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

$R= 18.5038062187$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.818716774
4 0.5
5 0.447213595
6 1.286026963
7 1.218166233
8 0.353553390
9 2.307730704
10 0.316227766
11 0.545616765
12 0.909358387
13 1.541876862
14 0.861373604
15 0.813354867
16 0.250000000
17 -1.169241821
18 1.631812030
19 -1.692888547
20 0.223606797
21 2.215499362
22 0.385809314
23 -0.659469810
24 0.643013481
25 0.200000000
26 1.090271585
27 2.378391767
28 0.609083116
29 -0.943464697
30 0.575128742
31 -0.267701992
32 0.176776695
33 0.992322362
34 -0.826778821
35 0.544780501
36 1.153865352
37 -0.261308215
38 -1.197052971
39 2.804237314
40 0.158113883
41 -0.109234391
42 1.566594622
43 -0.640264098
44 0.272808382
45 1.032048545
46 -0.466315575
47 -0.123181503
48 0.454679193
49 0.483928972
50 0.141421356
51 -2.126519714
52 0.770938431
53 -0.918882803
54 1.681776947
55 0.244007235
56 0.430686802
57 -3.078884797
58 -0.667130285
59 -1.396651528
60 0.406677433
61 0.112165506
62 -0.189293894
63 2.811199619
64 0.125000000
65 0.689548295
66 0.701677871
67 0.259734580
68 -0.584620910
69 -1.199388806
70 0.385217986
71 1.265682340
72 0.815906015
73 -0.743427160
74 -0.184772810
75 0.363743354
76 -0.846444273
77 0.664651919
78 1.982895220
79 1.262787308
80 0.111803398
81 2.017890298
82 -0.0772403788
83 0.117844240
84 1.107749681
85 -0.522900839
86 -0.452735085
87 -1.715895070
88 0.192904657
89 0.832978728
90 0.729768525
91 1.878262330
92 -0.329734905
93 -0.486874104
94 -0.0871024761
95 -0.757082774
96 0.321506740
97 0.777368881
98 0.342189457
99 1.259136561
100 0.100000000
101 -0.890800375
102 -1.503676510
103 0.211243915
104 0.545135792
105 0.990801435
106 -0.649748261
107 0.355288847
108 1.189195883
109 1.454226265
110 0.172539170
111 -0.475245629
112 0.304541558
113 -1.111911965
114 -2.177100319
115 -0.294923865
116 -0.471732348
117 3.558236576
118 -0.987581766
119 -1.424330868
120 0.287564371
121 -0.702302311
122 0.0793129902
123 -0.198666357
124 -0.133850996
125 0.0894427190
126 1.987818314
127 0.989097553
128 0.0883883476
129 -1.164458996
130 0.487584275
131 0.564365916
132 0.496161181
133 -2.062220089
134 0.183660083
135 1.063649133
136 -0.413389410
137 0.541116530
138 -0.848095958
139 -1.416830340
140 0.272390250
141 -0.224035028
142 0.894972565
143 0.841268886
144 0.576932676
145 -0.421930239
146 -0.525682386
147 0.880131585
148 -0.130654107
149 -1.517026938
150 0.257205392
151 0.582390910
152 -0.598526485
153 -2.698322361
154 0.469979879
155 -0.119719970
156 1.402118657
157 1.284694035
158 0.892925469
159 -1.670938769
160 0.0790569415
161 -0.803108642
162 1.426863913
163 0.586114392
164 -0.0546171957
165 0.443780051
166 0.0833284616
167 1.679888844
168 0.783297311
169 1.377921608
170 -0.369746729
171 -3.905039609
172 -0.320132049
173 0.409392871
174 -1.213321040
175 0.243633246
176 0.136404191
177 -2.536552228
178 0.589004907
179 -0.929315785
180 0.516024272
181 0.468530497
182 1.328132030
183 0.195959125
184 -0.233157787
185 -0.116860586
186 -0.344271980
187 -0.584815629
188 -0.0615907515
189 2.986676658
190 -0.535338363