↑
| Level |
1 |
| Symmetry |
odd |
| Weight |
0 |
| Character |
\( \chi_{1}(1,\cdot) \) |
| Multiplicity |
1 |
| Precision |
2e-13 |
| Fricke Eigenvalue |
undefined |
| Atkin-Lehner Eigenvalues |
1 |
$R= 9.53369526135$
| n | c(n) |
|
0
|
0 |
|
1
|
1 |
|
2
|
-1.068333551 |
|
3
|
-0.456197354 |
|
4
|
0.141336576 |
|
5
|
-0.290672554 |
|
6
|
0.487370939 |
|
7
|
-0.744941612 |
|
8
|
0.917338944 |
|
9
|
-0.791883973 |
|
10
|
0.310535242 |
|
11
|
0.166163596 |
|
12
|
-0.0644773723 |
|
13
|
-0.586688527 |
|
14
|
0.795846117 |
|
15
|
0.132604050 |
|
16
|
-1.121360548 |
|
17
|
0.570695802 |
|
18
|
0.845996217 |
|
19
|
-0.981938586 |
|
20
|
-0.0410826638 |
|
21
|
0.339840392 |
|
22
|
-0.177518145 |
|
23
|
0.662968958 |
|
24
|
-0.418487599 |
|
25
|
-0.915509465 |
|
26
|
0.626779038 |
|
27
|
0.817452728 |
|
28
|
-0.105287497 |
|
29
|
-1.048688563 |
|
30
|
-0.141665356 |
|
31
|
0.786268441 |
|
32
|
0.280648152 |
|
33
|
-0.0758033931 |
|
34
|
-0.609693473 |
|
35
|
0.216534081 |
|
36
|
-0.111922169 |
|
37
|
-0.448198119 |
|
38
|
1.049037937 |
|
39
|
0.267645754 |
|
40
|
-0.266645254 |
|
41
|
-1.198252638 |
|
42
|
-0.363062893 |
|
43
|
1.562030916 |
|
44
|
0.0234849938 |
|
45
|
0.230178937 |
|
46
|
-0.708271982 |
|
47
|
-0.603152239 |
|
48
|
0.511561716 |
|
49
|
-0.445061995 |
|
50
|
0.978069478 |
|
51
|
-0.260349913 |
|
52
|
-0.0829205481 |
|
53
|
0.594710328 |
|
54
|
-0.873312173 |
|
55
|
-0.0482991971 |
|
56
|
-0.683363952 |
|
57
|
0.447957785 |
|
58
|
1.120349177 |
|
59
|
0.240776400 |
|
60
|
0.0187418025 |
|
61
|
-1.269015756 |
|
62
|
-0.839996956 |
|
63
|
0.589907324 |
|
64
|
0.821534710 |
|
65
|
0.170534253 |
|
66
|
0.0809833082 |
|
67
|
-0.291094611 |
|
68
|
0.0806601910 |
|
69
|
-0.302444685 |
|
70
|
-0.231330624 |
|
71
|
0.185866954 |
|
72
|
-0.726426008 |
|
73
|
0.639072395 |
|
74
|
0.478825089 |
|
75
|
0.417652996 |
|
76
|
-0.138783838 |
|
77
|
-0.123782177 |
|
78
|
-0.285934939 |
|
79
|
-1.454497046 |
|
80
|
0.325948735 |
|
81
|
0.418964201 |
|
82
|
1.280133496 |
|
83
|
0.0744975083 |
|
84
|
0.0480318776 |
|
85
|
-0.165885606 |
|
86
|
-1.668770036 |
|
87
|
0.478408948 |
|
88
|
0.152428337 |
|
89
|
0.310514384 |
|
90
|
-0.245907881 |
|
91
|
0.437048695 |
|
92
|
0.0937017621 |
|
93
|
-0.358693583 |
|
94
|
0.644367774 |
|
95
|
0.285422594 |
|
96
|
-0.128030948 |
|
97
|
-1.777984562 |
|
98
|
0.475474661 |
|
99
|
-0.131582289 |
|
100
|
-0.129394973 |
|
101
|
1.315142260 |
|
102
|
0.278140549 |
|
103
|
0.383613736 |
|
104
|
-0.538192234 |
|
105
|
-0.0987822752 |
|
106
|
-0.635349002 |
|
107
|
-1.124295726 |
|
108
|
0.115535970 |
|
109
|
1.113235869 |
|
110
|
0.0515996529 |
|
111
|
0.204466796 |
|
112
|
0.835348134 |
|
113
|
-0.454156502 |
|
114
|
-0.478568331 |
|
115
|
-0.192706881 |
|
116
|
-0.148218051 |
|
117
|
0.464589242 |
|
118
|
-0.257229507 |
|
119
|
-0.425135051 |
|
120
|
0.121642859 |
|
121
|
-0.972389658 |
|
122
|
1.355732110 |
|
123
|
0.546639681 |
|
124
|
0.111128489 |
|
125
|
0.556786030 |
|
126
|
-0.630217784 |
|
127
|
-0.103330723 |
|
128
|
-1.158321247 |
|
129
|
-0.712594370 |
|
130
|
-0.182187467 |
|
131
|
1.376611493 |
|
132
|
-0.0107137936 |
|
133
|
0.731486917 |
|
134
|
0.310986138 |
|
135
|
-0.237611069 |
|
136
|
0.523521494 |
|
137
|
-1.441495842 |
|
138
|
0.323111804 |
|
139
|
-0.636311702 |
|
140
|
0.0306041860 |
|
141
|
0.275156455 |
|
142
|
-0.198567903 |
|
143
|
-0.0974862758 |
|
144
|
0.887987447 |
|
145
|
0.304824984 |
|
146
|
-0.682742481 |
|
147
|
0.203036104 |
|
148
|
-0.0633467879 |
|
149
|
1.053417513 |
|
150
|
-0.446192708 |
|
151
|
-0.294837230 |
|
152
|
-0.900770506 |
|
153
|
-0.451924860 |
|
154
|
0.132240653 |
|
155
|
-0.228546656 |
|
156
|
0.0378281353 |
|
157
|
1.014076484 |
|
158
|
1.553887995 |
|
159
|
-0.271305282 |
|
160
|
-0.0815767157 |
|
161
|
-0.493873165 |
|
162
|
-0.447593512 |
|
163
|
-1.051182294 |
|
164
|
-0.169356929 |
|
165
|
0.0220339693 |
|
166
|
-0.0795881889 |
|
167
|
1.174127370 |
|
168
|
0.311748827 |
|
169
|
-0.655796573 |
|
170
|
0.177221175 |
|
171
|
0.777581425 |
|
172
|
0.220772109 |
|
173
|
-0.735730789 |
|
174
|
-0.511100330 |
|
175
|
0.682001097 |
|
176
|
-0.186329302 |
|
177
|
-0.109841556 |
|
178
|
-0.331732934 |
|
179
|
-0.724159202 |
|
180
|
0.0325327029 |
|
181
|
0.669658248 |
|
182
|
-0.466913787 |
|
183
|
0.578921630 |
|
184
|
0.608167243 |
|
185
|
0.130278892 |
|
186
|
0.383204388 |
|
187
|
0.0948288678 |
|
188
|
-0.0852474722 |
|
189
|
-0.608954555 |
|
190
|
-0.304926539 |
|
191
|
-1.284991825 |
|
192
|
-0.374781960 |
|
193
|
-0.399953683 |
|
194
|
1.899480574 |
|
195
|
-0.0777972729 |
|
196
|
-0.0629035409 |
|
197
|
1.504636077 |
|
198
|
0.140573773 |
|
199
|
-0.306503987 |
|
200
|
-0.839832492 |
|
201
|
0.132796581 |
|
202
|
-1.405010605 |
|
203
|
0.781211746 |
|
204
|
-0.0367969636 |
|
205
|
0.348299177 |
|
206
|
-0.409827419 |
|
207
|
-0.524994492 |
|
208
|
0.657889369 |
|
209
|
-0.163162446 |
|
210
|
0.105532418 |
|
211
|
0.174904068 |
|
212
|
0.0840543229 |
|
213
|
-0.0847920131 |
|
214
|
1.201122847 |
|
215
|
-0.454039516 |
|
216
|
0.749881223 |
|
217
|
-0.585724079 |
|
218
|
-1.189307230 |
|
219
|
-0.291543137 |
|
220
|
-0.00682644437 |
|
221
|
-0.334820677 |
|
222
|
-0.218438738 |
|
223
|
0.454307380 |
|
224
|
-0.209066487 |
|
225
|
0.724977276 |
|
226
|
0.485190632 |
|
227
|
1.348675797 |
|
228
|
0.0633128216 |
|
229
|
-1.068621744 |
|
230
|
0.205875224 |
|
231
|
0.0564691026 |
|
232
|
-0.962002852 |
|
233
|
-0.682837379 |
|
234
|
-0.496336274 |
|
235
|
0.175319799 |
|
236
|
0.0340305184 |
|
237
|
0.663537698 |
|
238
|
0.454186038 |
|
239
|
0.171985973 |
|
240
|
-0.148696950 |
|
241
|
0.152517704 |
|
242
|
1.038836496 |
|
243
|
-1.008583088 |
|
244
|
-0.179358342 |
|
245
|
0.129367306 |
|
246
|
-0.583993510 |
|
247
|
0.576092104 |
|
248
|
0.721274656 |
|
249
|
-0.0339855684 |
|
250
|
-0.594833200 |
|
251
|
-1.523444053 |
|
252
|
0.0833754827 |
|
253
|
0.110161306 |
|
254
|
0.110391688 |
|
255
|
0.0756765765 |
|
256
|
0.415938734 |
|
257
|
0.549019149 |
|
258
|
0.761288474 |
|
259
|
0.333881431 |
|
260
|
0.0241027264 |
|
261
|
0.830439664 |
|
262
|
-1.470680230 |
|
263
|
-0.724568955 |
|
264
|
-0.0695374094 |
|
265
|
-0.172865947 |
|
266
|
-0.781472000 |
|
267
|
-0.141655841 |
|
268
|
-0.0411423145 |
|
269
|
0.394335452 |
|
270
|
0.253847880 |
|
271
|
1.447765918 |
|
272
|
-0.639955756 |
|
273
|
-0.199380458 |
|
274
|
1.539998371 |
|
275
|
-0.152124341 |
|
276
|
-0.0427465035 |
|
277
|
-1.589864716 |
|
278
|
0.679793147 |
|
279
|
-0.622633376 |
|
280
|
0.198635148 |
|
281
|
-0.0859443871 |
|
282
|
-0.293958864 |
|
283
|
-0.0870941815 |
|
284
|
0.0262697927 |
|
285
|
-0.130209027 |
|
286
|
0.104147864 |
|
287
|
0.892628250 |
|
288
|
-0.222240785 |
|
289
|
-0.674306303 |
|
290
|
-0.325654770 |
|
291
|
0.811111872 |
|
292
|
0.0903243019 |
|
293
|
1.461411459 |
|
294
|
-0.216910286 |
|
295
|
-0.0699871015 |
|
296
|
-0.411149591 |
|
297
|
0.135830885 |
|
298
|
-1.125401272 |
|
299
|
-0.388956278 |
|
300
|
0.0590296444 |
|
301
|
-1.163621831 |
|
302
|
0.314984508 |
|
303
|
-0.599964421 |
|
304
|
1.101107195 |
|
305
|
0.368868047 |
|
306
|
0.482806490 |
|
307
|
1.595684490 |
|
308
|
-0.0174949508 |
|
309
|
-0.175003566 |
|
310
|
0.244164062 |
|
311
|
-1.542056844 |
|
312
|
0.245521867 |
|
313
|
0.237160581 |
|
314
|
-1.083371938 |
|
315
|
-0.171469866 |
|
316
|
-0.205573636 |
|
317
|
0.199315632 |
|
318
|
0.289844520 |
|
319
|
-0.174253853 |
|
320
|
-0.238797589 |
|
321
|
0.512900727 |
|
322
|
0.527621278 |
|
323
|
-0.560388251 |
|
324
|
0.0592149676 |
|
325
|
0.537118896 |
|
326
|
1.123013318 |
|
327
|
-0.507855284 |
|
328
|
-1.099203809 |
|
329
|
0.449313202 |
|
330
|
-0.0235396249 |
|
331
|
0.415876236 |
|
332
|
0.0105292205 |
|
333
|
0.354920909 |
|
334
|
-1.254359664 |
|
335
|
0.0846132132 |
|
336
|
-0.381083610 |
|
337
|
-1.025842502 |
|
338
|
0.700609477 |
|
339
|
0.207184998 |
|
340
|
-0.0234457057 |
|
341
|
0.130649192 |
|
342
|
-0.830716326 |
|
343
|
1.076486809 |
|
344
|
1.432911795 |
|
345
|
0.0879123649 |
|
346
|
0.786005875 |
|
347
|
-0.401841517 |
|
348
|
0.0676166795 |
|
349
|
-0.792451863 |
|
350
|
-0.728604652 |
|
351
|
-0.479590145 |
|
352
|
0.0466335162 |
|
353
|
-1.218009905 |
|
354
|
0.117347412 |
|
355
|
-0.0540264113 |
|
356
|
0.0438870273 |
|
357
|
0.193945484 |
|
358
|
0.773643575 |
|
359
|
1.260432561 |
|
360
|
0.211152098 |
|
361
|
-0.0357966146 |
|
362
|
-0.715418385 |
|
363
|
0.443601589 |
|
364
|
0.0617709674 |
|
365
|
-0.185760805 |
|
366
|
-0.618481400 |
|
367
|
0.342157323 |
|
368
|
-0.743427234 |
|
369
|
0.948877058 |
|
370
|
-0.139181309 |
|
371
|
-0.443024474 |
|
372
|
-0.0506965266 |
|
373
|
-0.203869609 |
|
374
|
-0.101308865 |
|
375
|
-0.254004311 |
|
376
|
-0.553295039 |
|
377
|
0.615253548 |
|
378
|
0.650566583 |
|
379
|
-0.852030441 |
|
380
|
0.0403406550 |
|
381
|
0.0471392036 |
|
382
|
1.372799876 |
|
383
|
0.199354663 |
|
384
|
0.528423098 |
|
385
|
0.0359800734 |
|
386
|
0.427283933 |
|
387
|
-1.236947246 |
|
388
|
-0.251294258 |
|
389
|
-0.491391691 |
|
390
|
0.0831134323 |
|
391
|
0.378353594 |
|
392
|
-0.408272705 |
|
393
|
-0.628006515 |
|
394
|
-1.607453214 |
|
395
|
0.422782394 |
|
396
|
-0.0185974039 |
|
397
|
1.398594639 |
|
398
|
0.327448512 |
|
399
|
-0.333702433 |
|
400
|
1.026616214 |
|
401
|
1.281181526 |
|
402
|
-0.141871045 |
|
403
|
-0.461294673 |
|
404
|
0.185877703 |
|
405
|
-0.121781392 |
|
406
|
-0.834594723 |
|
407
|
-0.0744742114 |
|
408
|
-0.238829116 |
|
409
|
-1.052261913 |
|
410
|
-0.372099672 |
|
411
|
0.657606592 |
|
412
|
0.0542186499 |
|
413
|
-0.179364355 |
|
414
|
0.560869230 |
|
415
|
-0.0216543820 |
|
416
|
-0.164653049 |
|
417
|
0.290283711 |
|
418
|
0.174311919 |
|
419
|
0.0612158554 |
|
420
|
-0.0139615512 |
|
421
|
-0.192256900 |
|
422
|
-0.186855887 |
|
423
|
0.477626588 |
|
424
|
0.545550948 |
|
425
|
-0.522477409 |
|
426
|
0.0905861527 |
|
427
|
0.945342644 |
|
428
|
-0.158904109 |
|
429
|
0.0444729834 |
|
430
|
0.485065647 |
|
431
|
-1.523421383 |
|
432
|
-0.916659246 |
|
433
|
-0.804731839 |
|
434
|
0.625748680 |
|
435
|
-0.139060350 |
|
436
|
0.157340944 |
|
437
|
-0.650994788 |
|
438
|
0.311465320 |
|
439
|
0.921313089 |
|
440
|
-0.0443067312 |
|
441
|
0.352437466 |
|
442
|
0.357700165 |
|
443
|
1.606377627 |
|
444
|
0.0288986508 |
|
445
|
-0.0902580214 |
|
446
|
-0.485351814 |
|
447
|
-0.480566285 |
|
448
|
-0.611995388 |
|
449
|
0.396894250 |
|
450
|
-0.774517545 |
|
451
|
-0.199105965 |
|
452
|
-0.0641889271 |
|
453
|
0.134503969 |
|
454
|
-1.440835600 |
|
455
|
-0.127038060 |
|
456
|
0.410929120 |
|
457
|
0.00969847427 |
|
458
|
1.141644455 |
|
459
|
0.466516844 |
|
460
|
-0.0272365322 |
|
461
|
0.777679714 |
|
462
|
-0.0603278295 |
|
463
|
-1.237799460 |
|
464
|
1.175957985 |
|
465
|
0.104262378 |
|
466
|
0.729498070 |
|
467
|
-1.593845534 |
|
468
|
0.0656634473 |
|
469
|
0.216848480 |
|
470
|
-0.187300015 |
|
471
|
-0.462619014 |
|
472
|
0.220873568 |
|
473
|
0.259552673 |
|
474
|
-0.708879604 |
|
475
|
0.898974086 |
|
476
|
-0.0600871416 |
|
477
|
-0.470941573 |
|
478
|
-0.183738384 |
|
479
|
-0.864072202 |
|
480
|
0.0372150922 |
|
481
|
0.262952692 |
|
482
|
-0.162939785 |
|
483
|
0.225303627 |
|
484
|
-0.137434211 |
|
485
|
0.516811302 |
|
486
|
1.077503167 |
|
487
|
1.843367656 |
|
488
|
-1.164117567 |
|
489
|
0.479546579 |
|
490
|
-0.138207446 |
|
491
|
-0.544111017 |
|
492
|
0.0772601531 |
|
493
|
-0.598482157 |
|
494
|
-0.615458505 |
|
495
|
0.0382473574 |
|
496
|
-0.881690410 |
|
497
|
-0.138460028 |
|
498
|
0.0363079175 |
|
499
|
-1.117720323 |
