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

$R= 27.9703069143$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.0787993516
4 0.5
5 -0.447213595
6 -0.0557195558
7 1.731826195
8 -0.353553390
9 -0.993790662
10 0.316227766
11 0.751272706
12 0.0393996758
13 -1.823874551
14 -1.224586046
15 -0.0352401413
16 0.250000000
17 0.670382665
18 0.702716116
19 -1.943371202
20 -0.223606797
21 0.136466781
22 -0.531230024
23 -0.134947249
24 -0.0278597779
25 0.200000000
26 1.289674063
27 -0.157109411
28 0.865913097
29 1.061874122
30 0.0249185429
31 0.0921965451
32 -0.176776695
33 0.0591998021
34 -0.474032128
35 -0.774496219
36 -0.496895331
37 0.234697687
38 1.374170955
39 -0.143720132
40 0.158113883
41 -1.084626408
42 -0.0964965864
43 -0.923262227
44 0.375636353
45 0.444436695
46 0.0954221155
47 0.510151149
48 0.0196998379
49 1.999221971
50 -0.141421356
51 0.0528257194
52 -0.911937275
53 0.126112285
54 0.111093130
55 -0.335979368
56 -0.612293023
57 -0.153136390
58 -0.750858392
59 1.625785262
60 -0.0176200706
61 0.627185713
62 -0.0651928022
63 -1.721072701
64 0.125000000
65 0.815661495
66 -0.0418605815
67 1.469284987
68 0.335191332
69 -0.0106337558
70 0.547651528
71 -0.765647687
72 0.351358058
73 -0.665887039
74 -0.165956326
75 0.0157598703
76 -0.971685601
77 1.301073752
78 0.101625480
79 -1.216334573
80 -0.111803398
81 0.981410542
82 0.766946688
83 -1.126999981
84 0.0682333906
85 -0.299804242
86 0.652844982
87 0.0836749923
88 -0.265615012
89 1.126994802
90 -0.314264200
91 -3.158633725
92 -0.0674736249
93 0.00726502797
94 -0.360731336
95 0.869102022
96 -0.0139298889
97 -1.057814097
98 -1.413663413
99 -0.746607799
100 0.100000000
101 -1.402294452
102 -0.0373534244
103 1.081678765
104 0.644837031
105 -0.0610297999
106 -0.0891748525
107 -0.378529515
108 -0.0785547057
109 0.134329691
110 0.237573289
111 0.0184940255
112 0.432956548
113 -1.167483246
114 0.108283780
115 0.0603502448
116 0.530937061
117 1.812549498
118 -1.149603783
119 1.160986261
120 0.0124592714
121 -0.435589321
122 -0.443487271
123 -0.0854678576
124 0.0460982725
125 -0.0894427190
126 1.216982178
127 0.516313111
128 -0.0883883476
129 -0.0727524647
130 -0.576759774
131 1.334231842
132 0.0295999010
133 -3.365581156
134 -1.038941377
135 0.0702614647
136 -0.237016064
137 -0.593235824
138 0.00751920083
139 0.145726879
140 -0.387248109
141 0.0401995793
142 0.541394671
143 -1.370227169
144 -0.248447665
145 -0.474884544
146 0.470853241
147 0.157537395
148 0.117348843
149 0.676523468
150 -0.0111439111
151 0.219501897
152 0.687085477
153 -0.666220028
154 -0.919998073
155 -0.0412315484
156 -0.0718600660
157 -0.228912881
158 0.860078425
159 0.00993758593
160 0.0790569415
161 -0.233705169
162 -0.693962049
163 -0.139580840
164 -0.542313204
165 -0.0264749563
166 0.796909329
167 1.198858484
168 -0.0482482932
169 2.326518381
170 0.211993612
171 1.931304140
172 -0.461631113
173 0.556677852
174 -0.0591671544
175 0.346365239
176 0.187818176
177 0.128110848
178 -0.796905667
179 1.291939750
180 0.222218347
181 -0.566937083
182 2.233491326
183 0.0494230573
184 0.0477110577
185 -0.104959996
186 -0.00513715054
187 0.503639687
188 0.255075574
189 -0.272085452
190 -0.614547933
191 0.580541166
192 0.00984991895
193 0.676631369
194 0.747987521
195 0.0642735970
196 0.999610985
197 -0.974119132
198 0.527931438
199 1.030205489
200 -0.0707106781
201 0.115750697
202 0.991571916
203 1.839013410
204 0.0264128597
205 0.485059675
206 -0.764862389
207 0.133908777
208 -0.455968637
209 -1.459823977
210 0.0431545853
211 1.803939325
212 0.0630561429
213 -0.0604033639
214 0.267660787
215 0.412895420
216 0.0555465651
217 0.156278092
218 -0.0949854358
219 -0.0524640242
220 -0.167989684
221 -1.227410949
222 -0.0130772509
223 0.805158612
224 -0.306146511
225 -0.198758132
226 0.825535320
227 -0.0650212827
228 -0.0765681953
229 1.104437890
230 -0.0426740673
231 0.0894605828
232 -0.375429196