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

$R= 11.1924559787$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.530177261
4 0.5
5 -0.447213595
6 -1.081998717
7 1.291037956
8 0.353553390
9 1.341442450
10 -0.316227766
11 1.140191717
12 -0.765088630
13 -1.675699147
14 0.912901693
15 0.684316074
16 0.250000000
17 -0.937309026
18 0.948543053
19 0.563488712
20 -0.223606797
21 -1.975516923
22 0.806237295
23 -0.802406871
24 -0.540999358
25 0.200000000
26 -1.184898230
27 -0.522467473
28 0.645518978
29 -0.694427414
30 0.483884536
31 -1.452647879
32 0.176776695
33 -1.744695439
34 -0.662777568
35 -0.577369726
36 0.670721225
37 -0.369438870
38 0.398446689
39 2.564116731
40 -0.158113883
41 -0.905485737
42 -1.396901412
43 -0.134424450
44 0.570095858
45 -0.599911301
46 -0.567387339
47 -0.786436664
48 -0.382544315
49 0.666779004
50 0.141421356
51 1.434248958
52 -0.837849573
53 1.408516449
54 -0.369440293
55 -0.509909237
56 0.456450846
57 -0.862237614
58 -0.491034334
59 0.525918607
60 0.342158037
61 -0.271376014
62 -1.027177166
63 1.731853119
64 0.125000000
65 0.749395440
66 -1.233685976
67 -1.250161656
68 -0.468654513
69 1.227824748
70 -0.408262048
71 -1.045565153
72 0.474271526
73 0.336600709
74 -0.261232730
75 -0.306035452
76 0.281744356
77 1.472030783
78 1.813104328
79 0.168143721
80 -0.111803398
81 -0.541974603
82 -0.640275105
83 -1.436963553
84 -0.987758461
85 0.419177339
86 -0.0950524405
87 1.062597039
88 0.403118647
89 0.579507020
90 -0.424201349
91 -2.163391197
92 -0.401203435
93 2.222808746
94 -0.556094698
95 -0.251999813
96 -0.270499679
97 -1.547955348
98 0.471483955
99 1.529501349
100 0.100000000
101 0.735492797
102 1.014167164
103 -1.714297610
104 -0.592449115
105 0.883478026
106 0.995971532
107 -0.0261393026
108 -0.261233736
109 0.978779891
110 -0.360560279
111 0.565305995
112 0.322759489
113 -1.331500126
114 -0.609694064
115 0.358847261
116 -0.347213707
117 -2.247852561
118 0.371880613
119 -1.210115314
120 0.241942268
121 0.300038057
122 -0.191891820
123 1.385592846
124 -0.726323939
125 -0.0894427190
126 1.224605084
127 0.491748053
128 0.0883883476
129 0.205651907
130 0.529902597
131 1.309969555
132 -0.872347719
133 0.727277943
134 -0.883997784
135 0.233654557
136 -0.331388784
137 -0.812778293
138 0.868203205
139 -0.294120973
140 -0.288684863
141 1.202701660
142 -0.739326209
143 -1.908114773
144 0.335360612
145 0.310557380
146 0.238012643
147 -1.037827800
148 -0.184719435
149 0.00851343033
150 -0.216399743