Properties

Level 10
Symmetry even
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

$R= 7.41262473822$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.001383765
4 0.5
5 -0.447213595
6 -0.708085251
7 0.271646379
8 -0.353553390
9 0.00276944567
10 0.316227766
11 1.433911590
12 0.500691882
13 0.876818457
14 -0.192082997
15 -0.447832434
16 0.250000000
17 -0.0791591158
18 -0.00195829381
19 1.616812389
20 -0.223606797
21 0.272022274
22 -1.013928609
23 1.411615585
24 -0.354042625
25 0.200000000
26 -0.620004277
27 -0.998610487
28 0.135823189
29 -0.662609100
30 0.316665351
31 1.086004920
32 -0.176776695
33 1.435895787
34 0.0559739476
35 -0.121483954
36 0.00138472283
37 -0.585355923
38 -1.143259004
39 0.878031768
40 0.158113883
41 -1.695165337
42 -0.192348794
43 0.900750815
44 0.716955795
45 -0.00123853375
46 -0.998162953
47 1.241078434
48 0.250345941
49 -0.926208244
50 -0.141421356
51 -0.0792686535
52 0.438409228
53 0.0238021191
54 0.706124247
55 -0.641264757
56 -0.0960414985
57 1.619049678
58 0.468535388
59 -0.567135700
60 -0.223916217
61 -1.307179654
62 -0.767921443
63 0.000752309890
64 0.125000000
65 -0.392125135
66 -1.015331648
67 0.760850931
68 -0.0395795579
69 1.413568930
70 0.0859021277
71 -0.971319017
72 -0.000979146908
73 1.063883268
74 0.413909142
75 0.200276753
76 0.808406194
77 0.389516891
78 -0.620862217
79 -0.00811830000
80 -0.111803398
81 -1.002761775
82 1.198662905
83 -1.498778399
84 0.136011137
85 0.0354010328
86 -0.636927010
87 -0.663525995
88 -0.506964304
89 0.256865999
90 0.000875775618
91 0.238184559
92 0.705807792
93 1.087507696
94 -0.877574977
95 -0.723060481
96 -0.177021312
97 0.276079999
98 0.654928130
99 0.00397114025
100 0.100000000
101 0.422590000
102 0.0560514024
103 1.764019999
104 -0.310002138
105 -0.121652059
106 -0.0168306398
107 -1.060230000
108 -0.499305243
109 1.018389999
110 0.453442658
111 -0.586165918
112 0.0679115948
113 -0.634660000
114 -1.144841006
115 -0.631293681
116 -0.331304550
117 0.00242830108
118 0.401025499
119 -0.0215032872
120 0.158332675
121 1.056102448
122 0.924315597
123 -1.697511048
124 0.543002460
125 -0.0894427190
126 -0.000531963425