-
Notifications
You must be signed in to change notification settings - Fork 0
/
realsphnum.m
521 lines (518 loc) · 60.1 KB
/
realsphnum.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
function Y = realsphnum(theta,phi,l,m)
PI = pi;
if (l == 0 && m == 0)
Y = (1/PI)^(1/2)/2;
elseif (l == 1 && m == -1)
Y = (3^(1/2)*sin(phi)*(sin(theta)^2)^(1/2)*(1/PI)^(1/2))/2;
elseif (l == 1 && m == 0)
Y = (3^(1/2)*cos(theta)*(1/PI)^(1/2))/2;
elseif (l == 1 && m == 1)
Y = (3^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2))/2;
elseif (l == 2 && m == -2)
Y = (15^(1/2)*sin(2*phi)*sin(theta)^2*(1/PI)^(1/2))/4;
elseif (l == 2 && m == -1)
Y = (15^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2))/2;
elseif (l == 2 && m == 0)
Y = (5^(1/2)*(1/PI)^(1/2)*((3*cos(theta)^2)/2 - 1/2))/2;
elseif (l == 2 && m == 1)
Y = (15^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2))/2;
elseif (l == 2 && m == 2)
Y = -(15^(1/2)*cos(2*phi)*(1/PI)^(1/2)*(3*cos(theta)^2 - 3))/12;
elseif (l == 3 && m == -3)
Y = (70^(1/2)*sin(3*phi)*(sin(theta)^2)^(3/2)*(1/PI)^(1/2))/8;
elseif (l == 3 && m == -2)
Y = -(105^(1/2)*sin(2*phi)*cos(theta)*(cos(theta)^2 - 1)*(1/PI)^(1/2))/4;
elseif (l == 3 && m == -1)
Y = (42^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(360*cos(theta)^2 - 72))/576;
elseif (l == 3 && m == 0)
Y = (7^(1/2)*cos(theta)*(1/PI)^(1/2)*(5*cos(theta)^2 - 3))/4;
elseif (l == 3 && m == 1)
Y = (42^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(360*cos(theta)^2 - 72))/576;
elseif (l == 3 && m == 2)
Y = -(105^(1/2)*cos(2*phi)*cos(theta)*(cos(theta)^2 - 1)*(1/PI)^(1/2))/4;
elseif (l == 3 && m == 3)
Y = (70^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2))/8;
elseif (l == 4 && m == -4)
Y = (3*35^(1/2)*sin(4*phi)*sin(theta)^4*(1/PI)^(1/2))/16;
elseif (l == 4 && m == -3)
Y = (3*70^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2))/8;
elseif (l == 4 && m == -2)
Y = -(5^(1/2)*sin(2*phi)*(1/PI)^(1/2)*((105*cos(theta)^4)/2 - 60*cos(theta)^2 + 15/2))/20;
elseif (l == 4 && m == -1)
Y = (3*10^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(7*cos(theta)^2 - 3))/8;
elseif (l == 4 && m == 0)
Y = (3*(1/PI)^(1/2)*((35*cos(theta)^4)/8 - (15*cos(theta)^2)/4 + 3/8))/2;
elseif (l == 4 && m == 1)
Y = (3*10^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(7*cos(theta)^2 - 3))/8;
elseif (l == 4 && m == 2)
Y = -(5^(1/2)*cos(2*phi)*(1/PI)^(1/2)*((105*cos(theta)^4)/2 - 60*cos(theta)^2 + 15/2))/20;
elseif (l == 4 && m == 3)
Y = (3*70^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2))/8;
elseif (l == 4 && m == 4)
Y = (3*35^(1/2)*cos(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2))/16;
elseif (l == 5 && m == -5)
Y = (571939421694023565*22^(1/2)*sin(5*phi)*(sin(theta)^2)^(5/2)*(1/PI)^(1/2))/2305843009213693952;
elseif (l == 5 && m == -4)
Y = (3617262512385266115*22^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2))/4611686018427387904;
elseif (l == 5 && m == -3)
Y = (770^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(1814400*cos(theta)^2 - 201600))/6451200;
elseif (l == 5 && m == -2)
Y = -(1155^(1/2)*sin(2*phi)*cos(theta)*(1/PI)^(1/2)*(3*cos(theta)^4 - 4*cos(theta)^2 + 1))/8;
elseif (l == 5 && m == -1)
Y = (165^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(151200*cos(theta)^4 - 100800*cos(theta)^2 + 7200))/115200;
elseif (l == 5 && m == 0)
Y = (11^(1/2)*cos(theta)*(1/PI)^(1/2)*(63*cos(theta)^4 - 70*cos(theta)^2 + 15))/16;
elseif (l == 5 && m == 1)
Y = (165^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(151200*cos(theta)^4 - 100800*cos(theta)^2 + 7200))/115200;
elseif (l == 5 && m == 2)
Y = -(1155^(1/2)*cos(2*phi)*cos(theta)*(1/PI)^(1/2)*(3*cos(theta)^4 - 4*cos(theta)^2 + 1))/8;
elseif (l == 5 && m == 3)
Y = (770^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(1814400*cos(theta)^2 - 201600))/6451200;
elseif (l == 5 && m == 4)
Y = (3617262512385266115*22^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2))/4611686018427387904;
elseif (l == 5 && m == 5)
Y = (571939421694023565*22^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2))/2305843009213693952;
elseif (l == 6 && m == -6)
Y = (8761444901189466255*26^(1/2)*sin(6*phi)*sin(theta)^6*(1/PI)^(1/2))/36893488147419103232;
elseif (l == 6 && m == -5)
Y = (60701070866301748575*26^(1/2)*sin(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2))/73786976294838206464;
elseif (l == 6 && m == -4)
Y = (6847360736639263*26^(1/2)*sin(4*phi)*(239500800*cos(theta)^2 - 21772800)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2))/850025966916536138465280;
elseif (l == 6 && m == -3)
Y = (2730^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(11*cos(theta)^2 - 3))/32;
elseif (l == 6 && m == -2)
Y = -(2730^(1/2)*sin(2*phi)*(1/PI)^(1/2)*((1995*cos(theta)^2)/8 - (5355*cos(theta)^4)/8 + (3465*cos(theta)^6)/8 - 105/8))/840;
elseif (l == 6 && m == -1)
Y = (273^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(33*cos(theta)^4 - 30*cos(theta)^2 + 5))/16;
elseif (l == 6 && m == 0)
Y = (13^(1/2)*(1/PI)^(1/2)*((105*cos(theta)^2)/16 - (315*cos(theta)^4)/16 + (231*cos(theta)^6)/16 - 5/16))/2;
elseif (l == 6 && m == 1)
Y = (273^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(33*cos(theta)^4 - 30*cos(theta)^2 + 5))/16;
elseif (l == 6 && m == 2)
Y = -(2730^(1/2)*cos(2*phi)*(1/PI)^(1/2)*((1995*cos(theta)^2)/8 - (5355*cos(theta)^4)/8 + (3465*cos(theta)^6)/8 - 105/8))/840;
elseif (l == 6 && m == 3)
Y = (2730^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(11*cos(theta)^2 - 3))/32;
elseif (l == 6 && m == 4)
Y = (6847360736639263*26^(1/2)*cos(4*phi)*(239500800*cos(theta)^2 - 21772800)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2))/850025966916536138465280;
elseif (l == 6 && m == 5)
Y = (60701070866301748575*26^(1/2)*cos(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2))/73786976294838206464;
elseif (l == 6 && m == 6)
Y = -(8761444901189466255*26^(1/2)*cos(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2))/36893488147419103232;
elseif (l == 7 && m == -7)
Y = (622964223759633346403777810512315774125*30^(1/2)*sin(7*phi)*(sin(theta)^2)^(7/2)*(1/PI)^(1/2))/2722258935367507707706996859454145691648;
elseif (l == 7 && m == -6)
Y = -(291364836190765818430107208838450788125*30^(1/2)*sin(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2))/340282366920938463463374607431768211456;
elseif (l == 7 && m == -5)
Y = (17450802992556886343961966369545*30^(1/2)*sin(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(43589145600*cos(theta)^2 - 3353011200))/348449143727040986586495598010130648530944;
elseif (l == 7 && m == -4)
Y = (7142668198612885820212584399040269375*30^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(13*cos(theta)^2 - 3))/21267647932558653966460912964485513216;
elseif (l == 7 && m == -3)
Y = (21704162181270889411240392242285*30^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(3632428800*cos(theta)^4 - 1676505600*cos(theta)^2 + 76204800))/10889035741470030830827987437816582766592;
elseif (l == 7 && m == -2)
Y = -30240*70^(1/2)*sin(2*phi)*cos(theta)*((3660068268593165*cos(theta)^2)/2361183241434822606848 - 3660068268593165/2361183241434822606848)*(1/PI)^(1/2)*(143*cos(theta)^4 - 110*cos(theta)^2 + 15);
elseif (l == 7 && m == -1)
Y = (3660068268593165*105^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(38102400*cos(theta)^2 - 139708800*cos(theta)^4 + 121080960*cos(theta)^6 - 1411200))/66113130760175032991744;
elseif (l == 7 && m == 0)
Y = (1152921504606846975*15^(1/2)*cos(theta)*(1/PI)^(1/2)*(315*cos(theta)^2 - 693*cos(theta)^4 + 429*cos(theta)^6 - 35))/36893488147419103232;
elseif (l == 7 && m == 1)
Y = (3660068268593165*105^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(38102400*cos(theta)^2 - 139708800*cos(theta)^4 + 121080960*cos(theta)^6 - 1411200))/66113130760175032991744;
elseif (l == 7 && m == 2)
Y = -30240*70^(1/2)*cos(2*phi)*cos(theta)*((3660068268593165*cos(theta)^2)/2361183241434822606848 - 3660068268593165/2361183241434822606848)*(1/PI)^(1/2)*(143*cos(theta)^4 - 110*cos(theta)^2 + 15);
elseif (l == 7 && m == 3)
Y = (21704162181270889411240392242285*30^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(3632428800*cos(theta)^4 - 1676505600*cos(theta)^2 + 76204800))/10889035741470030830827987437816582766592;
elseif (l == 7 && m == 4)
Y = (7142668198612885820212584399040269375*30^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(13*cos(theta)^2 - 3))/21267647932558653966460912964485513216;
elseif (l == 7 && m == 5)
Y = (17450802992556886343961966369545*30^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(43589145600*cos(theta)^2 - 3353011200))/348449143727040986586495598010130648530944;
elseif (l == 7 && m == 6)
Y = -(291364836190765818430107208838450788125*30^(1/2)*cos(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2))/340282366920938463463374607431768211456;
elseif (l == 7 && m == 7)
Y = (622964223759633346403777810512315774125*30^(1/2)*cos(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2))/2722258935367507707706996859454145691648;
elseif (l == 8 && m == -8)
Y = (4825460127808181729739116385952141955625*34^(1/2)*sin(8*phi)*sin(theta)^8*(1/PI)^(1/2))/21778071482940061661655974875633165533184;
elseif (l == 8 && m == -7)
Y = (4825460127808181729739116385952141955625*34^(1/2)*sin(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2))/5444517870735015415413993718908291383296;
elseif (l == 8 && m == -6)
Y = -(10348316634736233594032770660625*34^(1/2)*sin(6*phi)*(10461394944000*cos(theta)^2 - 697426329600)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2))/44601490397061246283071436545296723011960832;
elseif (l == 8 && m == -5)
Y = (713695177656981865662037084986268271625*34^(1/2)*sin(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(5*cos(theta)^2 - 1))/680564733841876926926749214863536422912;
elseif (l == 8 && m == -4)
Y = (30225677415983538869803856712565*34^(1/2)*sin(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(871782912000*cos(theta)^4 - 348713164800*cos(theta)^2 + 13412044800))/2787593149816327892691964784081045188247552;
elseif (l == 8 && m == -3)
Y = (31942983265648761230587743870270355875*34^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(39*cos(theta)^4 - 26*cos(theta)^2 + 3))/85070591730234615865843651857942052864;
elseif (l == 8 && m == -2)
Y = -(1190^(1/2)*sin(2*phi)*((3660068268593165*cos(theta)^2)/37778931862957161709568 - 3660068268593165/37778931862957161709568)*(1/PI)^(1/2)*(6706022400*cos(theta)^2 - 29059430400*cos(theta)^4 + 29059430400*cos(theta)^6 - 203212800))/840;
elseif (l == 8 && m == -1)
Y = (3458764513820540925*17^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(385*cos(theta)^2 - 1001*cos(theta)^4 + 715*cos(theta)^6 - 35))/73786976294838206464;
elseif (l == 8 && m == 0)
Y = (17^(1/2)*(1/PI)^(1/2)*((3994873013462724768375*cos(theta)^4)/73786976294838206464 - (363170273951156797125*cos(theta)^2)/36893488147419103232 - (3462223278334361465925*cos(theta)^6)/36893488147419103232 + (7419049882145060284125*cos(theta)^8)/147573952589676412928 + 40352252661239644125/147573952589676412928))/2;
elseif (l == 8 && m == 1)
Y = (3458764513820540925*17^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(385*cos(theta)^2 - 1001*cos(theta)^4 + 715*cos(theta)^6 - 35))/73786976294838206464;
elseif (l == 8 && m == 2)
Y = -(1190^(1/2)*cos(2*phi)*((3660068268593165*cos(theta)^2)/37778931862957161709568 - 3660068268593165/37778931862957161709568)*(1/PI)^(1/2)*(6706022400*cos(theta)^2 - 29059430400*cos(theta)^4 + 29059430400*cos(theta)^6 - 203212800))/840;
elseif (l == 8 && m == 3)
Y = (31942983265648761230587743870270355875*34^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(39*cos(theta)^4 - 26*cos(theta)^2 + 3))/85070591730234615865843651857942052864;
elseif (l == 8 && m == 4)
Y = (30225677415983538869803856712565*34^(1/2)*cos(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(871782912000*cos(theta)^4 - 348713164800*cos(theta)^2 + 13412044800))/2787593149816327892691964784081045188247552;
elseif (l == 8 && m == 5)
Y = (713695177656981865662037084986268271625*34^(1/2)*cos(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(5*cos(theta)^2 - 1))/680564733841876926926749214863536422912;
elseif (l == 8 && m == 6)
Y = -(10348316634736233594032770660625*34^(1/2)*cos(6*phi)*(10461394944000*cos(theta)^2 - 697426329600)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2))/44601490397061246283071436545296723011960832;
elseif (l == 8 && m == 7)
Y = (4825460127808181729739116385952141955625*34^(1/2)*cos(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2))/5444517870735015415413993718908291383296;
elseif (l == 8 && m == 8)
Y = (4825460127808181729739116385952141955625*34^(1/2)*cos(8*phi)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2))/21778071482940061661655974875633165533184;
elseif (l == 9 && m == -9)
Y = (1200513104031725405598602863323714976522875*38^(1/2)*sin(9*phi)*(sin(theta)^2)^(9/2)*(1/PI)^(1/2))/5575186299632655785383929568162090376495104;
elseif (l == 9 && m == -8)
Y = (318334108786554070248790125246943707511875*38^(1/2)*sin(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2))/348449143727040986586495598010130648530944;
elseif (l == 9 && m == -7)
Y = (4750086872606176786212274606173*38^(1/2)*sin(7*phi)*(3201186852864000*cos(theta)^2 - 188305108992000)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2))/5708990770823839524233143877797980545530986496;
elseif (l == 9 && m == -6)
Y = -(15759886783033794785003033260970820571875*38^(1/2)*sin(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(17*cos(theta)^2 - 3))/43556142965880123323311949751266331066368;
elseif (l == 9 && m == -5)
Y = (7966137859632595715463359825357*38^(1/2)*sin(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(266765571072000*cos(theta)^4 - 94152554496000*cos(theta)^2 + 3138418483200))/178405961588244985132285746181186892047843328;
elseif (l == 9 && m == -4)
Y = (3191741864909601274273012629548582077425*38^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(17*cos(theta)^4 - 10*cos(theta)^2 + 1))/2722258935367507707706996859454145691648;
elseif (l == 9 && m == -3)
Y = (2299345185640089671314184348455*38^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(1569209241600*cos(theta)^2 - 7846046208000*cos(theta)^4 + 8892185702400*cos(theta)^6 - 40236134400))/696898287454081973172991196020261297061888;
elseif (l == 9 && m == -2)
Y = -4354560*2090^(1/2)*sin(2*phi)*cos(theta)*(1/PI)^(1/2)*((1626697008263629*cos(theta)^2)/302231454903657293676544 - 1626697008263629/302231454903657293676544)*(91*cos(theta)^2 - 273*cos(theta)^4 + 221*cos(theta)^6 - 7);
elseif (l == 9 && m == -1)
Y = (1626697008263629*95^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(130767436800*cos(theta)^4 - 20118067200*cos(theta)^2 - 261534873600*cos(theta)^6 + 158789030400*cos(theta)^8 + 457228800))/9066943647109718810296320;
elseif (l == 9 && m == 0)
Y = (4611686018427388215*19^(1/2)*cos(theta)*(1/PI)^(1/2)*(18018*cos(theta)^4 - 4620*cos(theta)^2 - 25740*cos(theta)^6 + 12155*cos(theta)^8 + 315))/1180591620717411303424;
elseif (l == 9 && m == 1)
Y = (1626697008263629*95^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(130767436800*cos(theta)^4 - 20118067200*cos(theta)^2 - 261534873600*cos(theta)^6 + 158789030400*cos(theta)^8 + 457228800))/9066943647109718810296320;
elseif (l == 9 && m == 2)
Y = -4354560*2090^(1/2)*cos(2*phi)*cos(theta)*(1/PI)^(1/2)*((1626697008263629*cos(theta)^2)/302231454903657293676544 - 1626697008263629/302231454903657293676544)*(91*cos(theta)^2 - 273*cos(theta)^4 + 221*cos(theta)^6 - 7);
elseif (l == 9 && m == 3)
Y = (2299345185640089671314184348455*38^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(1569209241600*cos(theta)^2 - 7846046208000*cos(theta)^4 + 8892185702400*cos(theta)^6 - 40236134400))/696898287454081973172991196020261297061888;
elseif (l == 9 && m == 4)
Y = (3191741864909601274273012629548582077425*38^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(17*cos(theta)^4 - 10*cos(theta)^2 + 1))/2722258935367507707706996859454145691648;
elseif (l == 9 && m == 5)
Y = (7966137859632595715463359825357*38^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(266765571072000*cos(theta)^4 - 94152554496000*cos(theta)^2 + 3138418483200))/178405961588244985132285746181186892047843328;
elseif (l == 9 && m == 6)
Y = -(15759886783033794785003033260970820571875*38^(1/2)*cos(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(17*cos(theta)^2 - 3))/43556142965880123323311949751266331066368;
elseif (l == 9 && m == 7)
Y = (4750086872606176786212274606173*38^(1/2)*cos(7*phi)*(3201186852864000*cos(theta)^2 - 188305108992000)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2))/5708990770823839524233143877797980545530986496;
elseif (l == 9 && m == 8)
Y = (318334108786554070248790125246943707511875*38^(1/2)*cos(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2))/348449143727040986586495598010130648530944;
elseif (l == 9 && m == 9)
Y = (1200513104031725405598602863323714976522875*38^(1/2)*cos(9*phi)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2))/5575186299632655785383929568162090376495104;
elseif (l == 10 && m == -10)
Y = (74887387732771042032024354341385578328853125*42^(1/2)*sin(10*phi)*sin(theta)^10*(1/PI)^(1/2))/356811923176489970264571492362373784095686656;
elseif (l == 10 && m == -9)
Y = (41863322406964975491969479079182563811060625*42^(1/2)*sin(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2))/44601490397061246283071436545296723011960832;
elseif (l == 10 && m == -8)
Y = (6951536451890890460676670442859*42^(1/2)*sin(8*phi)*(1216451004088320000*cos(theta)^2 - 64023737057280000)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2))/2923003274661805836407369665432566039311865085952;
elseif (l == 10 && m == -7)
Y = (1039674845667584616356293580318204120956875*42^(1/2)*sin(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(19*cos(theta)^2 - 3))/2787593149816327892691964784081045188247552;
elseif (l == 10 && m == -6)
Y = -(6581913442975880421282327855225*42^(1/2)*sin(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(101370917007360000*cos(theta)^4 - 32011868528640000*cos(theta)^2 + 941525544960000))/45671926166590716193865151022383844364247891968;
elseif (l == 10 && m == -5)
Y = (7048035632912807268949502889100798171875*42^(1/2)*sin(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(323*cos(theta)^4 - 170*cos(theta)^2 + 15))/87112285931760246646623899502532662132736;
elseif (l == 10 && m == -4)
Y = (4363233401916694712681775722097*42^(1/2)*sin(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(470762772480000*cos(theta)^2 - 2667655710720000*cos(theta)^4 + 3379030566912000*cos(theta)^6 - 10461394944000))/356811923176489970264571492362373784095686656;
elseif (l == 10 && m == -3)
Y = (984992923939612009700066693480278077375*42^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(105*cos(theta)^2 - 357*cos(theta)^4 + 323*cos(theta)^6 - 7))/5444517870735015415413993718908291383296;
elseif (l == 10 && m == -2)
Y = -(385^(1/2)*sin(2*phi)*(1/PI)^(1/2)*((1301357606610903*cos(theta)^2)/4835703278458516698824704 - 1301357606610903/4835703278458516698824704)*(39230231040000*cos(theta)^4 - 5230697472000*cos(theta)^2 - 88921857024000*cos(theta)^6 + 60339831552000*cos(theta)^8 + 100590336000))/660;
elseif (l == 10 && m == -1)
Y = (18446744073709550025*1155^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(4914*cos(theta)^4 - 1092*cos(theta)^2 - 7956*cos(theta)^6 + 4199*cos(theta)^8 + 63))/4722366482869645213696;
elseif (l == 10 && m == 0)
Y = (21^(1/2)*(1/PI)^(1/2)*((63917968215403590836625*cos(theta)^2)/4722366482869645213696 - (276977862266748893625375*cos(theta)^4)/2361183241434822606848 + (830933586800246680876125*cos(theta)^6)/2361183241434822606848 - (2017981567943456224984875*cos(theta)^8)/4722366482869645213696 + (852036662020570406104725*cos(theta)^10)/4722366482869645213696 - 1162144876643701651575/4722366482869645213696))/2;
elseif (l == 10 && m == 1)
Y = (18446744073709550025*1155^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(4914*cos(theta)^4 - 1092*cos(theta)^2 - 7956*cos(theta)^6 + 4199*cos(theta)^8 + 63))/4722366482869645213696;
elseif (l == 10 && m == 2)
Y = -(385^(1/2)*cos(2*phi)*(1/PI)^(1/2)*((1301357606610903*cos(theta)^2)/4835703278458516698824704 - 1301357606610903/4835703278458516698824704)*(39230231040000*cos(theta)^4 - 5230697472000*cos(theta)^2 - 88921857024000*cos(theta)^6 + 60339831552000*cos(theta)^8 + 100590336000))/660;
elseif (l == 10 && m == 3)
Y = (984992923939612009700066693480278077375*42^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(105*cos(theta)^2 - 357*cos(theta)^4 + 323*cos(theta)^6 - 7))/5444517870735015415413993718908291383296;
elseif (l == 10 && m == 4)
Y = (4363233401916694712681775722097*42^(1/2)*cos(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(470762772480000*cos(theta)^2 - 2667655710720000*cos(theta)^4 + 3379030566912000*cos(theta)^6 - 10461394944000))/356811923176489970264571492362373784095686656;
elseif (l == 10 && m == 5)
Y = (7048035632912807268949502889100798171875*42^(1/2)*cos(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(323*cos(theta)^4 - 170*cos(theta)^2 + 15))/87112285931760246646623899502532662132736;
elseif (l == 10 && m == 6)
Y = -(6581913442975880421282327855225*42^(1/2)*cos(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(101370917007360000*cos(theta)^4 - 32011868528640000*cos(theta)^2 + 941525544960000))/45671926166590716193865151022383844364247891968;
elseif (l == 10 && m == 7)
Y = (1039674845667584616356293580318204120956875*42^(1/2)*cos(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(19*cos(theta)^2 - 3))/2787593149816327892691964784081045188247552;
elseif (l == 10 && m == 8)
Y = (6951536451890890460676670442859*42^(1/2)*cos(8*phi)*(1216451004088320000*cos(theta)^2 - 64023737057280000)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2))/2923003274661805836407369665432566039311865085952;
elseif (l == 10 && m == 9)
Y = (41863322406964975491969479079182563811060625*42^(1/2)*cos(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2))/44601490397061246283071436545296723011960832;
elseif (l == 10 && m == 10)
Y = -(74887387732771042032024354341385578328853125*42^(1/2)*cos(10*phi)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2))/356811923176489970264571492362373784095686656;
elseif (l == 11 && m == -11)
Y = (18730395759487536822434794959070174570219029375*46^(1/2)*sin(11*phi)*(sin(theta)^2)^(11/2)*(1/PI)^(1/2))/91343852333181432387730302044767688728495783936;
elseif (l == 11 && m == -10)
Y = -(2745416983063446017740163437098377873199418125*46^(1/2)*sin(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2))/2854495385411919762116571938898990272765493248;
elseif (l == 11 && m == -9)
Y = (2074800265707897366042463818129*46^(1/2)*sin(9*phi)*(562000363888803840000*cos(theta)^2 - 26761922089943040000)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2))/374144419156711147060143317175368453031918731001856;
elseif (l == 11 && m == -8)
Y = (1640700461354974624257458057727956001452806875*46^(1/2)*sin(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(7*cos(theta)^2 - 1))/1427247692705959881058285969449495136382746624;
elseif (l == 11 && m == -7)
Y = (8756664963885168992117216248887*46^(1/2)*sin(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(46833363657400320000*cos(theta)^4 - 13380961044971520000*cos(theta)^2 + 352130553815040000))/23384026197294446691258957323460528314494920687616;
elseif (l == 11 && m == -6)
Y = -(3719653807054915633615234792146360897789375*46^(1/2)*sin(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(399*cos(theta)^4 - 190*cos(theta)^2 + 15))/44601490397061246283071436545296723011960832;
elseif (l == 11 && m == -5)
Y = (1638664756483810351684830071175*46^(1/2)*sin(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(176065276907520000*cos(theta)^2 - 1115080087080960000*cos(theta)^4 + 1561112121913344000*cos(theta)^6 - 3452260331520000))/45671926166590716193865151022383844364247891968;
elseif (l == 11 && m == -4)
Y = (182705965480187368334208982575135759184875*46^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(85*cos(theta)^2 - 323*cos(theta)^4 + 323*cos(theta)^6 - 5))/696898287454081973172991196020261297061888;
elseif (l == 11 && m == -3)
Y = (5936627086727416889369559767145*46^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(14672106408960000*cos(theta)^4 - 1726130165760000*cos(theta)^2 - 37169336236032000*cos(theta)^6 + 27877002177024000*cos(theta)^8 + 28768836096000))/1427247692705959881058285969449495136382746624;
elseif (l == 11 && m == -2)
Y = -159667200*49335^(1/2)*sin(2*phi)*cos(theta)*((1892883791434041*cos(theta)^2)/154742504910672534362390528 - 1892883791434041/154742504910672534362390528)*(1/PI)^(1/2)*(2142*cos(theta)^4 - 420*cos(theta)^2 - 3876*cos(theta)^6 + 2261*cos(theta)^8 + 21);
elseif (l == 11 && m == -1)
Y = (630961263811347*1518^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(14384418048000*cos(theta)^2 - 143844180480000*cos(theta)^4 + 489070213632000*cos(theta)^6 - 663738147072000*cos(theta)^8 + 309744468633600*cos(theta)^10 - 221298739200))/6808670216069591511945183232;
elseif (l == 11 && m == 0)
Y = (295147905179352842925*23^(1/2)*cos(theta)*(1/PI)^(1/2)*(15015*cos(theta)^2 - 90090*cos(theta)^4 + 218790*cos(theta)^6 - 230945*cos(theta)^8 + 88179*cos(theta)^10 - 693))/151115727451828646838272;
elseif (l == 11 && m == 1)
Y = (630961263811347*1518^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(14384418048000*cos(theta)^2 - 143844180480000*cos(theta)^4 + 489070213632000*cos(theta)^6 - 663738147072000*cos(theta)^8 + 309744468633600*cos(theta)^10 - 221298739200))/6808670216069591511945183232;
elseif (l == 11 && m == 2)
Y = -159667200*49335^(1/2)*cos(2*phi)*cos(theta)*((1892883791434041*cos(theta)^2)/154742504910672534362390528 - 1892883791434041/154742504910672534362390528)*(1/PI)^(1/2)*(2142*cos(theta)^4 - 420*cos(theta)^2 - 3876*cos(theta)^6 + 2261*cos(theta)^8 + 21);
elseif (l == 11 && m == 3)
Y = (5936627086727416889369559767145*46^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(14672106408960000*cos(theta)^4 - 1726130165760000*cos(theta)^2 - 37169336236032000*cos(theta)^6 + 27877002177024000*cos(theta)^8 + 28768836096000))/1427247692705959881058285969449495136382746624;
elseif (l == 11 && m == 4)
Y = (182705965480187368334208982575135759184875*46^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(85*cos(theta)^2 - 323*cos(theta)^4 + 323*cos(theta)^6 - 5))/696898287454081973172991196020261297061888;
elseif (l == 11 && m == 5)
Y = (1638664756483810351684830071175*46^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(176065276907520000*cos(theta)^2 - 1115080087080960000*cos(theta)^4 + 1561112121913344000*cos(theta)^6 - 3452260331520000))/45671926166590716193865151022383844364247891968;
elseif (l == 11 && m == 6)
Y = -(3719653807054915633615234792146360897789375*46^(1/2)*cos(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(399*cos(theta)^4 - 190*cos(theta)^2 + 15))/44601490397061246283071436545296723011960832;
elseif (l == 11 && m == 7)
Y = (8756664963885168992117216248887*46^(1/2)*cos(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(46833363657400320000*cos(theta)^4 - 13380961044971520000*cos(theta)^2 + 352130553815040000))/23384026197294446691258957323460528314494920687616;
elseif (l == 11 && m == 8)
Y = (1640700461354974624257458057727956001452806875*46^(1/2)*cos(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(7*cos(theta)^2 - 1))/1427247692705959881058285969449495136382746624;
elseif (l == 11 && m == 9)
Y = (2074800265707897366042463818129*46^(1/2)*cos(9*phi)*(562000363888803840000*cos(theta)^2 - 26761922089943040000)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2))/374144419156711147060143317175368453031918731001856;
elseif (l == 11 && m == 10)
Y = -(2745416983063446017740163437098377873199418125*46^(1/2)*cos(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2))/2854495385411919762116571938898990272765493248;
elseif (l == 11 && m == 11)
Y = (18730395759487536822434794959070174570219029375*46^(1/2)*cos(11*phi)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2))/91343852333181432387730302044767688728495783936;
elseif (l == 12 && m == -12)
Y = (733441098842147879561461543657255943751257015625*2^(1/2)*sin(12*phi)*sin(theta)^12*(1/PI)^(1/2))/730750818665451459101842416358141509827966271488;
elseif (l == 12 && m == -11)
Y = (3593112897098928385951021897837173248182517728125*2^(1/2)*sin(11*phi)*cos(theta)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2))/730750818665451459101842416358141509827966271488;
elseif (l == 12 && m == -10)
Y = -(5148183698591334802484249656035*2^(1/2)*sin(10*phi)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(310224200866619719680000*cos(theta)^2 - 13488008733331292160000))/95780971304118053647396689196894323976171195136475136;
elseif (l == 12 && m == -9)
Y = (44832471597844324878772516958837212331047696875*2^(1/2)*sin(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(23*cos(theta)^2 - 3))/22835963083295358096932575511191922182123945984;
elseif (l == 12 && m == -8)
Y = (11978864919211615476641114801535*2^(1/2)*sin(8*phi)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(25852016738884976640000*cos(theta)^4 - 6744004366665646080000*cos(theta)^2 + 160571532539658240000))/2993155353253689176481146537402947624255349848014848;
elseif (l == 12 && m == -7)
Y = (917179440576247400028342967130500849172169375*2^(1/2)*sin(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(161*cos(theta)^4 - 70*cos(theta)^2 + 5))/713623846352979940529142984724747568191373312;
elseif (l == 12 && m == -6)
Y = -(19984262205146118296418489875415*2^(1/2)*sin(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(80285766269829120000*cos(theta)^2 - 562000363888803840000*cos(theta)^4 + 861733891296165888000*cos(theta)^6 - 1408522215260160000))/46768052394588893382517914646921056628989841375232;
elseif (l == 12 && m == -5)
Y = (15066319882105332621238865005991661294650625*2^(1/2)*sin(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(95*cos(theta)^2 - 399*cos(theta)^4 + 437*cos(theta)^6 - 5))/11150372599265311570767859136324180752990208;
elseif (l == 12 && m == -4)
Y = (5109435075453142798279377425355*2^(1/2)*sin(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(6690480522485760000*cos(theta)^4 - 704261107630080000*cos(theta)^2 - 18733345462960128000*cos(theta)^6 + 15388105201717248000*cos(theta)^8 + 10356780994560000))/91343852333181432387730302044767688728495783936;
elseif (l == 12 && m == -3)
Y = (107660522628563128485192040991426125205625*2^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(5814*cos(theta)^4 - 1020*cos(theta)^2 - 11628*cos(theta)^6 + 7429*cos(theta)^8 + 45))/696898287454081973172991196020261297061888;
elseif (l == 12 && m == -2)
Y = -(5*3003^(1/2)*sin(2*phi)*((630961263811347*cos(theta)^2)/1237940039285380274899124224 - 630961263811347/1237940039285380274899124224)*(1/PI)^(1/2)*(5178390497280000*cos(theta)^2 - 58688425635840000*cos(theta)^4 + 223016017416192000*cos(theta)^6 - 334524026124288000*cos(theta)^8 + 170978946685747200*cos(theta)^10 - 69045206630400))/12012;
elseif (l == 12 && m == -1)
Y = (1475739525896764214625*78^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(5775*cos(theta)^2 - 39270*cos(theta)^4 + 106590*cos(theta)^6 - 124355*cos(theta)^8 + 52003*cos(theta)^10 - 231))/302231454903657293676544;
elseif (l == 12 && m == 0)
Y = (5*(1/PI)^(1/2)*((66474686944019744047783125*cos(theta)^4)/302231454903657293676544 - (2658987477760789761911325*cos(theta)^2)/151115727451828646838272 - (75337978536555709920820875*cos(theta)^6)/75557863725914323419136 + (613466396654810780783827125*cos(theta)^8)/302231454903657293676544 - (286284318438911697699119325*cos(theta)^10)/151115727451828646838272 + (199531494669544516578174075*cos(theta)^12)/302231454903657293676544 + 68179166096430506715675/302231454903657293676544))/2;
elseif (l == 12 && m == 1)
Y = (1475739525896764214625*78^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(5775*cos(theta)^2 - 39270*cos(theta)^4 + 106590*cos(theta)^6 - 124355*cos(theta)^8 + 52003*cos(theta)^10 - 231))/302231454903657293676544;
elseif (l == 12 && m == 2)
Y = -(5*3003^(1/2)*cos(2*phi)*((630961263811347*cos(theta)^2)/1237940039285380274899124224 - 630961263811347/1237940039285380274899124224)*(1/PI)^(1/2)*(5178390497280000*cos(theta)^2 - 58688425635840000*cos(theta)^4 + 223016017416192000*cos(theta)^6 - 334524026124288000*cos(theta)^8 + 170978946685747200*cos(theta)^10 - 69045206630400))/12012;
elseif (l == 12 && m == 3)
Y = (107660522628563128485192040991426125205625*2^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(5814*cos(theta)^4 - 1020*cos(theta)^2 - 11628*cos(theta)^6 + 7429*cos(theta)^8 + 45))/696898287454081973172991196020261297061888;
elseif (l == 12 && m == 4)
Y = (5109435075453142798279377425355*2^(1/2)*cos(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(6690480522485760000*cos(theta)^4 - 704261107630080000*cos(theta)^2 - 18733345462960128000*cos(theta)^6 + 15388105201717248000*cos(theta)^8 + 10356780994560000))/91343852333181432387730302044767688728495783936;
elseif (l == 12 && m == 5)
Y = (15066319882105332621238865005991661294650625*2^(1/2)*cos(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(95*cos(theta)^2 - 399*cos(theta)^4 + 437*cos(theta)^6 - 5))/11150372599265311570767859136324180752990208;
elseif (l == 12 && m == 6)
Y = -(19984262205146118296418489875415*2^(1/2)*cos(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(80285766269829120000*cos(theta)^2 - 562000363888803840000*cos(theta)^4 + 861733891296165888000*cos(theta)^6 - 1408522215260160000))/46768052394588893382517914646921056628989841375232;
elseif (l == 12 && m == 7)
Y = (917179440576247400028342967130500849172169375*2^(1/2)*cos(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(161*cos(theta)^4 - 70*cos(theta)^2 + 5))/713623846352979940529142984724747568191373312;
elseif (l == 12 && m == 8)
Y = (11978864919211615476641114801535*2^(1/2)*cos(8*phi)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(25852016738884976640000*cos(theta)^4 - 6744004366665646080000*cos(theta)^2 + 160571532539658240000))/2993155353253689176481146537402947624255349848014848;
elseif (l == 12 && m == 9)
Y = (44832471597844324878772516958837212331047696875*2^(1/2)*cos(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(23*cos(theta)^2 - 3))/22835963083295358096932575511191922182123945984;
elseif (l == 12 && m == 10)
Y = -(5148183698591334802484249656035*2^(1/2)*cos(10*phi)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(310224200866619719680000*cos(theta)^2 - 13488008733331292160000))/95780971304118053647396689196894323976171195136475136;
elseif (l == 12 && m == 11)
Y = (3593112897098928385951021897837173248182517728125*2^(1/2)*cos(11*phi)*cos(theta)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2))/730750818665451459101842416358141509827966271488;
elseif (l == 12 && m == 12)
Y = (733441098842147879561461543657255943751257015625*2^(1/2)*cos(12*phi)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2))/730750818665451459101842416358141509827966271488;
elseif (l == 13 && m == -13)
Y = (7070005673480593136345781719936905019112469995703125*6^(1/2)*sin(13*phi)*(sin(theta)^2)^(13/2)*(1/PI)^(1/2))/11972621413014756705924586149611790497021399392059392;
elseif (l == 13 && m == -12)
Y = (281641381955384747391787960570272827652067225078125*6^(1/2)*sin(12*phi)*cos(theta)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2))/93536104789177786765035829293842113257979682750464;
elseif (l == 13 && m == -11)
Y = (82848058981863135794330814644745*6^(1/2)*sin(11*phi)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(201645730563302817792000000*cos(theta)^2 - 8065829222532112711680000))/1569275433846670190958947355801916604025588861116008628224;
elseif (l == 13 && m == -10)
Y = -(56328276391076949478357592114054565530413445015625*6^(1/2)*sin(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(25*cos(theta)^2 - 3))/46768052394588893382517914646921056628989841375232;
elseif (l == 13 && m == -9)
Y = (105356788964328938302508501206275*6^(1/2)*sin(9*phi)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(16803810880275234816000000*cos(theta)^4 - 4032914611266056355840000*cos(theta)^2 + 87672056766653399040000))/24519928653854221733733552434404946937899825954937634816;
elseif (l == 13 && m == -8)
Y = (3849540637136966845325007103059598277429673009375*6^(1/2)*sin(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(115*cos(theta)^4 - 46*cos(theta)^2 + 3))/2923003274661805836407369665432566039311865085952;
elseif (l == 13 && m == -7)
Y = (24225579801450459881278708149885*6^(1/2)*sin(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(43836028383326699520000*cos(theta)^2 - 336076217605504696320000*cos(theta)^4 + 560127029342507827200000*cos(theta)^6 - 695809974338519040000))/47890485652059026823698344598447161988085597568237568;
elseif (l == 13 && m == -6)
Y = -(38041613621026810950877690184178178266762586875*6^(1/2)*sin(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(105*cos(theta)^2 - 483*cos(theta)^4 + 575*cos(theta)^6 - 5))/45671926166590716193865151022383844364247891968;
elseif (l == 13 && m == -5)
Y = (27608958387364525627403374930695*6^(1/2)*sin(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(3653002365277224960000*cos(theta)^4 - 347904987169259520000*cos(theta)^2 - 11202540586850156544000*cos(theta)^6 + 10002268381116211200000*cos(theta)^8 + 4577697199595520000))/374144419156711147060143317175368453031918731001856;
elseif (l == 13 && m == -4)
Y = (136364761038878505577574348878474754393829375*6^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(7182*cos(theta)^4 - 1140*cos(theta)^2 - 15732*cos(theta)^6 + 10925*cos(theta)^8 + 45))/1427247692705959881058285969449495136382746624;
elseif (l == 13 && m == -3)
Y = (143179885840419318883833251248575*6^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(2288848599797760000*cos(theta)^2 - 28992082264104960000*cos(theta)^4 + 121766745509240832000*cos(theta)^6 - 200045367622324224000*cos(theta)^8 + 111136315345735680000*cos(theta)^10 - 26927630585856000))/11692013098647223345629478661730264157247460343808;
elseif (l == 13 && m == -2)
Y = -149448499200*1365^(1/2)*sin(2*phi)*cos(theta)*((6212541674450185*cos(theta)^2)/316912650057057350374175801344 - 6212541674450185/316912650057057350374175801344)*(1/PI)^(1/2)*(2805*cos(theta)^2 - 21318*cos(theta)^4 + 63954*cos(theta)^6 - 81719*cos(theta)^8 + 37145*cos(theta)^10 - 99);
elseif (l == 13 && m == -1)
Y = (18637625023350555*273^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(190737383316480000*cos(theta)^4 - 13463815292928000*cos(theta)^2 - 966402742136832000*cos(theta)^6 + 2174406169807872000*cos(theta)^8 - 2222726306914713600*cos(theta)^10 + 841941782922240000*cos(theta)^12 + 149597947699200))/57678102310384437768099995844608;
elseif (l == 13 && m == 0)
Y = (113336795588871476246625*3^(1/2)*cos(theta)*(1/PI)^(1/2)*(765765*cos(theta)^4 - 90090*cos(theta)^2 - 2771340*cos(theta)^6 + 4849845*cos(theta)^8 - 4056234*cos(theta)^10 + 1300075*cos(theta)^12 + 3003))/77371252455336267181195264;
elseif (l == 13 && m == 1)
Y = (18637625023350555*273^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(190737383316480000*cos(theta)^4 - 13463815292928000*cos(theta)^2 - 966402742136832000*cos(theta)^6 + 2174406169807872000*cos(theta)^8 - 2222726306914713600*cos(theta)^10 + 841941782922240000*cos(theta)^12 + 149597947699200))/57678102310384437768099995844608;
elseif (l == 13 && m == 2)
Y = -149448499200*1365^(1/2)*cos(2*phi)*cos(theta)*((6212541674450185*cos(theta)^2)/316912650057057350374175801344 - 6212541674450185/316912650057057350374175801344)*(1/PI)^(1/2)*(2805*cos(theta)^2 - 21318*cos(theta)^4 + 63954*cos(theta)^6 - 81719*cos(theta)^8 + 37145*cos(theta)^10 - 99);
elseif (l == 13 && m == 3)
Y = (143179885840419318883833251248575*6^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(2288848599797760000*cos(theta)^2 - 28992082264104960000*cos(theta)^4 + 121766745509240832000*cos(theta)^6 - 200045367622324224000*cos(theta)^8 + 111136315345735680000*cos(theta)^10 - 26927630585856000))/11692013098647223345629478661730264157247460343808;
elseif (l == 13 && m == 4)
Y = (136364761038878505577574348878474754393829375*6^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(7182*cos(theta)^4 - 1140*cos(theta)^2 - 15732*cos(theta)^6 + 10925*cos(theta)^8 + 45))/1427247692705959881058285969449495136382746624;
elseif (l == 13 && m == 5)
Y = (27608958387364525627403374930695*6^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(3653002365277224960000*cos(theta)^4 - 347904987169259520000*cos(theta)^2 - 11202540586850156544000*cos(theta)^6 + 10002268381116211200000*cos(theta)^8 + 4577697199595520000))/374144419156711147060143317175368453031918731001856;
elseif (l == 13 && m == 6)
Y = -(38041613621026810950877690184178178266762586875*6^(1/2)*cos(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(105*cos(theta)^2 - 483*cos(theta)^4 + 575*cos(theta)^6 - 5))/45671926166590716193865151022383844364247891968;
elseif (l == 13 && m == 7)
Y = (24225579801450459881278708149885*6^(1/2)*cos(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(43836028383326699520000*cos(theta)^2 - 336076217605504696320000*cos(theta)^4 + 560127029342507827200000*cos(theta)^6 - 695809974338519040000))/47890485652059026823698344598447161988085597568237568;
elseif (l == 13 && m == 8)
Y = (3849540637136966845325007103059598277429673009375*6^(1/2)*cos(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(115*cos(theta)^4 - 46*cos(theta)^2 + 3))/2923003274661805836407369665432566039311865085952;
elseif (l == 13 && m == 9)
Y = (105356788964328938302508501206275*6^(1/2)*cos(9*phi)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(16803810880275234816000000*cos(theta)^4 - 4032914611266056355840000*cos(theta)^2 + 87672056766653399040000))/24519928653854221733733552434404946937899825954937634816;
elseif (l == 13 && m == 10)
Y = -(56328276391076949478357592114054565530413445015625*6^(1/2)*cos(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(25*cos(theta)^2 - 3))/46768052394588893382517914646921056628989841375232;
elseif (l == 13 && m == 11)
Y = (82848058981863135794330814644745*6^(1/2)*cos(11*phi)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(201645730563302817792000000*cos(theta)^2 - 8065829222532112711680000))/1569275433846670190958947355801916604025588861116008628224;
elseif (l == 13 && m == 12)
Y = (281641381955384747391787960570272827652067225078125*6^(1/2)*cos(12*phi)*cos(theta)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2))/93536104789177786765035829293842113257979682750464;
elseif (l == 13 && m == 13)
Y = (7070005673480593136345781719936905019112469995703125*6^(1/2)*cos(13*phi)*(1 - cos(theta)^2)^(13/2)*(1/PI)^(1/2))/11972621413014756705924586149611790497021399392059392;
elseif (l == 14 && m == -14)
Y = (296217930628498880696891075082998577265774569450046875*58^(1/2)*sin(14*phi)*sin(theta)^14*(1/PI)^(1/2))/1532495540865888858358347027150309183618739122183602176;
elseif (l == 14 && m == -13)
Y = (1530701129533575764034365299400877786922097390484375*58^(1/2)*sin(13*phi)*cos(theta)*(1 - cos(theta)^2)^(13/2)*(1/PI)^(1/2))/1496577676626844588240573268701473812127674924007424;
elseif (l == 14 && m == -12)
Y = (39613784091363503537041994060281*58^(1/2)*sin(12*phi)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2)*(152444172305856930250752000000*cos(theta)^2 - 5646080455772478898176000000))/1606938044258990275541962092341162602522202993782792835301376;
elseif (l == 14 && m == -11)
Y = (14717390426517210030580611528619387686137097495140625*58^(1/2)*sin(11*phi)*cos(theta)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(9*cos(theta)^2 - 1))/11972621413014756705924586149611790497021399392059392;
elseif (l == 14 && m == -10)
Y = -(54665541891447633101459662227409*58^(1/2)*sin(10*phi)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(12703681025488077520896000000*cos(theta)^4 - 2823040227886239449088000000*cos(theta)^2 + 56460804557724788981760000))/25108406941546723055343157692830665664409421777856138051584;
elseif (l == 14 && m == -9)
Y = (41984618355281529484099368550513611051471278911875*58^(1/2)*sin(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(135*cos(theta)^4 - 50*cos(theta)^2 + 3))/93536104789177786765035829293842113257979682750464;
elseif (l == 14 && m == -8)
Y = (27479185667654436608337704752337*58^(1/2)*sin(8*phi)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(28230402278862394490880000*cos(theta)^2 - 235253352323853287424000000*cos(theta)^4 + 423456034182935917363200000*cos(theta)^6 - 409136264911049195520000))/98079714615416886934934209737619787751599303819750539264;
elseif (l == 14 && m == -7)
Y = (593997016125439705100950952101425016736815573125*58^(1/2)*sin(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(161*cos(theta)^2 - 805*cos(theta)^4 + 1035*cos(theta)^6 - 7))/2923003274661805836407369665432566039311865085952;
elseif (l == 14 && m == -6)
Y = -(34530978900182371422074230128701*58^(1/2)*sin(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(2352533523238532874240000*cos(theta)^4 - 204568132455524597760000*cos(theta)^2 - 7841778410795109580800000*cos(theta)^6 + 7561714896123855667200000*cos(theta)^8 + 2435334910184816640000))/766247770432944429179173513575154591809369561091801088;
elseif (l == 14 && m == -5)
Y = (53798965917413186882379779145105780160443666375*58^(1/2)*sin(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(966*cos(theta)^4 - 140*cos(theta)^2 - 2300*cos(theta)^6 + 1725*cos(theta)^8 + 5))/182687704666362864775460604089535377456991567872;
elseif (l == 14 && m == -4)
Y = (12472456046983034856239217730917*58^(1/2)*sin(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(1217667455092408320000*cos(theta)^2 - 17047344371293716480000*cos(theta)^4 + 78417784107951095808000*cos(theta)^6 - 140031757335626956800000*cos(theta)^8 + 84019054401376174080000*cos(theta)^10 - 12817552158867456000))/1496577676626844588240573268701473812127674924007424;
elseif (l == 14 && m == -3)
Y = (43339566047328528088870412649328384661234625*58^(1/2)*sin(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(3135*cos(theta)^2 - 26334*cos(theta)^4 + 86526*cos(theta)^6 - 120175*cos(theta)^8 + 58995*cos(theta)^10 - 99))/2854495385411919762116571938898990272765493248;
elseif (l == 14 && m == -2)
Y = -(39585^(1/2)*sin(2*phi)*((7100047627943069*cos(theta)^2)/10141204801825835211973625643008 - 7100047627943069/10141204801825835211973625643008)*(1/PI)^(1/2)*(101472287924367360000*cos(theta)^4 - 6408776079433728000*cos(theta)^2 - 568244812376457216000*cos(theta)^6 + 1400317573356269568000*cos(theta)^8 - 1555908414840299520000*cos(theta)^10 + 636507987889213440000*cos(theta)^12 + 62831138033664000))/10920;
elseif (l == 14 && m == -1)
Y = (302231454903657288234225*3045^(1/2)*cos(theta)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(138567*cos(theta)^4 - 14586*cos(theta)^2 - 554268*cos(theta)^6 + 1062347*cos(theta)^8 - 965770*cos(theta)^10 + 334305*cos(theta)^12 + 429))/618970019642690137449562112;
elseif (l == 14 && m == 0)
Y = (29^(1/2)*(1/PI)^(1/2)*((13614015886135242548510665125*cos(theta)^2)/618970019642690137449562112 - (231438270064299123324681307125*cos(theta)^4)/618970019642690137449562112 + (1465775710407227781056314945125*cos(theta)^6)/618970019642690137449562112 - (4397327131221683343168944835375*cos(theta)^8)/618970019642690137449562112 + (6742568267873247792859048747575*cos(theta)^10)/618970019642690137449562112 - (5108006263540339237014430869375*cos(theta)^12)/618970019642690137449562112 + (1515562297973507246147138829375*cos(theta)^14)/618970019642690137449562112 - 129657294153668976652482525/618970019642690137449562112))/2;
elseif (l == 14 && m == 1)
Y = (302231454903657288234225*3045^(1/2)*cos(phi)*cos(theta)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(138567*cos(theta)^4 - 14586*cos(theta)^2 - 554268*cos(theta)^6 + 1062347*cos(theta)^8 - 965770*cos(theta)^10 + 334305*cos(theta)^12 + 429))/618970019642690137449562112;
elseif (l == 14 && m == 2)
Y = -(39585^(1/2)*cos(2*phi)*((7100047627943069*cos(theta)^2)/10141204801825835211973625643008 - 7100047627943069/10141204801825835211973625643008)*(1/PI)^(1/2)*(101472287924367360000*cos(theta)^4 - 6408776079433728000*cos(theta)^2 - 568244812376457216000*cos(theta)^6 + 1400317573356269568000*cos(theta)^8 - 1555908414840299520000*cos(theta)^10 + 636507987889213440000*cos(theta)^12 + 62831138033664000))/10920;
elseif (l == 14 && m == 3)
Y = (43339566047328528088870412649328384661234625*58^(1/2)*cos(3*phi)*cos(theta)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(3135*cos(theta)^2 - 26334*cos(theta)^4 + 86526*cos(theta)^6 - 120175*cos(theta)^8 + 58995*cos(theta)^10 - 99))/2854495385411919762116571938898990272765493248;
elseif (l == 14 && m == 4)
Y = (12472456046983034856239217730917*58^(1/2)*cos(4*phi)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(1217667455092408320000*cos(theta)^2 - 17047344371293716480000*cos(theta)^4 + 78417784107951095808000*cos(theta)^6 - 140031757335626956800000*cos(theta)^8 + 84019054401376174080000*cos(theta)^10 - 12817552158867456000))/1496577676626844588240573268701473812127674924007424;
elseif (l == 14 && m == 5)
Y = (53798965917413186882379779145105780160443666375*58^(1/2)*cos(5*phi)*cos(theta)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(966*cos(theta)^4 - 140*cos(theta)^2 - 2300*cos(theta)^6 + 1725*cos(theta)^8 + 5))/182687704666362864775460604089535377456991567872;
elseif (l == 14 && m == 6)
Y = -(34530978900182371422074230128701*58^(1/2)*cos(6*phi)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(2352533523238532874240000*cos(theta)^4 - 204568132455524597760000*cos(theta)^2 - 7841778410795109580800000*cos(theta)^6 + 7561714896123855667200000*cos(theta)^8 + 2435334910184816640000))/766247770432944429179173513575154591809369561091801088;
elseif (l == 14 && m == 7)
Y = (593997016125439705100950952101425016736815573125*58^(1/2)*cos(7*phi)*cos(theta)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(161*cos(theta)^2 - 805*cos(theta)^4 + 1035*cos(theta)^6 - 7))/2923003274661805836407369665432566039311865085952;
elseif (l == 14 && m == 8)
Y = (27479185667654436608337704752337*58^(1/2)*cos(8*phi)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(28230402278862394490880000*cos(theta)^2 - 235253352323853287424000000*cos(theta)^4 + 423456034182935917363200000*cos(theta)^6 - 409136264911049195520000))/98079714615416886934934209737619787751599303819750539264;
elseif (l == 14 && m == 9)
Y = (41984618355281529484099368550513611051471278911875*58^(1/2)*cos(9*phi)*cos(theta)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(135*cos(theta)^4 - 50*cos(theta)^2 + 3))/93536104789177786765035829293842113257979682750464;
elseif (l == 14 && m == 10)
Y = -(54665541891447633101459662227409*58^(1/2)*cos(10*phi)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(12703681025488077520896000000*cos(theta)^4 - 2823040227886239449088000000*cos(theta)^2 + 56460804557724788981760000))/25108406941546723055343157692830665664409421777856138051584;
elseif (l == 14 && m == 11)
Y = (14717390426517210030580611528619387686137097495140625*58^(1/2)*cos(11*phi)*cos(theta)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(9*cos(theta)^2 - 1))/11972621413014756705924586149611790497021399392059392;
elseif (l == 14 && m == 12)
Y = (39613784091363503537041994060281*58^(1/2)*cos(12*phi)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2)*(152444172305856930250752000000*cos(theta)^2 - 5646080455772478898176000000))/1606938044258990275541962092341162602522202993782792835301376;
elseif (l == 14 && m == 13)
Y = (1530701129533575764034365299400877786922097390484375*58^(1/2)*cos(13*phi)*cos(theta)*(1 - cos(theta)^2)^(13/2)*(1/PI)^(1/2))/1496577676626844588240573268701473812127674924007424;
elseif (l == 14 && m == 14)
Y = -(296217930628498880696891075082998577265774569450046875*58^(1/2)*cos(14*phi)*(cos(theta)^2 - 1)^7*(1/PI)^(1/2))/1532495540865888858358347027150309183618739122183602176;
elseif (l == 15 && m == -15)
Y = (149114431192082362039127074566116374295990905489544296875*62^(1/2)*sin(15*phi)*(sin(theta)^2)^(15/2)*(1/PI)^(1/2))/784637716923335095479473677900958302012794430558004314112;
elseif (l == 15 && m == -14)
Y = -(102091672016819338657352820170275065841243155353681015625*62^(1/2)*sin(14*phi)*cos(theta)*(cos(theta)^2 - 1)^7*(1/PI)^(1/2))/98079714615416886934934209737619787751599303819750539264;
elseif (l == 15 && m == -13)
Y = (384197172830287280810369758395*62^(1/2)*sin(13*phi)*(1 - cos(theta)^2)^(13/2)*(1/PI)^(1/2)*(132626429906095529318154240000000*cos(theta)^2 - 4573325169175707907522560000000))/12855504354071922204335696738729300820177623950262342682411008;
elseif (l == 15 && m == -12)
Y = (2559615464829691725528745187668246389415339777728046875*62^(1/2)*sin(12*phi)*cos(theta)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2)*(29*cos(theta)^2 - 3))/6129982163463555433433388108601236734474956488734408704;
elseif (l == 15 && m == -11)
Y = (9148411563507374103816224536361*62^(1/2)*sin(11*phi)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(11052202492174627443179520000000*cos(theta)^4 - 2286662584587853953761280000000*cos(theta)^2 + 42345603418293591736320000000))/3213876088517980551083924184682325205044405987565585670602752;
elseif (l == 15 && m == -10)
Y = -(26327268356077683297304301813603304479263252113234375*62^(1/2)*sin(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(261*cos(theta)^4 - 90*cos(theta)^2 + 5))/95780971304118053647396689196894323976171195136475136;
elseif (l == 15 && m == -9)
Y = (9980516804063164691340017776639*62^(1/2)*sin(9*phi)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(21172801709146795868160000000*cos(theta)^2 - 190555215382321162813440000000*cos(theta)^4 + 368406749739154248105984000000*cos(theta)^6 - 282304022788623944908800000))/25108406941546723055343157692830665664409421777856138051584;
elseif (l == 15 && m == -8)
Y = (38870203554599240399637315190494927165684090328125*62^(1/2)*sin(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(175*cos(theta)^2 - 945*cos(theta)^4 + 1305*cos(theta)^6 - 7))/187072209578355573530071658587684226515959365500928;
elseif (l == 15 && m == -7)
Y = (27418052809576490164537253997015*62^(1/2)*sin(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(1764400142428899655680000000*cos(theta)^4 - 141152011394311972454400000*cos(theta)^2 - 6351840512744038760448000000*cos(theta)^6 + 6578691959627754430464000000*cos(theta)^8 + 1534260993416434483200000))/392318858461667547739736838950479151006397215279002157056;
elseif (l == 15 && m == -6)
Y = -(6720309089709974818934425621515848621386183640625*62^(1/2)*sin(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(4830*cos(theta)^4 - 644*cos(theta)^2 - 12420*cos(theta)^6 + 10005*cos(theta)^8 + 21))/93536104789177786765035829293842113257979682750464;
elseif (l == 15 && m == -5)
Y = (21839308631958477549414048279783*62^(1/2)*sin(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(767130496708217241600000*cos(theta)^2 - 11762667616192664371200000*cos(theta)^4 + 58813338080963321856000000*cos(theta)^6 - 113425723441857835008000000*cos(theta)^8 + 73096577329197271449600000*cos(theta)^10 - 7306004730554449920000))/1532495540865888858358347027150309183618739122183602176;
elseif (l == 15 && m == -4)
Y = (102590602684704311595531244283631150457538878125*62^(1/2)*sin(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(385*cos(theta)^2 - 3542*cos(theta)^4 + 12650*cos(theta)^6 - 18975*cos(theta)^8 + 10005*cos(theta)^10 - 11))/730750818665451459101842416358141509827966271488;
elseif (l == 15 && m == -3)
Y = (4776587007872406734328798895741*62^(1/2)*sin(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(63927541392351436800000*cos(theta)^4 - 3653002365277224960000*cos(theta)^2 - 392088920539755479040000*cos(theta)^6 + 1050238180017202176000000*cos(theta)^8 - 1260285816020642611200000*cos(theta)^10 + 553761949463615692800000*cos(theta)^12 + 32043880397168640000))/1496577676626844588240573268701473812127674924007424;
elseif (l == 15 && m == -2)
Y = -5230697472000*55335^(1/2)*sin(2*phi)*cos(theta)*(1/PI)^(1/2)*((7573384136472607*cos(theta)^2)/324518553658426726783156020576256 - 7573384136472607/324518553658426726783156020576256)*(171171*cos(theta)^4 - 16302*cos(theta)^2 - 749892*cos(theta)^6 + 1562275*cos(theta)^8 - 1533870*cos(theta)^10 + 570285*cos(theta)^12 + 429);
elseif (l == 15 && m == -1)
Y = (7573384136472607*930^(1/2)*sin(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(16021940198584320000*cos(theta)^2 - 304416863773102080000*cos(theta)^4 + 2130918046411714560000*cos(theta)^6 - 7001587866781347840000*cos(theta)^8 + 11669313111302246400000*cos(theta)^10 - 9547619818338201600000*cos(theta)^12 + 3042648073975910400000*cos(theta)^14 - 134638152929280000))/38942226439011207213978722469150720;
elseif (l == 15 && m == 0)
Y = (4835703278458516654315125*31^(1/2)*cos(theta)*(1/PI)^(1/2)*(255255*cos(theta)^2 - 2909907*cos(theta)^4 + 14549535*cos(theta)^6 - 37182145*cos(theta)^8 + 50702925*cos(theta)^10 - 35102025*cos(theta)^12 + 9694845*cos(theta)^14 - 6435))/19807040628566084398385987584;
elseif (l == 15 && m == 1)
Y = (7573384136472607*930^(1/2)*cos(phi)*(1 - cos(theta)^2)^(1/2)*(1/PI)^(1/2)*(16021940198584320000*cos(theta)^2 - 304416863773102080000*cos(theta)^4 + 2130918046411714560000*cos(theta)^6 - 7001587866781347840000*cos(theta)^8 + 11669313111302246400000*cos(theta)^10 - 9547619818338201600000*cos(theta)^12 + 3042648073975910400000*cos(theta)^14 - 134638152929280000))/38942226439011207213978722469150720;
elseif (l == 15 && m == 2)
Y = -5230697472000*55335^(1/2)*cos(2*phi)*cos(theta)*(1/PI)^(1/2)*((7573384136472607*cos(theta)^2)/324518553658426726783156020576256 - 7573384136472607/324518553658426726783156020576256)*(171171*cos(theta)^4 - 16302*cos(theta)^2 - 749892*cos(theta)^6 + 1562275*cos(theta)^8 - 1533870*cos(theta)^10 + 570285*cos(theta)^12 + 429);
elseif (l == 15 && m == 3)
Y = (4776587007872406734328798895741*62^(1/2)*cos(3*phi)*(1 - cos(theta)^2)^(3/2)*(1/PI)^(1/2)*(63927541392351436800000*cos(theta)^4 - 3653002365277224960000*cos(theta)^2 - 392088920539755479040000*cos(theta)^6 + 1050238180017202176000000*cos(theta)^8 - 1260285816020642611200000*cos(theta)^10 + 553761949463615692800000*cos(theta)^12 + 32043880397168640000))/1496577676626844588240573268701473812127674924007424;
elseif (l == 15 && m == 4)
Y = (102590602684704311595531244283631150457538878125*62^(1/2)*cos(4*phi)*cos(theta)*(cos(theta)^2 - 1)^2*(1/PI)^(1/2)*(385*cos(theta)^2 - 3542*cos(theta)^4 + 12650*cos(theta)^6 - 18975*cos(theta)^8 + 10005*cos(theta)^10 - 11))/730750818665451459101842416358141509827966271488;
elseif (l == 15 && m == 5)
Y = (21839308631958477549414048279783*62^(1/2)*cos(5*phi)*(1 - cos(theta)^2)^(5/2)*(1/PI)^(1/2)*(767130496708217241600000*cos(theta)^2 - 11762667616192664371200000*cos(theta)^4 + 58813338080963321856000000*cos(theta)^6 - 113425723441857835008000000*cos(theta)^8 + 73096577329197271449600000*cos(theta)^10 - 7306004730554449920000))/1532495540865888858358347027150309183618739122183602176;
elseif (l == 15 && m == 6)
Y = -(6720309089709974818934425621515848621386183640625*62^(1/2)*cos(6*phi)*cos(theta)*(cos(theta)^2 - 1)^3*(1/PI)^(1/2)*(4830*cos(theta)^4 - 644*cos(theta)^2 - 12420*cos(theta)^6 + 10005*cos(theta)^8 + 21))/93536104789177786765035829293842113257979682750464;
elseif (l == 15 && m == 7)
Y = (27418052809576490164537253997015*62^(1/2)*cos(7*phi)*(1 - cos(theta)^2)^(7/2)*(1/PI)^(1/2)*(1764400142428899655680000000*cos(theta)^4 - 141152011394311972454400000*cos(theta)^2 - 6351840512744038760448000000*cos(theta)^6 + 6578691959627754430464000000*cos(theta)^8 + 1534260993416434483200000))/392318858461667547739736838950479151006397215279002157056;
elseif (l == 15 && m == 8)
Y = (38870203554599240399637315190494927165684090328125*62^(1/2)*cos(8*phi)*cos(theta)*(cos(theta)^2 - 1)^4*(1/PI)^(1/2)*(175*cos(theta)^2 - 945*cos(theta)^4 + 1305*cos(theta)^6 - 7))/187072209578355573530071658587684226515959365500928;
elseif (l == 15 && m == 9)
Y = (9980516804063164691340017776639*62^(1/2)*cos(9*phi)*(1 - cos(theta)^2)^(9/2)*(1/PI)^(1/2)*(21172801709146795868160000000*cos(theta)^2 - 190555215382321162813440000000*cos(theta)^4 + 368406749739154248105984000000*cos(theta)^6 - 282304022788623944908800000))/25108406941546723055343157692830665664409421777856138051584;
elseif (l == 15 && m == 10)
Y = -(26327268356077683297304301813603304479263252113234375*62^(1/2)*cos(10*phi)*cos(theta)*(cos(theta)^2 - 1)^5*(1/PI)^(1/2)*(261*cos(theta)^4 - 90*cos(theta)^2 + 5))/95780971304118053647396689196894323976171195136475136;
elseif (l == 15 && m == 11)
Y = (9148411563507374103816224536361*62^(1/2)*cos(11*phi)*(1 - cos(theta)^2)^(11/2)*(1/PI)^(1/2)*(11052202492174627443179520000000*cos(theta)^4 - 2286662584587853953761280000000*cos(theta)^2 + 42345603418293591736320000000))/3213876088517980551083924184682325205044405987565585670602752;
elseif (l == 15 && m == 12)
Y = (2559615464829691725528745187668246389415339777728046875*62^(1/2)*cos(12*phi)*cos(theta)*(cos(theta)^2 - 1)^6*(1/PI)^(1/2)*(29*cos(theta)^2 - 3))/6129982163463555433433388108601236734474956488734408704;
elseif (l == 15 && m == 13)
Y = (384197172830287280810369758395*62^(1/2)*cos(13*phi)*(1 - cos(theta)^2)^(13/2)*(1/PI)^(1/2)*(132626429906095529318154240000000*cos(theta)^2 - 4573325169175707907522560000000))/12855504354071922204335696738729300820177623950262342682411008;
elseif (l == 15 && m == 14)
Y = -(102091672016819338657352820170275065841243155353681015625*62^(1/2)*cos(14*phi)*cos(theta)*(cos(theta)^2 - 1)^7*(1/PI)^(1/2))/98079714615416886934934209737619787751599303819750539264;
elseif (l == 15 && m == 15)
Y = (149114431192082362039127074566116374295990905489544296875*62^(1/2)*cos(15*phi)*(1 - cos(theta)^2)^(15/2)*(1/PI)^(1/2))/784637716923335095479473677900958302012794430558004314112;
else
fprintf('Not found (l,m) = (15,15)\n');
end
end