↑
| Level |
3 |
| Symmetry |
even |
| Weight |
0 |
| Character |
\( \chi_{3}(1,\cdot) \) |
| Multiplicity |
1 |
| Precision |
5e-12 |
| Fricke Eigenvalue |
1 |
| Atkin-Lehner Eigenvalues |
1,1 |
$R= 5.09874190873$
| n | c(n) |
|
0
|
0 |
|
1
|
1 |
|
2
|
1.342406731 |
|
3
|
-0.577350269 |
|
4
|
0.802055834 |
|
5
|
-0.0624853167 |
|
6
|
-0.775038885 |
|
7
|
0.753838133 |
|
8
|
-0.265721491 |
|
9
|
0.333332814 |
|
10
|
-0.0838776769 |
|
11
|
-0.408349071 |
|
12
|
-0.463067151 |
|
13
|
0.527645078 |
|
14
|
1.011957405 |
|
15
|
0.0360759141 |
|
16
|
-1.158762273 |
|
17
|
-0.967583197 |
|
18
|
0.447468910 |
|
19
|
1.560205624 |
|
20
|
-0.0501167124 |
|
21
|
-0.435228657 |
|
22
|
-0.548146758 |
|
23
|
0.285124949 |
|
24
|
0.153414426 |
|
25
|
-0.996095585 |
|
26
|
0.708314305 |
|
27
|
-0.192450089 |
|
28
|
0.604620284 |
|
29
|
-0.216424251 |
|
30
|
0.0484285500 |
|
31
|
1.154221603 |
|
32
|
-1.289808695 |
|
33
|
0.235750217 |
|
34
|
-1.298890198 |
|
35
|
-0.0471038150 |
|
36
|
0.267351944 |
|
37
|
0.254344444 |
|
38
|
2.094430534 |
|
39
|
-0.304636027 |
|
40
|
0.0166036970 |
|
41
|
-1.105075659 |
|
42
|
-0.584253881 |
|
43
|
-0.126149776 |
|
44
|
-0.327504541 |
|
45
|
-0.0208284407 |
|
46
|
0.382753645 |
|
47
|
1.008106189 |
|
48
|
0.669011723 |
|
49
|
-0.431728034 |
|
50
|
-1.337165440 |
|
51
|
0.558634401 |
|
52
|
0.423200841 |
|
53
|
0.247646995 |
|
54
|
-0.258346252 |
|
55
|
0.0255146117 |
|
56
|
-0.200311064 |
|
57
|
-0.900785137 |
|
58
|
-0.290529372 |
|
59
|
0.0689514842 |
|
60
|
0.0289348976 |
|
61
|
0.485289996 |
|
62
|
1.549434850 |
|
63
|
0.251279382 |
|
64
|
-0.572685602 |
|
65
|
-0.0329700686 |
|
66
|
0.316472679 |
|
67
|
-0.692441699 |
|
68
|
-0.776055750 |
|
69
|
-0.164616966 |
|
70
|
-0.0632324762 |
|
71
|
-1.106816140 |
|
72
|
-0.0885738618 |
|
73
|
1.507834831 |
|
74
|
0.341433698 |
|
75
|
0.575096056 |
|
76
|
1.251372019 |
|
77
|
-0.307815754 |
|
78
|
-0.408945455 |
|
79
|
-1.278016269 |
|
80
|
0.0724056223 |
|
81
|
0.111111099 |
|
82
|
-1.483461002 |
|
83
|
1.611629487 |
|
84
|
-0.349077669 |
|
85
|
0.0604596848 |
|
86
|
-0.169344399 |
|
87
|
0.124952628 |
|
88
|
0.108502588 |
|
89
|
-0.414761438 |
|
90
|
-0.0279604065 |
|
91
|
0.397758953 |
|
92
|
0.228686240 |
|
93
|
-0.666389909 |
|
94
|
1.353290009 |
|
95
|
-0.0974895890 |
|
96
|
0.744671392 |
|
97
|
-0.0802764464 |
|
98
|
-0.579554644 |
|
99
|
-0.136110442 |
|
100
|
-0.798924279 |
|
101
|
-1.225551630 |
|
102
|
0.749914614 |
|
103
|
-0.951498165 |
|
104
|
-0.140206665 |
|
105
|
0.0271953784 |
|
106
|
0.332442913 |
|
107
|
1.925346998 |
|
108
|
-0.154355727 |
|
109
|
1.398246600 |
|
110
|
0.0342510829 |
|
111
|
-0.146845784 |
|
112
|
-0.873519252 |
|
113
|
0.139699984 |
|
114
|
-1.209220031 |
|
115
|
-0.0178161729 |
|
116
|
-0.173584240 |
|
117
|
0.175881580 |
|
118
|
0.0925610361 |
|
119
|
-0.729401174 |
|
120
|
-0.00958607257 |
|
121
|
-0.833265497 |
|
122
|
0.651456386 |
|
123
|
0.638015997 |
|
124
|
0.925750117 |
|
125
|
0.124727211 |
|
126
|
0.337319072 |
|
127
|
-0.806325713 |
|
128
|
0.521031907 |
|
129
|
0.0728330343 |
|
130
|
-0.0442611053 |
|
131
|
-1.093897488 |
|
132
|
0.189085103 |
|
133
|
1.176142515 |
|
134
|
-0.929538412 |
|
135
|
0.0120253086 |
|
136
|
0.257107712 |
|
137
|
-0.0796738031 |
|
138
|
-0.220982932 |
|
139
|
0.516707932 |
|
140
|
-0.0377798934 |
|
141
|
-0.582030405 |
|
142
|
-1.485797428 |
|
143
|
-0.215454088 |
|
144
|
-0.386254047 |
|
145
|
0.0135233459 |
|
146
|
2.024127691 |
|
147
|
0.249258339 |
|
148
|
0.203998458 |
|
149
|
1.206022461 |
|
150
|
0.772012753 |
|
151
|
-0.297011115 |
|
152
|
-0.414580356 |
|
153
|
-0.322527720 |
|
154
|
-0.413213973 |
|
155
|
-0.0721216344 |
|
156
|
-0.244334957 |
|
157
|
-0.435163360 |
|
158
|
-1.715617583 |
|
159
|
-0.142978959 |
|
160
|
0.0805929616 |
|
161
|
0.214937794 |
|
162
|
0.149156281 |
|
163
|
0.772708312 |
|
164
|
-0.886331232 |
|
165
|
-0.0147309340 |
|
166
|
2.163462278 |
|
167
|
0.710903524 |
|
168
|
0.115649676 |
|
169
|
-0.721590667 |
|
170
|
0.0811614830 |
|
171
|
0.520068466 |
|
172
|
-0.101179212 |
|
173
|
-1.148051509 |
|
174
|
0.167737338 |
|
175
|
-0.750894758 |
|
176
|
0.473159038 |
|
177
|
-0.0398092422 |
|
178
|
-0.556778528 |
|
179
|
0.820122827 |
|
180
|
-0.0167056522 |
|
181
|
-0.796799267 |
|
182
|
0.533954595 |
|
183
|
-0.280182061 |
|
184
|
-0.0757638851 |
|
185
|
-0.0158929185 |
|
186
|
-0.894566999 |
|
187
|
0.395094298 |
|
188
|
0.808557562 |
|
189
|
-0.145075914 |
|
190
|
-0.130870375 |
|
191
|
-0.869847100 |
|
192
|
0.330639856 |
|
193
|
1.902885263 |
|
194
|
-0.107763794 |
|
195
|
0.0190352266 |
|
196
|
-0.346269940 |
|
197
|
0.177586448 |
|
198
|
-0.182715419 |
|
199
|
0.588553095 |
|
200
|
0.264683977 |
|
201
|
0.399781146 |
|
202
|
-1.645188966 |
|
203
|
-0.163148865 |
|
204
|
0.448056195 |
|
205
|
0.0690514060 |
|
206
|
-1.277297281 |
|
207
|
0.0950416441 |
|
208
|
-0.611415755 |
|
209
|
-0.637081321 |
|
210
|
0.0365070601 |
|
211
|
-1.128067857 |
|
212
|
0.198627360 |
|
213
|
0.639021056 |
|
214
|
2.584599070 |
|
215
|
0.00788227218 |
|
216
|
0.0511374893 |
|
217
|
0.870095585 |
|
218
|
1.877015575 |
|
219
|
-0.870548213 |
|
220
|
0.0204642247 |
|
221
|
-0.510540447 |
|
222
|
-0.197126837 |
|
223
|
-1.076530856 |
|
224
|
-0.972307060 |
|
225
|
-0.332031938 |
|
226
|
0.187534148 |
|
227
|
0.784357915 |
|
228
|
-0.722479985 |
|
229
|
-1.027329122 |
|
230
|
-0.0239165777 |
|
231
|
0.177717326 |
|
232
|
0.0575085118 |
|
233
|
0.836205668 |
|
234
|
0.236105013 |
|
235
|
-0.0629915889 |
|
236
|
0.0553031008 |
|
237
|
0.737863386 |
|
238
|
-0.979152782 |
|
239
|
0.653409812 |
|
240
|
-0.0418031861 |
|
241
|
0.397367376 |
|
242
|
-1.118581185 |
|
243
|
-0.0641499920 |
|
244
|
0.389229673 |
|
245
|
0.0269766149 |
|
246
|
0.856476578 |
|
247
|
0.823234871 |
|
248
|
-0.306701614 |
|
249
|
-0.930474719 |
|
250
|
0.167433993 |
|
251
|
0.439771749 |
|
252
|
0.201539963 |
|
253
|
-0.116425537 |
|
254
|
-1.082417335 |
|
255
|
-0.0349064390 |
|
256
|
1.272122046 |
|
257
|
-1.197697596 |
|
258
|
0.0977710748 |
|
259
|
0.191734432 |
|
260
|
-0.0264442492 |
|
261
|
-0.0721414725 |
|
262
|
-1.468452592 |
|
263
|
-1.228125242 |
|
264
|
-0.0626439713 |
|
265
|
-0.0154745934 |
|
266
|
1.578861747 |
|
267
|
0.239462228 |
|
268
|
-0.555376031 |
|
269
|
1.697438032 |
|
270
|
0.0161428844 |
|
271
|
0.408358648 |
|
272
|
1.121198857 |
|
273
|
-0.229646237 |
|
274
|
-0.106954643 |
|
275
|
0.406737000 |
|
276
|
-0.132032022 |
|
277
|
-0.989424487 |
|
278
|
0.693632188 |
|
279
|
0.384740488 |
|
280
|
0.0125165057 |
|
281
|
-1.342783165 |
|
282
|
-0.781321578 |
|
283
|
0.477636027 |
|
284
|
-0.887728410 |
|
285
|
0.0562859485 |
|
286
|
-0.289227002 |
|
287
|
-0.833048133 |
|
288
|
-0.429936081 |
|
289
|
-0.0637826867 |
|
290
|
0.0181535752 |
|
291
|
0.0463475694 |
|
292
|
1.209367820 |
|
293
|
0.442779999 |
|
294
|
0.334605953 |
|
295
|
-0.00430805953 |
|
296
|
-0.0675843505 |
|
297
|
0.0785831676 |
|
298
|
1.618972857 |
|
299
|
0.150444910 |
|
300
|
0.461259179 |
|
301
|
-0.0950966759 |
|
302
|
-0.398709968 |
|
303
|
0.707572687 |
|
304
|
-1.807907539 |
|
305
|
-0.0303236409 |
|
306
|
-0.432963237 |
|
307
|
-0.581760437 |
|
308
|
-0.246885557 |
|
309
|
0.549347718 |
|
310
|
-0.0968166824 |
|
311
|
-0.189702832 |
|
312
|
0.0809480215 |
|
313
|
1.237173273 |
|
314
|
-0.584165416 |
|
315
|
-0.0157014424 |
|
316
|
-1.025040611 |
|
317
|
1.623571511 |
|
318
|
-0.191935726 |
|
319
|
0.0883723971 |
|
320
|
0.0357844068 |
|
321
|
-1.111599227 |
|
322
|
0.288534120 |
|
323
|
-1.509629287 |
|
324
|
0.0891174814 |
|
325
|
-0.525584648 |
|
326
|
1.037293058 |
|
327
|
-0.807278664 |
|
328
|
0.293643065 |
|
329
|
0.759949681 |
|
330
|
-0.0197753749 |
|
331
|
0.394459783 |
|
332
|
1.292616850 |
|
333
|
0.0847813790 |
|
334
|
0.954321501 |
|
335
|
0.0432674921 |
|
336
|
0.504326579 |
|
337
|
-0.128547995 |
|
338
|
-0.968668167 |
|
339
|
-0.0806556374 |
|
340
|
0.0484921089 |
|
341
|
-0.471305002 |
|
342
|
0.698143536 |
|
343
|
-1.079291165 |
|
344
|
0.0335205531 |
|
345
|
0.0102860306 |
|
346
|
-1.541152045 |
|
347
|
0.226857659 |
|
348
|
0.100218809 |
|
349
|
-0.225472255 |
|
350
|
-1.008005908 |
|
351
|
-0.101545365 |
|
352
|
0.526669082 |
|
353
|
-0.471510224 |
|
354
|
-0.0534400007 |
|
355
|
0.0691594967 |
|
356
|
-0.332661943 |
|
357
|
0.421120055 |
|
358
|
1.100939115 |
|
359
|
1.363390675 |
|
360
|
0.00553469345 |
|
361
|
1.434242177 |
|
362
|
-1.069628726 |
|
363
|
0.481086032 |
|
364
|
0.319024956 |
|
365
|
-0.0942172962 |
|
366
|
-0.376119096 |
|
367
|
0.784712794 |
|
368
|
-0.330391987 |
|
369
|
-0.368358465 |
|
370
|
-0.0213344110 |
|
371
|
0.186685802 |
|
372
|
-0.534482055 |
|
373
|
-1.748413726 |
|
374
|
0.530377450 |
|
375
|
-0.0720111435 |
|
376
|
-0.267875732 |
|
377
|
-0.114195260 |
|
378
|
-0.194751218 |
|
379
|
-0.367644992 |
|
380
|
-0.0781921460 |
|
381
|
0.465532744 |
|
382
|
-1.167688882 |
|
383
|
0.970787001 |
|
384
|
-0.300817941 |
|
385
|
0.0192336972 |
|
386
|
2.554446501 |
|
387
|
-0.0420501374 |
|
388
|
-0.0643863792 |
|
389
|
-1.803787843 |
|
390
|
0.0255532089 |
|
391
|
-0.275881756 |
|
392
|
0.114719485 |
|
393
|
0.631560936 |
|
394
|
0.238392956 |
|
395
|
0.0798569185 |
|
396
|
-0.109168568 |
|
397
|
0.000333383989 |
|
398
|
0.790077275 |
|
399
|
-0.679045935 |
|
400
|
1.154238042 |
|
401
|
-1.173383133 |
|
402
|
0.536669896 |
|
403
|
0.609019918 |
|
404
|
-0.982960355 |
|
405
|
-0.00694313917 |
|
406
|
-0.219012100 |
|
407
|
-0.103856771 |
|
408
|
-0.148441335 |
|
409
|
1.793048405 |
|
410
|
0.0926944571 |
|
411
|
0.0459996874 |
|
412
|
-0.763154555 |
|
413
|
0.0519781609 |
|
414
|
0.127584667 |
|
415
|
-0.100703223 |
|
416
|
-0.680561261 |
|
417
|
-0.298321350 |
|
418
|
-0.855221790 |
|
419
|
-0.933503818 |
|
420
|
0.0218123295 |
|
421
|
-0.583139464 |
|
422
|
-1.514325732 |
|
423
|
0.336035247 |
|
424
|
-0.0658050983 |
|
425
|
0.963805513 |
|
426
|
0.857825324 |
|
427
|
0.365830275 |
|
428
|
1.544235652 |
|
429
|
0.124392324 |
|
430
|
0.0105817090 |
|
431
|
0.573317536 |
|
432
|
0.223003975 |
|
433
|
-0.0523646822 |
|
434
|
1.168022842 |
|
435
|
-0.00780741321 |
|
436
|
1.121471650 |
|
437
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499
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