Properties

Level 1
Symmetry even
Weight 0
Character \( \chi_{1}(1,\cdot) \)
Multiplicity 1
Precision 6e-15
Fricke Eigenvalue undefined
Atkin-Lehner Eigenvalues 1

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Spectral parameter

$R= 13.7797513519$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 1.549304477
3 0.246899772
4 1.400344365
5 0.737060385
6 0.382522923
7 -0.261420075
8 0.620255318
9 -0.939040502
10 1.141930961
11 -0.953564652
12 0.345744705
13 0.278827029
14 -0.405019294
15 0.181980041
16 -0.439380023
17 1.307341714
18 -1.454859655
19 0.0925585825
20 1.032138357
21 -0.0645445572
22 -1.477361986
23 1.138068521
24 0.153140896
25 -0.456741988
26 0.431987964
27 -0.478748658
28 -0.366078130
29 0.752113845
30 0.281942493
31 0.0248519535
32 -1.300988756
33 -0.235434895
34 2.025470372
35 -0.192682381
36 -1.314980076
37 0.199265655
38 0.143401426
39 0.0688423300
40 0.457165623
41 -0.304032996
42 -0.0999991715
43 0.783239363
44 -1.335318888
45 -0.692129554
46 1.763214656
47 0.360568410
48 -0.108482827
49 -0.931659544
50 -0.707632407
51 0.322782371
52 0.390453859
53 1.398065718
54 -0.741727442
55 -0.702834728
56 -0.162147186
57 0.0228526929
58 1.165253348
59 -1.587730961
60 0.254834725
61 1.167275968
62 0.0385032428
63 0.245484039
64 -1.576247682
65 0.205512357
66 -0.364760338
67 -0.0270938862
68 1.830728603
69 0.280988858
70 -0.298523676
71 -1.633423858
72 -0.582444865
73 1.067847736
74 0.308723172
75 -0.112769492
76 0.129613889
77 0.249280943
78 0.106657730
79 -0.531173888
80 -0.323849609
81 0.820837567
82 -0.471039683
83 -0.904532379
84 -0.0903846070
85 0.963589787
86 1.213476252
87 0.185696737
88 -0.591453546
89 -1.067353171
90 -1.072319417
91 -0.0728909849
92 1.593687841
93 0.00613594290
94 0.558630251
95 0.0682212660
96 -0.321213823
97 -0.00325711706
98 -1.443424306
99 0.895435828
100 -0.639596071
101 0.864185296
102 0.500088174
103 -1.231844841
104 0.172943947
105 -0.0475732362
106 2.166029479
107 -0.812652045
108 -0.670412986
109 -0.153741680
110 -1.088904994
111 0.0491986450
112 0.114862759
113 0.811772544
114 0.0354057795
115 0.838825222
116 1.053218385
117 -0.261829873
118 -2.459878688
119 -0.341765369
120 0.112874088
121 -0.0907144531
122 1.808465885
123 -0.0750656770
124 0.0348012928
125 -1.073706811
126 0.380329520
127 1.169661030
128 -1.141098835
129 0.193381619
130 0.318401215
131 -0.611125873
132 -0.329689930
133 -0.0241966697
134 -0.0419766788
135 -0.352866673
136 0.810885651
137 0.771802674
138 0.435337298
139 0.0953561695
140 -0.269821682
141 0.0890242652
142 -2.530670897
143 -0.265879599
144 0.412595638
145 0.554353320
146 1.654421280
147 -0.230026529
148 0.279040537
149 -0.186967522
150 -0.174714280
151 -0.283609628
152 0.0574099530
153 -1.227646820
154 0.386212082
155 0.0183173904
156 0.0964029691
157 1.146454208
158 -0.822950084
159 0.345182106
160 -0.958907273
161 -0.297513959
162 1.271727318
163 1.503612982
164 -0.425750895
165 -0.173529731
166 -1.401396068
167 -0.724341129
168 -0.0400341032
169 -0.922255489
170 1.492893970
171 -0.0869162587
172 1.096804834
173 0.0377358338
174 0.287700779
175 0.119401526
176 0.418977260
177 -0.392010409
178 -1.653655031
179 -0.592479080
180 -0.969219722
181 1.892818855
182 -0.112930326
183 0.288200170
184 0.705893052
185 0.146870821
186 0.00950644207
187 -1.246634847
188 0.504919941
189 0.125154510
190 0.105695510
191 0.454923599
192 -0.389175193
193 -0.351065362
194 -0.00504626321
195 0.0507409537
196 -1.304644190
197 -0.493490010
198 1.387302741
199 0.761559327
200 -0.283296647
201 -0.00668947162
202 1.338886148
203 -0.196617661
204 0.452006477
205 -0.224090677
206 -1.908502733
207 -1.068692435
208 -0.122511026
209 -0.0882605901
210 -0.0737054366
211 1.633495547
212 1.957773458
213 -0.403291973
214 -1.259045439
215 0.577294687
216 -0.296946401
217 -0.00649679940
218 -0.238192675
219 0.263651364
220 -0.984210654
221 0.364522206
222 0.0762236815
223 -0.889835255
224 0.340104581
225 0.428899222
226 1.257682838
227 -1.117022838
228 0.0320016407
229 -1.123129434
230 1.299595671
231 0.0615474090
232 0.466502606
233 1.131828876
234 -0.405654195
235 0.265760691
236 -2.223370105
237 -0.131146711
238 -0.529498613
239 -0.611250250
240 -0.0799583959
241 1.616881847
242 -0.140544311
243 0.681413276
244 1.634588326
245 -0.686689345
246 -0.116299608
247 0.0258078292
248 0.0154145608
249 -0.223328849
250 -1.663498770
251 -0.439756562
252 0.343762192
253 -1.085221914
254 1.812161073
255 0.237910102
256 -0.191661853
257 0.378139948
258 0.299607010
259 -0.0520920446
260 0.287788074
261 -0.706265362
262 -0.946820053
263 1.027402009
264 -0.146029749
265 1.030458859
266 -0.0374880121
267 -0.263529248
268 -0.0379407683
269 -1.481531880
270 -0.546697917
271 0.504065533
272 -0.574419820
273 -0.0179967660
274 1.195757326
275 0.435533016
276 0.393481165
277 0.0799184256
278 0.147735774
279 -0.0233369780
280 -0.119512272
281 1.266155550
282 0.137925683
283 -1.613726541
284 -2.287355896
285 0.0168438156
286 -0.411928454
287 0.0794803233
288 1.221681136
289 0.709142359
290 0.858862078
291 -0.000804182681
292 1.495354562
293 -0.996264515
294 -0.356381138
295 -1.170253594
296 0.123595577
297 0.456517794
298 -0.289669616
299 0.317324266
300 -0.157916106
301 -0.204754511
302 -0.439397669
303 0.213367156
304 -0.0406683966
305 0.860352873
306 -1.901998712
307 1.124432662
308 0.349079139
309 -0.304142200
310 0.0283792153
311 -0.00399673211
312 0.0426998237
313 0.478964510
314 1.776206637
315 0.180936560
316 -0.743826361
317 -1.583557030
318 0.534792183
319 -0.717189176
320 -1.161789726
321 -0.200643604
322 -0.460939709
323 0.121005698
324 1.149455267
325 -0.127352018
326 2.329554331
327 -0.0379587878
328 -0.188578088
329 -0.0942598231
330 -0.268850394
331 1.115206237
332 -1.266656811
333 -0.187118539
334 -1.122224955
335 -0.0199698226
336 0.0283595711
337 0.439003183
338 -1.428854552
339 0.200426447
340 1.349357549
341 -0.0236979707
342 -0.134659714
343 0.504974570
344 0.485808381
345 0.207105756
346 0.0584642935
347 -1.431567590
348 0.260039379
349 -0.350135308
350 0.184989318
351 -0.133488066
352 1.240576889
353 1.762560582
354 -0.607343487
355 -1.203932020
356 -1.494662001
357 -0.0843817938
358 -0.917930479
359 0.532518498
360 -0.429297036
361 -0.991432913
362 2.932552736
363 -0.0223973860
364 -0.102072479
365 0.787068264
366 0.446509812
367 -0.00334167972
368 -0.500044586
369 0.285499321
370 0.227547615
371 -0.365482437
372 0.00859243128
373 -0.987646262
374 -1.931416941
375 -0.265097990
376 0.223644487
377 0.209709670
378 0.193902451
379 1.593305018
380 0.0955332828
381 0.288789043
382 0.704815172
383 0.0502016858
384 -0.281737043
385 0.183735107
386 -0.543907138
387 -0.735493490
388 -0.00456108180
389 -0.327358995
390 0.0786131878
391 1.487844454
392 -0.577866787
393 -0.150886837
394 -0.764566281
395 -0.391507227
396 1.253918518
397 -1.893151273
398 1.179887269
399 -0.00597414794
400 0.200683303
401 -0.812603436
402 -0.0103640325
403 0.00692939108
404 1.210157016
405 0.605006850
406 -0.304620622
407 -0.190012695
408 0.200207480
409 1.475395940
410 -0.347184677
411 0.190557906
412 -1.725006973
413 0.415064753
414 -1.655729975
415 -0.666694996
416 -0.362750851
417 0.0235434228
418 -0.136742524
419 0.739679660
420 -0.0666189182
421 0.879251406
422 2.530781966
423 -0.338588340
424 0.867157698
425 -0.597117853
426 -0.624822070
427 -0.305149370
428 -1.137992713
429 -0.0656456133
430 0.894405275
431 -1.208366785
432 0.210352597
433 -0.157137548
434 -0.0100655189
435 0.136869711
436 -0.215291300
437 0.105338011
438 0.408476232
439 -0.602099033
440 -0.435936979
441 0.874866047
442 0.564755887
443 1.013229818
444 0.0688950462
445 -0.786703748
446 -1.378625731
447 -0.0461622403
448 0.412062802
449 0.446168311
450 0.664495496
451 0.289915118
452 1.136761105
453 -0.0700231466
454 -1.730608498
455 -0.0537250406
456 0.0141745024
457 -0.708176045
458 -1.740069465
459 -0.625888092
460 1.174644164
461 0.330080932
462 0.0953556572
463 1.272649229
464 -0.330463784
465 0.00452255556
466 1.753547560
467 0.148114658
468 -0.366651967
469 0.00708288704
470 0.411744228
471 0.283059283
472 -0.984798573
473 -0.746869370
474 -0.203186190
475 -0.0422753909
476 -0.478589207
477 -1.312840335
478 -0.947012748
479 1.148279194
480 -0.236753986
481 0.0555606467
482 2.505042291
483 -0.0734561267
484 -0.127031471
485 -0.00240068832
486 1.055716626
487 -1.138192956
488 0.724009123
489 0.371241704
490 -1.063890873
491 -1.488741870
492 -0.105117799
493 0.983269800
494 0.0399841987
495 0.659990269
496 -0.0109194377
497 0.427009791
498 -0.346004368
499 0.435917006