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

$R= 6.01171674499$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.703815723
4 0.499999999
5 -0.447213595
6 -0.497672870
7 -0.475201469
8 -0.353553390
9 -0.504643427
10 0.316227766
11 -0.784174717
12 0.351907861
13 -1.461180564
14 0.336018181
15 -0.314755960
16 0.249999999
17 1.136169558
18 0.356836789
19 -0.643496018
20 -0.223606797
21 -0.334454265
22 0.554495260
23 -1.272332876
24 -0.248836435
25 0.200000000
26 1.033210685
27 -1.058991702
28 -0.237600734
29 1.113671949
30 0.222566073
31 1.490684208
32 -0.176776695
33 -0.551914495
34 -0.803393199
35 0.212516557
36 -0.252321713
37 -1.319026063
38 0.455020398
39 -1.028401855
40 0.158113883
41 1.340568616
42 0.236494879
43 0.0378001182
44 -0.392087358
45 0.225683401
46 0.899675204
47 -0.119762491
48 0.175953930
49 -0.774183563
50 -0.141421356
51 0.799653999
52 -0.730590282
53 -0.400446721
54 0.748820213
55 0.350693594
56 0.168009090
57 -0.452902615
58 -0.787484987
59 0.884184069
60 -0.157377980
61 -1.392490529
62 -1.054072912
63 0.239807298
64 0.124999999
65 0.653459813
66 0.390262482
67 0.831415169
68 0.568084779
69 -0.895487883
70 -0.150271899
71 1.552544099
72 0.178418394
73 -1.101723000
74 0.932692274
75 0.140763144
76 -0.321748009
77 0.372640977
78 0.727189925
79 -1.798084000
80 -0.111803398
81 -0.240691582
82 -0.947925159
83 -0.289819999
84 -0.167227132
85 -0.508110473
86 -0.0267287199
87 0.783819828
88 0.277247630
89 -0.0295599999
90 -0.159582263
91 0.694355150
92 -0.636166438
93 1.049166984
94 0.0846848700
95 0.287780168
96 -0.124418217
97 0.214100000
98 0.547430447
99 0.395728617
100 0.100000000
101 -0.242999999
102 -0.565440765
103 -0.511000000
104 0.516605342
105 0.149572494
106 0.283158592
107 -0.179999999
108 -0.529495851
109 0.0970000000
110 -0.247977819
111 -0.928351283
112 -0.118800367
113 -1.649999999
114 0.320250510
115 0.569004560
116 0.556835974
117 0.737375168
118 -0.625212551
119 -0.539909443
120 0.111283036
121 -0.385070012
122 0.984639496
123 0.943513270
124 0.745342104
125 -0.0894427190
126 -0.169569366