,0.0921956,0.0922753,0.0923543,0.0924324,0.0925097,0.0925861,0.0926616,0.0927361,0.0928096,0.0928821,0.0929535,0.0931268,0.093292,0.0934484,0.0935949,0.0937302,0.0938532,0.0939623,0.0940559,0.0941321,0.0941887,0.0942233,0.094233,0.0942145,0.094164,0.0940768,0.0939478,0.0937705,0.0935374,0.0932393,0.092865,0.0924006,0.0918287,0.0911274,0.0902679,0.0892124,0.0879094,0.086287,0.0842401,0.0832692,0.0821917,0.0809905,0.0796442,0.0781255,0.0763992,0.0744185,0.0721192,0.0694103,0.066156,0.0621396,0.056982,0.0537633,0.0499111,0.0451315,0.0422323,0.0388376,0.037297,0.0356236,0.0337901,0.0317587,0.0294747,0.0268643,0.0238503,0.0221678,0.0203555,0.0184036,0.0173723,0.0163026,0.0151931,0.0149663,0.0147379,0.0145079,0.0142761,0.0140427,0.0135708,0.0130921,0.0128502,0.0126066 } };
2760 
2761  /* 4, 3 mode */
2762 
2763  const double reomegaqnm43[1][107] =
2764  { { 0.6693003,0.6693096,0.669319,0.6693378,0.6693566,0.669366,0.6693754,0.6693847,0.6693941,0.6694035,0.6694505,0.6694975,0.6695445,0.6696385,0.6697326,0.6698268,0.6700154,0.6702042,0.6703932,0.6705825,0.6707721,0.6709619,0.671152,0.6716283,0.6721062,0.6730669,0.6740342,0.6750081,0.6769759,0.6789709,0.6809934,0.6830442,0.6851236,0.6872322,0.6893706,0.6915394,0.6937392,0.6959706,0.6982341,0.7005306,0.7064203,0.7125313,0.718876,0.7254679,0.7323219,0.7394544,0.7468833,0.7546284,0.762712,0.7711586,0.7799957,0.789254,0.7989685,0.8091784,0.8199287,0.8312708,0.8432641,0.8559777,0.8694922,0.8839034,0.8993256,0.9158968,0.9337868,0.9532065,0.9744241,0.9977881,1.0237636,1.0529941,1.0657927,1.0793335,1.0937094,1.1090333,1.125444,1.1431159,1.1622721,1.1832067,1.2063199,1.2321809,1.2616477,1.2961279,1.3159845,1.3382581,1.3638397,1.3783312,1.3943717,1.4013335,1.4086741,1.4164573,1.4247668,1.4337213,1.4434439,1.4540576,1.4597371,1.4656856,1.4719184,1.4751462,1.4784509,1.4818344,1.4825207,1.4832103,1.4839031,1.4845992,1.4852986,1.4867073,1.4881293,1.4888454,1.4895648 } };
2765 
2766  const double imomegaqnm43[1][107] =
2767  { { 0.0909037,0.0909044,0.090905,0.0909063,0.0909076,0.0909082,0.0909088,0.0909095,0.0909101,0.0909107,0.0909139,0.0909171,0.0909203,0.0909267,0.090933,0.0909394,0.090952,0.0909647,0.0909773,0.0909899,0.0910025,0.0910151,0.0910276,0.0910588,0.0910899,0.0911517,0.0912128,0.0912734,0.0913929,0.09151,0.0916249,0.0917376,0.091848,0.0919562,0.0920622,0.0921659,0.0922675,0.0923668,0.0924639,0.0925588,0.0927862,0.0929995,0.0931982,0.0933819,0.09355,0.0937018,0.0938363,0.0939523,0.0940485,0.0941233,0.0941747,0.0942005,0.094198,0.094164,0.0940946,0.0939853,0.0938306,0.0936239,0.0933572,0.0930204,0.0926012,0.092084,0.0914489,0.0906697,0.089712,0.0885284,0.0870525,0.0851868,0.0843003,0.0833153,0.0822157,0.0809813,0.0795864,0.0779977,0.0761705,0.0740437,0.0715299,0.0684982,0.0647384,0.0598795,0.0568286,0.0531572,0.0485691,0.0457669,0.0424661,0.0409602,0.0393192,0.0375143,0.0355057,0.0332342,0.030638,0.0276553,0.0259997,0.0242243,0.0223214,0.0213197,0.0202832,0.019211,0.0189922,0.0187719,0.0185501,0.0183269,0.0181021,0.017648,0.0171879,0.0169555,0.0167216 } };
2768 
2769  /* 5, 5 mode */
2770 
2771  const double reomegaqnm55[1][107] =
2772  { { 0.7722084,0.772225,0.7722417,0.7722749,0.7723082,0.7723249,0.7723415,0.7723582,0.7723748,0.7723915,0.7724747,0.772558,0.7726413,0.772808,0.7729748,0.7731417,0.7734757,0.7738101,0.774145,0.7744802,0.7748158,0.7751518,0.7754882,0.7763309,0.777176,0.7788738,0.7805816,0.7822995,0.7857661,0.7892744,0.7928254,0.7964199,0.8000589,0.8037434,0.8074743,0.8112526,0.8150796,0.8189561,0.8228834,0.8268627,0.8370462,0.8475822,0.8584928,0.8698019,0.8815359,0.893724,0.9063981,0.9195938,0.9333504,0.9477121,0.9627282,0.9784541,0.9949527,1.0122953,1.0305636,1.0498516,1.0702682,1.0919408,1.1150193,1.1396824,1.166145,1.1946693,1.2255796,1.2592842,1.2963072,1.3373388,1.383315,1.4355536,1.4586087,1.4831307,1.5093194,1.5374201,1.5677389,1.6006659,1.6367095,1.6765525,1.721146,1.7718796,1.8309191,1.9019707,1.9440292,1.9923892,2.0497724,2.0833278,2.1215386,2.1385228,2.1567323,2.1764116,2.1978973,2.2216752,2.2483857,2.2786917,2.2954002,2.3132563,2.3323427,2.3423732,2.3527424,2.3634606,2.365647,2.3678479,2.3700633,2.3722934,2.3745382,2.3790722,2.383666,2.3859855,2.3883203 } };
2773 
2774  const double imomegaqnm55[1][107] =
2775  { { 0.0921596,0.09216,0.0921605,0.0921613,0.0921622,0.0921627,0.0921631,0.0921635,0.092164,0.0921644,0.0921666,0.0921688,0.0921711,0.0921755,0.0921799,0.0921843,0.0921931,0.0922019,0.0922107,0.0922195,0.0922283,0.0922371,0.0922459,0.0922679,0.0922898,0.0923335,0.092377,0.0924205,0.0925068,0.0925926,0.0926777,0.092762,0.0928457,0.0929286,0.0930106,0.0930918,0.0931722,0.0932516,0.09333,0.0934074,0.0935961,0.0937773,0.09395,0.0941133,0.094266,0.0944066,0.0945339,0.094646,0.0947411,0.0948169,0.0948709,0.0949002,0.0949014,0.0948705,0.094803,0.0946932,0.0945348,0.0943198,0.0940389,0.0936804,0.0932301,0.09267,0.0919774,0.0911228,0.0900671,0.0887575,0.0871199,0.0850466,0.0840612,0.0829665,0.0817451,0.0803751,0.0788289,0.0770706,0.0750526,0.0727103,0.0699513,0.0666388,0.0625545,0.0573174,0.054054,0.0501531,0.0453206,0.0423931,0.038969,0.0374162,0.0357305,0.0338844,0.0318402,0.0295431,0.026921,0.0238989,0.0222145,0.0204021,0.0184523,0.0174229,0.0163557,0.0152495,0.0150235,0.0147958,0.0145665,0.0143356,0.0141031,0.013633,0.0131562,0.0129153,0.0126727 } };
2776 
2777 
2778  /* To actually calculate the ringdown, we will use the following pointers to point to the correct mode */
2779  const double (*reomegaqnm)[107] = NULL;
2780  const double (*imomegaqnm)[107] = NULL;
2781 
2782  /* Stuff for interpolating the data */
2783  gsl_spline *spline = NULL;
2784  gsl_interp_accel *acc = NULL;
2785 
2786  UINT4 i;
2787  REAL8 signm = m < 0 ? -1.0 : 1.0;
2788 
2789  /* Check we do not require more overtones than we have */
2790  if (nmodes > 8) {
2791  XLALPrintError("Requesting more overtones than we have data to generate!\n");
2792  XLAL_ERROR(XLAL_EINVAL);
2793  }
2794 
2795  /* Choose the appropriate data bases on the user requested l and m */
2796  switch (l) {
2797  case 2:
2798  if (abs(m) == 2) {
2799  reomegaqnm = reomegaqnm22;
2800  imomegaqnm = imomegaqnm22;
2801  } else if (abs(m) == 1) {
2802  reomegaqnm = reomegaqnm21;
2803  imomegaqnm = imomegaqnm21;
2804  } else if (abs(m) == 0) {
2805  reomegaqnm = reomegaqnm20;
2806  imomegaqnm = imomegaqnm20;
2807  } else {
2808  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2809  XLAL_ERROR(XLAL_EINVAL);
2810  }
2811  break;
2812  case 3:
2813  if (abs(m) == 3) {
2814  reomegaqnm = reomegaqnm33;
2815  imomegaqnm = imomegaqnm33;
2816  } else if (abs(m) == 2) {
2817  reomegaqnm = reomegaqnm32;
2818  imomegaqnm = imomegaqnm32;
2819  } else {
2820  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2821  XLAL_ERROR(XLAL_EINVAL);
2822  }
2823  break;
2824  case 4:
2825  if (abs(m) == 4) {
2826  reomegaqnm = reomegaqnm44;
2827  imomegaqnm = imomegaqnm44;
2828  } else if (abs(m) == 3) {
2829  reomegaqnm = reomegaqnm43;
2830  imomegaqnm = imomegaqnm43;
2831  } else {
2832  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2833  XLAL_ERROR(XLAL_EINVAL);
2834  }
2835  break;
2836  case 5:
2837  if (abs(m) == 5) {
2838  reomegaqnm = reomegaqnm55;
2839  imomegaqnm = imomegaqnm55;
2840  } else {
2841  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2842  XLAL_ERROR(XLAL_EINVAL);
2843  }
2844  break;
2845  default:
2846  XLALPrintError("Unsupported combination of l, m (%d, %d)\n", l, m);
2847  XLAL_ERROR(XLAL_EINVAL);
2848  break;
2849  }
2850 
2851  spline = gsl_spline_alloc(gsl_interp_cspline, 107);
2852  acc = gsl_interp_accel_alloc();
2853 
2854  /* finalSpin interpolation is available only between -0.9996 and 0.9996 */
2855  /* Set finalSpin to +/- 0.9996 if it is out of this range */
2856  if (finalSpin < -0.9996 || finalSpin > 0.9996) {
2857  XLALPrintError("Final spin must be between -0.9996 and 0.9996");
2858  XLAL_ERROR(XLAL_EINVAL);
2859  }
2860  /* Now get the QNM frequencies from interpolating the above data */
2861  for (i = 0; i < nmodes; i++) {
2862  gsl_spline_init(spline, afinallist, reomegaqnm[i], 107);
2863  gsl_interp_accel_reset(acc);
2864 
2865  modefreqs->data[i] = signm * gsl_spline_eval(spline, signm * finalSpin, acc);
2866 
2867  gsl_spline_init(spline, afinallist, imomegaqnm[i], 107);
2868  gsl_interp_accel_reset(acc);
2869 
2870  modefreqs->data[i] += I * gsl_spline_eval(spline, signm * finalSpin, acc);
2871 
2872  /* Scale by the appropriate mass factors */
2873  modefreqs->data[i] *= 1. / (finalMass * LAL_MTSUN_SI);
2874  }
2875  /* Free memory and exit */
2876  gsl_spline_free(spline);
2877  gsl_interp_accel_free(acc);
2878 
2879  return XLAL_SUCCESS;
2880 }
XLALSimBlackHoleRingdownModeRadialCoefficientsLeaver
static int XLALSimBlackHoleRingdownModeRadialCoefficientsLeaver(COMPLEX16 *alp, COMPLEX16 *bet, COMPLEX16 *gam, double a, int UNUSED l, int m, int n, int s, COMPLEX16 A, COMPLEX16 omega)
Definition: LALSimBlackHoleRingdown.c:64
XLALSimIMREOBGenerateQNMFreqV5
INT4 XLALSimIMREOBGenerateQNMFreqV5(COMPLEX16Vector *modefreqs, const REAL8 mass1, const REAL8 mass2, const REAL8 spin1[3], const REAL8 spin2[3], UINT4 l, INT4 m, UINT4 nmodes, Approximant approximant)
These functions generate the quasinormal mode frequencies for a black hole ringdown,...
Definition: LALSimBlackHoleRingdown.c:2654
XLALSimBlackHoleRingdownModeSchwarzschildEigenvalueSolveResid
static int XLALSimBlackHoleRingdownModeSchwarzschildEigenvalueSolveResid(const gsl_vector *x, void *params, gsl_vector *f)
Definition: LALSimBlackHoleRingdown.c:129
XLALSimBlackHoleRingdownModeKerrEigenvalueSolveResid
static int XLALSimBlackHoleRingdownModeKerrEigenvalueSolveResid(const gsl_vector *x, void *params, gsl_vector *f)
Definition: LALSimBlackHoleRingdown.c:148
XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver
static COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunction1Leaver(double mu, double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega)
Definition: LALSimBlackHoleRingdown.c:306
XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver
static COMPLEX16 XLALSimBlackHoleRingdownModeEigenvalueEvaluateContinuedFractionLeaver(double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega, int(*coef)(COMPLEX16 *, COMPLEX16 *, COMPLEX16 *, double, int, int, int, int, COMPLEX16, COMPLEX16))
Definition: LALSimBlackHoleRingdown.c:86
XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver
static COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunctionNormLeaver(double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega)
Definition: LALSimBlackHoleRingdown.c:360
EPS
#define EPS
Definition: LALSimBlackHoleRingdown.c:17
XLALSimBlackHoleRingdownModeEigenvalueSolveKerr
static int XLALSimBlackHoleRingdownModeEigenvalueSolveKerr(COMPLEX16 *A, COMPLEX16 *omega, double a, int l, int m, int s)
Definition: LALSimBlackHoleRingdown.c:238
XLALSimBlackHoleRingdownModeSphericalCoefficientsLeaver
static int XLALSimBlackHoleRingdownModeSphericalCoefficientsLeaver(COMPLEX16 *alp, COMPLEX16 *bet, COMPLEX16 *gam, double UNUSED a, int l, int UNUSED m, int n, int s, COMPLEX16 UNUSED A, COMPLEX16 omega)
Definition: LALSimBlackHoleRingdown.c:38
XLALSimBlackHoleRingdownModeEigenvalueSolveSchwarzschild
static int XLALSimBlackHoleRingdownModeEigenvalueSolveSchwarzschild(COMPLEX16 *omega, int l, int m, int s)
Definition: LALSimBlackHoleRingdown.c:173
XLALSimBlackHoleRingdownSpheriodalWaveFunctionNormIntegrand
static double XLALSimBlackHoleRingdownSpheriodalWaveFunctionNormIntegrand(double mu, void *params)
Definition: LALSimBlackHoleRingdown.c:344
MAXITER
#define MAXITER
Definition: LALSimBlackHoleRingdown.c:19
TINY
#define TINY
Definition: LALSimBlackHoleRingdown.c:18
XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver
static int XLALSimBlackHoleRingdownModeAngularCoefficientsLeaver(COMPLEX16 *alp, COMPLEX16 *bet, COMPLEX16 *gam, double a, int UNUSED l, int m, int n, int s, COMPLEX16 A, COMPLEX16 omega)
Definition: LALSimBlackHoleRingdown.c:50
XLALSimIMREOBGenerateQNMFreqV5fromFinal
INT4 XLALSimIMREOBGenerateQNMFreqV5fromFinal(COMPLEX16Vector *modefreqs, const REAL8 finalMass, const REAL8 finalSpin, UINT4 l, INT4 m, UINT4 nmodes)
Definition: LALSimBlackHoleRingdown.c:2691
k11
static const REAL8 k11
Definition: LALSimBlackHoleRingdown.h:98
s5coeff
static const REAL8 s5coeff
Definition: LALSimBlackHoleRingdown.h:78
s4v2coeff
static const REAL8 s4v2coeff
Definition: LALSimBlackHoleRingdown.h:85
t2v2coeff
static const REAL8 t2v2coeff
Definition: LALSimBlackHoleRingdown.h:88
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
s7coeff
static const REAL8 s7coeff
Definition: LALSimBlackHoleRingdown.h:82
t3v2coeff
static const REAL8 t3v2coeff
Definition: LALSimBlackHoleRingdown.h:87
p1coeff
static const REAL8 p1coeff
Definition: LALSimBlackHoleRingdown.h:71
k24
static const REAL8 k24
Definition: LALSimBlackHoleRingdown.h:106
k30
static const REAL8 k30
Definition: LALSimBlackHoleRingdown.h:107
t3coeff
static const REAL8 t3coeff
Definition: LALSimBlackHoleRingdown.h:76
s5v2coeff
static const REAL8 s5v2coeff
Definition: LALSimBlackHoleRingdown.h:84
k02
static const REAL8 k02
Definition: LALSimBlackHoleRingdown.h:94
t0coeff
static const REAL8 t0coeff
Definition: LALSimBlackHoleRingdown.h:74
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
t2coeff
static const REAL8 t2coeff
Definition: LALSimBlackHoleRingdown.h:75
k23
static const REAL8 k23
Definition: LALSimBlackHoleRingdown.h:105
k20
static const REAL8 k20
Definition: LALSimBlackHoleRingdown.h:102
s6coeff
static const REAL8 s6coeff
Definition: LALSimBlackHoleRingdown.h:83
s8coeff
static const REAL8 s8coeff
Definition: LALSimBlackHoleRingdown.h:81
k00
static const REAL8 k00
Definition: LALSimBlackHoleRingdown.h:92
k22
static const REAL8 k22
Definition: LALSimBlackHoleRingdown.h:104
s9coeff
static const REAL8 s9coeff
Definition: LALSimBlackHoleRingdown.h:80
k21
static const REAL8 k21
Definition: LALSimBlackHoleRingdown.h:103
k03
static const REAL8 k03
Definition: LALSimBlackHoleRingdown.h:95
t0v2coeff
static const REAL8 t0v2coeff
Definition: LALSimBlackHoleRingdown.h:86
p0coeff
static const REAL8 p0coeff
Definition: LALSimBlackHoleRingdown.h:70
k10
static const REAL8 k10
Definition: LALSimBlackHoleRingdown.h:97
p2coeff
static const REAL8 p2coeff
Definition: LALSimBlackHoleRingdown.h:72
s4coeff
static const REAL8 s4coeff
Definition: LALSimBlackHoleRingdown.h:77
c1
const double c1
Definition: LALSimIMRLackeyTidal2013.c:51
c2
const double c2
Definition: LALSimIMRLackeyTidal2013.c:52
c0
const double c0
Definition: LALSimIMRLackeyTidal2013.c:50
delta
static double double delta
Definition: LALSimIMRPhenomTHM_fits.h:105
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
error
static REAL8TimeSeries * error(const REAL8TimeSeries *s1, const REAL8TimeSeries *s0)
Definition: LALSimulationTest.c:88
sum
static REAL8 sum(REAL8 *arr1, REAL8 *arr2, int k)
Definition: PNCoefficients.c:118
fprintf
#define fprintf
main
int main(int argc, char *argv[])
Definition: bh_qnmode.c:226
s
int s
Definition: bh_qnmode.c:137
l
int l
Definition: bh_qnmode.c:135
M
REAL8 M
Definition: bh_qnmode.c:133
dt
double dt
Definition: bh_ringdown.c:113
i
double i
Definition: bh_ringdown.c:118
e
double e
Definition: bh_ringdown.c:117
theta
double theta
Definition: bh_sphwf.c:118
k2
coeffs k2
Definition: exact_derivatives-HrealHeader.c:40
a2
const double a2
Definition: exact_derivatives-HrealHeader.c:33
w
const double w
Definition: exact_derivatives-HrealHeader.c:106
k1
coeffs k1
Definition: exact_derivatives-HrealHeader.c:39
csi
const double csi
Definition: exact_derivatives-HrealHeader.c:125
LAL_C_SI
#define LAL_C_SI
LAL_MSUN_SI
#define LAL_MSUN_SI
LAL_REAL8_EPS
#define LAL_REAL8_EPS
LAL_PI
#define LAL_PI
LAL_TWOPI
#define LAL_TWOPI
LAL_MTSUN_SI
#define LAL_MTSUN_SI
LAL_PC_SI
#define LAL_PC_SI
LAL_G_SI
#define LAL_G_SI
XLAL_NUM_ELEM
#define XLAL_NUM_ELEM(x)
COMPLEX16
double complex COMPLEX16
REAL8
double REAL8
UINT4
uint32_t UINT4
INT4
int32_t INT4
XLALbbh_final_mass_non_precessing_UIB2016
REAL8 XLALbbh_final_mass_non_precessing_UIB2016(const REAL8 m1, const REAL8 m2, const REAL8 chi1, const REAL8 chi2)
Calculate the final mass with the aligned-spin NR fit.
Definition: LALSimBHNSRemnantFits.c:174
XLALSimBlackHoleRingdownMode
int XLALSimBlackHoleRingdownMode(double *frequency, double *quality, double mass, double dimensionless_spin, int l, int m, int s)
Computes the frequency and quality factor of a specified quasinormal mode (l,m) of spin weight s pert...
Definition: LALSimBlackHoleRingdown.c:551
XLALSimIMREOBGenerateQNMFreqV2fromFinal
INT4 XLALSimIMREOBGenerateQNMFreqV2fromFinal(COMPLEX16Vector *modefreqs, const REAL8 finalMass, const REAL8 finalSpin, UINT4 l, INT4 m, UINT4 nmodes)
Definition: LALSimBlackHoleRingdown.c:895
XLALSimIMREOBFinalMassSpin
INT4 XLALSimIMREOBFinalMassSpin(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: LALSimBlackHoleRingdown.c:721
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
XLALSimBlackHoleRingdownModeEigenvaluesLeaver
int XLALSimBlackHoleRingdownModeEigenvaluesLeaver(COMPLEX16 *A, COMPLEX16 *omega, double a, int l, int m, int s)
Low-level routine that computes the black hole quasinormal mode eigenefrequency, omega,...
Definition: LALSimBlackHoleRingdown.c:434
XLALSimIMREOBGenerateQNMFreqV2
INT4 XLALSimIMREOBGenerateQNMFreqV2(COMPLEX16Vector *modefreqs, const REAL8 mass1, const REAL8 mass2, const REAL8 spin1[3], const REAL8 spin2[3], UINT4 l, INT4 m, UINT4 nmodes, Approximant approximant)
These functions generate the quasinormal mode frequencies for a black hole ringdown.
Definition: LALSimBlackHoleRingdown.c:858
XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver
COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunctionLeaver(double mu, double a, int l, int m, int s, COMPLEX16 A, COMPLEX16 omega)
Low-level routine that evaluates the spheroidal wave function at a specified value of mu = cos(theta)...
Definition: LALSimBlackHoleRingdown.c:503
XLALSimBlackHoleRingdownSpheroidalWaveFunction
COMPLEX16 XLALSimBlackHoleRingdownSpheroidalWaveFunction(double theta, double dimensionless_spin, int l, int m, int s)
Evaluates the value of spheroidal wave function at a given polar angle theta for a specified mode (l,...
Definition: LALSimBlackHoleRingdown.c:585
XLALSimBlackHoleRingdown
int XLALSimBlackHoleRingdown(REAL8TimeSeries **hplus, REAL8TimeSeries **hcross, const LIGOTimeGPS *t0, double phi0, double deltaT, double mass, double dimensionless_spin, double fractional_mass_loss, double distance, double inclination, int l, int m)
Computes the waveform for the ringdown of a black hole quasinormal mode (l,m).
Definition: LALSimBlackHoleRingdown.c:612
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
SEOBNRv4
@ SEOBNRv4
Spin nonprecessing EOBNR model v4.
Definition: LALSimInspiral.h:338
EOBNRv2
@ EOBNRv2
UNDOCUMENTED.
Definition: LALSimInspiral.h:314
EOBNR
@ EOBNR
UNDOCUMENTED.
Definition: LALSimInspiral.h:312
SEOBNRv5_ROM
@ SEOBNRv5_ROM
Time domain, precessing phenomenological IMR waveform model with subdominant modes ([arXiv: 20XY....
Definition: LALSimInspiral.h:440
r
static const INT4 r
m
static const INT4 m
q
static const INT4 q
eps
static const REAL4 eps
a
static const INT4 a
XLALCreateREAL8TimeSeries
REAL8TimeSeries * XLALCreateREAL8TimeSeries(const CHAR *name, const LIGOTimeGPS *epoch, REAL8 f0, REAL8 deltaT, const LALUnit *sampleUnits, size_t length)
XLALDestroyREAL8TimeSeries
void XLALDestroyREAL8TimeSeries(REAL8TimeSeries *series)
lalStrainUnit
const LALUnit lalStrainUnit
XLAL_ERROR_REAL8
#define XLAL_ERROR_REAL8(...)
XLALAbortErrorHandler
void XLALAbortErrorHandler(const char *func, const char *file, int line, int errnum)
XLAL_ERROR
#define XLAL_ERROR(...)
XLAL_TRY
#define XLAL_TRY(statement, errnum)
XLALPrintError
int XLALPrintError(const char *fmt,...) _LAL_GCC_PRINTF_FORMAT_(1
XLALSetErrorHandler
XLALErrorHandlerType * XLALSetErrorHandler(XLALErrorHandlerType *newHandler)
XLAL_EBADLEN
XLAL_EBADLEN
XLAL_ENOMEM
XLAL_ENOMEM
XLAL_SUCCESS
XLAL_SUCCESS
XLAL_EFUNC
XLAL_EFUNC
XLAL_EMAXITER
XLAL_EMAXITER
XLAL_EINVAL
XLAL_EINVAL
XLAL_FAILURE
XLAL_FAILURE
x
list x
p
list p
mu
list mu
status
string status
COMPLEX16Vector::data
COMPLEX16 * data
REAL8TimeSeries::data
REAL8Sequence * data
REAL8Vector::data
REAL8 * data
params
Definition: burst.c:245
fp
FILE * fp
epoch
LIGOTimeGPS epoch
Definition: unicorn.c:20
deltaT
double deltaT
Definition: unicorn.c:24