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

$R= 23.638281764$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.349380818
4 0.5
5 -0.447213595
6 -0.247049546
7 -0.588930958
8 0.353553390
9 -0.877933043
10 -0.316227766
11 -0.0574364455
12 -0.174690409
13 1.009537889
14 -0.416437074
15 0.156247852
16 0.250000000
17 1.085531239
18 -0.620792408
19 0.252109668
20 -0.223606797
21 0.205761180
22 -0.0406137001
23 1.245672780
24 -0.123524773
25 0.200000000
26 0.713851087
27 0.656113784
28 -0.294465479
29 -1.318929338
30 0.110483915
31 -0.119216807
32 0.176776695
33 0.0200671923
34 0.767586500
35 0.263377931
36 -0.438966521
37 -1.574367062
38 0.178268456
39 -0.352713174
40 -0.158113883
41 -0.413247622
42 0.145495126
43 1.346517298
44 -0.0287182227
45 0.392623593
46 0.880823670
47 0.818844194
48 -0.0873452046
49 -0.653160325
50 0.141421356
51 -0.379263793
52 0.504768944
53 -0.282479303
54 0.463942505
55 0.0256863593
56 -0.208218537
57 -0.0880822825
58 -0.932623879
59 -1.218130233
60 0.0781239260
61 0.284532101
62 -0.0842990130
63 0.517041949
64 0.125000000
65 -0.451479069
66 0.0141896477
67 0.0963903896
68 0.542765619
69 -0.435214175
70 0.186236321
71 -1.289194806
72 -0.310396204
73 -0.191470885
74 -1.113245626
75 -0.0698761637
76 0.126054834
77 0.0338261009
78 -0.249405877
79 -1.853846583
80 -0.111803398
81 0.648699472
82 -0.292210195
83 -0.239042490
84 0.102880590
85 -0.485464328
86 0.952131512
87 0.460808612
88 -0.0203068500
89 0.397409609
90 0.277626805
91 -0.594548117
92 0.622836390
93 0.0416520658
94 0.579010282
95 -0.112746871
96 -0.0617623865
97 0.857048608
98 -0.461854095
99 0.0504253534
100 0.100000000
101 1.030771293
102 -0.268179999
103 0.432592274
104 0.356925543
105 -0.0920191973
106 -0.199743030
107 0.725962015
108 0.328056892
109 -0.913956385
110 0.0181629988
111 0.550053653
112 -0.147232739
113 -1.210032876
114 -0.0622835792
115 -0.557081803
116 -0.659464669
117 -0.886306671
118 -0.861348148
119 -0.639302953
120 0.0552419578
121 -0.996701054
122 0.201194578
123 0.144380793
124 -0.0596084037
125 -0.0894427190
126 0.365603868
127 0.117606344
128 0.0883883476
129 -0.470447314
130 -0.319243911
131 -1.939992500
132 0.0100335961
133 -0.148475187
134 0.0681582981
135 -0.293423004
136 0.383793250
137 -1.972115717
138 -0.307742895
139 -1.452767853
140 0.131688965
141 -0.286088437
142 -0.911598390
143 -0.0579842495
144 -0.219483260
145 0.589843131
146 -0.135390361
147 0.228201660
148 -0.787183531
149 1.010102494
150 -0.0494099092
151 0.0605255105
152 0.0891342282
153 -0.953023860
154 0.0239186653
155 0.0533153771
156 -0.176356587
157 1.150596949
158 -1.310867490
159 0.0986931239
160 -0.0790569415
161 -0.733615048
162 0.458699795
163 -0.0680743742
164 -0.206623811
165 -0.00897432124
166 -0.169028566
167 -1.610430874
168 0.0727475630
169 0.0191675282
170 -0.343275118
171 -0.221337008
172 0.673258649
173 -0.140971976
174 0.325840894
175 -0.117786191
176 -0.0143591113
177 0.425545666
178 0.281011030
179 0.0158318924
180 0.196311796
181 -0.355512934
182 -0.420409005
183 -0.0994279555
184 0.440411835
185 0.704078354
186 0.0294524581
187 -0.0626584056
188 0.409422097
189 -0.386240063
190 -0.0797240773
191 0.259647939
192 -0.0436726023
193 -1.073243514
194 0.606024883
195 0.157738126
196 -0.326580162
197 -1.958678913
198 0.0356561093
199 0.289256787
200 0.0707106781
201 -0.0408599486
202 0.728865371
203 0.772431351
204 -0.189631896
205 0.184809954
206 0.305888930
207 -1.088400980
208 0.252384472
209 -0.0196447225
210 -0.0650673984
211 -0.648747753
212 -0.141239651
213 0.466500203
214 0.513332663
215 -0.602180842
216 0.231971252
217 0.130956395
218 -0.646264758