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

$R= 20.2676618424$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.353444776
4 0.5
5 -0.447213595
6 0.957029979
7 -0.510640443
8 -0.353553390
9 0.831812763
10 0.316227766
11 -0.572456626
12 -0.676722388
13 0.604548629
14 0.361077320
15 0.605278904
16 0.250000000
17 -1.050487645
18 -0.588180445
19 0.458338662
20 -0.223606797
21 0.691123640
22 0.404787962
23 0.734765488
24 0.478514989
25 0.200000000
26 -0.427480435
27 0.227632136
28 -0.255320221
29 -1.698245453
30 -0.427996818
31 -1.399912793
32 -0.176776695
33 0.774788430
34 0.742806938
35 0.228365348
36 0.415906381
37 -1.234894803
38 -0.324094376
39 -0.818223184
40 0.158113883
41 -1.181780432
42 -0.488698212
43 0.612492786
44 -0.286228313
45 -0.371997976
46 -0.519557659
47 -1.053054111
48 -0.338361194
49 -0.739246337
50 -0.141421356
51 1.421777017
52 0.302274314
53 -0.157701405
54 -0.160960227
55 0.256010386
56 0.180538660
57 -0.620336068
58 1.200840875
59 -1.795981906
60 0.302639452
61 -0.786193541
62 0.989887829
63 -0.424757238
64 0.125000000
65 -0.270362366
66 -0.547858153
67 -1.024928795
68 -0.525243822
69 -0.994464512
70 -0.161478686
71 -0.730723441
72 -0.294090222
73 1.263340999
74 0.873202489
75 -0.270688955
76 0.229169331
77 0.292319505
78 0.578571162
79 0.161250179
80 -0.111803398
81 -1.139900290
82 0.835644957
83 -1.119649296
84 0.345561820
85 0.469792357
86 -0.433097802
87 2.298481437
88 0.202393981
89 0.665810441
90 0.263042291
91 -0.308706979
92 0.367382744
93 1.894704657
94 0.744621703
95 -0.204975281
96 0.239257494
97 0.921702768
98 0.522726098
99 -0.476176728
100 0.100000000
101 1.425865393
102 -1.005348170
103 0.0156657171
104 -0.213740217
105 -0.309079888
106 0.111511733
107 0.0872417607
108 0.113816068
109 1.627226562
110 -0.181026680
111 1.671361921
112 -0.127660110
113 -0.320957598
114 0.438643840
115 -0.328597115
116 -0.849122726
117 0.502871265
118 1.269950984
119 0.536421475
120 -0.213998409
121 -0.672293408
122 0.555922784
123 1.599474564
124 -0.699956396
125 -0.0894427190
126 0.300348723
127 -1.561206577
128 -0.0883883476
129 -0.828975170
130 0.191175062
131 -0.761962650
132 0.387394215
133 -0.234046148
134 0.724734101
135 -0.101800186
136 0.371403469
137 1.443516827
138 0.703192600
139 -1.962434126
140 0.114182674
141 1.425250834
142 0.516699500
143 -0.346078278
144 0.207953190
145 0.759478455
146 -0.893316987
147 1.000527671
148 -0.617447401
149 -1.729430851
150 0.191405995
151 0.521347045
152 -0.162047188
153 -0.873816774
154 -0.206701104
155 0.626060033
156 -0.409111592
157 0.307185315
158 -0.114021095
159 0.213438815
160 0.0790569415
161 -0.375224859
162 0.806031224
163 -0.186251179
164 -0.590890216
165 -0.346495919
166 0.791711610
167 1.492152127
168 -0.244349106
169 -0.634355810
170 -0.332193361
171 0.381106726
172 0.306246393
173 -1.026436481
174 -1.625271811
175 -0.102128088
176 -0.143114156
177 2.430732643
178 -0.470799078
179 0.843675949
180 -0.185998988
181 0.392691416
182 0.218288798
183 1.067278901
184 -0.259778829
185 0.552261745
186 -1.339758511
187 0.605151204
188 -0.526527055
189 -0.108811254
190 0.144939411
191 -1.012608747
192 -0.169180597
193 -1.343607277
194 -0.651742277
195 0.365920532
196 -0.369623168