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

$R= 24.9540594028$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.068845121
4 0.5
5 -0.447213595
6 0.755787633
7 -0.420215629
8 0.353553390
9 0.142429893
10 -0.316227766
11 -1.401210132
12 0.534422560
13 1.215813371
14 -0.297137321
15 -0.478002069
16 0.250000000
17 0.266957379
18 0.100713143
19 0.829228641
20 -0.223606797
21 -0.449145425
22 -0.990805186
23 -0.246645340
24 0.377893816
25 0.200000000
26 0.859709879
27 -0.916609624
28 -0.210107814
29 0.265801770
30 -0.337998504
31 0.767349848
32 0.176776695
33 -1.497676614
34 0.188767373
35 0.187926142
36 0.0712149468
37 0.268261185
38 0.586353195
39 1.299516191
40 -0.158113883
41 -0.740748736
42 -0.317593776
43 -1.775721970
44 -0.700605066
45 -0.0636965849
46 -0.174404592
47 -1.525392611
48 0.267211280
49 -0.823418824
50 0.141421356
51 0.285336092
52 0.607906685
53 -0.493380817
54 -0.648140881
55 0.626640221
56 -0.148568660
57 0.886316988
58 0.187950234
59 -0.879403590
60 -0.239001034
61 -1.739281976
62 0.542598281
63 -0.0598512674
64 0.125000000
65 -0.543728269
66 -1.059017290
67 0.0425880156
68 0.133478689
69 -0.263625668
70 0.132883849
71 -0.812502162
72 0.0503565718
73 -0.653763394
74 0.189689303
75 0.213769024
76 0.414614320
77 0.588810397
78 0.918896711
79 -0.583861481
80 -0.111803398
81 -1.122143619
82 -0.523788455
83 -1.172977473
84 -0.224572712
85 -0.119386969
86 -1.255625046
87 0.284100925
88 -0.495402593
89 0.672497930
90 -0.0450402871
91 -0.510903781
92 -0.123322670
93 0.820178141
94 -1.078615459
95 -0.370842322
96 0.188946908
97 0.633734952
98 -0.582245034
99 -0.199574210
100 0.100000000
101 1.768849126
102 0.201763086
103 -1.083462519
104 0.429854939
105 0.200863940
106 -0.348872921
107 0.949027919
108 -0.458304812
109 0.146135443
110 0.443101550
111 0.286729659
112 -0.105053907
113 1.916682164
114 0.626720752
115 0.110303149
116 0.132900885
117 0.173168169
118 -0.621832242
119 -0.112179662
120 -0.168999252
121 0.963389837
122 -1.229858079
123 -0.791745672
124 0.383674924
125 -0.0894427190
126 -0.0423212370
127 -1.608715981
128 0.0883883476
129 -1.897971764
130 -0.384473946
131 1.502661906
132 -0.748838307
133 -0.348454833
134 0.0301142746
135 0.409920285
136 0.0943836866
137 1.472673178
138 -0.186411497
139 -1.071626968
140 0.0939630712
141 -1.630408443
142 -0.574525788
143 -1.703609996
144 0.0356074734
145 -0.118870165
146 -0.462280529
147 -0.880107186
148 0.134130592
149 -1.845119510
150 0.151157526
151 -1.180517472
152 0.293176597
153 0.0380226861
154 0.416351825
155 -0.343169284
156 0.649758095
157 -0.0149254751
158 -0.412852412
159 -0.527347657
160 -0.0790569415
161 0.103643923
162 -0.793475362
163 0.0919304775
164 -0.370374368
165 0.669781343
166 -0.829420325
167 -0.396253042
168 -0.158796888
169 0.478200764
170 -0.0844193357
171 0.118100144
172 -0.887860985
173 -1.049175286
174 0.200889690
175 -0.0840431258
176 -0.350302533
177 -0.939943488
178 0.475527847
179 1.749983031
180 -0.0318482924
181 0.297285498
182 -0.361263528
183 -1.859100532
184 -0.0872022963
185 -0.119970049
186 0.579953525
187 -0.374007597
188 -0.762696305
189 0.384814182
190 -0.262225120
191 -0.182928397
192 0.133605640
193 1.559346379
194 0.448118282
195 -0.581161308
196 -0.411709412
197 -0.0523787991
198 -0.141120277
199 0.0902791417
200 0.0707106781
201 0.0409328299
202 1.250765212
203 -0.113682666
204 0.142668046
205 0.331272906
206 -0.766123694
207 -0.0390577837
208 0.303953342
209 -1.173372139
210 0.142032254
211 -1.363939102
212 -0.246690408
213 -0.895663151
214 0.671064077
215 0.794127006
216 -0.324070440
217 -0.289446164
218 0.103333363
219 -0.739519022
220 0.313320110
221 0.177437137
222 0.202748486