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

$R= 5.45975729468$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.801440802
4 0.499999999
5 0.447213595
6 1.273811007
7 -0.939838994
8 -0.353553390
9 2.245188965
10 -0.316227766
11 0.164122617
12 -0.900720401
13 0.844818178
14 0.664566525
15 -0.805628818
16 0.249999999
17 0.193064121
18 -1.587588342
19 -0.0981072790
20 0.223606797
21 1.693064311
22 -0.116052215
23 0.482532280
24 0.636905503
25 0.200000000
26 -0.597376662
27 -2.243134209
28 -0.469919497
29 -0.508577218
30 0.569665600
31 1.844803435
32 -0.176776695
33 -0.295657180
34 -0.136516949
35 -0.420308775
36 1.122594482
37 1.086660452
38 0.0693723222
39 -1.521889937
40 -0.158113883
41 0.606225997
42 -1.197177255
43 0.607905952
44 0.0820613088
45 1.004079029
46 -0.341201847
47 -1.192300486
48 -0.450360200
49 -0.116702665
50 -0.141421356
51 -0.347793586
52 0.422409089
53 -0.0764913063
54 1.586135410
55 0.0733978659
56 0.332283262
57 0.176734455
58 0.359618400
59 -0.0551323400
60 -0.402814409
61 1.187307020
62 -1.304473019
63 -2.110116138
64 0.124999999
65 0.377814175
66 0.209061197
67 1.851355599
68 0.0965320607
69 -0.869253338
70 0.297203185
71 -1.510516600
72 -0.793794171
73 1.277995439
74 -0.768384974
75 -0.360288160
76 -0.0490536395
77 -0.154248836
78 1.076138694
79 -0.895210999
80 0.111803398
81 1.795684524
82 -0.428666513
83 1.195138800
84 0.846532155
85 0.0863408999
86 -0.429854421
87 0.916171753
88 -0.0580261079
89 -0.356256999
90 -0.709991090
91 -0.793993067
92 0.241266140
93 -3.323304182
94 0.843083759
95 -0.0438749089
96 0.318452751
97 -1.509686000
98 0.0825212458
99 0.368486290
100 0.100000000
101 1.225400000
102 0.245927203
103 1.487900000
104 -0.298688331
105 0.757161378
106 0.0540875213
107 0.130000000
108 -1.121567104
109 0.752800000
110 -0.0519001287
111 -1.957554478
112 -0.234959748
113 1.135000000
114 -0.124970131
115 0.215794996
116 -0.254288609
117 1.896776451
118 0.0389844514
119 -0.181449189
120 0.284832800
121 -0.973063766
122 -0.839552845
123 -1.092080247
124 0.922401717
125 0.0894427190
126 1.492077430
127 -0.569999999
128 -0.0883883476
129 -1.095106586
130 -0.267154965