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grpp_specfunc_scaled_mod_sph_bessel.c
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1/*----------------------------------------------------------------------------*/
2/* CP2K: A general program to perform molecular dynamics simulations */
3/* Copyright 2000-2025 CP2K developers group <https://cp2k.org> */
4/* */
5/* SPDX-License-Identifier: MIT */
6/*----------------------------------------------------------------------------*/
7
8/*
9 * libgrpp - a library for the evaluation of integrals over
10 * generalized relativistic pseudopotentials.
11 *
12 * Copyright (C) 2021-2023 Alexander Oleynichenko
13 */
14#include <math.h>
15
16#ifndef M_PI
17#define M_PI 3.1415926535897932384626433
18#endif
19
20#include "grpp_specfunc.h"
21#include "libgrpp.h"
22
23/*
24 * assumed max angular momentum
25 */
26#define LMAX (LIBGRPP_MAX_BASIS_L + LIBGRPP_MAX_RPP_L)
27
28/*
29 * number of pretabulated points
30 */
31#define NPOINTS 2000
32
33/*
34 * array containing pre-tabulated values of the Bessel function Kn(z).
35 * 1st dim: number of point (z)
36 * 2nd dim: order of Bessel function
37 * 3rd dim: order of derivative
38 */
39double bessel_table[NPOINTS][3 * LMAX][10];
40
41static double modified_scaled_bessel_derivative(int n, int lambda, int ix);
42
43static double bessel_asymptotic_R_function(int n, double x);
44
45extern const double rfun_coeffs[50][50];
46extern const double bessel_table_0[1601][60];
47
48void libgrpp_pretabulate_bessel() {
49 for (int i = 0; i <= 1600; i++) {
50
51 // Bessel functions
52 for (int lam = 0; lam <= 3 * LMAX - 1; lam++) {
53 bessel_table[i][lam][0] = bessel_table_0[i][lam];
54 }
55
56 // and their 1st, 2nd, 3rd, 4th derivatives
57 for (int k = 1; k < 5; k++) {
58 for (int lam = 0; lam <= 3 * LMAX - 1 - 5; lam++) {
59 bessel_table[i][lam][k] = modified_scaled_bessel_derivative(k, lam, i);
60 }
61 }
62 }
63}
64
65/*
66 * evaluates scaled modified spherical Bessel function of the n-th order.
67 */
68double libgrpp_modified_bessel_scaled(int n, double x) {
69 // static int bessel_pretabulated = 0;
70
71 /*
72 * pre-tabulation step.
73 * this code is invoked only once at start of the LIBGRPP library
74 */
75 /*if (bessel_pretabulated == 0) {
76 pretabulate_bessel();
77 bessel_pretabulated = 1;
78 }*/
79
80 /*
81 * use Taylor expansion
82 */
83 if (x <= 1e-7) {
84 switch (n) {
85 case 0:
86 return 1.0 - x;
87 case 1:
88 return (1.0 - x) * x * (1.0 / 3.0);
89 case 2:
90 return (1.0 - x) * x * x * (1.0 / 15.0);
91 default:
92 return 0.0;
93 }
94 } else if (x <= 16.0) {
95
96 int i0 = (int)(round(x * 100) + 1e-5);
97 double x0 = i0 * 0.01;
98 double dx = x - x0;
99
100 double *k_derivatives = bessel_table[i0][n];
101
102 double d0 = k_derivatives[0];
103 double d1 = k_derivatives[1];
104 double d2 = k_derivatives[2];
105 double d3 = k_derivatives[3];
106 double d4 = k_derivatives[4];
107
108 double dx2 = dx * dx;
109 double dx3 = dx2 * dx;
110 double dx4 = dx3 * dx;
111
112 double sum = d0 + d1 * dx + d2 * dx2 * 0.5 + d3 * dx3 * (1.0 / 6.0) +
113 d4 * dx4 * (1.0 / 24.0);
114
115 return sum;
116 } else {
117 return bessel_asymptotic_R_function(n, -x) / (2.0 * x);
118 }
119}
120
121/**
122 * Calculates n-th order derivative on the scaled modified spherical Bessel
123 * function K_lambda(z).
124 *
125 * Note that the formula (45) for derivatives in the paper of Flores-Moreno et
126 * al is wrong (you must also add: - K^(n-1)_{lambda}).
127 *
128 * R. Flores-Moreno, R. J. Alvarez-Mendez, A. Vela, A. M. Koster,
129 * Half-numerical evaluation of pseudopotential integrals.
130 * J. Comput. Chem. 27 (9), 1009 (2006), doi: 10.1002/jcc.20410
131 */
132static double modified_scaled_bessel_derivative(int n, int lambda, int ix) {
133 /*
134 * base of recursion
135 */
136 if (n == 0) {
137 return bessel_table[ix][lambda][0];
138 }
139
140 /*
141 * upward recursion
142 */
143 double deriv = 0.0;
144
145 if (lambda > 0) {
146 deriv +=
147 lambda / (2.0 * lambda + 1.0) * bessel_table[ix][lambda - 1][n - 1];
148 }
149 deriv += (lambda + 1.0) / (2.0 * lambda + 1.0) *
150 bessel_table[ix][lambda + 1][n - 1];
151 deriv -= bessel_table[ix][lambda][n - 1];
152
153 return deriv;
154}
155
156/**
157 * Asymptotic formula for the scaled spherical modified Bessel function of order
158 * 'n'.
159 *
160 * For the formula, see:
161 * R. Flores-Moreno, R. J. Alvarez-Mendez, A. Vela, A. M. Koster,
162 * Half-numerical evaluation of pseudopotential integrals.
163 * J. Comput. Chem. 27 (9), 1009 (2006), doi: 10.1002/jcc.20410
164 *
165 * In the optimized version all factors used are pretabulated above in the
166 * 'rfun_coeffs' array. Unoptimized version of this code:
167 *
168 * double sum = 0.0;
169 *
170 * for (int k = 0; k <= n; k++) {
171 * sum += factorial(k + n) / (factorial(k) * factorial(n - k) * pow(2 * x,
172 * k));
173 * }
174 */
175static double bessel_asymptotic_R_function(int n, double x) {
176 double sum = 0.0;
177
178 double denom = 1.0;
179 double inv_x = 1.0 / x;
180 const double *coeffs = rfun_coeffs[n];
181
182 for (int k = 0; k <= n; k++) {
183 sum += coeffs[k] * denom;
184 denom *= inv_x;
185 }
186
187 return sum;
188}
189
190/*
191 * pretabulated coefficients which are required for the fast calculation
192 * of the R_lambda(z) asymptotic relation.
193 */
194const double rfun_coeffs[50][50] = {
195 // lambda = 0
196 {1.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
197 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
198 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
199 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
200 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
201 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
202 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
203 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
204 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
205 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
206 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
207 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
208 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
209 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
210 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
211 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
212 0.0000000000000000e+00, 0.0000000000000000e+00},
213 // lambda = 1
214 {1.0000000000000000e+00, 1.0000000000000000e+00, 0.0000000000000000e+00,
215 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
216 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
217 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
218 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
219 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
220 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
221 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
222 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
223 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
224 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
225 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
226 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
227 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
228 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
229 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
230 0.0000000000000000e+00, 0.0000000000000000e+00},
231 // lambda = 2
232 {1.0000000000000000e+00, 3.0000000000000000e+00, 3.0000000000000000e+00,
233 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
234 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
235 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
236 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
237 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
238 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
239 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
240 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
241 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
242 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
243 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
244 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
245 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
246 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
247 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
248 0.0000000000000000e+00, 0.0000000000000000e+00},
249 // lambda = 3
250 {1.0000000000000000e+00, 6.0000000000000000e+00, 1.5000000000000000e+01,
251 1.5000000000000000e+01, 0.0000000000000000e+00, 0.0000000000000000e+00,
252 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
253 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
254 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
255 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
256 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
257 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
258 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
259 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
260 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
261 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
262 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
263 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
264 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
265 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
266 0.0000000000000000e+00, 0.0000000000000000e+00},
267 // lambda = 4
268 {1.0000000000000000e+00, 1.0000000000000000e+01, 4.5000000000000000e+01,
269 1.0500000000000000e+02, 1.0500000000000000e+02, 0.0000000000000000e+00,
270 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
271 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
272 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
273 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
274 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
275 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
276 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
277 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
278 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
279 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
280 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
281 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
282 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
283 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
284 0.0000000000000000e+00, 0.0000000000000000e+00},
285 // lambda = 5
286 {1.0000000000000000e+00, 1.5000000000000000e+01, 1.0500000000000000e+02,
287 4.2000000000000000e+02, 9.4500000000000000e+02, 9.4500000000000000e+02,
288 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
289 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
290 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
291 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
292 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
293 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
294 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
295 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
296 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
297 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
298 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
299 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
300 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
301 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
302 0.0000000000000000e+00, 0.0000000000000000e+00},
303 // lambda = 6
304 {1.0000000000000000e+00, 2.1000000000000000e+01, 2.1000000000000000e+02,
305 1.2600000000000000e+03, 4.7250000000000000e+03, 1.0395000000000000e+04,
306 1.0395000000000000e+04, 0.0000000000000000e+00, 0.0000000000000000e+00,
307 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
308 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
309 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
310 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
311 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
312 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
313 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
314 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
315 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
316 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
317 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
318 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
319 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
320 0.0000000000000000e+00, 0.0000000000000000e+00},
321 // lambda = 7
322 {1.0000000000000000e+00, 2.8000000000000000e+01, 3.7800000000000000e+02,
323 3.1500000000000000e+03, 1.7325000000000000e+04, 6.2370000000000000e+04,
324 1.3513500000000000e+05, 1.3513500000000000e+05, 0.0000000000000000e+00,
325 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
326 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
327 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
328 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
329 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
330 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
331 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
332 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
333 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
334 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
335 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
336 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
337 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
338 0.0000000000000000e+00, 0.0000000000000000e+00},
339 // lambda = 8
340 {1.0000000000000000e+00, 3.6000000000000000e+01, 6.3000000000000000e+02,
341 6.9300000000000000e+03, 5.1975000000000000e+04, 2.7027000000000000e+05,
342 9.4594500000000000e+05, 2.0270250000000000e+06, 2.0270250000000000e+06,
343 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
344 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
345 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
346 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
347 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
348 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
349 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
350 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
351 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
352 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
353 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
354 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
355 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
356 0.0000000000000000e+00, 0.0000000000000000e+00},
357 // lambda = 9
358 {1.0000000000000000e+00, 4.5000000000000000e+01, 9.9000000000000000e+02,
359 1.3860000000000000e+04, 1.3513500000000000e+05, 9.4594500000000000e+05,
360 4.7297250000000000e+06, 1.6216200000000000e+07, 3.4459425000000000e+07,
361 3.4459425000000000e+07, 0.0000000000000000e+00, 0.0000000000000000e+00,
362 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
363 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
364 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
365 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
366 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
367 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
368 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
369 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
370 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
371 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
372 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
373 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
374 0.0000000000000000e+00, 0.0000000000000000e+00},
375 // lambda = 10
376 {1.0000000000000000e+00, 5.5000000000000000e+01, 1.4850000000000000e+03,
377 2.5740000000000000e+04, 3.1531500000000000e+05, 2.8378350000000000e+06,
378 1.8918900000000000e+07, 9.1891800000000000e+07, 3.1013482500000000e+08,
379 6.5472907500000000e+08, 6.5472907500000000e+08, 0.0000000000000000e+00,
380 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
381 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
382 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
383 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
384 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
385 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
386 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
387 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
388 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
389 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
390 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
391 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
392 0.0000000000000000e+00, 0.0000000000000000e+00},
393 // lambda = 11
394 {1.0000000000000000e+00, 6.6000000000000000e+01, 2.1450000000000000e+03,
395 4.5045000000000000e+04, 6.7567500000000000e+05, 7.5675600000000000e+06,
396 6.4324260000000000e+07, 4.1351310000000000e+08, 1.9641872250000000e+09,
397 6.5472907500000000e+09, 1.3749310575000000e+10, 1.3749310575000000e+10,
398 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
399 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
400 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
401 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
402 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
403 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
404 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
405 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
406 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
407 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
408 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
409 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
410 0.0000000000000000e+00, 0.0000000000000000e+00},
411 // lambda = 12
412 {1.0000000000000000e+00, 7.8000000000000000e+01, 3.0030000000000000e+03,
413 7.5075000000000000e+04, 1.3513500000000000e+06, 1.8378360000000000e+07,
414 1.9297278000000000e+08, 1.5713497800000000e+09, 9.8209361250000000e+09,
415 4.5831035250000000e+10, 1.5124241632500000e+11, 3.1623414322500000e+11,
416 3.1623414322500000e+11, 0.0000000000000000e+00, 0.0000000000000000e+00,
417 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
418 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
419 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
420 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
421 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
422 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
423 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
424 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
425 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
426 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
427 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
428 0.0000000000000000e+00, 0.0000000000000000e+00},
429 // lambda = 13
430 {1.0000000000000000e+00, 9.1000000000000000e+01, 4.0950000000000000e+03,
431 1.2012000000000000e+05, 2.5525500000000000e+06, 4.1351310000000000e+07,
432 5.2378326000000000e+08, 5.2378326000000000e+09, 4.1247931725000000e+10,
433 2.5207069387500000e+11, 1.1595251918250000e+12, 3.7948097187000000e+12,
434 7.9058535806250000e+12, 7.9058535806250000e+12, 0.0000000000000000e+00,
435 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
436 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
437 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
438 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
439 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
440 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
441 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
442 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
443 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
444 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
445 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
446 0.0000000000000000e+00, 0.0000000000000000e+00},
447 // lambda = 14
448 {1.0000000000000000e+00, 1.0500000000000000e+02, 5.4600000000000000e+03,
449 1.8564000000000000e+05, 4.5945900000000000e+06, 8.7297210000000000e+07,
450 1.3094581500000000e+09, 1.5713497800000000e+10, 1.5124241632500000e+11,
451 1.1595251918250000e+12, 6.9571511509500000e+12, 3.1623414322500000e+13,
452 1.0277609654812500e+14, 2.1345804667687500e+14, 2.1345804667687500e+14,
453 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
454 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
455 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
456 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
457 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
458 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
459 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
460 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
461 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
462 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
463 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
464 0.0000000000000000e+00, 0.0000000000000000e+00},
465 // lambda = 15
466 {1.0000000000000000e+00, 1.2000000000000000e+02, 7.1400000000000000e+03,
467 2.7846000000000000e+05, 7.9361100000000000e+06, 1.7459442000000000e+08,
468 3.0554023500000000e+09, 4.3212118950000000e+10, 4.9693936792500000e+11,
469 4.6381007673000000e+12, 3.4785755754750000e+13, 2.0555219309625000e+14,
470 9.2498486893312500e+14, 2.9884126534762500e+15, 6.1902833536293750e+15,
471 6.1902833536293750e+15, 0.0000000000000000e+00, 0.0000000000000000e+00,
472 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
473 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
474 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
475 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
476 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
477 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
478 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
479 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
480 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
481 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
482 0.0000000000000000e+00, 0.0000000000000000e+00},
483 // lambda = 16
484 {1.0000000000000000e+00, 1.3600000000000000e+02, 9.1800000000000000e+03,
485 4.0698000000000000e+05, 1.3226850000000000e+07, 3.3331662000000000e+08,
486 6.7218851700000000e+09, 1.1043097065000000e+11, 1.4908181037750000e+12,
487 1.6564645597500000e+13, 1.5073827493725000e+14, 1.1099818427197500e+15,
488 6.4748940825318750e+15, 2.8887988983603752e+16, 9.2854250304440624e+16,
489 1.9189878396251062e+17, 1.9189878396251062e+17, 0.0000000000000000e+00,
490 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
491 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
492 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
493 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
494 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
495 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
496 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
497 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
498 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
499 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
500 0.0000000000000000e+00, 0.0000000000000000e+00},
501 // lambda = 17
502 {1.0000000000000000e+00, 1.5300000000000000e+02, 1.1628000000000000e+04,
503 5.8140000000000000e+05, 2.1366450000000000e+07, 6.1108047000000000e+08,
504 1.4054850810000000e+10, 2.6503432956000000e+11, 4.1411613993750000e+12,
505 5.3835098191875000e+13, 5.8141906047225000e+14, 5.1799152660255000e+15,
506 3.7554385678684872e+16, 2.1665991737702813e+17, 9.5949391981255309e+17,
507 3.0703805434001700e+18, 6.3326598707628503e+18, 6.3326598707628503e+18,
508 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
509 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
510 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
511 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
512 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
513 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
514 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
515 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
516 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
517 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
518 0.0000000000000000e+00, 0.0000000000000000e+00},
519 // lambda = 18
520 {1.0000000000000000e+00, 1.7100000000000000e+02, 1.4535000000000000e+04,
521 8.1396000000000000e+05, 3.3575850000000000e+07, 1.0811423700000000e+09,
522 2.8109701620000000e+10, 6.0235074900000000e+11, 1.0767019638375000e+13,
523 1.6150529457562500e+14, 2.0349667116528750e+15, 2.1459648959248500e+16,
524 1.8777192839342438e+17, 1.3432914877375744e+18, 7.6759513585004247e+18,
525 3.3774185977401868e+19, 1.0765521780296847e+20, 2.2164309547669976e+20,
526 2.2164309547669976e+20, 0.0000000000000000e+00, 0.0000000000000000e+00,
527 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
528 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
529 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
530 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
531 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
532 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
533 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
534 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
535 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
536 0.0000000000000000e+00, 0.0000000000000000e+00},
537 // lambda = 19
538 {1.0000000000000000e+00, 1.9000000000000000e+02, 1.7955000000000000e+04,
539 1.1191950000000000e+06, 5.1482970000000000e+07, 1.8533869200000000e+09,
540 5.4057118500000000e+10, 1.3050932895000000e+12, 2.6428139112375000e+13,
541 4.5221482481175000e+14, 6.5571149597703750e+15, 8.0473683597181872e+16,
542 8.3156139717087936e+17, 7.1642212679337298e+18, 5.0661278966102802e+19,
543 2.8708058080791590e+20, 1.2559775410346320e+21, 3.9895757185805960e+21,
544 8.2007945326378919e+21, 8.2007945326378919e+21, 0.0000000000000000e+00,
545 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
546 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
547 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
548 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
549 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
550 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
551 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
552 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
553 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
554 0.0000000000000000e+00, 0.0000000000000000e+00},
555 // lambda = 20
556 {1.0000000000000000e+00, 2.1000000000000000e+02, 2.1945000000000000e+04,
557 1.5142050000000000e+06, 7.7224455000000000e+07, 3.0889782000000000e+09,
558 1.0039179150000000e+11, 2.7105783705000000e+12, 6.1665657928875000e+13,
559 1.1922027199582500e+15, 1.9671344879311124e+16, 2.7718713239029312e+17,
560 3.3262455886835174e+18, 3.3774185977401868e+19, 2.8708058080791590e+20,
561 2.0095640656554112e+21, 1.1303797869311689e+22, 4.9204767195827347e+22,
562 1.5581509612011996e+23, 3.1983098677287775e+23, 3.1983098677287775e+23,
563 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
564 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
565 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
566 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
567 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
568 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
569 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
570 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
571 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
572 0.0000000000000000e+00, 0.0000000000000000e+00},
573 // lambda = 21
574 {1.0000000000000000e+00, 2.3100000000000000e+02, 2.6565000000000000e+04,
575 2.0189400000000000e+06, 1.1356537500000000e+08, 5.0195895750000000e+09,
576 1.8070522470000000e+11, 5.4211567410000000e+12, 1.3756185230287500e+14,
577 2.9805067998956250e+15, 5.5437426478058624e+16, 8.8699882364893798e+17,
578 1.2196233825172898e+19, 1.4354029040395795e+20, 1.4354029040395795e+21,
579 1.2057384393932467e+22, 8.3648104232906486e+22, 4.6744528836035980e+23,
580 2.0255962495615593e+24, 6.3966197354575558e+24, 1.3113070457687988e+25,
581 1.3113070457687988e+25, 0.0000000000000000e+00, 0.0000000000000000e+00,
582 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
583 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
584 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
585 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
586 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
587 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
588 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
589 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
590 0.0000000000000000e+00, 0.0000000000000000e+00},
591 // lambda = 22
592 {1.0000000000000000e+00, 2.5300000000000000e+02, 3.1878000000000000e+04,
593 2.6565000000000000e+06, 1.6403887500000000e+08, 7.9722893250000000e+09,
594 3.1623414322500000e+11, 1.0480903032600000e+13, 2.9477539779187500e+14,
595 7.1073623689818750e+15, 1.4783313727482301e+17, 2.6609964709468140e+18,
596 4.1467195005587849e+19, 5.5821224045983649e+20, 6.4593130681781075e+21,
597 6.3731888939357331e+22, 5.2977132680840781e+23, 3.6460732492108065e+24,
598 2.0255962495615594e+25, 8.7420469717919930e+25, 2.7537447961144777e+26,
599 5.6386202968058351e+26, 5.6386202968058351e+26, 0.0000000000000000e+00,
600 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
601 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
602 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
603 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
604 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
605 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
606 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
607 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
608 0.0000000000000000e+00, 0.0000000000000000e+00},
609 // lambda = 23
610 {1.0000000000000000e+00, 2.7600000000000000e+02, 3.7950000000000000e+04,
611 3.4534500000000000e+06, 2.3310787500000000e+08, 1.2401338950000000e+10,
612 5.3945824432500000e+11, 1.9651693186125000e+13, 6.0920248876987500e+14,
613 1.6245399700530000e+16, 3.7526873308224301e+17, 7.5394900010159729e+18,
614 1.3194107501777953e+20, 2.0095640656554112e+21, 2.6554953724732222e+22,
615 3.0272647246194728e+23, 2.9515831065039861e+24, 2.4307154994738711e+25,
616 1.6609889246404785e+26, 9.1791493203815915e+26, 3.9470342077640844e+27,
617 1.2404964652972836e+28, 2.5373791335626256e+28, 2.5373791335626256e+28,
618 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
619 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
620 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
621 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
622 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
623 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
624 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
625 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
626 0.0000000000000000e+00, 0.0000000000000000e+00},
627 // lambda = 24
628 {1.0000000000000000e+00, 3.0000000000000000e+02, 4.4850000000000000e+04,
629 4.4401500000000000e+06, 3.2635102500000000e+08, 1.8928359450000000e+10,
630 8.9909707387500000e+11, 3.5835440515875000e+13, 1.2184049775397500e+15,
631 3.5739879341166000e+16, 9.1136692319973299e+17, 2.0298626925812236e+19,
632 3.9582322505333860e+20, 6.7594427662954744e+21, 1.0090882415398244e+23,
633 1.3118147140017716e+24, 1.4757915532519932e+25, 1.4237047925489816e+26,
634 1.1626922472483349e+27, 7.8940684155281688e+27, 4.3417376285404926e+28,
635 1.8607446979459256e+29, 5.8359720071940396e+29, 1.1925681927744342e+30,
636 1.1925681927744342e+30, 0.0000000000000000e+00, 0.0000000000000000e+00,
637 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
638 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
639 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
640 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
641 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
642 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
643 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
644 0.0000000000000000e+00, 0.0000000000000000e+00},
645 // lambda = 25
646 {1.0000000000000000e+00, 3.2500000000000000e+02, 5.2650000000000000e+04,
647 5.6511000000000000e+06, 4.5067522500000000e+08, 2.8392539175000000e+10,
648 1.4669478573750000e+12, 6.3707449806000000e+13, 2.3651390740477500e+15,
649 7.5947243599977744e+16, 2.1265228207993769e+18, 5.2196469237802893e+19,
650 1.1265737943825791e+21, 2.1404902093269001e+22, 3.5776764927321044e+23,
651 5.2472588560070862e+24, 6.7230504092590799e+25, 7.4744501608821538e+26,
652 7.1422523759540579e+27, 5.7889835047206574e+28, 3.9075638656864439e+29,
653 2.1398564026378145e+30, 9.1430228112706621e+30, 2.8621636626586418e+31,
654 5.8435841445947271e+31, 5.8435841445947271e+31, 0.0000000000000000e+00,
655 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
656 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
657 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
658 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
659 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
660 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
661 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
662 0.0000000000000000e+00, 0.0000000000000000e+00},
663 // lambda = 26
664 {1.0000000000000000e+00, 3.5100000000000000e+02, 6.1425000000000000e+04,
665 7.1253000000000000e+06, 6.1455712500000000e+08, 4.1912795925000000e+10,
666 2.3471165718000000e+12, 1.1064978124200000e+14, 4.4674849176457500e+15,
667 1.5636197211760125e+17, 4.7846763467985981e+18, 1.2875129078658046e+20,
668 3.0578431561812861e+21, 6.4214706279807002e+22, 1.1925588309107015e+24,
669 1.9557964826935507e+25, 2.8236811718888136e+26, 3.5711261879770289e+27,
670 3.9282388067747316e+28, 3.7214893958918512e+29, 2.9957989636929402e+30,
671 2.0114650184795456e+31, 1.0971627373524793e+32, 4.6748673156757817e+32,
672 1.4608960361486818e+33, 2.9802279137433107e+33, 2.9802279137433107e+33,
673 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
674 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
675 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
676 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
677 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
678 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
679 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
680 0.0000000000000000e+00, 0.0000000000000000e+00},
681 // lambda = 27
682 {1.0000000000000000e+00, 3.7800000000000000e+02, 7.1253000000000000e+04,
683 8.9066250000000000e+06, 8.2831612500000000e+08, 6.0964066800000000e+10,
684 3.6883260414000000e+12, 1.8810462811140000e+14, 8.2295774798737500e+15,
685 3.1272394423520250e+17, 1.0413707343032244e+19, 3.0578431561812863e+20,
686 7.9503922060713431e+21, 1.8347058937087716e+23, 3.7611470821029817e+24,
687 6.8452876894274268e+25, 1.1038026399201726e+27, 1.5712955227098926e+28,
688 1.9641194033873659e+29, 2.1398564026378145e+30, 2.0114650184795456e+31,
689 1.6091720147836365e+32, 1.0752194826054298e+33, 5.8435841445947272e+33,
690 2.4835232614527592e+34, 7.7485925757326079e+34, 1.5795207942839547e+35,
691 1.5795207942839547e+35, 0.0000000000000000e+00, 0.0000000000000000e+00,
692 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
693 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
694 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
695 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
696 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
697 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
698 0.0000000000000000e+00, 0.0000000000000000e+00},
699 // lambda = 28
700 {1.0000000000000000e+00, 4.0600000000000000e+02, 8.2215000000000000e+04,
701 1.1044215000000000e+07, 1.1044215000000000e+09, 8.7470182800000000e+10,
702 5.7001402458000000e+12, 3.1350771351900000e+14, 1.4813239463772750e+16,
703 6.0898873351065754e+17, 2.1984493279734735e+19, 7.0150519465335390e+20,
704 1.9875980515178361e+22, 5.0148627761373093e+23, 1.1283441246308945e+25,
705 2.2642105434259949e+26, 4.0472763463739662e+27, 6.4280271383586516e+28,
706 9.0349492555818833e+29, 1.1174805658219697e+31, 1.2068790110877273e+32,
707 1.1264204103485455e+33, 8.9601623550452488e+33, 5.9604558274866214e+34,
708 3.2285802398885867e+35, 1.3689180217127607e+36, 4.2647061445666780e+36,
709 8.6873643685617512e+36, 8.6873643685617512e+36, 0.0000000000000000e+00,
710 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
711 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
712 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
713 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
714 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
715 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
716 0.0000000000000000e+00, 0.0000000000000000e+00},
717 // lambda = 29
718 {1.0000000000000000e+00, 4.3500000000000000e+02, 9.4395000000000000e+04,
719 1.3592880000000000e+07, 1.4578363800000000e+09, 1.2391609230000000e+11,
720 8.6741264610000000e+12, 5.1301262212200000e+14, 2.6099517150456752e+16,
721 1.1570785936702492e+18, 4.5126065153139720e+19, 1.5589004325630084e+21,
722 4.7936188301312512e+22, 1.3164014787360436e+24, 3.2345864906085645e+25,
723 7.1160902793388421e+26, 1.4009802737448345e+28, 2.4640770697041499e+29,
724 3.8603874092031681e+30, 5.3639067159454546e+31, 6.5707857270331817e+32,
725 7.0401275646784093e+33, 6.5281182872472521e+34, 5.1657283838217391e+35,
726 3.4222950542819017e+36, 1.8480393293122271e+37, 7.8186279317055763e+37,
727 2.4324620231972902e+38, 4.9517976900801979e+38, 4.9517976900801979e+38,
728 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
729 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
730 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
731 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
732 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
733 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
734 0.0000000000000000e+00, 0.0000000000000000e+00},
735 // lambda = 30
736 {1.0000000000000000e+00, 4.6500000000000000e+02, 1.0788000000000000e+05,
737 1.6613520000000000e+07, 1.9064014200000000e+09, 1.7348252922000000e+11,
738 1.3011189691500000e+13, 8.2528117471800000e+14, 4.5080984168970752e+16,
739 2.1488602453876058e+18, 9.0252130306279440e+19, 3.3639430386885974e+21,
740 1.1185110603639586e+23, 3.3297213873911694e+24, 8.8951128491735526e+25,
741 2.1348270838016525e+27, 4.6032208994473134e+28, 8.9085863289303885e+29,
742 1.5441549636812672e+31, 2.3893766280120661e+32, 3.2853928635165913e+33,
743 3.9894056199844321e+34, 4.2432768867107142e+35, 3.9111943477507451e+36,
744 3.0800655488537117e+37, 2.0328432622434498e+38, 1.0946079104387807e+39,
745 4.6216778440748515e+39, 1.4360213301232574e+40, 2.9215606371473171e+40,
746 2.9215606371473171e+40, 0.0000000000000000e+00, 0.0000000000000000e+00,
747 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
748 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
749 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
750 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
751 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
752 0.0000000000000000e+00, 0.0000000000000000e+00},
753 // lambda = 31
754 {1.0000000000000000e+00, 4.9600000000000000e+02, 1.2276000000000000e+05,
755 2.0173560000000000e+07, 2.4712611000000000e+09, 2.4020657892000000e+11,
756 1.9256560743420000e+13, 1.3066951933035000e+15, 7.6441668808254752e+16,
757 3.9070186279774648e+18, 1.7620654012178366e+20, 7.0642803812460543e+21,
758 2.5313671366131695e+23, 8.1393189469561908e+24, 2.3545886953694697e+26,
759 6.1376278659297511e+27, 1.4423425484934914e+29, 3.0543724556332761e+30,
760 5.8202764015678539e+31, 9.9557359500502762e+32, 1.5232276003576923e+34,
761 2.0744909223919045e+35, 2.4988186110629760e+36, 2.6400561847317531e+37,
762 2.4200515026707736e+38, 1.8973203780938864e+39, 1.2478530179002099e+40,
763 6.7014328739085347e+40, 2.8241752825757396e+41, 8.7646819114419503e+41,
764 1.7821519886598634e+42, 1.7821519886598634e+42, 0.0000000000000000e+00,
765 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
766 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
767 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
768 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
769 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
770 0.0000000000000000e+00, 0.0000000000000000e+00},
771 // lambda = 32
772 {1.0000000000000000e+00, 5.2800000000000000e+02, 1.3912800000000000e+05,
773 2.4347400000000000e+07, 3.1773357000000000e+09, 3.2917197852000000e+11,
774 2.8144204163460000e+13, 2.0384445015534600e+15, 1.2740278134709125e+17,
775 6.9646853803076547e+18, 3.3639430386885971e+20, 1.4464955066360969e+22,
776 5.5690077005489726e+23, 1.9277334348054137e+25, 6.0172822214997554e+26,
777 1.6968735864629310e+28, 4.3270276454804741e+29, 9.9776166884020347e+30,
778 2.0786701434170907e+32, 3.9057117957889542e+33, 6.6006529348833326e+34,
779 9.9952744442519035e+35, 1.3493620499740072e+37, 1.6133676684471823e+38,
780 1.6940360518695416e+39, 1.5449608793050218e+40, 1.2062579173035363e+41,
781 7.9076907912120706e+41, 4.2362629238636097e+42, 1.7821519886598633e+43,
782 5.5246711648455764e+43, 1.1227557528557138e+44, 1.1227557528557138e+44,
783 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
784 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
785 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
786 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
787 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
788 0.0000000000000000e+00, 0.0000000000000000e+00},
789 // lambda = 33
790 {1.0000000000000000e+00, 5.6100000000000000e+02, 1.5708000000000000e+05,
791 2.9216880000000000e+07, 4.0538421000000000e+09, 4.4673339942000000e+11,
792 4.0652739347220000e+13, 3.1360684639284000e+15, 2.0894056140922966e+17,
793 1.2188199415538397e+19, 6.2891108984178121e+20, 2.8929910132721939e+22,
794 1.1933587929747799e+24, 4.4337869000524515e+25, 1.4884856021604660e+27,
795 4.5249962305678166e+28, 1.2472020860502543e+30, 3.1180052151256360e+31,
796 7.0674784876181083e+32, 1.4506929527216116e+34, 2.6910354272985894e+35,
797 4.4978734999133567e+36, 6.7468102498700352e+37, 9.0348589433042215e+38,
798 1.0728894995173763e+40, 1.1200966374961408e+41, 1.0167031017272664e+42,
799 7.9076907912120706e+42, 5.1682407671136041e+43, 2.7623355824227882e+44,
800 1.1601809446175710e+45, 3.5928184091382843e+45, 7.2979123935621403e+45,
801 7.2979123935621403e+45, 0.0000000000000000e+00, 0.0000000000000000e+00,
802 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
803 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
804 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
805 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
806 0.0000000000000000e+00, 0.0000000000000000e+00},
807 // lambda = 34
808 {1.0000000000000000e+00, 5.9500000000000000e+02, 1.7671500000000000e+05,
809 3.4871760000000000e+07, 5.1348666600000000e+09, 6.0077939922000000e+11,
810 5.8075341924600000e+13, 4.7621780378172000e+15, 3.3751936843029408e+17,
811 2.0963702994726040e+19, 1.1530036647099323e+21, 5.6601998085760311e+22,
812 2.4952047489472671e+24, 9.9232373477364390e+25, 3.5723654451851181e+27,
813 1.1669727120938052e+29, 3.4644502390284845e+30, 9.3540156453769076e+31,
814 2.2969305084758852e+33, 5.1257817662830279e+34, 1.0379708076723131e+36,
815 1.9029464807325740e+37, 3.1485114499393499e+38, 4.6816996342576421e+39,
816 6.2227590972007826e+40, 7.3428557346969232e+41, 7.6252732629544975e+42,
817 6.8909876894848052e+43, 5.3405154593507234e+44, 3.4805428338527132e+45,
818 1.8562895113881136e+46, 7.7844398864662830e+46, 2.4083110898755061e+47,
819 4.8896013036866339e+47, 4.8896013036866339e+47, 0.0000000000000000e+00,
820 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
821 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
822 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
823 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
824 0.0000000000000000e+00, 0.0000000000000000e+00},
825 // lambda = 35
826 {1.0000000000000000e+00, 6.3000000000000000e+02, 1.9813500000000000e+05,
827 4.1410215000000000e+07, 6.4599935400000000e+09, 8.0103919896000000e+11,
828 8.2106517893400000e+13, 7.1432670567258000e+15, 5.3753084601861645e+17,
829 3.5477035837228687e+19, 2.0754065964778780e+21, 1.0848716299770726e+23,
830 5.0988966608922417e+24, 2.1650699667788595e+26, 8.3355193720986085e+27,
831 2.9174317802345130e+29, 9.2993137994975104e+30, 2.7022711864422177e+32,
832 7.1610186440718767e+33, 1.7299513461205220e+35, 3.8058929614651479e+36,
833 7.6117859229302960e+37, 1.3805011742041766e+39, 2.2628214898911938e+40,
834 3.3376616975895104e+41, 4.4057134408181539e+42, 5.1682407671136041e+43,
835 5.3405154593507234e+44, 4.8064639134156512e+45, 3.7125790227762272e+46,
836 2.4131763648045479e+47, 1.2844325812669368e+48, 5.3785614340552972e+48,
837 1.6624644432534555e+49, 3.3738248995437775e+49, 3.3738248995437775e+49,
838 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
839 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
840 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
841 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
842 0.0000000000000000e+00, 0.0000000000000000e+00},
843 // lambda = 36
844 {1.0000000000000000e+00, 6.6600000000000000e+02, 2.2144500000000000e+05,
845 4.8939345000000000e+07, 8.0749919250000000e+09, 1.0594389405600000e+12,
846 1.1494912505076000e+14, 1.0591740808248600e+16, 8.4469132945782579e+17,
847 5.9128393062047810e+19, 3.6718732091531691e+21, 2.0395586643568966e+23,
848 1.0197793321784483e+25, 4.6125403640071350e+26, 1.8944362209315020e+28,
849 7.0851914662838170e+29, 2.4178215878693527e+31, 7.5379143621809230e+32,
850 2.1483055932215630e+34, 5.5969014139193357e+35, 1.3320625365128018e+37,
851 2.8924786507135127e+38, 5.7192191502744452e+39, 1.0269728300275418e+41,
852 1.6688308487947554e+42, 2.4431683626355217e+43, 3.2043092756104344e+44,
853 3.7383608215455063e+45, 3.8451711307325209e+46, 3.4473948068636396e+47,
854 2.6544940012850026e+48, 1.7211396588976951e+49, 9.1435544378940057e+49,
855 3.8236682194829480e+50, 1.1808387148403220e+51, 2.3954156786760820e+51,
856 2.3954156786760820e+51, 0.0000000000000000e+00, 0.0000000000000000e+00,
857 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
858 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
859 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
860 0.0000000000000000e+00, 0.0000000000000000e+00},
861 // lambda = 37
862 {1.0000000000000000e+00, 7.0300000000000000e+02, 2.4675300000000000e+05,
863 5.7575700000000000e+07, 1.0032565725000000e+10, 1.3905136094850000e+12,
864 1.5944556055428000e+14, 1.5534553185431280e+16, 1.3107279250207642e+18,
865 9.7139502887649968e+19, 6.3917792900073684e+21, 3.7653390726588858e+23,
866 1.9987674910697586e+25, 9.6094590916815319e+26, 4.2007064029350700e+28,
867 1.6746816193034478e+30, 6.1021211503369381e+31, 2.0352368777888494e+33,
868 6.2187793487992616e+34, 1.7412582176637932e+36, 4.4663273283076299e+37,
869 1.0485235108836483e+39, 2.2495595324412818e+40, 4.4013121286894641e+41,
870 7.8306678289600057e+42, 1.2623036540283529e+44, 1.8351953123950669e+45,
871 2.3925509257891243e+46, 2.7770680388623764e+47, 2.8441007156625026e+48,
872 2.5407299726585025e+49, 1.9506249467507211e+50, 1.2618105124293728e+51,
873 6.6914193840951586e+51, 2.7946516251220958e+52, 8.6234964432338948e+52,
874 1.7486534454335398e+53, 1.7486534454335398e+53, 0.0000000000000000e+00,
875 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
876 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
877 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
878 0.0000000000000000e+00, 0.0000000000000000e+00},
879 // lambda = 38
880 {1.0000000000000000e+00, 7.4100000000000000e+02, 2.7417000000000000e+05,
881 6.7445820000000000e+07, 1.2393169425000000e+10, 1.8118813699350000e+12,
882 2.1923764576213500e+14, 2.2550157849819600e+16, 2.0097828183651720e+18,
883 1.5743298743860514e+20, 1.0957335925726917e+22, 6.8333931318624231e+23,
884 3.8437836366726128e+25, 1.9603296547030326e+27, 9.1015305396926512e+28,
885 3.8590489488296838e+30, 1.4977933732645212e+32, 5.3303822989707952e+33,
886 1.7412582176637933e+35, 5.2237746529913798e+36, 1.4391499168991251e+38,
887 3.6389933613020737e+39, 8.4358482466548073e+40, 1.7898669323337157e+42,
888 3.4678671813965737e+43, 6.1173177079835560e+44, 9.7877083327736896e+45,
889 1.4137800925117553e+47, 1.8328649056491685e+48, 2.1172749772154188e+49,
890 2.1596204767597270e+50, 1.9227588760828539e+51, 1.4721122645009349e+52,
891 9.5018155254151250e+52, 5.0303729252197726e+53, 2.0983841345202479e+54,
892 6.4700177481040970e+54, 1.3114900840751548e+55, 1.3114900840751548e+55,
893 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
894 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
895 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
896 0.0000000000000000e+00, 0.0000000000000000e+00},
897 // lambda = 39
898 {1.0000000000000000e+00, 7.8000000000000000e+02, 3.0381000000000000e+05,
899 7.8686790000000000e+07, 1.5225893865000000e+10, 2.3447876552100000e+12,
900 2.9896042603927500e+14, 3.2415851909115676e+16, 3.0470900794568735e+18,
901 2.5189277990176820e+20, 1.8514119322779964e+22, 1.2202487735468612e+24,
902 7.2604802026038244e+25, 3.9206593094060651e+27, 1.9295244744148420e+29,
903 8.6828601348667891e+30, 3.5816798056325503e+32, 1.3568245851925663e+34,
904 4.7262723050874392e+35, 1.5148946493675002e+37, 4.4689392156341257e+38,
905 1.2129977871006912e+40, 3.0269808414467250e+41, 6.9357343627931483e+42,
906 1.4565042161865610e+44, 2.7964880950781971e+45, 4.8938541663868447e+46,
907 7.7757905088146541e+47, 1.1163813516226753e+49, 1.4397469845064846e+50,
908 1.6557090321824573e+51, 1.6824140165724971e+52, 1.4931424397080912e+53,
909 1.1402178630498150e+54, 7.3443444708208672e+54, 3.8820106488624587e+55,
910 1.6175044370260244e+56, 4.9836623194855884e+56, 1.0098473647378693e+57,
911 1.0098473647378693e+57, 0.0000000000000000e+00, 0.0000000000000000e+00,
912 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
913 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
914 0.0000000000000000e+00, 0.0000000000000000e+00},
915 // lambda = 40
916 {1.0000000000000000e+00, 8.2000000000000000e+02, 3.3579000000000000e+05,
917 9.1446810000000000e+07, 1.8609425835000000e+10, 3.0147269852700000e+12,
918 4.0447587052372500e+14, 4.6168031506922328e+16, 4.5706351191853102e+18,
919 3.9815310371569815e+20, 3.0856865537966605e+22, 2.1459547396858593e+24,
920 1.3483748947692816e+26, 7.6961090147600541e+27, 4.0074739084000568e+29,
921 1.9102292296706936e+31, 8.3572528798092841e+32, 3.3625652763467943e+34,
922 1.2460172440685066e+36, 4.2561325863182151e+37, 1.3406817646902376e+39,
923 3.8943613164811663e+40, 1.0426267342760942e+42, 2.5703015579762841e+43,
924 5.8260168647462440e+44, 1.2118115078672187e+46, 2.3071026784395125e+47,
925 4.0075228006967830e+48, 6.3261609925284934e+49, 9.0311401755406768e+50,
926 1.1589963225277201e+52, 1.3272377241849699e+53, 1.3438281957372820e+54,
927 1.1890843428948071e+55, 9.0580248473457363e+55, 5.8230159732936878e+56,
928 3.0732584303494464e+57, 1.2791399953346345e+58, 3.9384047224776901e+58,
929 7.9777941814291672e+58, 7.9777941814291672e+58, 0.0000000000000000e+00,
930 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
931 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
932 0.0000000000000000e+00, 0.0000000000000000e+00},
933 // lambda = 41
934 {1.0000000000000000e+00, 8.6100000000000000e+02, 3.7023000000000000e+05,
935 1.0588578000000000e+08, 2.2633085475000000e+10, 3.8521511478450000e+12,
936 5.4315331184614500e+14, 6.5178397421537400e+16, 6.7867006315175813e+18,
937 6.2211422455577838e+20, 5.0764520723751509e+22, 3.7196548821221565e+24,
938 2.4642713594059285e+26, 1.4842495957037247e+28, 8.1633727763704851e+29,
939 4.1143398792907248e+31, 1.9054536565965168e+33, 8.1261994178380867e+34,
940 3.1963051043496476e+36, 1.1607634326322404e+38, 3.8943613164811664e+39,
941 1.2072520081091615e+41, 3.4571307504944172e+42, 9.1388499839156768e+43,
942 2.2275946835794461e+45, 4.9987224699522775e+46, 1.0305058630363156e+48,
943 1.9465110746241519e+49, 3.3577316037266620e+50, 5.2681651023987281e+51,
944 7.4807944454061944e+52, 9.5561116141317828e+53, 1.0899939809869065e+55,
945 1.0999030171776966e+56, 9.7050266221561463e+56, 7.3758202328386708e+57,
946 4.7328179827381474e+58, 2.4943229909025372e+59, 1.0371132435857918e+60,
947 3.1911176725716667e+60, 6.4620132869576254e+60, 6.4620132869576254e+60,
948 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
949 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
950 0.0000000000000000e+00, 0.0000000000000000e+00},
951 // lambda = 42
952 {1.0000000000000000e+00, 9.0300000000000000e+02, 4.0725300000000000e+05,
953 1.2217590000000000e+08, 2.7397945575000000e+10, 4.8932730796950000e+12,
954 7.2420441579486000e+14, 9.1249756390152352e+16, 9.9804421051729142e+18,
955 9.6144925613165747e+20, 8.2492346176096214e+22, 6.3594099597572353e+24,
956 4.4356884469306716e+26, 2.8149561297829258e+28, 1.6326745552740970e+30,
957 8.6858286340581957e+31, 4.2506273877922301e+33, 1.9177830626097884e+35,
958 7.9907627608741190e+36, 3.0785464952420287e+38, 1.0975018255537833e+40,
959 3.6217560243274846e+41, 1.1062818401582135e+43, 3.1264486787079947e+44,
960 8.1678471731246364e+45, 1.9700847381576624e+47, 4.3796499179043412e+48,
961 8.9539509432710981e+49, 1.6788658018633310e+51, 2.8772286328485359e+52,
962 4.4884766672437164e+53, 6.3417831621056375e+54, 8.0659554593031079e+55,
963 9.1658584764808051e+56, 9.2197752910483396e+57, 8.1134022561225381e+58,
964 6.1526633775595913e+59, 3.9410303256260089e+60, 2.0742264871715836e+61,
965 8.6160177159435002e+61, 2.6494254476526262e+62, 5.3634710281748292e+62,
966 5.3634710281748292e+62, 0.0000000000000000e+00, 0.0000000000000000e+00,
967 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
968 0.0000000000000000e+00, 0.0000000000000000e+00},
969 // lambda = 43
970 {1.0000000000000000e+00, 9.4600000000000000e+02, 4.4698500000000000e+05,
971 1.4050228500000000e+08, 3.3018036975000000e+10, 6.1809765217200000e+12,
972 9.5908152362022000e+14, 1.2673577276410050e+17, 1.4542929924680532e+19,
973 1.4704518034954760e+21, 1.3248770749494239e+23, 1.0731504307090333e+25,
974 7.8697698251995782e+26, 5.2545847755947955e+28, 3.2090499879525356e+30,
975 1.7992073599120551e+32, 9.2884079955459836e+33, 4.4256532214072039e+35,
976 1.9497461136532850e+37, 7.9529117793752411e+38, 3.0062006526038411e+40,
977 1.0536017525316319e+42, 3.4242056957278036e+43, 1.0317280639736383e+45,
978 2.8802408452597401e+46, 7.4425423441511693e+47, 1.7776226137376445e+49,
979 3.9173535376811057e+50, 7.9466314621530998e+51, 1.4797175826078185e+53,
980 2.5204522823753176e+54, 3.9107662832984770e+55, 5.4995150858884829e+56,
981 6.9660524421254113e+57, 7.8880299712302451e+58, 7.9105671997194750e+59,
982 6.9437200975315386e+60, 5.2547071008346777e+61, 3.3602469092179653e+62,
983 1.7662836317684177e+63, 7.3300770718389326e+63, 2.2526578318334282e+64,
984 4.5589503739486049e+64, 4.5589503739486049e+64, 0.0000000000000000e+00,
985 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
986 0.0000000000000000e+00, 0.0000000000000000e+00},
987 // lambda = 44
988 {1.0000000000000000e+00, 9.9000000000000000e+02, 4.8955500000000000e+05,
989 1.6106359500000000e+08, 3.9621644370000000e+10, 7.7658422965200000e+12,
990 1.2619493731845000e+15, 1.7468984894511149e+17, 2.1006454335649657e+19,
991 2.2266841595788638e+21, 2.1042165308020262e+23, 1.7885840511817223e+25,
992 1.3772097194099262e+27, 9.6616558777065585e+28, 6.2041633100415692e+30,
993 3.6604563529245253e+32, 1.9903731419027108e+34, 9.9986980187347942e+35,
994 4.6493945787116795e+37, 2.0041337684025609e+39, 8.0165350736102435e+40,
995 2.9775701701980905e+42, 1.0272617087183411e+44, 3.2917038231539888e+45,
996 9.7928188738831166e+46, 2.7028180091917401e+48, 6.9129768312019513e+49,
997 1.6360711833844617e+51, 3.5759841579688950e+52, 7.2012922353580503e+53,
998 1.3322390635412394e+55, 2.2562113172875826e+56, 3.4830262210627056e+57,
999 4.8762367094877882e+58, 6.1526633775595913e+59, 6.9437200975315386e+60,
1000 6.9437200975315394e+61, 6.0804467881086989e+62, 4.5923374425978860e+63,
1001 2.9320308287355731e+64, 1.5393161850861759e+65, 6.3825305235280469e+65,
1002 1.9603486607978999e+66, 3.9662868253352865e+66, 3.9662868253352865e+66,
1003 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00,
1004 0.0000000000000000e+00, 0.0000000000000000e+00},
1005 // lambda = 45
1006 {1.0000000000000000e+00, 1.0350000000000000e+03, 5.3509500000000000e+05,
1007 1.8407268000000000e+08, 4.7352696930000000e+10, 9.7073028706500000e+12,
1008 1.6502414880105000e+15, 2.3904926697752099e+17, 3.0090326480795455e+19,
1009 3.3400262393682954e+21, 3.3066259769746125e+23, 2.9459031431228367e+25,
1010 2.3788167880716906e+27, 1.7511751278343138e+29, 1.1807923719111372e+31,
1011 7.3209127058490507e+32, 4.1866469536574267e+34, 2.2139974184341332e+36,
1012 1.0848587350327252e+38, 4.9332523529909190e+39, 2.0842991191386631e+41,
1013 8.1883179680447479e+42, 2.9924580210490806e+44, 1.0174357271566874e+46,
1014 3.2176404871330240e+47, 9.4598630321710909e+48, 2.5832702895544132e+50,
1015 6.5442847335378469e+51, 1.5355696678337018e+53, 3.3305976588530985e+54,
1016 6.6611953177061970e+55, 1.2248004293846877e+57, 2.0630232232448336e+58,
1017 3.1695538611670622e+59, 4.4187309711564336e+60, 5.5549760780252308e+61,
1018 6.2493480877783854e+62, 6.2324579578114167e+63, 5.4452001105089213e+64,
1019 4.1048431602298024e+65, 2.6168375146464991e+66, 1.3722440625585301e+67,
1020 5.6850111163139101e+67, 1.7451662031475260e+68, 3.5299952745484048e+68,
1021 3.5299952745484048e+68, 0.0000000000000000e+00, 0.0000000000000000e+00,
1022 0.0000000000000000e+00, 0.0000000000000000e+00},
1023 // lambda = 46
1024 {1.0000000000000000e+00, 1.0810000000000000e+03, 5.8374000000000000e+05,
1025 2.0975724000000000e+08, 5.6372258250000000e+10, 1.2074937717150000e+13,
1026 2.1453139344136500e+15, 3.2486182435406701e+17, 4.2759937630604067e+19,
1027 4.9649038693312506e+21, 5.1436404086271749e+23, 4.7976136902286196e+25,
1028 4.0579815796517076e+27, 3.1308888649158942e+29, 2.2139856973333827e+31,
1029 1.4405666937315875e+33, 8.6524037042253478e+34, 4.8097185297017371e+36,
1030 2.4796771086462288e+38, 1.1876348257200359e+40, 5.2909131485827601e+41,
1031 2.1944692154359926e+43, 8.4786310596390627e+44, 3.0523071814700622e+46,
1032 1.0237947004514167e+48, 3.1983346442102258e+49, 9.2997730423958877e+50,
1033 2.5143830818329623e+52, 6.3128975233163300e+53, 1.4693813200822492e+55,
1034 3.1640677759104434e+56, 6.2873088708413973e+57, 1.1493986529506929e+59,
1035 1.9261135002476763e+60, 2.9458206474376228e+61, 4.0904823847276701e+62,
1036 5.1244654319782758e+63, 5.7477112277594171e+64, 5.7174601160343675e+65,
1037 4.9844524088504742e+66, 3.7508004376599823e+67, 2.3877046688518421e+68,
1038 1.2507024455890602e+69, 5.1773264026709932e+69, 1.5884978735467820e+70,
1039 3.2122956998390481e+70, 3.2122956998390481e+70, 0.0000000000000000e+00,
1040 0.0000000000000000e+00, 0.0000000000000000e+00},
1041 // lambda = 47
1042 {1.0000000000000000e+00, 1.1280000000000000e+03, 6.3562800000000000e+05,
1043 2.3836050000000000e+08, 6.6860120250000000e+10, 1.4949922887900000e+13,
1044 2.7732106957054500e+15, 4.3856346287799046e+17, 6.0302476145723687e+19,
1045 7.3167004390144743e+21, 7.9239865754526747e+23, 7.7294887231461096e+25,
1046 6.8405975199843072e+27, 5.5250979969104019e+29, 4.0925190162829194e+31,
1047 2.7910979691049507e+33, 1.7583917205361192e+35, 1.0260732863363706e+37,
1048 5.5578969676553410e+38, 2.7994249463400848e+40, 1.3129302998334999e+42,
1049 5.7393810249864419e+43, 2.3401021724603811e+45, 8.9025626126210148e+46,
1050 3.1604097274804605e+48, 1.0467277017415285e+50, 3.2327782480709515e+51,
1051 9.3032174027819598e+52, 2.4919332328880251e+54, 6.2040544625694973e+55,
1052 1.4331365808535538e+57, 3.0650630745351811e+58, 6.0534995722069831e+59,
1053 1.1006362858558150e+61, 1.8354728649419034e+62, 2.7951629628972415e+63,
1054 3.8666420986745172e+64, 4.8280774313179104e+65, 5.3998234429213471e+66,
1055 5.3582863395142599e+67, 4.6617091153774061e+68, 3.5019668476493689e+69,
1056 2.2262503531485273e+70, 1.1648984406009735e+71, 4.8184435497585726e+71,
1057 1.4776560219259621e+72, 2.9874350008503150e+72, 2.9874350008503150e+72,
1058 0.0000000000000000e+00, 0.0000000000000000e+00},
1059 // lambda = 48
1060 {1.0000000000000000e+00, 1.1760000000000000e+03, 6.9090000000000000e+05,
1061 2.7014190000000000e+08, 7.9016505750000000e+10, 1.8426649140900000e+13,
1062 3.5655566087641500e+15, 5.8831684044608474e+17, 8.4423466604013158e+19,
1063 1.0693639103175000e+22, 1.2094505825690927e+24, 1.2325400936908661e+26,
1064 1.1400995866640512e+28, 9.6294565089009858e+29, 7.4628287943982639e+31,
1065 5.3284597592003606e+33, 3.5167834410722384e+35, 2.1514439874794866e+37,
1066 1.2227373328841749e+39, 6.4676369449926094e+40, 3.1885450138813566e+42,
1067 1.4667307063854240e+44, 6.3002750797010264e+45, 2.5283277819843683e+47,
1068 9.4812291824413815e+48, 3.3222227055274598e+50, 1.0873890470784109e+52,
1069 3.3225776438506998e+53, 9.4693462849744954e+54, 2.5142747032518486e+56,
1070 6.2102585170320663e+57, 1.4243528405192900e+59, 3.0267497861034914e+60,
1071 5.9434359436214007e+61, 1.0750626780374005e+63, 1.7846040455420849e+64,
1072 2.7066494690721621e+65, 3.7307871060183856e+66, 4.6438481609123586e+67,
1073 5.1796767948637847e+68, 5.1278800269151473e+69, 4.4525007062970545e+70,
1074 3.3393755297227907e+71, 2.1201151618937719e+72, 1.1082420164444717e+73,
1075 4.5807336679704831e+73, 1.4040944503996481e+74, 2.8380632508077990e+74,
1076 2.8380632508077990e+74, 0.0000000000000000e+00},
1077 // lambda = 49
1078 {1.0000000000000000e+00, 1.2250000000000000e+03, 7.4970000000000000e+05,
1079 3.0537780000000000e+08, 9.3063884550000000e+10, 2.2614523945650000e+13,
1080 4.5605956623727500e+15, 7.8442245392811302e+17, 1.1736920966899391e+20,
1081 1.5505776699603750e+22, 1.8296816505532427e+24, 1.9461159374066307e+26,
1082 1.8796236428785709e+28, 1.6584063987551699e+30, 1.3433091829916875e+32,
1083 1.0030041899671267e+34, 6.9269976869604691e+35, 4.4373532241764414e+37,
1084 2.6426903646206363e+39, 1.4659977075316582e+41, 7.5865381364763308e+42,
1085 3.6668267659635603e+44, 1.6567390024398995e+46, 7.0015230885720968e+47,
1086 2.7685189212728831e+49, 1.0243520008709669e+51, 3.5458338491687312e+52,
1087 1.1477995496938781e+54, 3.4720936378239817e+55, 9.8056713426822102e+56,
1088 2.5821601202396487e+58, 6.3304570689746226e+59, 1.4421572510257811e+61,
1089 3.0460109211059682e+62, 5.9486801518069496e+63, 1.0707624273252509e+65,
1090 1.7697323451625674e+66, 2.6737307593131764e+67, 3.6728617272670476e+68,
1091 4.5581155794801306e+69, 5.0709035821716453e+70, 5.0090632945841862e+71,
1092 4.3411881886396280e+72, 3.2508432482371166e+73, 2.0613301505867174e+74,
1093 1.0764724119730636e+75, 4.4462990929322190e+75, 1.3622703603877436e+76,
1094 2.7529213532835652e+76, 2.7529213532835652e+76},
1095};
i
static void const int const int i
Definition grid_cpu_collint.h:38
grpp_specfunc.h
NPOINTS
#define NPOINTS
Definition grpp_specfunc_scaled_mod_sph_bessel.c:31
bessel_asymptotic_R_function
static double bessel_asymptotic_R_function(int n, double x)
Definition grpp_specfunc_scaled_mod_sph_bessel.c:175
rfun_coeffs
const double rfun_coeffs[50][50]
Definition grpp_specfunc_scaled_mod_sph_bessel.c:194
LMAX
#define LMAX
Definition grpp_specfunc_scaled_mod_sph_bessel.c:26
libgrpp_modified_bessel_scaled
double libgrpp_modified_bessel_scaled(int n, double x)
Definition grpp_specfunc_scaled_mod_sph_bessel.c:68
bessel_table
double bessel_table[NPOINTS][3 *LMAX][10]
Definition grpp_specfunc_scaled_mod_sph_bessel.c:39
libgrpp_pretabulate_bessel
void libgrpp_pretabulate_bessel()
Definition grpp_specfunc_scaled_mod_sph_bessel.c:48
modified_scaled_bessel_derivative
static double modified_scaled_bessel_derivative(int n, int lambda, int ix)
Definition grpp_specfunc_scaled_mod_sph_bessel.c:132
bessel_table_0
const double bessel_table_0[1601][60]
Definition grpp_specfunc_bessel_table.c:34