forked from boostorg/math
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathlanczos_generator.cpp
More file actions
4361 lines (4310 loc) · 189 KB
/
Copy pathlanczos_generator.cpp
File metadata and controls
4361 lines (4310 loc) · 189 KB
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
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
// (C) Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/precision.hpp>
#include <boost/math/tools/polynomial.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/cstdint.hpp>
#include <boost/bind.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/array.hpp>
#include "mp_t.hpp"
//
// this is a sort of recursive include, since this file
// is used to create the contents of gamma.hpp.
// However, we will be using the "generic" version of gamma
// which doesn't use a lanczos approximation.
//
#include <boost/math/special_functions/gamma.hpp>
#include <iostream>
#include <iomanip>
#include <vector>
using boost::numeric::ublas::matrix;
using boost::numeric::ublas::vector;
struct lanczos_spot_data
{
int N;
double g;
double err;
};
lanczos_spot_data sweet_spots[] = {
// a few selected spots from Pugh's thesis:
3, 2.03209, 6.4e-7,
4, 3.655180, 8.5e-8,
9, 8.406094, 6.9e-15,
10, 9.656578, 2.1e-16,
11, 10.900511, 6.1e-18,
12, 12.066012, 1.1e-19,
13, 13.144565, 5.2e-21,
14, 13.726821, 4.0e-22,
15, 14.977863, 1.2e-23,
20, 20.298892, 7.8e-31,
21, 21.508926, 2.1e-32,
22, 22.618910, 1.8e-34,
23, 23.118012, 5.2e-35,
// some more we've found, these are all the points where the first
// negleted term from the Lanczos series changes sign, there is one
// point just above that point, and one just below:
3, 0.58613894134759903, 0.00036580426080686315,
3, 0.58613894879817963, 0.00036580416320668711,
3, 1.249951496720314, 4.2305536798953929e-005,
3, 1.2499515041708946, 4.2305534015367749e-005,
3, 1.8384982049465179, 1.164778449938813e-005,
3, 1.8384982123970985, 1.1647786529958048e-005,
3, 2.3276706635951996, 5.3732582230468998e-006,
3, 2.3276706710457802, 5.3732600294516588e-006,
3, 2.6038404405117035, 7.4060771171390379e-007,
3, 2.6038404479622841, 7.406058543248471e-007,
4, 0.62704569846391678, 0.00012800533557793425,
4, 0.62704570591449738, 0.00012800531551557324,
4, 1.3344274088740349, 9.0166140418663663e-006,
4, 1.3344274163246155, 9.0166116338646694e-006,
4, 1.9880444705486298, 1.4955557778725745e-006,
4, 1.9880444779992104, 1.4955557079994109e-006,
4, 2.5835030898451805, 4.5877676859600527e-007,
4, 2.5835030972957611, 4.5877667876325684e-007,
4, 3.1086832508444786, 2.1441725587707906e-007,
4, 3.1086832582950592, 2.1441723688775765e-007,
4, 3.5476611852645874, 1.0813760990515544e-007,
4, 3.547661192715168, 1.0813766234070327e-007,
4, 3.6492579728364944, 1.047642251124206e-007,
4, 3.649257980287075, 1.0476415796074403e-007,
5, 0.65435918420553207, 5.5274429026631278e-005,
5, 0.65435919165611267, 5.527441185903385e-005,
5, 1.389187254011631, 2.6307833416554052e-006,
5, 1.3891872614622116, 2.6307826816540255e-006,
5, 2.0801975876092911, 2.9014694764756466e-007,
5, 2.0801975950598717, 2.9014696142909125e-007,
5, 2.7272208333015442, 5.9176544536206063e-008,
5, 2.7272208407521248, 5.9176528019009275e-008,
5, 3.3269794136285782, 1.9379184595472579e-008,
5, 3.3269794210791588, 1.9379189057179851e-008,
5, 3.8722873777151108, 9.0123694745032944e-009,
5, 3.8722873851656914, 9.0123661007867372e-009,
5, 4.3516943231225014, 4.9816097608842378e-009,
5, 4.351694330573082, 4.9816087871575021e-009,
6, 0.67425807565450668, 2.7371903086326379e-005,
6, 0.67425808310508728, 2.7371893712684938e-005,
6, 1.4284561350941658, 9.4138428977455083e-007,
6, 1.4284561425447464, 9.4138417896969612e-007,
6, 2.1447814926505089, 7.4109049995920916e-008,
6, 2.1447815001010895, 7.4109044064461768e-008,
6, 2.8244904428720474, 1.0708333024058614e-008,
6, 2.824490450322628, 1.0708333661155651e-008,
6, 3.4669468700885773, 2.4940116660002578e-009,
6, 3.4669468775391579, 2.4940118560592828e-009,
6, 4.0696377158164978, 8.5267622527507512e-010,
6, 4.0696377232670784, 8.5267624048985822e-010,
6, 4.6278460025787354, 3.9323405231792876e-010,
6, 4.6278460100293159, 3.9323393550021793e-010,
6, 5.1345816180109978, 2.1943462473419721e-010,
6, 5.1345816254615784, 2.1943458105218707e-010,
6, 5.5917193591594696, 1.242916896389048e-010,
6, 5.5917193666100502, 1.2429175679293363e-010,
7, 0.68959406018257141, 1.4934177419305624e-005,
7, 0.68959406763315201, 1.4934171696393048e-005,
7, 1.4584139510989189, 3.8891482410396904e-007,
7, 1.4584139585494995, 3.8891475436265016e-007,
7, 2.1934122517704964, 2.2977989848570384e-008,
7, 2.193412259221077, 2.2977982819591052e-008,
7, 2.8964230641722679, 2.4742239281355561e-009,
7, 2.8964230716228485, 2.4742234478616864e-009,
7, 3.5678729563951492, 4.2816138965285379e-010,
7, 3.5678729638457298, 4.2816128067858218e-010,
7, 4.2069913893938065, 1.0931003472338519e-010,
7, 4.2069913968443871, 1.0931004659777642e-010,
7, 4.8118086308240891, 3.8518213120095777e-011,
7, 4.8118086382746696, 3.8518212172324096e-011,
7, 5.3790060579776764, 1.7613602961109952e-011,
7, 5.379006065428257, 1.7613603275796266e-011,
7, 5.9039439857006073, 9.7098281187573355e-012,
7, 5.9039439931511879, 9.7098271522398387e-012,
7, 6.3838147521018982, 5.7878801570305524e-012,
7, 6.3838147595524788, 5.7878771973838702e-012,
7, 6.7833591029047966, 2.829092368392454e-012,
7, 6.7833591103553772, 2.8290901754246269e-012,
8, 0.70188850909471512, 8.7610752024780369e-006,
8, 0.70188851654529572, 8.7610704217796693e-006,
8, 1.4822541922330856, 1.7881701068328982e-007,
8, 1.4822541996836662, 1.7881694190606741e-007,
8, 2.231784276664257, 8.2272386690167009e-009,
8, 2.2317842841148376, 8.2272367814664617e-009,
8, 2.9525627419352531, 6.8591536474980462e-010,
8, 2.9525627493858337, 6.8591515664364383e-010,
8, 3.6455128863453865, 9.1549235855884194e-011,
8, 3.6455128937959671, 9.1549217088498416e-011,
8, 4.3106606528162956, 1.8015466799942756e-011,
8, 4.3106606602668762, 1.8015467001952356e-011,
8, 4.9472371935844421, 4.918149362493385e-012,
8, 4.9472372010350227, 4.9181495178774722e-012,
8, 5.553666315972805, 1.7720036810370511e-012,
8, 5.5536663234233856, 1.7720035779693502e-012,
8, 6.1274929493665695, 8.0403304333886761e-013,
8, 6.1274929568171501, 8.0403274526493467e-013,
8, 6.6654317826032639, 4.3551924163930176e-013,
8, 6.6654317900538445, 4.3551918580885179e-013,
8, 7.1646013185381889, 2.6142608803934048e-013,
8, 7.1646013259887695, 2.6142610866873453e-013,
8, 7.6312204822897911, 1.5767278184484503e-013,
8, 7.6312204897403717, 1.576728292094547e-013,
8, 7.8779716044664383, 6.0579161144149095e-014,
8, 7.8779716119170189, 6.0579145495868576e-014,
9, 0.7120363786816597, 5.4383680639900953e-006,
9, 0.7120363861322403, 5.4383647430909934e-006,
9, 1.5018193200230598, 8.9331552269793478e-008,
9, 1.5018193274736404, 8.9331529217486569e-008,
9, 2.2630845010280609, 3.2922940247769628e-009,
9, 2.2630845084786415, 3.2922936681951672e-009,
9, 2.9980199560523033, 2.1887825488935961e-010,
9, 2.9980199635028839, 2.1887818854849753e-010,
9, 3.7078000977635384, 2.3213138957857667e-011,
9, 3.707800105214119, 2.3213132917173771e-011,
9, 4.3928612694144249, 3.6226509291513855e-012,
9, 4.3928612768650055, 3.6226507116549233e-012,
9, 5.0530400574207306, 7.8472620106742312e-013,
9, 5.0530400648713112, 7.8472599177745781e-013,
9, 5.6876183524727821, 2.2542091218064693e-013,
9, 5.6876183599233627, 2.2542085472082343e-013,
9, 6.2953110262751579, 8.261026286619692e-014,
9, 6.2953110337257385, 8.2610267677539022e-014,
9, 6.8742315545678139, 3.7226229880661886e-014,
9, 6.8742315620183945, 3.722621661830273e-014,
9, 7.4219388365745544, 1.9804198141916339e-014,
9, 7.421938844025135, 1.9804197841080089e-014,
9, 7.936030775308609, 1.1800366216622659e-014,
9, 7.9360307827591896, 1.1800362381207757e-014,
9, 8.4175376817584038, 7.341772297716249e-015,
9, 8.4175376892089844, 7.3417744970482286e-015,
10, 0.72060277312994003, 3.5324438420494327e-006,
10, 0.72060278058052063, 3.5324425213780505e-006,
10, 1.5182576552033424, 4.7690979892410133e-008,
10, 1.518257662653923, 4.7690968887170632e-008,
10, 2.2892609387636185, 1.4396365431590603e-009,
10, 2.2892609462141991, 1.4396363283470758e-009,
10, 3.0358340814709663, 7.8118059457005561e-011,
10, 3.0358340889215469, 7.8118048721726738e-011,
10, 3.7592824399471283, 6.7417155809106958e-012,
10, 3.7592824473977089, 6.7417147580480395e-012,
10, 4.4602697342634201, 8.5434024476488055e-013,
10, 4.4602697417140007, 8.5434000006256964e-013,
10, 5.1389683187007904, 1.5015237157428729e-013,
10, 5.138968326151371, 1.5015232503714518e-013,
10, 5.795127771794796, 3.5035278065891386e-014,
10, 5.7951277792453766, 3.5035266685032581e-014,
10, 6.4280949085950851, 1.0474518584578706e-014,
10, 6.4280949160456657, 1.047451900091486e-014,
10, 7.0368044599890709, 3.8902615249132166e-015,
10, 7.0368044674396515, 3.8902605386615012e-015,
10, 7.6197631657123566, 1.742442940023884e-015,
10, 7.6197631731629372, 1.7424426824540998e-015,
10, 8.1750892177224159, 9.1144555287546294e-016,
10, 8.1750892251729965, 9.1144560389833963e-016,
10, 8.7008367404341698, 5.3541847847332351e-016,
10, 8.7008367478847504, 5.3541844723127514e-016,
10, 9.1965094059705734, 3.3560389199894529e-016,
10, 9.196509413421154, 3.3560370421140035e-016,
10, 9.6678015515208244, 2.1059571242602905e-016,
10, 9.667801558971405, 2.1059579862533338e-016,
11, 0.72796426713466644, 2.3816013324880167e-006,
11, 0.72796427458524704, 2.3816003939892356e-006,
11, 1.5323273167014122, 2.6884539057733283e-008,
11, 1.5323273241519928, 2.6884532967611841e-008,
11, 2.3115825653076172, 6.7682186491374862e-010,
11, 2.3115825727581978, 6.768217495558193e-010,
11, 3.0679489448666573, 3.0544688315708309e-011,
11, 3.0679489523172379, 3.054468452617125e-011,
11, 3.8027990683913231, 2.186949692679853e-012,
11, 3.8027990758419037, 2.1869496552307528e-012,
11, 4.5169280469417572, 2.2947351040888336e-013,
11, 4.5169280543923378, 2.2947348773371414e-013,
11, 5.2107065990567207, 3.3353640359739479e-014,
11, 5.2107066065073013, 3.335363154144172e-014,
11, 5.8841593414545059, 6.4351159890193404e-015,
11, 5.8841593489050865, 6.435115249418266e-015,
11, 6.5370001494884491, 1.5930548620019077e-015,
11, 6.5370001569390297, 1.59305482454352e-015,
11, 7.1686412021517754, 4.9183710858836462e-016,
11, 7.168641209602356, 4.9183713116224844e-016,
11, 7.7781866490840912, 1.8464804238726119e-016,
11, 7.7781866565346718, 1.8464801709489452e-016,
11, 8.3644260391592979, 8.2263320775918765e-017,
11, 8.3644260466098785, 8.2263297787354186e-017,
11, 8.9258662387728691, 4.2375346461043962e-017,
11, 8.9258662462234497, 4.2375329267920249e-017,
11, 9.4609249979257584, 2.4482616150935944e-017,
11, 9.460925005376339, 2.4482619419420328e-017,
11, 9.968697115778923, 1.5254006021629585e-017,
11, 9.9686971232295036, 1.5254009931381535e-017,
11, 10.451380550861359, 9.7234265908062383e-018,
11, 10.451380558311939, 9.7234241296957717e-018,
11, 10.909898526966572, 6.3147967493977272e-018,
11, 10.909898534417152, 6.3147961332742783e-018,
12, 0.73438271880149841, 1.6566052109275983e-006,
12, 0.73438272625207901, 1.6566045155548952e-006,
12, 1.5445517003536224, 1.5860666784152459e-008,
12, 1.544551707804203, 1.5860658867525684e-008,
12, 2.33091701567173, 3.380059232629492e-010,
12, 2.3309170231223106, 3.3800585031437757e-010,
12, 3.095676377415657, 1.2884951580384992e-011,
12, 3.0956763848662376, 1.2884947453406877e-011,
12, 3.8402339816093445, 7.7768150022424858e-013,
12, 3.8402339890599251, 7.776814490345326e-013,
12, 4.5654622465372086, 6.8670097741098332e-014,
12, 4.5654622539877892, 6.8670083429297199e-014,
12, 5.2718541026115417, 8.38897478481124e-015,
12, 5.2718541100621223, 8.3889742372884196e-015,
12, 5.9596048966050148, 1.3595098759195538e-015,
12, 5.9596049040555954, 1.3595098086325987e-015,
12, 6.6286550611257553, 2.827608125932321e-016,
12, 6.6286550685763359, 2.8276074709416868e-016,
12, 7.2787091657519341, 7.3455425966950088e-017,
12, 7.2787091732025146, 7.3455407058460195e-017,
12, 7.9092400223016739, 2.3285371485286439e-017,
12, 7.9092400297522545, 2.3285373002934362e-017,
12, 8.5194846615195274, 8.8196897130872609e-018,
12, 8.519484668970108, 8.8196870510698361e-018,
12, 9.1084426045417786, 3.9108299199270105e-018,
12, 9.1084426119923592, 3.9108294386613317e-018,
12, 9.6749012768268585, 1.9869557945423399e-018,
12, 9.6749012842774391, 1.9869552330025425e-018,
12, 10.217559166252613, 1.1287442348688164e-018,
12, 10.217559173703194, 1.1287443889939456e-018,
12, 10.735452570021152, 6.9443548691210419e-019,
12, 10.735452577471733, 6.944357314519752e-019,
12, 11.229217991232872, 4.4666546191302752e-019,
12, 11.229217998683453, 4.4666540313320006e-019,
12, 11.70328252017498, 2.9048073087968165e-019,
12, 11.703282527625561, 2.9048072811110897e-019,
12, 12.068153090775013, 1.1197702118472231e-019,
12, 12.068153098225594, 1.1197723483874788e-019,
13, 0.74004656821489334, 1.1833107184182451e-006,
13, 0.74004657566547394, 1.1833097788321784e-006,
13, 1.5553053691983223, 9.7255030271643972e-009,
13, 1.5553053766489029, 9.7254989421162363e-009,
13, 2.3478806391358376, 1.7766237223855854e-010,
13, 2.3478806465864182, 1.7766232949140296e-010,
13, 3.1199393272399902, 5.7956070959333847e-012,
13, 3.1199393346905708, 5.7956067491263655e-012,
13, 3.8728964179754257, 2.9884476000191141e-013,
13, 3.8728964254260063, 2.9884474795319482e-013,
13, 4.6076695621013641, 2.2511499024927438e-014,
13, 4.6076695695519447, 2.2511492228003123e-014,
13, 5.3248289301991463, 2.3433299337790734e-015,
13, 5.3248289376497269, 2.3433296697120652e-015,
13, 6.024680033326149, 3.2334220967999432e-016,
13, 6.0246800407767296, 3.2334220842696106e-016,
13, 6.7073097303509712, 5.7246438539858037e-017,
13, 6.7073097378015518, 5.7246428548181273e-017,
13, 7.3726105690002441, 1.2665024613881524e-017,
13, 7.3726105764508247, 1.2665026479377931e-017,
13, 8.0202914103865623, 3.4243381685006812e-018,
13, 8.0202914178371429, 3.4243378550191225e-018,
13, 8.6498793810606003, 1.1097375058286432e-018,
13, 8.6498793885111809, 1.1097372565619852e-018,
13, 9.2607174664735794, 4.2345371873704953e-019,
13, 9.26071747392416, 4.234535720073341e-019,
13, 9.8519651964306831, 1.8698553775808502e-019,
13, 9.8519652038812637, 1.8698556036241362e-019,
13, 10.4226189032197, 9.3834845010114218e-020,
13, 10.42261891067028, 9.3834849389696859e-020,
13, 10.971594020724297, 5.2445253216776838e-020,
13, 10.971594028174877, 5.244524330346984e-020,
13, 11.497980736196041, 3.1824489086388546e-020,
13, 11.497980743646622, 3.1824504032698097e-020,
13, 12.001743614673615, 2.0418153275918044e-020,
13, 12.001743622124195, 2.0418144824511038e-020,
13, 12.485165499150753, 1.322118298528861e-020,
13, 12.485165506601334, 1.3221186083014843e-020,
13, 12.954543322324753, 8.948147552026443e-021,
13, 12.954543329775333, 8.9481497369716256e-021,
13, 13.141756847500801, 6.2261736884111559e-021,
13, 13.141756854951382, 6.22616137965588e-021,
14, 0.74509535729885101, 8.6479103419423106e-007,
14, 0.74509536474943161, 8.6479038219181041e-007,
14, 1.5648643523454666, 6.1650149037400714e-009,
14, 1.5648643597960472, 6.1650125500027851e-009,
14, 2.3629250749945641, 9.7577785849465913e-011,
14, 2.3629250824451447, 9.7577755012051767e-011,
14, 3.1414090842008591, 2.7542691144474049e-012,
14, 3.1414090916514397, 2.754268644924632e-012,
14, 3.9017298147082329, 1.2272153763375018e-013,
14, 3.9017298221588135, 1.2272152123703597e-013,
14, 4.6448303312063217, 7.978322520490151e-015,
14, 4.6448303386569023, 7.9783225037342658e-015,
14, 5.3713301867246628, 7.1601479759177548e-016,
14, 5.3713301941752434, 7.1601474269921559e-016,
14, 6.0816079154610634, 8.5112993423908193e-017,
14, 6.081607922911644, 8.5112990415141843e-017,
14, 6.775848351418972, 1.2975876577628266e-017,
14, 6.7758483588695526, 1.2975877961248016e-017,
14, 7.454069696366787, 2.472008704163831e-018,
14, 7.4540697038173676, 2.4720086738065271e-018,
14, 8.1161380037665367, 5.7588911760227473e-019,
14, 8.1161380112171173, 5.7588919455128341e-019,
14, 8.7617733329534531, 1.6104402650810633e-019,
14, 8.7617733404040337, 1.6104400596562633e-019,
14, 9.3905506879091263, 5.3175849261375426e-020,
14, 9.3905506953597069, 5.3175840555484183e-020,
14, 10.001898743212223, 2.0418615673652841e-020,
14, 10.001898750662804, 2.0418619107744165e-020,
14, 10.595101684331894, 8.9828277730487657e-021,
14, 10.595101691782475, 8.9828244400191064e-021,
14, 11.169315472245216, 4.4582227129137701e-021,
14, 11.169315479695797, 4.4582210840169188e-021,
14, 11.723624959588051, 2.4539473008929182e-021,
14, 11.723624967038631, 2.4539478386423601e-021,
14, 12.25720601528883, 1.4682386166943286e-021,
14, 12.25720602273941, 1.4682385418038961e-021,
14, 12.76973832398653, 9.3346251997410079e-022,
14, 12.769738331437111, 9.3346223359077701e-022,
14, 13.262287445366383, 6.0874087090840453e-022,
14, 13.262287452816963, 6.0874060113413987e-022,
14, 13.73819725215435, 4.0622784880680064e-022,
14, 13.738197259604931, 4.0622806176204874e-022,
15, 0.74963488429784775, 6.4472609076683897e-007,
15, 0.74963489174842834, 6.4472546314886359e-007,
15, 1.5734371542930603, 4.0226647054678587e-009,
15, 1.5734371617436409, 4.0226622606167611e-009,
15, 2.3763899058103561, 5.5678382926067953e-011,
15, 2.3763899132609367, 5.5678366001298979e-011,
15, 3.1605874672532082, 1.3728924222156093e-012,
15, 3.1605874747037888, 1.3728922232543816e-012,
15, 3.9274342954158783, 5.3378856950128611e-014,
15, 3.9274343028664589, 5.3378843159211659e-014,
15, 4.6778862848877907, 3.0250264329161316e-015,
15, 4.6778862923383713, 3.0250255465237931e-015,
15, 5.4125945195555687, 2.3643655178483816e-016,
15, 5.4125945270061493, 2.364365094900239e-016,
15, 6.1319867372512817, 2.4459487536429736e-017,
15, 6.1319867447018623, 2.4459487650611821e-017,
15, 6.8363150134682655, 3.2436206211824709e-018,
15, 6.8363150209188461, 3.2436197176022979e-018,
15, 7.5256842151284218, 5.3739371041542508e-019,
15, 7.5256842225790024, 5.3739376909794387e-019,
15, 8.2000685408711433, 1.088934674475772e-019,
15, 8.2000685483217239, 1.0889347191934601e-019,
15, 8.8593204915523529, 2.6504714435038781e-020,
15, 8.8593204990029335, 2.6504716387206021e-020,
15, 9.5031745359301567, 7.6282884779808578e-021,
15, 9.5031745433807373, 7.6282871890206407e-021,
15, 10.131247609853745, 2.5596033506939261e-021,
15, 10.131247617304325, 2.5596033059431966e-021,
15, 10.743038579821587, 9.8815320291260219e-022,
15, 10.743038587272167, 9.881528789722149e-022,
15, 11.337930642068386, 4.3327572929097578e-022,
15, 11.337930649518967, 4.3327579478065768e-022,
15, 11.91520432382822, 2.1290839700926256e-022,
15, 11.915204331278801, 2.1290844593454176e-022,
15, 12.47407853603363, 1.1555853827459651e-022,
15, 12.474078543484211, 1.1555851200022939e-022,
15, 13.013818167150021, 6.8144327801967497e-023,
15, 13.013818174600601, 6.814431722582805e-023,
15, 13.533991023898125, 4.2798966509192708e-023,
15, 13.533991031348705, 4.279897117134478e-023,
15, 14.035010702908039, 2.7914921195937233e-023,
15, 14.03501071035862, 2.7914916878659476e-023,
15, 14.518910378217697, 1.833772281462441e-023,
15, 14.518910385668278, 1.8337712497676989e-023,
15, 14.989013738930225, 1.2608384937256306e-023,
15, 14.989013746380806, 1.2608378195451462e-023,
16, 0.75374705344438553, 4.8915337496543224e-007,
16, 0.75374706089496613, 4.8915306793373716e-007,
16, 1.5811846181750298, 2.6923132475156358e-009,
16, 1.5811846256256104, 2.692312137537266e-009,
16, 2.3885360583662987, 3.2852614483624288e-011,
16, 2.3885360658168793, 3.2852599884042077e-011,
16, 3.1778582483530045, 7.1354837117579206e-013,
16, 3.1778582558035851, 7.1354819499657137e-013,
16, 3.9505422189831734, 2.4415794649042575e-014,
16, 3.950542226433754, 2.4415790464100997e-014,
16, 4.7075485289096832, 1.2166614671909252e-015,
16, 4.7075485363602638, 1.2166612061656969e-015,
16, 5.4495479688048363, 8.3551487091643194e-017,
16, 5.4495479762554169, 8.3551474485434551e-017,
16, 6.1770017296075821, 7.5892566535084655e-018,
16, 6.1770017370581627, 7.5892568568026215e-018,
16, 6.890208899974823, 8.8323530753260686e-019,
16, 6.8902089074254036, 8.8323505679897636e-019,
16, 7.5893355086445808, 1.2838109403040181e-019,
16, 7.5893355160951614, 1.2838108671707829e-019,
16, 8.2744322568178177, 2.2821684437156804e-020,
16, 8.2744322642683983, 2.282168749495082e-020,
16, 8.9454451054334641, 4.8744259157716707e-021,
16, 8.9454451128840446, 4.8744247029595045e-021,
16, 9.6022209450602531, 1.2319495868217162e-021,
16, 9.6022209525108337, 1.2319494772820823e-021,
16, 10.244509845972061, 3.6348978875812834e-022,
16, 10.244509853422642, 3.6348985260615e-022,
16, 10.871965378522873, 1.2367742746291744e-022,
16, 10.871965385973454, 1.2367739126564003e-022,
16, 11.484144628047943, 4.7970119302772392e-023,
16, 11.484144635498524, 4.7970127598781626e-023,
16, 12.080510623753071, 2.0970543482083159e-023,
16, 12.080510631203651, 2.0970540591110336e-023,
16, 12.660443000495434, 1.0212748080573996e-023,
16, 12.660443007946014, 1.0212749016622482e-023,
16, 13.223268158733845, 5.4721418402402487e-024,
16, 13.223268166184425, 5.4721424729500052e-024,
16, 13.768333427608013, 3.1810966077030606e-024,
16, 13.768333435058594, 3.181096582631882e-024,
16, 14.295174412429333, 1.9706877841945116e-024,
16, 14.295174419879913, 1.9706884118909232e-024,
16, 14.803859077394009, 1.2794879837821395e-024,
16, 14.803859084844589, 1.2794882377473996e-024,
16, 15.295545108616352, 8.4344716828413924e-025,
16, 15.295545116066933, 8.4344683346343458e-025,
16, 15.772794611752033, 5.7392825698566701e-025,
16, 15.772794619202614, 5.7392822347696177e-025,
16, 16.216887570917606, 3.6997343524479107e-025,
16, 16.216887578368187, 3.6997346587299121e-025,
17, 0.75749634951353073, 3.7692745372019008e-007,
17, 0.75749635696411133, 3.7692700070692814e-007,
17, 1.5882330387830734, 1.8429395479824224e-009,
17, 1.588233046233654, 1.8429387676315583e-009,
17, 2.3995678052306175, 1.9967644390215291e-011,
17, 2.3995678126811981, 1.9967637238366132e-011,
17, 3.1935207024216652, 3.8482056723979746e-013,
17, 3.1935207098722458, 3.8482046172543379e-013,
17, 3.9714667573571205, 1.1675233373393322e-014,
17, 3.9714667648077011, 1.167523092849099e-014,
17, 4.7343658432364464, 5.1547822958137584e-016,
17, 4.734365850687027, 5.1547809052809859e-016,
17, 5.4829004630446434, 3.1343625323079668e-017,
17, 5.482900470495224, 3.1343618068151562e-017,
17, 6.2175545245409012, 2.5193828294777807e-018,
17, 6.2175545319914818, 2.5193819999045696e-018,
17, 6.9386604055762291, 2.5933718219907985e-019,
17, 6.9386604130268097, 2.5933719595613529e-019,
17, 7.6464280635118484, 3.3330158772752984e-020,
17, 7.646428070962429, 3.3330160862180195e-020,
17, 8.3409634903073311, 5.2379397998875143e-021,
17, 8.3409634977579117, 5.2379386588488221e-021,
17, 9.0222802385687828, 9.8908851451647746e-022,
17, 9.0222802460193634, 9.8908823476058462e-022,
17, 9.6903063133358955, 2.2108045577850313e-022,
17, 9.6903063207864761, 2.2108041448570457e-022,
17, 10.344887860119343, 5.7731399489054422e-023,
17, 10.344887867569923, 5.773138110616153e-023,
17, 10.98579066246748, 1.7407181648032493e-023,
17, 10.98579066991806, 1.7407180865759728e-023,
17, 11.6127003505826, 5.9955236166794974e-024,
17, 11.61270035803318, 5.9955216352412096e-024,
17, 12.225222736597061, 2.3349804655788398e-024,
17, 12.225222744047642, 2.3349807732238287e-024,
17, 12.82288621366024, 1.0179952851287067e-024,
17, 12.822886221110821, 1.0179953150198629e-024,
17, 13.405150465667248, 4.9176017252558557e-025,
17, 13.405150473117828, 4.9176033251919074e-025,
17, 13.971429191529751, 2.6038182860572718e-025,
17, 13.971429198980331, 2.603818076773733e-025,
17, 14.521142840385437, 1.4930454888989484e-025,
17, 14.521142847836018, 1.4930452390494677e-025,
17, 15.053831778466702, 9.123082958623521e-026,
17, 15.053831785917282, 9.1230791767726492e-026,
17, 15.569381833076477, 5.8751079623571136e-026,
17, 15.569381840527058, 5.8751075038868982e-026,
17, 16.068407364189625, 3.8749149875575966e-026,
17, 16.068407371640205, 3.8749167349006019e-026,
17, 16.552637793123722, 2.5963438998656586e-026,
17, 16.552637800574303, 2.5963440101195602e-026,
17, 17.024716928601265, 1.7949322494851864e-026,
17, 17.024716936051846, 1.7949319523018589e-026,
17, 17.346179291605949, 2.8309800520891487e-027,
17, 17.34617929905653, 2.8309773118757838e-027,
18, 0.76093439012765884, 2.9450240370798458e-007,
18, 0.76093439757823944, 2.9450203771031953e-007,
18, 1.5946831777691841, 1.2871185298229725e-009,
18, 1.5946831852197647, 1.2871177488403049e-009,
18, 2.4096476435661316, 1.2461251822064865e-011,
18, 2.4096476510167122, 1.2461248257070009e-011,
18, 3.207812137901783, 2.1447968570473172e-013,
18, 3.2078121453523636, 2.1447959182366632e-013,
18, 3.9905342757701874, 5.8079896477904645e-015,
18, 3.990534283220768, 5.8079874820498712e-015,
18, 4.7587697133421898, 2.2873919040338732e-016,
18, 4.7587697207927704, 2.2873918091132165e-016,
18, 5.5132071524858475, 1.2399411155563791e-017,
18, 5.5132071599364281, 1.2399410449684862e-017,
18, 6.2543457671999931, 8.8806343367361896e-019,
18, 6.2543457746505737, 8.8806339445463331e-019,
18, 6.9825416058301926, 8.1418645242373546e-020,
18, 6.9825416132807732, 8.1418638978404545e-020,
18, 7.6980366632342339, 9.3166546160183016e-021,
18, 7.6980366706848145, 9.316653065404742e-021,
18, 8.4009775668382645, 1.3033282065831878e-021,
18, 8.4009775742888451, 1.303327910841165e-021,
18, 9.0914276838302612, 2.1906432409842348e-022,
18, 9.0914276912808418, 2.1906432254533542e-022,
18, 9.7693748101592064, 4.3589910796802725e-023,
18, 9.769374817609787, 4.3589901608432619e-023,
18, 10.434735849499702, 1.0137066700093108e-023,
18, 10.434735856950283, 1.0137066734442173e-023,
18, 11.087359227240086, 2.7240107890987674e-024,
18, 11.087359234690666, 2.7240105244068185e-024,
18, 11.727025918662548, 8.371655684372496e-025,
18, 11.727025926113129, 8.3716527086860413e-025,
18, 12.353449679911137, 2.9146730821631173e-025,
18, 12.353449687361717, 2.9146728028573778e-025,
18, 12.966277495026588, 1.1392339405640447e-025,
18, 12.966277502477169, 1.1392339608927589e-025,
18, 13.565091922879219, 4.9545881072919797e-026,
18, 13.5650919303298, 4.9545866952502942e-026,
18, 14.149418227374554, 2.3758167105055241e-026,
18, 14.149418234825134, 2.3758158313872783e-026,
18, 14.718741856515408, 1.2442765527084641e-026,
18, 14.718741863965988, 1.244276230271342e-026,
18, 15.272546909749508, 7.0424811711899878e-027,
18, 15.272546917200089, 7.0424832994636221e-027,
18, 15.810395196080208, 4.2497327978932225e-027,
18, 15.810395203530788, 4.2497340544704781e-027,
18, 16.332078844308853, 2.7060819868792312e-027,
18, 16.332078851759434, 2.7060823827611486e-027,
18, 16.83788288384676, 1.778958105553305e-027,
18, 16.83788289129734, 1.7789585636337179e-027,
18, 17.328916251659393, 1.1828714637450282e-027,
18, 17.328916259109974, 1.182871994927067e-027,
18, 17.807191208004951, 8.1726141746863567e-028,
18, 17.807191215455532, 8.1726174566351736e-028,
18, 18.284037873148918, 5.6912247207101229e-028,
18, 18.284037880599499, 5.691222218060101e-028,
18, 18.392694972455502, 5.2831137523744097e-028,
18, 18.392694979906082, 5.2831145046877764e-028,
19, 0.764103002846241, 2.3298449147644669e-007,
19, 0.76410301029682159, 2.3298424269489823e-007,
19, 1.6006165370345116, 9.1529116957755399e-010,
19, 1.6006165444850922, 9.1529068365546486e-010,
19, 2.4189066812396049, 7.9633891310433137e-012,
19, 2.4189066886901855, 7.9633842469171524e-012,
19, 3.220923513174057, 1.2312031507978179e-013,
19, 3.2209235206246376, 1.2312028082814339e-013,
19, 4.0080065280199051, 2.9933906948263948e-015,
19, 4.0080065354704857, 2.9933899839494794e-015,
19, 4.7811048328876495, 1.0579214187674311e-016,
19, 4.7811048403382301, 1.0579211525173792e-016,
19, 5.5409095361828804, 5.1437209226821869e-018,
19, 5.540909543633461, 5.1437201098803477e-018,
19, 6.2879297584295273, 3.30285370901757e-019,
19, 6.2879297658801079, 3.3028526990782213e-019,
19, 7.022538423538208, 2.7137393350465049e-020,
19, 7.0225384309887886, 2.7137390145037245e-020,
19, 7.7450010478496552, 2.7820488626315749e-021,
19, 7.7450010553002357, 2.7820487012081861e-021,
19, 8.4554945304989815, 3.4859333557441231e-022,
19, 8.4554945379495621, 3.4859329845518359e-022,
19, 9.1541195586323738, 5.2474008771752571e-023,
19, 9.1541195660829544, 5.2474000384032056e-023,
19, 9.8409088104963303, 9.3512638696111626e-024,
19, 9.8409088179469109, 9.3512648493398201e-024,
19, 10.515832215547562, 1.9479937239944536e-024,
19, 10.515832222998142, 1.9479938575974556e-024,
19, 11.178800173103809, 4.69085412141189e-025,
19, 11.17880018055439, 4.6908548720156987e-025,
19, 11.829665213823318, 1.2928024618486752e-025,
19, 11.829665221273899, 1.2928026753018633e-025,
19, 12.468222707509995, 4.0409290148689646e-026,
19, 12.468222714960575, 4.04092946286875e-026,
19, 13.094211108982563, 1.4204369152574e-026,
19, 13.094211116433144, 1.4204368039399753e-026,
19, 13.707312539219856, 5.5697729454842655e-027,
19, 13.707312546670437, 5.5697729267586886e-027,
19, 14.307154916226864, 2.4168995964876991e-027,
19, 14.307154923677444, 2.4168993118015141e-027,
19, 14.893317893147469, 1.151182873307859e-027,
19, 14.893317900598049, 1.151183249370605e-027,
19, 15.465346492826939, 5.9684896488404262e-028,
19, 15.465346500277519, 5.9684880973262032e-028,
19, 16.022779874503613, 3.3368863785415361e-028,
19, 16.022779881954193, 3.3368858888570371e-028,
19, 16.565208047628403, 1.988896282534073e-028,
19, 16.565208055078983, 1.9888966397094828e-028,
19, 17.092378154397011, 1.2511355195873936e-028,
19, 17.092378161847591, 1.2511357084655119e-028,
19, 17.604376800358295, 8.1764674788794317e-029,
19, 17.604376807808876, 8.1764689419338323e-029,
19, 18.101884864270687, 5.4403818799662857e-029,
19, 18.101884871721268, 5.4403811124044756e-029,
19, 18.586358889937401, 3.703368785213425e-029,
19, 18.586358897387981, 3.7033672461047739e-029,
19, 19.059829846024513, 2.5704197367132541e-029,
19, 19.059829853475094, 2.5704186883245258e-029,
20, 0.76703650504350662, 1.8640212188134082e-007,
20, 0.76703651249408722, 1.8640189110524636e-007,
20, 1.6060998290777206, 6.6157054588464647e-010,
20, 1.6060998365283012, 6.6157015121944875e-010,
20, 2.4274520501494408, 5.1991605763036711e-012,
20, 2.4274520576000214, 5.1991575903475782e-012,
20, 3.2330104410648346, 7.2582820146985349e-014,
20, 3.2330104485154152, 7.2582783832962019e-014,
20, 4.0240962356328964, 1.5927986670250318e-015,
20, 4.024096243083477, 1.5927979999140583e-015,
20, 4.8016504645347595, 5.0788048744312721e-017,
20, 4.8016504719853401, 5.0788029685345059e-017,
20, 5.5663639381527901, 2.2269814628583385e-018,
20, 5.5663639456033707, 2.2269809381302064e-018,
20, 6.3187519386410713, 1.2891132499721331e-019,
20, 6.3187519460916519, 1.2891130172541847e-019,
20, 7.0591993033885956, 9.5451218618123886e-021,
20, 7.0591993108391762, 9.5451218640099815e-021,
20, 7.7879889234900475, 8.8158015376044649e-022,
20, 7.7879889309406281, 8.8158004848661898e-022,
20, 8.5053204819560051, 9.9494735027566205e-023,
20, 8.5053204894065857, 9.9494722416437504e-023,
20, 9.2113229855895042, 1.3487881180413846e-023,
20, 9.2113229930400848, 1.3487880891331086e-023,
20, 9.9060632660984993, 2.1645350197982161e-024,
20, 9.9060632735490799, 2.1645348970951956e-024,
20, 10.589551687240601, 4.0607366596729865e-025,
20, 10.589551694691181, 4.0607361603086007e-025,
20, 11.26174583286047, 8.808202739315011e-026,
20, 11.26174584031105, 8.8082017838145519e-026,
20, 11.922552742063999, 2.1876047727436381e-026,
20, 11.92255274951458, 2.1876050426774313e-026,
20, 12.571830086410046, 6.1662495078304429e-027,
20, 12.571830093860626, 6.1662499348774014e-027,
20, 13.209386698901653, 1.9567173794914837e-027,
20, 13.209386706352234, 1.9567170332738984e-027,
20, 13.834982834756374, 6.9373607598036741e-028,
20, 13.834982842206955, 6.9373595897190232e-028,
20, 14.448330782353878, 2.7280690089401278e-028,
20, 14.448330789804459, 2.7280680945996177e-028,
20, 15.049096845090389, 1.1813689543546431e-028,
20, 15.04909685254097, 1.181369139348639e-028,
20, 15.636906251311302, 5.5924252241628636e-029,
20, 15.636906258761883, 5.5924267990651051e-029,
20, 16.211354024708271, 2.8725730797162321e-029,
20, 16.211354032158852, 2.8725722552333354e-029,
20, 16.772026851773262, 1.5875830143022102e-029,
20, 16.772026859223843, 1.5875829520216891e-029,
20, 17.318544775247574, 9.3495852893429768e-030,
20, 17.318544782698154, 9.3495854282408101e-030,
20, 17.850637152791023, 5.8080378869545303e-030,
20, 17.850637160241604, 5.8080398155538604e-030,
20, 18.36827152967453, 3.766778846313291e-030,
20, 18.368271537125111, 3.766779811191838e-030,
20, 18.871843047440052, 2.5002689211421573e-030,
20, 18.871843054890633, 2.5002682344308047e-030,
20, 19.362363085150719, 1.674243648785181e-030,
20, 19.362363092601299, 1.6742442653555633e-030,
20, 19.841450870037079, 1.1710157057806629e-030,
20, 19.841450877487659, 1.1710152732309025e-030,
20, 20.30974967777729, 8.0586953650643033e-031,
20, 20.309749685227871, 8.0586997818188476e-031,
21, 0.76976337283849716, 1.5066428073454916e-007,
21, 0.76976338028907776, 1.5066414246643623e-007,
21, 1.6111882776021957, 4.8530823596591033e-010,
21, 1.6111882850527763, 4.8530796828419519e-010,
21, 2.4353722333908081, 3.4610451821120009e-012,
21, 2.4353722408413887, 3.4610441424017983e-012,
21, 3.2442012280225754, 4.3835042623395894e-014,
21, 3.244201235473156, 4.3835023934688873e-014,
21, 4.0389783605933189, 8.7240487039547189e-016,
21, 4.0389783680438995, 8.7240461492198342e-016,
21, 4.820635624229908, 2.5219465898201733e-017,
21, 4.8206356316804886, 2.5219460854936753e-017,
21, 5.5898616313934326, 1.0022039268504888e-018,
21, 5.5898616388440132, 1.0022036172718784e-018,
21, 6.3471750691533089, 5.2559389652856588e-020,
21, 6.3471750766038895, 5.2559375594443955e-020,
21, 7.0929690599441528, 3.5247425965088507e-021,
21, 7.0929690673947334, 3.5247425089738368e-021,
21, 7.827539324760437, 2.9476660458905233e-022,
21, 7.8275393322110176, 2.9476655571904849e-022,
21, 8.551102802157402, 3.0115631228572582e-023,
21, 8.5511028096079826, 3.011562652643058e-023,
21, 9.2638102099299431, 3.6952283110718485e-024,
21, 9.2638102173805237, 3.6952283319575928e-024,
21, 9.9657547101378441, 5.3669656457006436e-025,
21, 9.9657547175884247, 5.3669649762144234e-025,
21, 10.656977899372578, 9.1124256917763825e-026,
21, 10.656977906823158, 9.1124268540483906e-026,
21, 11.337473809719086, 1.7890692227696762e-026,
21, 11.337473817169666, 1.7890693666894125e-026,
21, 12.007191583514214, 4.0227743879756425e-027,
21, 12.007191590964794, 4.0227743211391833e-027,
21, 12.666037052869797, 1.0270242765644747e-027,
21, 12.666037060320377, 1.0270242120978496e-027,
21, 13.313873596489429, 2.9538104523737974e-028,
21, 13.31387360394001, 2.9538105861327128e-028,
21, 13.950522527098656, 9.5012147708737886e-029,
21, 13.950522534549236, 9.5012121359051193e-029,
21, 14.575763396918774, 3.3946835963332503e-029,
21, 14.575763404369354, 3.3946830842745097e-029,
21, 15.189334601163864, 1.338384258083857e-029,
21, 15.189334608614445, 1.3383838228935191e-029,
21, 15.790935188531876, 5.7848622633191873e-030,
21, 15.790935195982456, 5.7848637716726903e-030,
21, 16.380228973925114, 2.7230499400143476e-030,
21, 16.380228981375694, 2.7230500761171659e-030,
21, 16.956853300333023, 1.3866916070525852e-030,
21, 16.956853307783604, 1.3866911116291402e-030,
21, 17.520435951650143, 7.5812793671458848e-031,
21, 17.520435959100723, 7.5812815048755598e-031,
21, 18.070626437664032, 4.4134618820380508e-031,
21, 18.070626445114613, 4.4134600003014153e-031,
21, 18.607151560485363, 2.7073121862111579e-031,
21, 18.607151567935944, 2.7073119631598685e-031,
21, 19.129908226430416, 1.7405231919358924e-031,
21, 19.129908233880997, 1.7405224578827498e-031,
21, 19.639103204011917, 1.149909852362787e-031,
21, 19.639103211462498, 1.1499093604025187e-031,
21, 20.135416276752949, 7.7057380617546439e-032,
21, 20.135416284203529, 7.7057377584979628e-032,
21, 20.62007824331522, 5.313635434227207e-032,
21, 20.6200782507658, 5.313638182607342e-032,
21, 21.09471806883812, 3.6998772136443968e-032,
21, 21.0947180762887, 3.6998750382256628e-032,
21, 21.513655178248882, 2.1423087294246753e-032,
21, 21.513655185699463, 2.1423066695903474e-032,
22, 0.77230742573738098, 1.229185164418409e-007,
22, 0.77230743318796158, 1.2291832454378835e-007,
22, 1.6159280240535736, 3.6084429032500014e-010,
22, 1.6159280315041542, 3.6084396590066408e-010,
22, 2.4427410438656807, 2.3451786403587014e-012,
22, 2.4427410513162613, 2.3451775949384816e-012,
22, 3.2546027079224586, 2.7062134880156874e-014,
22, 3.2546027153730392, 2.7062125966134374e-014,
22, 4.0527982860803604, 4.9058357404375516e-016,
22, 4.052798293530941, 4.9058348176902023e-016,
22, 4.8382501602172852, 1.2913921603181287e-017,
22, 4.8382501676678658, 1.2913917228554348e-017,
22, 5.6116434335708618, 4.6717185843067393e-019,
22, 5.6116434410214424, 4.6717179776425538e-019,
22, 6.3734981417655945, 2.2296903198511069e-020,
22, 6.3734981492161751, 2.2296900974904039e-020,
22, 7.1242129951715469, 1.3604387314615133e-021,
22, 7.1242130026221275, 1.3604385613902272e-021,
22, 7.8640931621193886, 1.0348631251961015e-022,
22, 7.8640931695699692, 1.03486285303848e-022,
22, 8.5933686941862106, 9.6152630844306075e-024,
22, 8.5933687016367912, 9.6152607923175558e-024,
22, 9.3122070804238319, 1.0727676244494742e-024,
22, 9.3122070878744125, 1.0727675822781486e-024,
22, 10.020721986889839, 1.4165824772693852e-025,
22, 10.02072199434042, 1.416582491355437e-025,
22, 10.718979395925999, 2.1866391305081649e-026,
22, 10.718979403376579, 2.1866388838497643e-026,
22, 11.407001882791519, 3.9031522459423558e-027,
22, 11.4070018902421, 3.9031521089045438e-027,
22, 12.084771521389484, 7.9802702761510913e-028,
22, 12.084771528840065, 7.980269670975788e-028,
22, 12.752231821417809, 1.8530613678900598e-028,
22, 12.752231828868389, 1.8530616824287783e-028,
22, 13.409288860857487, 4.8494798585916549e-029,
22, 13.409288868308067, 4.8494785536449382e-029,
22, 14.05581197142601, 1.4202884091535673e-029,
22, 14.055811978876591, 1.4202885442138583e-029,
22, 14.691633984446526, 4.6247809754088509e-030,
22, 14.691633991897106, 4.6247795457938258e-030,
22, 15.316551595926285, 1.6639745508668973e-030,
22, 15.316551603376865, 1.6639743599938902e-030,
22, 15.93032594025135, 6.5756901693418488e-031,
22, 15.930325947701931, 6.575690654043178e-031,
22, 16.532684214413166, 2.8372660249774888e-031,
22, 16.532684221863747, 2.8372664253810075e-031,
22, 17.123323194682598, 1.3286347918438753e-031,
22, 17.123323202133179, 1.328634334065038e-031,
22, 17.701916337013245, 6.7120509402607989e-032,
22, 17.701916344463825, 6.7120512896479518e-032,
22, 18.268127046525478, 3.6325184300463703e-032,
22, 18.268127053976059, 3.6325181235491734e-032,
22, 18.821632660925388, 2.0914308743910646e-032,
22, 18.821632668375969, 2.0914299057002497e-032,
22, 19.362165823578835, 1.2686800121696762e-032,
22, 19.362165831029415, 1.2686799446403407e-032,
22, 19.88958266377449, 8.0696445865656865e-033,
22, 19.889582671225071, 8.0696450863153928e-033,
22, 20.403966307640076, 5.2979414488418604e-033,
22, 20.403966315090656, 5.2979393097828398e-033,
22, 20.905758522450924, 3.5438052686101887e-033,
22, 20.905758529901505, 3.5438058521502753e-033,
22, 21.39586365967989, 2.4059587559014193e-033,
22, 21.39586366713047, 2.4059592126750793e-033,
22, 21.87561222910881, 1.686377885007472e-033,
22, 21.875612236559391, 1.6863776494421034e-033,
22, 22.346770018339157, 1.1684307972912237e-033,
22, 22.346770025789738, 1.1684310754271521e-033,
22, 22.618329457938671, 3.0366386951575348e-034,
22, 22.618329465389252, 3.0366315962617322e-034,
23, 0.77468881756067276, 1.0114160950347676e-007,
23, 0.77468882501125336, 1.0114149032370741e-007,
23, 1.6203579902648926, 2.7163743073571882e-010,
23, 1.6203579977154732, 2.7163720774540249e-010,
23, 2.4496206343173981, 1.6150650901954226e-012,
23, 2.4496206417679787, 1.6150639831714421e-012,
23, 3.2643046677112579, 1.7046911971326696e-014,
23, 3.2643046751618385, 1.7046904575466703e-014,
23, 4.0656779706478119, 2.8259863440888197e-016,
23, 4.0656779780983925, 2.8259849772579011e-016,
23, 4.8546530231833458, 6.8011510032153151e-018,
23, 4.8546530306339264, 6.8011494716482078e-018,
23, 5.6319104433059692, 2.2488464281640756e-019,
23, 5.6319104507565498, 2.2488459534517975e-019,
23, 6.3979701548814774, 9.8079791952490223e-021,
23, 6.397970162332058, 9.8079765385497614e-021,
23, 7.1532344222068787, 5.4671937485617472e-022,
23, 7.1532344296574593, 5.4671917378843881e-022,
23, 7.8980152830481529, 3.7986233108918277e-023,
23, 7.8980152904987335, 3.7986220021765903e-023,
23, 8.6325527653098106, 3.2231569433958688e-024,
23, 8.6325527727603912, 3.2231565617086114e-024,
23, 9.3570273742079735, 3.2834969778924849e-025,
23, 9.3570273816585541, 3.2834965760335941e-025,
23, 10.071568876504898, 3.9585335209485738e-026,
23, 10.071568883955479, 3.958533284993818e-026,
23, 10.776262499392033, 5.5783111048939248e-027,
23, 10.776262506842613, 5.5783106522452834e-027,
23, 11.471153371036053, 9.0901545746996052e-028,
23, 11.471153378486633, 9.0901530603778864e-028,
23, 12.156249642372131, 1.6968039360579984e-028,
23, 12.156249649822712, 1.6968035736701341e-028,
23, 12.831524632871151, 3.5977409707902412e-029,
23, 12.831524640321732, 3.5977400460720119e-029,
23, 13.496918246150017, 8.5996241514863787e-030,
23, 13.496918253600597, 8.5996216693376864e-030,
23, 14.152337834239006, 2.301386888748009e-030,
23, 14.152337841689587, 2.3013866363420915e-030,
23, 14.797658666968346, 6.8517867573579195e-031,
23, 14.797658674418926, 6.8517865061112645e-031,
23, 15.432724215090275, 2.2560267724720382e-031,
23, 15.432724222540855, 2.2560264136538832e-031,
23, 16.057346440851688, 8.1688281380273512e-032,
23, 16.057346448302269, 8.1688278348171516e-032,
23, 16.671306401491165, 3.2350057586674508e-032,
23, 16.671306408941746, 3.2350061703509374e-032,
23, 17.274355687201023, 1.3935974246555884e-032,
23, 17.274355694651604, 1.3935975649494885e-032,
23, 17.86621943116188, 6.494692001260146e-033,
23, 17.866219438612461, 6.4946923994178033e-033,
23, 18.446602113544941, 3.2567180669074382e-033,
23, 18.446602120995522, 3.2567169178931394e-033,
23, 19.015198193490505, 1.7458070339763389e-033,
23, 19.015198200941086, 1.7458065238164995e-033,
23, 19.571710675954819, 9.946196118534568e-034,
23, 19.571710683405399, 9.9461948954570997e-034,
23, 20.11588254570961, 5.9690525712299976e-034,
23, 20.115882553160191, 5.9690500193873946e-034,
23, 20.647547744214535, 3.7545858767414626e-034,
23, 20.647547751665115, 3.7545848159991635e-034,
23, 21.166708528995514, 2.4468390226112094e-034,
23, 21.166708536446095, 2.4468378891837283e-034,
23, 21.673638753592968, 1.6305350714270763e-034,
23, 21.673638761043549, 1.6305353199615473e-034,
23, 22.168985672295094, 1.0990783133763909e-034,
23, 22.168985679745674, 1.0990780643508099e-034,
23, 22.653797566890717, 7.660709966183589e-035,
23, 22.653797574341297, 7.6607108605632843e-035,
23, 23.129408702254295, 5.3481086344930933e-035,
23, 23.129408709704876, 5.3481086507387228e-035,
24, 0.77692466974258423, 8.3878559509491768e-008,
24, 0.77692467719316483, 8.3878444500950374e-008,
24, 1.6245112344622612, 2.0682132657809845e-010,
24, 1.6245112419128418, 2.068211277333234e-010,
24, 2.4560637548565865, 1.1289636914686017e-012,
24, 2.4560637623071671, 1.1289631400035527e-012,
24, 3.2733832001686096, 1.0938619422732816e-014,
24, 3.2733832076191902, 1.0938612911479053e-014,
24, 4.077720619738102, 1.6643113288659459e-016,
24, 4.0777206271886826, 1.6643108721731801e-016,
24, 4.8699784204363823, 3.6754217074679444e-018,
24, 4.8699784278869629, 3.6754201672840378e-018,
24, 5.6508321389555931, 1.1149437498689269e-019,
24, 5.6508321464061737, 1.1149432883776919e-019,
24, 6.4208004623651505, 4.4601526574819404e-021,
24, 6.420800469815731, 4.4601509330870358e-021,
24, 7.1802876740694046, 2.279941873373783e-022,
24, 7.1802876815199852, 2.2799412884161901e-022,
24, 7.9296107068657875, 1.4524227687620892e-023,
24, 7.9296107143163681, 1.4524227325357687e-023,
24, 8.6690171509981155, 1.1297516597255878e-024,
24, 8.6690171584486961, 1.1297516022917642e-024,
24, 9.398697666823864, 1.05489876857462e-025,
24, 9.3986976742744446, 1.0548984739860872e-025,
24, 10.118794731795788, 1.1655531704609301e-026,
24, 10.118794739246368, 1.1655532065990126e-026,
24, 10.82940886169672, 1.5051895754488702e-027,
24, 10.829408869147301, 1.5051892821133279e-027,
24, 11.53060320019722, 2.2476895295962268e-028,
24, 11.5306032076478, 2.2476889060302806e-028,
24, 12.22240673750639, 3.844876383499449e-029,
24, 12.22240674495697, 3.8448759550255258e-029,
24, 12.904816634953022, 7.4714391018572407e-030,
24, 12.904816642403603, 7.4714395302486889e-030,
24, 13.577799834311008, 1.6370125904554994e-030,
24, 13.577799841761589, 1.6370124695278897e-030,
24, 14.241294123232365, 4.0168128083279772e-031,
24, 14.241294130682945, 4.016811469349949e-031,
24, 14.895208783447742, 1.0969746370532075e-031,
24, 14.895208790898323, 1.0969744744608578e-031,
24, 15.539424940943718, 3.315109989109058e-032,
24, 15.539424948394299, 3.3151090923815311e-032,
24, 16.173795841634274, 1.1026485108254938e-032,
24, 16.173795849084854, 1.1026484499551487e-032,
24, 16.798147104680538, 4.0158085477948419e-033,
24, 16.798147112131119, 4.0158088226660865e-033,
24, 17.412277333438396, 1.5934132234896702e-033,
24, 17.412277340888977, 1.5934135053593853e-033,
24, 18.015959389507771, 6.8540171917222488e-034,
24, 18.015959396958351, 6.8540185876176649e-034,
24, 18.608942970633507, 3.1800628171362954e-034,
24, 18.608942978084087, 3.1800629680378069e-034,
24, 19.190959438681602, 1.5836246914151322e-034,
24, 19.190959446132183, 1.5836252472988316e-034,
24, 19.76173035800457, 8.4137600917291117e-035,
24, 19.761730365455151, 8.4137587940032584e-035,
24, 20.320982187986374, 4.745679482731015e-035,
24, 20.320982195436954, 4.7456809155199022e-035,
24, 20.868470467627048, 2.8185196647984626e-035,
24, 20.868470475077629, 2.8185199366681781e-035,
24, 21.404018573462963, 1.7531167534135375e-035,
24, 21.404018580913544, 1.7531173016947469e-035,
24, 21.927576221525669, 1.1332672002404092e-035,
24, 21.92757622897625, 1.1332675797508253e-035,
24, 22.439299717545509, 7.5125238131908317e-036,
24, 22.43929972499609, 7.5125236509015167e-036,
24, 22.939641229808331, 5.0568780187314363e-036,
24, 22.939641237258911, 5.0568784513528091e-036,
24, 23.429403953254223, 3.4736003627413405e-036,
24, 23.429403960704803, 3.4735987495009831e-036,
24, 23.90970042347908, 2.4387081321665308e-036,
24, 23.909700430929661, 2.4387083910949941e-036,
24, 24.38177253305912, 1.694733860647387e-036,
24, 24.381772540509701, 1.694733324885658e-036,
25, 0.77902968227863312, 7.0067469371321597e-008,
25, 0.77902968972921371, 7.0067352105092841e-008,
25, 1.6284160688519478, 1.5913112796142118e-010,
25, 1.6284160763025284, 1.5913095865429296e-010,
25, 2.4621154814958572, 8.0010005048491295e-013,
25, 2.4621154889464378, 8.0009951288958997e-013,
25, 3.2819032743573189, 7.1398107739385184e-015,
25, 3.2819032818078995, 7.1398064213538464e-015,
25, 4.0890141874551773, 1.0003569839311091e-016,
25, 4.0890141949057579, 1.0003565214949822e-016,
25, 4.8843406066298485, 2.0339987591563894e-018,
25, 4.8843406140804291, 2.0339981157202125e-018,
25, 5.6685525178909302, 5.6799254581074817e-020,
25, 5.6685525253415108, 5.6799245689717146e-020,
25, 6.4421665593981743, 2.0912595308116639e-021,
25, 6.4421665668487549, 2.0912591224302577e-021,