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LALSimulation 6.2.0.1-5e288d3
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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
27struct 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). */
38static 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). */
50static 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). */
64static 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). */
86static 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). */
129static 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. */
148static 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. */
173static 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. */
238static 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) */
306static 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. */
344static 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. */
360static 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 */
434int 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 */
503COMPLEX16 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 */
551int 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 */
585COMPLEX16 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 */
612int 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
676REAL8 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
691REAL8 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
699REAL8 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 */
721INT4 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 */
858INT4 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
895INT4 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>
2481int 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
2510int 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
2540int 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
2566int 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
2599int 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
2632int 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 */
2654INT4 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
2691INT4 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
XLALDestroyREAL8TimeSeries
void XLALDestroyREAL8TimeSeries(REAL8TimeSeries *series)
XLALCreateREAL8TimeSeries
REAL8TimeSeries * XLALCreateREAL8TimeSeries(const CHAR *name, const LIGOTimeGPS *epoch, REAL8 f0, REAL8 deltaT, const LALUnit *sampleUnits, size_t length)
lalStrainUnit
const LALUnit lalStrainUnit
XLAL_ERROR_REAL8
#define XLAL_ERROR_REAL8(...)
XLALAbortErrorHandler
void XLALAbortErrorHandler(const char *func, const char *file, int line, int errnum)
XLALSetErrorHandler
XLALErrorHandlerType * XLALSetErrorHandler(XLALErrorHandlerType *newHandler)
XLAL_ERROR
#define XLAL_ERROR(...)
XLAL_TRY
#define XLAL_TRY(statement, errnum)
XLALPrintError
int XLALPrintError(const char *fmt,...) _LAL_GCC_PRINTF_FORMAT_(1
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
mu
list mu
status
string status
p
p
x
x
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