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

$R= 12.657894507$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.270748837
4 0.5
5 -0.447213595
6 -0.191448339
7 1.110518447
8 -0.353553390
9 -0.926695066
10 0.316227766
11 -0.403726281
12 0.135374418
13 0.0154219697
14 -0.785255124
15 -0.121082561
16 0.250000000
17 0.434902066
18 0.655272365
19 0.259963704
20 -0.223606797
21 0.300671579
22 0.285477591
23 1.783044510
24 -0.0957241696
25 0.200000000
26 -0.0109049793
27 -0.521650450
28 0.555259223
29 -0.585006516
30 0.0856183001
31 -1.759695378
32 -0.176776695
33 -0.109308421
34 -0.307522200
35 -0.496638947
36 -0.463347533
37 -0.923238285
38 -0.183822098
39 0.00417548038
40 0.158113883
41 0.575302159
42 -0.212606912
43 -1.869003696
44 -0.201863140
45 0.414430632
46 -1.260802864
47 -0.470790966
48 0.0676872094
49 0.233251221
50 -0.141421356
51 0.117749229
52 0.00771098486
53 0.723008521
54 0.368862570
55 0.180551881
56 -0.392627562
57 0.0703848708
58 0.413662074
59 -0.975643154
60 -0.0605412806
61 -1.500858457
62 1.244292534
63 -1.029111966
64 0.125000000
65 -0.00689691453
66 0.0772927261
67 -0.667035496
68 0.217451033
69 0.482757229
70 0.351176767
71 1.243715708
72 0.327636182
73 -0.772151521
74 0.652828052
75 0.0541497675
76 0.129981852
77 -0.448345483
78 -0.00295251049
79 -1.351076906
80 -0.111803398
81 0.785458814
82 -0.406800058
83 -1.027489912
84 0.150335789
85 -0.194494116
86 1.321585188
87 -0.158389827
88 0.142738795
89 -0.618166067
90 -0.293046710
91 0.0171263691
92 0.891522255
93 -0.476435426
94 0.332899484
95 -0.116259302
96 -0.0478620848
97 1.326524579
98 -0.164933520
99 0.374131190
100 0.100000000
101 -0.305231296
102 -0.0832612784
103 -0.859079798
104 -0.00545248968
105 -0.134464417
106 -0.511244228
107 -0.186543354
108 -0.260825225
109 1.464853156
110 -0.127669460
111 -0.249968401
112 0.277629611
113 -0.667863702
114 -0.0497696194
115 -0.797401746
116 -0.292503258
117 -0.0142937434
118 0.689883890
119 0.482968255
120 0.0428091500
121 -0.836981732
122 1.061267192
123 0.155742144
124 -0.879847689
125 -0.0894427190
126 0.727692050
127 1.173938283
128 -0.0883883476
129 -0.505996629
130 0.00487685503
131 0.851598177
132 -0.0546542107
133 0.288942597
134 0.471665322
135 0.233289173
136 -0.153761100
137 -1.151767546
138 -0.341360910
139 -1.374710572
140 -0.248319473
141 -0.126634981
142 -0.879439811
143 -0.00439263637
144 -0.231673766
145 0.261622867
146 0.545993577
147 0.0667865049
148 -0.461619142
149 1.142131480
150 -0.0382896678
151 0.494812242
152 -0.0919110490
153 -0.401690422
154 0.317028131
155 0.786959697
156 0.00208774019
157 -0.488984533
158 0.955355642
159 0.304138078
160 0.0790569415
161 1.873017369
162 -0.555403254