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

$R= 22.490200783$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.626116247
4 0.5
5 -0.447213595
6 0.442731044
7 1.135474736
8 -0.353553390
9 -0.607978444
10 0.316227766
11 -0.758822369
12 -0.313058123
13 -0.467692681
14 -0.802901885
15 0.280007698
16 0.250000000
17 0.426406682
18 0.429905680
19 1.566633873
20 -0.223606797
21 -0.710939181
22 0.536568443
23 -1.554746723
24 0.221365522
25 0.200000000
26 0.330708666
27 1.006781430
28 0.567737368
29 -1.302553050
30 -0.197995342
31 1.627864838
32 -0.176776695
33 0.475111014
34 -0.301515056
35 -0.507799739
36 -0.303989222
37 -0.0714477901
38 -1.107777435
39 0.292829986
40 0.158113883
41 -1.092952762
42 0.502709916
43 0.383788704
44 -0.379411184
45 0.271896225
46 1.099371951
47 -0.264505671
48 -0.156529061
49 0.289302876
50 -0.141421356
51 -0.266980152
52 -0.233846340
53 -1.437764993
54 -0.711901976
55 0.339355680
56 -0.401450942
57 -0.980894922
58 0.921044094
59 -0.648266445
60 0.140003849
61 -0.722418939
62 -1.151074266
63 -0.690344163
64 0.125000000
65 0.209158525
66 -0.335954220
67 0.946383511
68 0.213203341
69 0.973452185
70 0.359068639
71 0.605103993
72 0.214952840
73 -1.487969124
74 0.0505212169
75 -0.125223249
76 0.783316936
77 -0.861623630
78 -0.207062069
79 -1.302242084
80 -0.111803398
81 -0.0223837674
82 0.772834309
83 -1.606420987
84 -0.355469590
85 -0.190694865
86 -0.271379595
87 0.815549628
88 0.268284221
89 0.520464235
90 -0.192259665
91 -0.531053223
92 -0.777373361
93 -1.019232624
94 0.187033754
95 -0.700619967
96 0.110682761
97 0.363273830
98 -0.204568026
99 0.461347643
100 0.100000000
101 0.775623255
102 0.188783475
103 -0.247411975
104 0.165354333
105 0.317941667
106 1.016653376
107 1.665767479
108 0.503390715
109 0.400560506
110 -0.239960702
111 0.0447346230
112 0.283868684
113 0.149500137
114 0.693597451
115 0.695303872
116 -0.651276525
117 0.284347070
118 0.458393599
119 0.484174018
120 -0.0989976711
121 -0.424188610
122 0.510827330
123 0.684315479
124 0.813932419
125 -0.0894427190
126 0.488147039
127 1.060790153
128 -0.0883883476
129 -0.240296324
130 -0.147897411
131 1.760347900
132 0.237555507
133 1.778873195
134 -0.669194198
135 -0.450246343
136 -0.150757528
137 -0.196444836
138 -0.688334641
139 0.866473432
140 -0.253899869
141 0.165611366
142 -0.427873137
143 0.354896083
144 -0.151994611
145 0.582519432
146 1.052153058
147 -0.181136635
148 -0.0357238950
149 -0.721741776
150 0.0885462089
151 0.627121469
152 -0.553888717
153 -0.259245857
154 0.609259911
155 -0.728003287
156 0.146414993
157 0.536912203
158 0.920824208
159 0.900211549
160 0.0790569415
161 -1.765362761
162 0.0158277137
163 0.763235539
164 -0.546476381
165 -0.212476105
166 1.135911173
167 1.012672888
168 0.251354958
169 -0.781265685
170 0.134841632
171 -0.952548601
172 0.191894352
173 0.422268095
174 -0.576680672
175 0.227094947
176 -0.189705592
177 0.405832528
178 -0.368023790
179 -1.823253103
180 0.135948112
181 -1.375278777
182 0.375511335
183 0.451445958
184 0.549685975
185 0.0319524231
186 0.720706300
187 -0.326715740
188 -0.132252835
189 1.135704153
190 0.495413130
191 1.760977486
192 -0.0782645309
193 -0.295334708
194 -0.256873389
195 -0.130957551
196 0.144651438
197 0.810432106
198 -0.326222047
199 -0.599363677
200 -0.0707106781
201 -0.596616287
202 -0.548448463
203 -1.297065460
204 -0.133490076
205 0.488783334
206 0.174946685
207 1.073577933
208 -0.116923170
209 -0.545844442
210 -0.224818709
211 1.517074560
212 -0.718882496
213 0.0154871670