↑
| Level |
2 |
| Symmetry |
odd |
| Weight |
0 |
| Character |
\( \chi_{2}(1,\cdot) \) |
| Multiplicity |
1 |
| Precision |
3e-09 |
| Fricke Eigenvalue |
-1 |
| Atkin-Lehner Eigenvalues |
1,-1 |
$R= 5.41733480684$
| n | c(n) |
|
0
|
0 |
|
1
|
1 |
|
2
|
0.707106781 |
|
3
|
-0.380538572 |
|
4
|
0.500000000 |
|
5
|
-0.253812464 |
|
6
|
-0.269081407 |
|
7
|
0.397600583 |
|
8
|
0.353553390 |
|
9
|
-0.855190394 |
|
10
|
-0.179472514 |
|
11
|
1.201833974 |
|
12
|
-0.190269286 |
|
13
|
-0.948703217 |
|
14
|
0.281146052 |
|
15
|
0.0965854328 |
|
16
|
0.250000000 |
|
17
|
0.472807317 |
|
18
|
-0.604710927 |
|
19
|
-0.231256664 |
|
20
|
-0.126906232 |
|
21
|
-0.151302349 |
|
22
|
0.849824952 |
|
23
|
0.398077371 |
|
24
|
-0.134540702 |
|
25
|
-0.935579232 |
|
26
|
-0.670834478 |
|
27
|
0.705971504 |
|
28
|
0.198800279 |
|
29
|
0.830299583 |
|
30
|
0.0682962145 |
|
31
|
-0.985533801 |
|
32
|
0.176776695 |
|
33
|
-0.457344184 |
|
34
|
0.334325260 |
|
35
|
-0.100915977 |
|
36
|
-0.427595197 |
|
37
|
1.217345916 |
|
38
|
-0.163523155 |
|
39
|
0.361018168 |
|
40
|
-0.0897362573 |
|
41
|
-1.213893128 |
|
42
|
-0.106986917 |
|
43
|
-0.208503006 |
|
44
|
0.600916987 |
|
45
|
0.217057982 |
|
46
|
0.281483208 |
|
47
|
0.872905391 |
|
48
|
-0.0951346455 |
|
49
|
-0.841913787 |
|
50
|
-0.661554405 |
|
51
|
-0.179921421 |
|
52
|
-0.474351586 |
|
53
|
1.010367541 |
|
54
|
0.499197238 |
|
55
|
-0.305040442 |
|
56
|
0.140573026 |
|
57
|
0.0880020811 |
|
58
|
0.587110466 |
|
59
|
-0.823124818 |
|
60
|
0.0482927164 |
|
61
|
0.141375520 |
|
62
|
-0.696877633 |
|
63
|
-0.340024179 |
|
64
|
0.124999999 |
|
65
|
0.240792701 |
|
66
|
-0.323391174 |
|
67
|
1.611398664 |
|
68
|
0.236403658 |
|
69
|
-0.151483795 |
|
70
|
-0.0713583725 |
|
71
|
-0.662064805 |
|
72
|
-0.302355461 |
|
73
|
-1.524518974 |
|
74
|
0.860793551 |
|
75
|
0.356023986 |
|
76
|
-0.115628337 |
|
77
|
0.477849863 |
|
78
|
0.255278402 |
|
79
|
0.466176760 |
|
80
|
-0.0634531137 |
|
81
|
0.586540998 |
|
82
|
-0.858352069 |
|
83
|
-0.497617328 |
|
84
|
-0.0756511857 |
|
85
|
-0.120004402 |
|
86
|
-0.147433904 |
|
87
|
-0.315961044 |
|
88
|
0.424912530 |
|
89
|
0.315840081 |
|
90
|
0.153483287 |
|
91
|
-0.377205293 |
|
92
|
0.199038685 |
|
93
|
0.375033625 |
|
94
|
0.617237323 |
|
95
|
0.0586958235 |
|
96
|
-0.0672703505 |
|
97
|
-0.162357949 |
|
98
|
-0.595322953 |
|
99
|
-1.027796870 |
|
100
|
-0.467789617 |
|
101
|
0.128533754 |
|
102
|
-0.127223657 |
|
103
|
1.642947834 |
|
104
|
-0.335417237 |
|
105
|
0.0384024208 |
|
106
|
0.714437739 |
|
107
|
0.590326134 |
|
108
|
0.352985749 |
|
109
|
-1.193901507 |
|
110
|
-0.215696164 |
|
111
|
-0.463247077 |
|
112
|
0.0994001447 |
|
113
|
-0.759787797 |
|
114
|
0.0622268605 |
|
115
|
-0.101036976 |
|
116
|
0.415149783 |
|
117
|
0.811321836 |
|
118
|
-0.582037158 |
|
119
|
0.187988413 |
|
120
|
0.0341481080 |
|
121
|
0.444404954 |
|
122
|
0.0999674504 |
|
123
|
0.461933078 |
|
124
|
-0.492766846 |
|
125
|
0.491274135 |
|
126
|
-0.240433404 |
|
127
|
-1.144569597 |
|
128
|
0.0883883509 |
|
129
|
0.0793434340 |
|
130
|
0.170266149 |
|
131
|
-0.769099489 |
|
132
|
-0.228672096 |
|
133
|
-0.0919477813 |
|
134
|
1.139430923 |
|
135
|
-0.179184367 |
|
136
|
0.167162628 |
|
137
|
0.360856575 |
|
138
|
-0.107115212 |
|
139
|
1.540298168 |
|
140
|
-0.0504579813 |
|
141
|
-0.332174150 |
|
142
|
-0.468150504 |
|
143
|
-1.140183808 |
|
144
|
-0.213797589 |
|
145
|
-0.210740361 |
|
146
|
-1.077997706 |
|
147
|
0.320380762 |
|
148
|
0.608672945 |
|
149
|
0.123745404 |
|
150
|
0.251747119 |
|
151
|
1.198021429 |
|
152
|
-0.0817615345 |
|
153
|
-0.404340438 |
|
154
|
0.337890757 |
|
155
|
0.250140949 |
|
156
|
0.180508535 |
|
157
|
-0.908057784 |
|
158
|
0.329636898 |
|
159
|
-0.384483820 |
|
160
|
-0.0448681268 |
|
161
|
0.158275788 |
|
162
|
0.414747126 |
|
163
|
-1.012321539 |
|
164
|
-0.606946561 |
|
165
|
0.116079647 |
|
166
|
-0.351868604 |
|
167
|
1.134997795 |
|
168
|
-0.0534934548 |
|
169
|
-0.0999621908 |
|
170
|
-0.0848559257 |
|
171
|
0.197768481 |
|
172
|
-0.104251516 |
|
173
|
1.580219072 |
|
174
|
-0.223418161 |
|
175
|
-0.371986843 |
|
176
|
0.300458516 |
|
177
|
0.313230738 |
|
178
|
0.223332710 |
|
179
|
-1.944423784 |
|
180
|
0.108528949 |
|
181
|
-0.512271098 |
|
182
|
-0.266724129 |
|
183
|
-0.0537988600 |
|
184
|
0.140741586 |
|
185
|
-0.308977441 |
|
186
|
0.265188807 |
|
187
|
0.568235879 |
|
188
|
0.436452705 |
|
189
|
0.280694661 |
|
190
|
0.0415042095 |
|
191
|
0.565123516 |
|
192
|
-0.0475673252 |
|
193
|
0.785438782 |
|
194
|
-0.114804412 |
|
195
|
-0.0916308993 |
|
196
|
-0.420956903 |
|
197
|
-1.342195919 |
|
198
|
-0.726762121 |
|
199
|
0.884566070 |
|
200
|
-0.330777205 |
|
201
|
-0.613199344 |
|
202
|
0.0908871024 |
|
203
|
0.330127575 |
|
204
|
-0.0899607089 |
|
205
|
0.308101258 |
|
206
|
1.161739533 |
|
207
|
-0.340431983 |
|
208
|
-0.237175775 |
|
209
|
-0.277932192 |
|
210
|
0.0271546301 |
|
211
|
-0.0475778653 |
|
212
|
0.505183921 |
|
213
|
0.251941306 |
|
214
|
0.417423663 |
|
215
|
0.0529206648 |
|
216
|
0.249598615 |
|
217
|
-0.391848789 |
|
218
|
-0.844215850 |
|
219
|
0.580138266 |
|
220
|
-0.152520226 |
|
221
|
-0.448553806 |
|
222
|
-0.327565152 |
|
223
|
-1.539370469 |
|
224
|
0.0702865238 |
|
225
|
0.800098385 |
|
226
|
-0.537251111 |
|
227
|
0.912887960 |
|
228
|
0.0440010588 |
|
229
|
0.901960640 |
|
230
|
-0.0714439348 |
|
231
|
-0.181840342 |
|
232
|
0.293555228 |
|
233
|
0.793970702 |
|
234
|
0.573691237 |
|
235
|
-0.221554497 |
|
236
|
-0.411562472 |
|
237
|
-0.177398357 |
|
238
|
0.132927889 |
|
239
|
-0.861040125 |
|
240
|
0.0241463460 |
|
241
|
-1.050837222 |
|
242
|
0.314241728 |
|
243
|
-0.929172977 |
|
244
|
0.0706877382 |
|
245
|
0.213688202 |
|
246
|
0.326636061 |
|
247
|
0.219393957 |
|
248
|
-0.348438805 |
|
249
|
0.189362570 |
|
250
|
0.347383259 |
|
251
|
1.448663057 |
|
252
|
-0.170012080 |
|
253
|
0.478422923 |
|
254
|
-0.809332914 |
|
255
|
0.0456663775 |
|
256
|
0.0625000703 |
|
257
|
-0.260423008 |
|
258
|
0.0561042970 |
|
259
|
0.484017276 |
|
260
|
0.120396313 |
|
261
|
-0.710064085 |
|
262
|
-0.543835473 |
|
263
|
0.140625435 |
|
264
|
-0.161695359 |
|
265
|
-0.256444118 |
|
266
|
-0.0650168870 |
|
267
|
-0.120189346 |
|
268
|
0.805699331 |
|
269
|
-1.343029807 |
|
270
|
-0.126702483 |
|
271
|
0.980472013 |
|
272
|
0.118201821 |
|
273
|
0.143541014 |
|
274
|
0.255164124 |
|
275
|
-1.124410897 |
|
276
|
-0.0757418719 |
|
277
|
0.656524283 |
|
278
|
1.089155262 |
|
279
|
0.842819037 |
|
280
|
-0.0356792047 |
|
281
|
0.790860762 |
|
282
|
-0.234882624 |
|
283
|
-0.904475288 |
|
284
|
-0.331032385 |
|
285
|
-0.0223359831 |
|
286
|
-0.806231621 |
|
287
|
-0.482644581 |
|
288
|
-0.151177725 |
|
289
|
-0.776453277 |
|
290
|
-0.149015961 |
|
291
|
0.0617834054 |
|
292
|
-0.762259571 |
|
293
|
1.199923455 |
|
294
|
0.226543276 |
|
295
|
0.208919341 |
|
296
|
0.430396778 |
|
297
|
0.848460530 |
|
298
|
0.0875013493 |
|
299
|
-0.377657291 |
|
300
|
0.178012004 |
|
301
|
-0.0829009245 |
|
302
|
0.847129125 |
|
303
|
-0.0489120374 |
|
304
|
-0.0578141796 |
|
305
|
-0.0358828416 |
|
306
|
-0.285911775 |
|
307
|
-0.630769920 |
|
308
|
0.238924928 |
|
309
|
-0.625205032 |
|
310
|
0.176876255 |
|
311
|
-0.254590446 |
|
312
|
0.127639236 |
|
313
|
-0.530063178 |
|
314
|
-0.642093149 |
|
315
|
0.0863023663 |
|
316
|
0.233088376 |
|
317
|
0.194188015 |
|
318
|
-0.271871089 |
|
319
|
0.997882264 |
|
320
|
-0.0317266449 |
|
321
|
-0.224641725 |
|
322
|
0.111917869 |
|
323
|
-0.109339858 |
|
324
|
0.293270481 |
|
325
|
0.887586943 |
|
326
|
-0.715819469 |
|
327
|
0.454325574 |
|
328
|
-0.429176031 |
|
329
|
0.347067677 |
|
330
|
0.0820807188 |
|
331
|
0.972617769 |
|
332
|
-0.248808688 |
|
333
|
-1.041062540 |
|
334
|
0.802564635 |
|
335
|
-0.408993055 |
|
336
|
-0.0378255844 |
|
337
|
-1.023314314 |
|
338
|
-0.0706839639 |
|
339
|
0.289128601 |
|
340
|
-0.0600021756 |
|
341
|
-1.184447970 |
|
342
|
0.139843418 |
|
343
|
-0.732345961 |
|
344
|
-0.0737169291 |
|
345
|
0.0384484254 |
|
346
|
1.117383615 |
|
347
|
0.870240398 |
|
348
|
-0.157980472 |
|
349
|
0.845160774 |
|
350
|
-0.263034393 |
|
351
|
-0.669757494 |
|
352
|
0.212456207 |
|
353
|
1.718217144 |
|
354
|
0.221487572 |
|
355
|
0.168040132 |
|
356
|
0.157920034 |
|
357
|
-0.0715369232 |
|
358
|
-1.374915176 |
|
359
|
-0.270569171 |
|
360
|
0.0767417354 |
|
361
|
-0.946520223 |
|
362
|
-0.362230366 |
|
363
|
-0.169113200 |
|
364
|
-0.188602459 |
|
365
|
0.386941911 |
|
366
|
-0.0380415217 |
|
367
|
-1.151570606 |
|
368
|
0.0995193335 |
|
369
|
1.038109740 |
|
370
|
-0.218480135 |
|
371
|
0.401722715 |
|
372
|
0.187516800 |
|
373
|
0.736465032 |
|
374
|
0.401803468 |
|
375
|
-0.186948759 |
|
376
|
0.308618675 |
|
377
|
-0.787707897 |
|
378
|
0.198481094 |
|
379
|
-0.436187057 |
|
380
|
0.0293479030 |
|
381
|
0.435552932 |
|
382
|
0.399602629 |
|
383
|
0.211837240 |
|
384
|
-0.0336351950 |
|
385
|
-0.121284275 |
|
386
|
0.555389100 |
|
387
|
0.178309794 |
|
388
|
-0.0811790550 |
|
389
|
-1.727605303 |
|
390
|
-0.0647928713 |
|
391
|
0.188213876 |
|
392
|
-0.297661428 |
|
393
|
0.292671943 |
|
394
|
-0.949075819 |
|
395
|
-0.118321454 |
|
396
|
-0.513898383 |
|
397
|
0.749313173 |
|
398
|
0.625482884 |
|
399
|
0.0349896939 |
|
400
|
-0.233894758 |
|
401
|
-0.229089430 |
|
402
|
-0.433597415 |
|
403
|
0.934979087 |
|
404
|
0.0642668798 |
|
405
|
-0.148871417 |
|
406
|
0.233435459 |
|
407
|
1.463047675 |
|
408
|
-0.0636118443 |
|
409
|
-0.267529157 |
|
410
|
0.217860453 |
|
411
|
-0.137319844 |
|
412
|
0.821473909 |
|
413
|
-0.327274893 |
|
414
|
-0.240721725 |
|
415
|
0.126301487 |
|
416
|
-0.167708624 |
|
417
|
-0.586142841 |
|
418
|
-0.196527674 |
|
419
|
-1.543396781 |
|
420
|
0.0192012104 |
|
421
|
0.0572228903 |
|
422
|
-0.0336426211 |
|
423
|
-0.746500291 |
|
424
|
0.357218886 |
|
425
|
-0.442348696 |
|
426
|
0.178149336 |
|
427
|
0.0562109812 |
|
428
|
0.295163121 |
|
429
|
0.433883881 |
|
430
|
0.0374205232 |
|
431
|
1.529726664 |
|
432
|
0.176492889 |
|
433
|
0.637921335 |
|
434
|
-0.277078906 |
|
435
|
0.0801948712 |
|
436
|
-0.596950781 |
|
437
|
-0.0920581326 |
|
438
|
0.410219698 |
|
439
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447
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449
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450
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491
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498
|
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499
|
1.350535248 |
