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

$R= 21.4106668814$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.998141553
4 0.5
5 0.447213595
6 0.705792661
7 -1.342707789
8 0.353553390
9 -0.00371343879
10 0.316227766
11 -1.266508738
12 0.499070776
13 1.197713449
14 -0.949437782
15 0.446382473
16 0.250000000
17 1.069359012
18 -0.00262579775
19 -0.947891855
20 0.223606797
21 -1.340212438
22 -0.895556917
23 0.858368339
24 0.352896330
25 0.200000000
26 0.846911302
27 -1.001848091
28 -0.671353894
29 -0.811445337
30 0.315640073
31 -0.938913403
32 0.176776695
33 -1.264154999
34 0.756151009
35 -0.600477178
36 -0.00185671939
37 -0.665793954
38 -0.670260759
39 1.195487563
40 0.158113883
41 -0.284096423
42 -0.947673303
43 -0.642367710
44 -0.633254369
45 -0.00166070031
46 0.606958073
47 -1.692308121
48 0.249535388
49 0.802864206
50 0.141421356
51 1.067371666
52 0.598856724
53 -1.658525989
54 -0.708413579
55 -0.566399926
56 -0.474718891
57 -0.946130249
58 -0.573778500
59 -0.822657882
60 0.223191236
61 0.785139736
62 -0.663912034
63 0.00498606319
64 0.125000000
65 0.535633738
66 -0.893892572
67 -1.837608402
68 0.534679506
69 0.856773107
70 -0.424601484
71 0.269358105
72 -0.00131289887
73 1.219459131
74 -0.470787420
75 0.199628310
76 -0.473945927
77 1.700551147
78 0.845337363
79 0.316580429
80 0.111803398
81 -0.996272771
82 -0.200886507
83 1.623302301
84 -0.670106219
85 0.478231888
86 -0.454222564
87 -0.809937310
88 -0.447778458
89 1.565204102
90 -0.00117429245
91 -1.608179178
92 0.429184169
93 -0.937168483
94 -1.196642548
95 -0.423910125
96 0.176448165
97 -1.041297254
98 0.567710725
99 0.00470310269
100 0.100000000
101 -0.775899674
102 0.754745743
103 -0.654895900
104 0.423455651
105 -0.599361223
106 -1.172754973
107 -1.551016569
108 -0.500924045
109 0.0478682717
110 -0.400505228
111 -0.664556612
112 -0.335676947
113 0.161318679
114 -0.669015115
115 0.383873991
116 -0.405722668
117 -0.00444763598
118 -0.581706967
119 -1.435836675
120 0.157820036
121 0.604044386
122 0.555177631
123 -0.283568448
124 -0.469456701
125 0.0894427190
126 0.00352567909
127 0.120688799
128 0.0883883476
129 -0.641173899
130 0.378750248
131 -0.638637026
132 -0.632077499
133 1.272741777
134 -1.299385362
135 -0.448040087
136 0.378075504
137 0.592815830
138 0.605830074
139 -0.749246977
140 -0.300238589
141 -1.689163203
142 0.190464942
143 -1.516914829
144 -0.000928359699
145 -0.362889387
146 0.862287821
147 0.801372094
148 -0.332896977
149 1.808934091
150 0.141158532
151 0.754753600
152 -0.335130379
153 -0.00397191986
154 1.202471248
155 -0.419894838
156 0.597743781
157 -0.677036838
158 0.223856168
159 -1.655442222
160 0.0790569415
161 -1.152534296
162 -0.704471232
163 0.654614869
164 -0.142048211
165 -0.565347302
166 1.147848065
167 -0.945520708
168 -0.473836651
169 0.434562819
170 0.338161011
171 0.00351192220
172 -0.321183855
173 1.014922662
174 -0.572712164
175 -0.268541557
176 -0.316627184
177 -0.821120533
178 1.106766435
179 1.551226340
180 -0.000830350157
181 1.885322301
182 -1.137154402
183 0.783748757
184 0.303479036
185 -0.297752108
186 -0.662678189
187 -1.357811437
188 -0.846154060
189 1.346515352
190 -0.299749724
191 -1.211002641
192 0.124767694
193 0.161680988
194 -0.736308349
195 0.534638291
196 0.401432103
197 1.039218271
198 0.00332559580