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

$R= 25.2524967393$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.520180571
4 0.5
5 0.447213595
6 -1.074929990
7 1.508623190
8 -0.353553390
9 1.310948969
10 -0.316227766
11 0.205261311
12 0.760090285
13 1.227673000
14 -1.066757688
15 0.679845419
16 0.250000000
17 0.734915692
18 -0.926980906
19 1.250532490
20 0.223606797
21 2.293379663
22 -0.145141665
23 -1.043233519
24 -0.537464995
25 0.200000000
26 -0.868095903
27 0.472698581
28 0.754311595
29 -0.435004329
30 -0.480723306
31 1.157136061
32 -0.176776695
33 0.312034258
34 -0.519663870
35 0.674676801
36 0.655474484
37 -1.382501552
38 -0.884260003
39 1.866284643
40 -0.158113883
41 0.235412385
42 -1.621664311
43 1.174052146
44 0.102630655
45 0.586274202
46 0.737677496
47 0.491983751
48 0.380045142
49 1.275943930
50 -0.141421356
51 1.117204557
52 0.613836500
53 1.111326033
54 -0.334248372
55 0.0917956492
56 -0.533378844
57 1.901035195
58 0.307594510
59 -1.629201676
60 0.339922709
61 1.196726690
62 -0.818218755
63 1.977728016
64 0.125000000
65 0.549032056
66 -0.220641539
67 0.372958278
68 0.367457846
69 -1.585903328
70 -0.477068541
71 -1.842624393
72 -0.463490453
73 -1.343626376
74 0.977576223
75 0.304036114
76 0.625266245
77 0.309661974
78 -1.319662526
79 -0.631336345
80 0.111803398
81 -0.592361769
82 -0.166461694
83 -1.581302553
84 1.146689831
85 0.328664289
86 -0.830180234
87 -0.661285129
88 -0.0725708327
89 1.418901926
90 -0.414558463
91 1.852095958
92 -0.521616759
93 1.759055759
94 -0.347885047
95 0.559255131
96 -0.268732497
97 -0.650575347
98 -0.902228605
99 0.269087105
100 0.100000000
101 -1.634002983
102 -0.789982918
103 1.586709124
104 -0.434047951
105 1.025630565
106 -0.785826174
107 -0.728593040
108 0.236349290
109 0.285642239
110 -0.0649093260
111 -2.101652000
112 0.377155797
113 -1.032533641
114 -1.344234878
115 -0.466548213
116 -0.217502164
117 1.609416654
118 1.152019553
119 1.108710857
120 -0.240361653
121 -0.957867793
122 -0.846213558
123 0.357869335
124 0.578568030
125 0.0894427190
126 -1.398464891
127 -1.221234994
128 -0.0883883476
129 1.784771264
130 -0.388224290
131 0.259026854
132 0.156017129
133 1.886582314
134 -0.263721327
135 0.211397232
136 -0.259831935
137 1.146598340
138 1.121402997
139 -0.750017690
140 0.337338400
141 0.747904154
142 1.302932204
143 0.251993773
144 0.327737242
145 -0.194539850
146 0.950087322
147 1.939665167
148 -0.691250776
149 -0.133062356
150 -0.214985998
151 -1.438774941
152 -0.442130001
153 0.963436971
154 -0.218964082
155 0.517486978
156 0.933142321
157 1.461478503
158 0.446422211
159 1.689415861
160 -0.0790569415
161 -1.573845868
162 0.418863023
163 -0.0389910474
164 0.117706192
165 0.139545962
166 1.118149758
167 0.712471890
168 -0.810832155
169 0.507183235
170 -0.232400747
171 1.639377589
172 0.587026073
173 0.359984276
174 0.467599199
175 0.301724638
176 0.0513153279
177 -2.476666059
178 -1.003315173
179 0.884677271
180 0.293137101
181 0.548355189
182 -1.309629611
183 1.819214695
184 0.368838748
185 -0.618273490
186 -1.243840255
187 0.150721222
188 0.245991875
189 0.713305339
190 -0.395453095
191 -1.062516797
192 0.190022571
193 1.245880480
194 0.460026240
195 0.834627865
196 0.637971965
197 -0.845813976
198 -0.190273316
199 1.184732360
200 -0.0707106781
201 0.568829042
202 1.155414590
203 -0.657985876
204 0.558602278
205 0.105279619
206 -1.121972781
207 -1.376794241
208 0.306918250
209 0.283042419
210 -0.725230327
211 -0.564564731
212 0.555663016
213 -2.796705924
214 0.515193079
215 0.525052081
216 -0.167124186
217 1.797579881
218 -0.201979564
219 -2.122528352
220 0.0458978246
221 1.173438864
222 1.486092381