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

$R= 2.55636946085$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.487312018
4 0.5
5 -0.447213595
6 -0.344581632
7 1.517108059
8 0.353553390
9 -0.762526996
10 -0.316227766
11 -0.791899181
12 -0.243656009
13 -0.112246478
14 1.072757396
15 0.217932559
16 0.250000000
17 0.408280719
18 -0.539188010
19 0.736844584
20 -0.223606797
21 -0.739304990
22 -0.559957281
23 -0.317970898
24 -0.172290816
25 0.200000000
26 -0.0793702463
27 0.858900587
28 0.758554029
29 -1.490060798
30 0.154101590
31 0.955018950
32 0.176776695
33 0.385901988
34 0.288698065
35 -0.678471350
36 -0.381263498
37 -0.419539974
38 0.521027802
39 0.0546990581
40 -0.158113883
41 0.154836228
42 -0.522767572
43 -0.906923135
44 -0.395949590
45 0.341012439
46 -0.224839378
47 0.492278050
48 -0.121828004
49 1.301616864
50 0.141421356
51 -0.198960101
52 -0.0561232394
53 0.638587800
54 0.607334430
55 0.354148080
56 0.536378698
57 -0.359073221
58 -1.053632095
59 -0.738583630
60 0.108966279
61 -1.565414279
62 0.675300376
63 -1.156835852
64 0.125000000
65 0.0501981513
66 0.272873912
67 0.413540000
68 0.204140359
69 0.154951040
70 -0.479751692
71 0.950605999
72 -0.269594005
73 1.736350000
74 -0.296659560
75 -0.0974624036
76 0.368422292
77 -1.201396631
78 0.0386780749
79 -0.00266999999
80 -0.111803398
81 0.343974418
82 0.109485747
83 0.857700000
84 -0.369652495
85 -0.182588688
86 -0.641291499
87 0.726124534
88 -0.279978640
89 -1.558199999
90 0.241132208
91 -0.170290037
92 -0.158985449
93 -0.465392212
94 0.348093147
95 -0.329526916
96 -0.0861454081
97 0.308999999
98 0.920382111
99 0.603844505
100 0.100000000
101 0.130000000
102 -0.140686036
103 -1.520000000
104 -0.0396851231
105 0.330627242
106 0.451549763
107 0.460000000
108 0.429450293
109 0.955999999
110 0.250420509
111 0.204446871
112 0.379277014
113 -0.920000000
114 -0.253903110
115 0.142200908
116 -0.745030399
117 0.0855909704
118 -0.522257493
119 0.619405970
120 0.0770507954
121 -0.372895685
122 -1.106915052
123 -0.0754535552
124 0.477509475
125 -0.0894427190
126 -0.818006476