Properties

Level 1
Symmetry odd
Weight 0
Character \( \chi_{1}(1,\cdot) \)
Multiplicity 1
Precision 2e-13
Fricke Eigenvalue undefined
Atkin-Lehner Eigenvalues 1

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Spectral parameter

$R= 9.53369526135$

The first few Fourier Coefficients

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