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

$R= 21.0284013311$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.155719811
4 0.5
5 0.447213595
6 0.817217315
7 1.705157748
8 0.353553390
9 0.335688282
10 0.316227766
11 -1.289702231
12 0.577859905
13 0.841152749
14 1.205728607
15 0.516853612
16 0.250000000
17 0.550280526
18 0.237367461
19 1.344448766
20 0.223606797
21 1.970684592
22 -0.911957193
23 -1.384664525
24 0.408608657
25 0.200000000
26 0.594784813
27 -0.767758212
28 0.852578874
29 1.244944180
30 0.365470694
31 1.198020906
32 0.176776695
33 -1.490534419
34 0.389107091
35 0.762569727
36 0.167844141
37 0.0947085051
38 0.950668839
39 0.972136897
40 0.158113883
41 -1.158378443
42 1.393484438
43 0.245851336
44 -0.644851115
45 0.150124363
46 -0.979105675
47 0.276031677
48 0.288929952
49 1.907562948
50 0.141421356
51 0.635970106
52 0.420576374
53 -1.023601862
54 -0.542887038
55 -0.576772372
56 0.602864303
57 1.553806075
58 0.880308471
59 1.450819423
60 0.258426806
61 -1.010074140
62 0.847128706
63 0.572401476
64 0.125000000
65 0.376174945
66 -1.053966995
67 -0.725647204
68 0.275140263
69 -1.600284224
70 0.539218225
71 -1.287304281
72 0.118683730
73 0.514956958
74 0.0669690262
75 0.231143962
76 0.672224383
77 -2.199145753
78 0.687404592
79 0.127817875
80 0.111803398
81 -1.223001659
82 -0.819097252
83 0.694691870
84 0.985342296
85 0.246092932
86 0.173843147
87 1.438806653
88 -0.455978596
89 -1.714161245
90 0.106153955
91 1.434298128
92 -0.692332262
93 1.384576496
94 0.195183870
95 0.601255766
96 0.204304328
97 0.712545594
98 1.348850696
99 -0.432937927
100 0.100000000
101 1.443946356
102 0.449698774
103 0.296842247
104 0.297392406
105 0.881316942
106 -0.723795818
107 -0.196957779
108 -0.383879106
109 1.121553063
110 -0.407839655
111 0.109456494
112 0.426289437
113 -0.118977933
114 1.098706812
115 -0.619240801
116 0.622472090
117 0.282365120
118 1.025884252
119 0.938315108
120 0.182735347
121 0.663331844
122 -0.714230274
123 -1.338760913
124 0.599010453
125 0.0894427190
126 0.404748965
127 0.658028763
128 0.0883883476
129 0.284135248
130 0.265995854
131 -0.843007082
132 -0.745267209
133 2.292497260
134 -0.513110059
135 -0.343351910
136 0.194553545
137 -1.217073773
138 -1.131571827
139 0.997824512
140 0.381284863
141 0.319015605
142 -0.910261587
143 -1.084836751
144 0.0839220707
145 0.556755962
146 0.364129557
147 2.204608603
148 0.0473542525
149 0.937356093
150 0.163443463
151 -0.959767802
152 0.475334419
153 0.184721452
154 -1.555030875
155 0.535771237
156 0.486068448
157 1.704586697
158 0.0903808863
159 -1.182972853
160 0.0790569415
161 -2.361098202
162 -0.864792766
163 -0.455964325
164 -0.579189221
165 -0.666587257
166 0.491221332
167 1.527478751
168 0.696742219
169 -0.292328275
170 0.174013981
171 0.451219251
172 0.122925668
173 -0.731018237
174 1.017389941
175 0.341031549
176 -0.322425557
177 1.676882776
178 -1.212095041
179 -0.456044331
180 0.0750621819
181 1.015559696
182 1.014201933
183 -1.168557487
184 -0.489552837
185 0.0423549311
186 0.979043429
187 -0.703391092
188 0.138015838
189 -1.328007370
190 0.425152029
191 -0.484272364
192 0.144464976
193 -1.803657333
194 0.503845821
195 0.434752837
196 0.953781474