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

$R= 23.425167202$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.473620500
4 0.5
5 0.447213595
6 -0.334900267
7 1.494030640
8 -0.353553390
9 -0.775683621
10 -0.316227766
11 -0.480772154
12 0.236810250
13 -1.627555338
14 -1.056439197
15 0.211809526
16 0.250000000
17 0.180711993
18 0.548491149
19 -0.372779118
20 0.223606797
21 0.707603538
22 0.339957250
23 -0.752250871
24 -0.167450133
25 0.200000000
26 1.150855416
27 -0.841000164
28 0.747015320
29 0.252765261
30 -0.149771952
31 0.790218569
32 -0.176776695
33 -0.227703548
34 -0.127782676
35 0.668150814
36 -0.387841810
37 0.947263251
38 0.263594642
39 -0.770843573
40 -0.158113883
41 1.264799789
42 -0.500351260
43 1.193038082
44 -0.240386077
45 -0.346896261
46 0.531921692
47 -0.282017987
48 0.118405125
49 1.232127554
50 -0.141421356
51 0.0855889048
52 -0.813777669
53 1.930600637
54 0.594676919
55 -0.215007843
56 -0.528219598
57 -0.176555832
58 -0.178732030
59 -1.171635784
60 0.105904763
61 -0.993924388
62 -0.558768909
63 -1.158895098
64 0.125000000
65 -0.727864874
66 0.161010723
67 0.264565034
68 0.0903559968
69 -0.356281433
70 -0.472453971
71 0.768439298
72 0.274245574
73 0.270121811
74 -0.669816268
75 0.0947241000
76 -0.186389559
77 -0.718288330
78 0.545068717
79 0.219494967
80 0.111803398
81 0.377368703
82 -0.894348507
83 1.777131230
84 0.353801769
85 0.0808168604
86 -0.843605318
87 0.119714809
88 0.169978625
89 -1.697928375
90 0.245292698
91 -2.431617544
92 -0.376125435
93 0.374263714
94 0.199416831
95 -0.166711889
96 -0.0837250668
97 -0.772994837
98 -0.871245749
99 0.372927086
100 0.100000000
101 0.213477094
102 -0.0605204949
103 1.930574106
104 0.575427708
105 0.316449922
106 -1.365140802
107 -0.889544449
108 -0.420500082
109 -0.635876393
110 0.152033504
111 0.448643294
112 0.373507660
113 1.667360934
114 0.124843826
115 -0.336416816
116 0.126382630
117 1.262468020
118 0.828471608
119 0.269989255
120 -0.0748859763
121 -0.768858135
122 0.702810674
123 0.599035108
124 0.395109284
125 0.0894427190
126 0.819462582
127 1.350936703
128 -0.0883883476
129 0.565047294
130 0.514678188
131 1.568121138
132 -0.113851774
133 -0.556943422
134 -0.187075729
135 -0.376106707
136 -0.0638913380
137 -0.0506677943
138 0.251929017
139 1.734159442
140 0.334075407
141 -0.133569495
142 -0.543368639
143 0.782483297
144 -0.193920905
145 0.113040061
146 -0.191004964
147 0.583560829
148 0.473631625
149 -0.249077388
150 -0.0669800534
151 1.397667829
152 0.131797321
153 -0.140175354
154 0.507906549
155 0.353396487
156 -0.385421786
157 0.552044890
158 -0.155206380
159 0.914371815
160 -0.0790569415
161 -1.123886184
162 -0.266839969
163 0.870530740
164 0.632399894
165 -0.101832122
166 -1.256621543
167 -1.153015544
168 -0.250175630
169 1.648931944
170 -0.0571461500
171 0.289151971
172 0.596519041
173 -1.679152329
174 -0.0846511536
175 0.298806128
176 -0.120193038
177 -0.554908798
178 1.200616667
179 -0.844528944
180 -0.173448130
181 1.783159985
182 1.719413255
183 -0.470798911
184 0.265960846
185 0.423629004
186 -0.264644410
187 -0.0870599285
188 -0.141008993
189 -1.256722972
190 0.117883107
191 0.808420583
192 0.0592025625
193 -1.355936069
194 0.546589891
195 -0.344731726
196 0.616063777
197 -0.823023148
198 -0.263699271
199 -0.560212760
200 -0.0707106781
201 0.129672752
202 -0.150951101
203 0.378375900
204 0.0427944524
205 0.565635661
206 -1.365122042
207 0.581541980
208 -0.406888834
209 0.198155985
210 -0.223763886