↑
| Level |
1 |
| Symmetry |
odd |
| Weight |
0 |
| Character |
\( \chi_{1}(1,\cdot) \) |
| Multiplicity |
1 |
| Precision |
5e-14 |
| Fricke Eigenvalue |
undefined |
| Atkin-Lehner Eigenvalues |
1 |
$R= 12.1730083247$
| n | c(n) |
|
0
|
0 |
|
1
|
1 |
|
2
|
0.289251871 |
|
3
|
-1.201858761 |
|
4
|
-0.916333354 |
|
5
|
0.0395527072 |
|
6
|
-0.347639895 |
|
7
|
0.448133104 |
|
8
|
-0.554303009 |
|
9
|
0.444464481 |
|
10
|
0.0114406946 |
|
11
|
-0.691450783 |
|
12
|
1.101303270 |
|
13
|
-0.802780003 |
|
14
|
0.129623339 |
|
15
|
-0.0475367677 |
|
16
|
0.756000172 |
|
17
|
-1.037675373 |
|
18
|
0.128562183 |
|
19
|
0.637178807 |
|
20
|
-0.0362434649 |
|
21
|
-0.538592697 |
|
22
|
-0.200003433 |
|
23
|
0.508798692 |
|
24
|
0.666193927 |
|
25
|
-0.998435583 |
|
26
|
-0.232205618 |
|
27
|
0.667675230 |
|
28
|
-0.410639311 |
|
29
|
0.779996881 |
|
30
|
-0.0137500990 |
|
31
|
-1.598013583 |
|
32
|
0.772977473 |
|
33
|
0.831026181 |
|
34
|
-0.300149543 |
|
35
|
0.0177248775 |
|
36
|
-0.407277629 |
|
37
|
-0.429215160 |
|
38
|
0.184305162 |
|
39
|
0.964828180 |
|
40
|
-0.0219241846 |
|
41
|
-0.548524187 |
|
42
|
-0.155788945 |
|
43
|
-0.489355022 |
|
44
|
0.633599416 |
|
45
|
0.0175797734 |
|
46
|
0.147170974 |
|
47
|
0.816868005 |
|
48
|
-0.908605430 |
|
49
|
-0.799176720 |
|
50
|
-0.288799360 |
|
51
|
1.247139238 |
|
52
|
0.735614092 |
|
53
|
-0.978756047 |
|
54
|
0.193126313 |
|
55
|
-0.0273487635 |
|
56
|
-0.248401523 |
|
57
|
-0.765798931 |
|
58
|
0.225615557 |
|
59
|
1.342931384 |
|
60
|
0.0435595258 |
|
61
|
-0.451739345 |
|
62
|
-0.462228419 |
|
63
|
0.199179247 |
|
64
|
-0.532414991 |
|
65
|
-0.0317521224 |
|
66
|
0.240375878 |
|
67
|
0.407059646 |
|
68
|
0.950856556 |
|
69
|
-0.611504166 |
|
70
|
0.00512695399 |
|
71
|
-1.218362389 |
|
72
|
-0.246367999 |
|
73
|
0.847623229 |
|
74
|
-0.124151288 |
|
75
|
1.199978553 |
|
76
|
-0.583868194 |
|
77
|
-0.309861986 |
|
78
|
0.279078356 |
|
79
|
-0.152197859 |
|
80
|
0.0299018535 |
|
81
|
-1.246915806 |
|
82
|
-0.158661647 |
|
83
|
1.512681485 |
|
84
|
0.493530453 |
|
85
|
-0.0410428702 |
|
86
|
-0.141546855 |
|
87
|
-0.937446085 |
|
88
|
0.383273250 |
|
89
|
-0.351411890 |
|
90
|
0.00508498046 |
|
91
|
-0.359752294 |
|
92
|
-0.466229211 |
|
93
|
1.920586624 |
|
94
|
0.236280600 |
|
95
|
0.0252021467 |
|
96
|
-0.929009751 |
|
97
|
-0.434877624 |
|
98
|
-0.231163364 |
|
99
|
-0.307325314 |
|
100
|
0.914899827 |
|
101
|
-0.428540668 |
|
102
|
0.360737358 |
|
103
|
0.136140070 |
|
104
|
0.444983371 |
|
105
|
-0.0213027993 |
|
106
|
-0.283107018 |
|
107
|
0.318195539 |
|
108
|
-0.611813083 |
|
109
|
-1.051614670 |
|
110
|
-0.00791067726 |
|
111
|
0.515856001 |
|
112
|
0.338788704 |
|
113
|
1.230036743 |
|
114
|
-0.221508774 |
|
115
|
0.0201243657 |
|
116
|
-0.714737158 |
|
117
|
-0.356807197 |
|
118
|
0.388445416 |
|
119
|
-0.465016686 |
|
120
|
0.0263497735 |
|
121
|
-0.521895814 |
|
122
|
-0.130666451 |
|
123
|
0.659248600 |
|
124
|
1.464313148 |
|
125
|
-0.0790435381 |
|
126
|
0.0576129708 |
|
127
|
-1.036459334 |
|
128
|
-0.926979506 |
|
129
|
0.588135621 |
|
130
|
-0.00918436151 |
|
131
|
0.314430908 |
|
132
|
-0.761497011 |
|
133
|
0.285540917 |
|
134
|
0.117742765 |
|
135
|
0.0264083628 |
|
136
|
0.575186579 |
|
137
|
1.154299357 |
|
138
|
-0.176878723 |
|
139
|
-1.144207004 |
|
140
|
-0.0162419027 |
|
141
|
-0.981759969 |
|
142
|
-0.352413601 |
|
143
|
0.555082862 |
|
144
|
0.336015224 |
|
145
|
0.0308509881 |
|
146
|
0.245176605 |
|
147
|
0.960497543 |
|
148
|
0.393304168 |
|
149
|
-1.414908027 |
|
150
|
0.347096042 |
|
151
|
0.208857471 |
|
152
|
-0.353190130 |
|
153
|
-0.461209847 |
|
154
|
-0.0896281587 |
|
155
|
-0.0632057634 |
|
156
|
-0.884104243 |
|
157
|
1.143195921 |
|
158
|
-0.0440235158 |
|
159
|
1.176326530 |
|
160
|
0.0305733517 |
|
161
|
0.228009537 |
|
162
|
-0.360672730 |
|
163
|
-1.433929039 |
|
164
|
0.502631011 |
|
165
|
0.0328693343 |
|
166
|
0.437545951 |
|
167
|
-1.044990120 |
|
168
|
0.298543554 |
|
169
|
-0.355544269 |
|
170
|
-0.0118717318 |
|
171
|
0.283203350 |
|
172
|
0.448412325 |
|
173
|
1.904636093 |
|
174
|
-0.271158041 |
|
175
|
-0.447432045 |
|
176
|
-0.522736891 |
|
177
|
-1.614013848 |
|
178
|
-0.101646547 |
|
179
|
0.537915463 |
|
180
|
-0.0161089329 |
|
181
|
0.336326778 |
|
182
|
-0.104059024 |
|
183
|
0.542926890 |
|
184
|
-0.282028646 |
|
185
|
-0.0169766218 |
|
186
|
0.555533275 |
|
187
|
0.717501450 |
|
188
|
-0.748523400 |
|
189
|
0.299207373 |
|
190
|
0.00728976686 |
|
191
|
-1.254886027 |
|
192
|
0.639887621 |
|
193
|
-1.044430269 |
|
194
|
-0.125789168 |
|
195
|
0.0381615664 |
|
196
|
0.732312286 |
|
197
|
0.354186207 |
|
198
|
-0.0888944213 |
|
199
|
0.618998534 |
|
200
|
0.553435848 |
|
201
|
-0.489228206 |
|
202
|
-0.123956192 |
|
203
|
0.349542424 |
|
204
|
-1.142795285 |
|
205
|
-0.0216956107 |
|
206
|
0.0393787745 |
|
207
|
0.226142940 |
|
208
|
-0.606901822 |
|
209
|
-0.440577785 |
|
210
|
-0.00616187657 |
|
211
|
0.0232932731 |
|
212
|
0.896866804 |
|
213
|
1.464299511 |
|
214
|
0.0920386548 |
|
215
|
-0.0193553153 |
|
216
|
-0.370094389 |
|
217
|
-0.716122788 |
|
218
|
-0.304181511 |
|
219
|
-1.018723404 |
|
220
|
0.0250605738 |
|
221
|
0.833025039 |
|
222
|
0.149212314 |
|
223
|
-0.354326068 |
|
224
|
0.346396793 |
|
225
|
-0.443769151 |
|
226
|
0.355790429 |
|
227
|
-0.998837987 |
|
228
|
0.701727103 |
|
229
|
1.637393927 |
|
230
|
0.00582100961 |
|
231
|
0.372410344 |
|
232
|
-0.432354620 |
|
233
|
-1.210009705 |
|
234
|
-0.103207147 |
|
235
|
0.0323093414 |
|
236
|
-1.230572825 |
|
237
|
0.182920325 |
|
238
|
-0.134506933 |
|
239
|
1.433407802 |
|
240
|
-0.0359378046 |
|
241
|
-0.358208763 |
|
242
|
-0.150959333 |
|
243
|
0.830941447 |
|
244
|
0.413943829 |
|
245
|
-0.0316095880 |
|
246
|
0.190688891 |
|
247
|
-0.511514404 |
|
248
|
0.885783736 |
|
249
|
-1.818029495 |
|
250
|
-0.0228634909 |
|
251
|
0.140754032 |
|
252
|
-0.182514589 |
|
253
|
-0.351809253 |
|
254
|
-0.299797801 |
|
255
|
0.0493277325 |
|
256
|
0.264284433 |
|
257
|
1.521660531 |
|
258
|
0.170119329 |
|
259
|
-0.192345526 |
|
260
|
0.0290955281 |
|
261
|
0.346680909 |
|
262
|
0.0909497321 |
|
263
|
-0.957417253 |
|
264
|
-0.460640307 |
|
265
|
-0.0387124565 |
|
266
|
0.0825932501 |
|
267
|
0.422347462 |
|
268
|
-0.373002330 |
|
269
|
-0.209315948 |
|
270
|
0.00763865039 |
|
271
|
-0.119245916 |
|
272
|
-0.784482753 |
|
273
|
0.432371453 |
|
274
|
0.333883238 |
|
275
|
0.690369065 |
|
276
|
0.560341665 |
|
277
|
1.490381238 |
|
278
|
-0.330964015 |
|
279
|
-0.710260278 |
|
280
|
-0.00982495248 |
|
281
|
-1.779211530 |
|
282
|
-0.283975910 |
|
283
|
-0.683180752 |
|
284
|
1.116426094 |
|
285
|
-0.0302894207 |
|
286
|
0.160558759 |
|
287
|
-0.245811850 |
|
288
|
0.343561026 |
|
289
|
0.0767701823 |
|
290
|
0.00892370200 |
|
291
|
0.522661490 |
|
292
|
-0.776705434 |
|
293
|
1.153046776 |
|
294
|
0.277825710 |
|
295
|
0.0531165709 |
|
296
|
0.237915251 |
|
297
|
-0.461664554 |
|
298
|
-0.409264788 |
|
299
|
-0.408453415 |
|
300
|
-1.099580365 |
|
301
|
-0.219296204 |
|
302
|
0.0604124401 |
|
303
|
0.515045342 |
|
304
|
0.481707294 |
|
305
|
-0.0178675145 |
|
306
|
-0.133405811 |
|
307
|
0.490159654 |
|
308
|
0.283936873 |
|
309
|
-0.163621134 |
|
310
|
-0.0182823852 |
|
311
|
1.090177349 |
|
312
|
-0.534807164 |
|
313
|
-0.464620530 |
|
314
|
0.330671559 |
|
315
|
0.00787807701 |
|
316
|
0.139463974 |
|
317
|
-1.251819433 |
|
318
|
0.340254653 |
|
319
|
-0.539329451 |
|
320
|
-0.0210584588 |
|
321
|
-0.382426089 |
|
322
|
0.0659521803 |
|
323
|
-0.661184767 |
|
324
|
1.142590549 |
|
325
|
0.801524113 |
|
326
|
-0.414766651 |
|
327
|
1.263892317 |
|
328
|
0.304048600 |
|
329
|
0.366065596 |
|
330
|
0.00950750563 |
|
331
|
-0.716097552 |
|
332
|
-1.386120479 |
|
333
|
-0.190770915 |
|
334
|
-0.302265353 |
|
335
|
0.0161003095 |
|
336
|
-0.407176179 |
|
337
|
1.672811235 |
|
338
|
-0.102841844 |
|
339
|
-1.478330436 |
|
340
|
0.0376089511 |
|
341
|
1.104947744 |
|
342
|
0.0819170967 |
|
343
|
-0.806270649 |
|
344
|
0.271250961 |
|
345
|
-0.0241866454 |
|
346
|
0.550919550 |
|
347
|
1.292517720 |
|
348
|
0.859013113 |
|
349
|
-0.992972179 |
|
350
|
-0.129420556 |
|
351
|
-0.535996327 |
|
352
|
-0.534475878 |
|
353
|
-0.841434800 |
|
354
|
-0.466856527 |
|
355
|
-0.0481895306 |
|
356
|
0.322010437 |
|
357
|
0.558884378 |
|
358
|
0.155593058 |
|
359
|
0.199941682 |
|
360
|
-0.00974451440 |
|
361
|
-0.594003178 |
|
362
|
0.0972831618 |
|
363
|
0.627245061 |
|
364
|
0.329653007 |
|
365
|
0.0335258019 |
|
366
|
0.157042624 |
|
367
|
0.495808551 |
|
368
|
0.384651895 |
|
369
|
-0.243799497 |
|
370
|
-0.00491053342 |
|
371
|
-0.438612992 |
|
372
|
-1.759897567 |
|
373
|
-0.0346719904 |
|
374
|
0.207538635 |
|
375
|
0.0949991707 |
|
376
|
-0.452792395 |
|
377
|
-0.626165899 |
|
378
|
0.0865462926 |
|
379
|
1.731918080 |
|
380
|
-0.0230935692 |
|
381
|
1.245677730 |
|
382
|
-0.362978131 |
|
383
|
-0.960394592 |
|
384
|
1.114098438 |
|
385
|
-0.0122558788 |
|
386
|
-0.302103411 |
|
387
|
-0.217500927 |
|
388
|
0.398492875 |
|
389
|
-0.902617736 |
|
390
|
0.0110383027 |
|
391
|
-0.527967869 |
|
392
|
0.442986060 |
|
393
|
-0.377901541 |
|
394
|
0.102449025 |
|
395
|
-0.00601983777 |
|
396
|
0.281612445 |
|
397
|
-0.795400395 |
|
398
|
0.179046491 |
|
399
|
-0.343179858 |
|
400
|
-0.754817466 |
|
401
|
1.659325614 |
|
402
|
-0.141510172 |
|
403
|
1.282853347 |
|
404
|
0.392686111 |
|
405
|
-0.0493188879 |
|
406
|
0.101105797 |
|
407
|
0.296781165 |
|
408
|
-0.691293050 |
|
409
|
-0.824874134 |
|
410
|
-0.00627551312 |
|
411
|
-1.387304761 |
|
412
|
-0.124749696 |
|
413
|
0.601812022 |
|
414
|
0.0654122793 |
|
415
|
0.0598306376 |
|
416
|
-0.620530857 |
|
417
|
1.375175214 |
|
418
|
-0.127437948 |
|
419
|
-0.792174988 |
|
420
|
0.0195204678 |
|
421
|
0.215639198 |
|
422
|
0.00673762055 |
|
423
|
0.363068816 |
|
424
|
0.542527420 |
|
425
|
1.036052018 |
|
426
|
0.423551375 |
|
427
|
-0.202439350 |
|
428
|
-0.291573189 |
|
429
|
-0.667131197 |
|
430
|
-0.00559856135 |
|
431
|
-1.260010329 |
|
432
|
0.504762587 |
|
433
|
-1.481134828 |
|
434
|
-0.207139851 |
|
435
|
-0.0370785326 |
|
436
|
0.963629591 |
|
437
|
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447
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497
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498
|
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499
|
1.298984105 |
