Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 5e-14
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1,0,0

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Spectral parameter

$R= 4.58236150313$

The first few Fourier Coefficients

n c(n)
0  0
1  1.0
2  0.7071067
3 -1.6631754
4  0.5
5 -0.4472135
6 -1.1760426
7 -1.1260064
8  0.3535533
9  1.7661526
10 -0.3162277
11 -0.4387835
12 -0.8315877
13  0.2247263
14 -0.7962068
15  0.7437946
16  0.25
17 -1.1292698
18  1.2488584
19 -0.3407921
20 -0.2236067
21  1.8727463
22 -0.3102668
23 -0.8395854
24 -0.5880213
25  0.2
26  0.1589054
27 -1.2742462
28 -0.5630032
29  1.2823499
30  0.5259422
31 -0.5121479
32  0.1767766
33  0.7297741
34 -0.7985143
35  0.5035653
36  0.8830763
37 -0.5968957
38 -0.2409764
39 -0.3737592
40 -0.1581138
41  0.4223083
42  1.3242316
43 -0.3726852
44 -0.2193917
45 -0.7898474
46 -0.5936765
47 -1.7165799
48 -0.4157938
49  0.2678905
50  0.1414213
51  1.8781738
52  0.1123631
53  1.9066831
54 -0.9010281
55  0.1962299
56 -0.3981034
57  0.5667971
58  0.9067583
59  0.1580893
60  0.3718973
61 -1.92731
62 -0.3621432
63 -1.9886992
64  0.125
65 -0.1005006
66  0.5160282
67 -0.2519683
68 -0.5646349
69  1.3963778
70  0.3560744
71  0.784884
72  0.6244292
73 -0.9154629
74 -0.422069
75 -0.3326352
76 -0.1703963
77  0.4940748
78 -0.2642876
79 -0.3025586
80 -0.1118033
81  0.3531424
82  0.2986171
83  1.6837347
84  0.9363731
85  0.5050248
86 -0.2635282
87 -2.1327729
88 -0.1551334
89 -0.0034998
90 -0.5585064
91 -0.2530432
92 -0.4197927
93  0.8517918
94 -1.2138053
95  0.1524068
96 -0.2940106
97  0.5619619
98  0.1894272
99 -0.7749587
100  0.1
101 -0.5963275
102  1.3280694
103  0.548698
104  0.0794528
105 -0.8375175
106  1.3482285
107  0.6094432
108 -0.6371232
109 -0.9316245
110  0.1387557
111  0.9927424
112 -0.2815018
113 -0.9385138
114  0.400789
115  0.3754716
116  0.6411709
117  0.3969009
118  0.111786
119  1.271565
120  0.2629711
121 -0.8074689
122 -1.362814
123 -0.7023729
124 -0.2560739
125 -0.0894427
126 -1.4062227
127 -0.0962762
128  0.0883883
129  0.6198408
130 -0.0710647
131 -1.4707648
132  0.364887
133  0.383734
134 -0.1781685
135  0.5698603
136 -0.3992571
137 -0.9125971
138  0.9873885
139  0.6556089
140  0.2517827
141  2.8549758
142  0.5549969
143 -0.0986061
144  0.4415389
145 -0.573484
146 -0.6473272
147 -0.4455514
148 -0.2984451
149  1.210277
150 -0.23521
151 -0.534354
152 -0.1204882
153 -1.9944628
154  0.3493624
155  0.2290395
156 -0.1868796
157  1.1442979
158 -0.2139412
159 -3.1711485
160 -0.0790569
161  0.9453788
162  0.2497096
163  0.7137533
164  0.2111542
165 -0.3263652
166  1.1905804
167  0.1923975
168  0.6621158
169 -0.9494979
170  0.3571056
171 -0.6018915
172 -0.1863423
173  0.4692536
174 -1.5080974
175 -0.2252045
176 -0.1096943
177 -0.2629261
178 -0.0024725
179  1.3420775
180 -0.3949263
181 -1.6637337
182 -0.1789286
183  3.2054547
184 -0.2968382
185  0.2669399
186  0.6023077
187  0.4955051
188 -0.8582899
189  1.4348094
190  0.1077679
191 -0.018876
192 -0.2078971
193 -0.3530214
194  0.3973671
195  0.16715
196  0.1339454
197 -0.2376212
198 -0.5479785
199 -1.7611127
200  0.0707103
201  0.4190684
202 -0.4216672
203 -1.443934
204  0.939087
205 -0.188861
206  0.3879881
207 -1.4828356
208  0.0561818
209  0.149534
210 -0.5922143
211  0.5840678
212  0.9533415
213 -1.3053997
214  0.4309414
215  0.1666698
216 -0.4505139
217  0.5766819
218 -0.6587581
219  1.5225753
220  0.0981149
221 -0.2537771
222  0.7019748
223  1.2095889
224 -0.199051
225  0.35323
226 -0.6636267
227 -0.4695116
228  0.2833987
229 -0.2152661
230  0.2655
231 -0.8217318
232  0.4533789
233 -1.3575874
234  0.2806513
235  0.7676778
236  0.0790446
237  0.5032081
238  0.8991322
239  1.1966667
240  0.1859486
241  0.9612512
242 -0.5709669
243  0.6869083
244 -0.9636551
245 -0.1198041
246 -0.4966525
247 -0.0765851
248 -0.1810716
249 -2.8003469
250 -0.0632463
251 -1.9346053
252 -0.9943491
253  0.3683952
254 -0.0680781
255 -0.8399433
256  0.0625005
257  1.2039944
258  0.4382938
259  0.6721085
260 -0.0502503
261  2.2648256
262 -1.0399875
263 -0.1432458
264  0.2580141
265 -0.8526946
266  0.271341
267  0.0058212
268 -0.125984
269  0.8317476
270  0.402952
271  1.5326336
272 -0.2823171
273  0.4208557
274 -0.6453038
275 -0.0877565
276  0.6981892
277  0.0025691
278  0.4635841
279 -0.9045312
280  0.178037
281 -1.0041492
282  2.0187697
283 -1.8193621
284  0.3924405
285 -0.2534792
286 -0.0697251
287 -0.4755219
288  0.3122146
289  0.2752502
290 -0.4055146
291 -0.9346413
292 -0.4577314
293  1.1718987
294 -0.3150507
295 -0.0706996
296 -0.2110344
297  0.5591182
298  0.8557991
299 -0.188677
300 -0.1663174
301  0.419646
302 -0.3778454
303  0.9917972
304 -0.0851979
305  0.8619194
306 -1.4102982
307 -1.4057096
308  0.2470365
309 -0.912581
310  0.1619551
311  0.6224401
312 -0.1321438
313 -1.0924522
314  0.8091412
315  0.8893741
316 -0.1512795
317 -0.4161466
318 -2.2423406
319 -0.562674
320 -0.0559016
321 -1.013611
322  0.6684836
323  0.3848462
324  0.1765711
325  0.0449452
326  0.5047
327  1.5494554
328  0.1493085
329  1.9328801
330 -0.2307748
331  0.2656669
332  0.8418673
333 -1.0542088
334  0.1360458
335  0.1126836
336  0.4681865
337 -0.2251618
338 -0.6713962
339  1.5609079
340  0.2525127
341  0.2247222
342 -0.4256014
343  0.8243588
344 -0.131764
345 -0.6244791
346  0.3318118
347  0.2459338
348 -1.0663862
349  0.5842856
350 -0.1592416
351 -0.2863566
352 -0.0775667
353 -0.9837803
354 -0.1859197
355 -0.3510108
356 -0.0017499
357 -2.1148357
358  0.9489934
359 -1.9690777
360 -0.2792532
361 -0.8838607
362 -1.1764374
363  1.3429625
364 -0.1265216
365  0.4094074
366  2.2665988
367  1.1726148
368 -0.2098963
369  0.745861
370  0.188755
371 -2.1469375
372  0.4258959
373 -0.1948894
374  0.3503749
375  0.1487589
376 -0.6069026
377  0.2881777
378  1.0145635
379 -0.8641474
380  0.0762034
381  0.1601244
382 -0.0133473
383  0.3251652
384 -0.1470053
385 -0.2209561
386 -0.2496238
387 -0.6582189
388  0.280981
389 -0.3061193
390  0.118193
391  0.9481185
392  0.0947136
393  2.4461397
394 -0.1680237
395  0.1353083
396 -0.3874794
397  0.8230016
398 -1.2452952
399 -0.6382173
400  0.0499999
401  1.7752464
402  0.2963254
403 -0.115093
404 -0.2981636
405 -0.1579302
406 -1.0210158
407  0.2619079
408  0.6640346
409 -0.7070764
410 -0.1335455
411  1.5178093
412  0.2743489
413 -0.1780093
414 -1.0485235
415 -0.7529902
416  0.0397263
417 -1.0903909
418  0.1057363
419 -0.3912666
420 -0.4187578
421 -0.3600337
422  0.4129983
423 -3.0317413
424  0.6741138
425 -0.2258541
426 -0.9230568
427  2.1701633
428  0.3047205
429  0.1639991
430  0.1178509
431 -0.0889061
432 -0.3185615
433 -0.9491076
434  0.4077756
435  0.953805
436 -0.4658124
437  0.286124
438  1.0766233
439  0.8502422
440  0.0693777
441  0.4731355
442 -0.1794471
443 -0.4643545
444  0.4963711
445  0.0015651
446  0.8553084
447 -2.0129128
448 -0.1407508
449  0.4099827
450  0.2497716
451 -0.185302
452 -0.4692553
453  0.8887244
454 -0.3319947
455  0.1131643
456  0.200393
457 -0.7878948
458 -0.1522142
459  1.4389676
460  0.1877374
461 -0.1968252
462 -0.5810512
463  1.2925366
464  0.3205875
465 -0.3809331
466 -0.9599592
467 -1.137616
468  0.1984506
469  0.2837176
470  0.5428302
471 -1.9031682
472  0.0558934
473  0.1635282
474  0.3558218
475 -0.0681583
476  0.6357828
477  3.367493
478  0.8461711
479  0.6511843
480  0.1314855
481 -0.1341381
482  0.679707
483 -1.5723305
484 -0.4037345
485 -0.251317
486  0.4857175
487 -0.7606902
488 -0.6814071
489 -1.1870972
490 -0.0847144
491 -0.1711371
492 -0.3511864
493 -1.448119
494 -0.0541537
495  0.346572
496 -0.128037
497 -0.8837844
498 -1.9801439
499  0.5096467