Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 19.3298732$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.956286320
4 0.5
5 -0.447213595
6 -0.676196542
7 -0.636592291
8 -0.353553390
9 -0.0769299903
10 0.316227766
11 -0.509544625
12 0.478143160
13 1.166808995
14 0.450138725
15 -0.427664243
16 0.250000000
17 1.586111725
18 0.0543977178
19 -0.238021712
20 -0.223606797
21 -0.619723570
22 0.360302460
23 0.982949824
24 -0.338098271
25 0.200000000
26 -0.825058552
27 -1.034485546
28 -0.318296145
29 -0.807371244
30 0.302404286
31 -1.280594903
32 -0.176776695
33 -0.481807120
34 -1.121550356
35 0.284692727
36 -0.0384649951
37 1.364825172
38 0.168306766
39 1.125842142
40 0.158113883
41 -0.603976642
42 0.438210739
43 1.052172458
44 -0.254772312
45 0.0344041376
46 -0.695050486
47 -0.639555118
48 0.239071580
49 -0.585912597
50 -0.141421356
51 1.519953181
52 0.583404497
53 -0.915466706
54 0.731491744
55 0.227875284
56 0.225069362
57 -0.228808138
58 0.570897681
59 0.986250795
60 -0.213832121
61 -0.237766642
62 0.905517340
63 0.0562728384
64 0.125000000
65 -0.521812845
66 0.340689081
67 -0.0500952325
68 0.793055862
69 0.941841512
70 -0.201308158
71 -0.235876624
72 0.0271988589
73 -1.514380311
74 -0.965077134
75 0.191257264
76 -0.119010856
77 0.320770266
78 -0.796090613
79 -1.378147589
80 -0.111803398
81 -0.913303959
82 0.427075979
83 0.0274200435
84 -0.309861785
85 -0.709330727
86 -0.743998280
87 -0.782317098
88 0.180151230
89 0.230454735
90 -0.0243273990
91 -0.763929917
92 0.491474912
93 -1.225850476
94 0.452233761
95 0.106446545
96 -0.169049135