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

$R= 20.1661566994$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.370989114
4 0.5
5 -0.447213595
6 0.262328918
7 -0.160619135
8 -0.353553390
9 -0.862367076
10 0.316227766
11 1.119386323
12 -0.185494557
13 -0.312623967
14 0.113574880
15 0.165911375
16 0.250000000
17 -0.352270782
18 0.609785607
19 0.718801390
20 -0.223606797
21 0.0595879510
22 -0.791525660
23 -1.059709828
24 0.131164459
25 0.200000000
26 0.221058527
27 0.690917913
28 -0.0803095678
29 0.149689607
30 -0.117317059
31 0.0841935420
32 -0.176776695
33 -0.415280141
34 0.249093059
35 0.0718310612
36 -0.431183538
37 -0.388010132
38 -0.508269337
39 0.115980088
40 0.158113883
41 1.921356200
42 -0.0421350442
43 0.778202024
44 0.559693161
45 0.385662280
46 0.749328005
47 -0.0209174481
48 -0.0927472787
49 -0.974201493
50 -0.141421356
51 0.130688625
52 -0.156311983
53 1.359795002
54 -0.488552741
55 -0.500604782
56 0.0567874400
57 -0.266667491
58 -0.105846536
59 0.586972866
60 0.0829556879
61 1.312105434
62 -0.0595338245
63 0.138512654
64 0.125000000
65 0.139809688
66 0.293647404
67 0.530601644
68 -0.176135391
69 0.393140811
70 -0.0507922304
71 -0.453792407
72 0.304892803
73 1.408753543
74 0.274364595
75 -0.0741978229
76 0.359400695
77 -0.179794863
78 -0.0820103073
79 -1.266713839
80 -0.111803398
81 0.606044051
82 -1.358603998
83 -1.580499801
84 0.0297939755
85 0.157540283
86 -0.550271928
87 -0.0555332148
88 -0.395762830
89 -0.742770993
90 -0.272704414
91 0.0502133915
92 -0.529854914
93 -0.0312348876
94 0.0147908694
95 -0.321457754
96 0.0655822297
97 -0.658441318
98 0.688864482
99 -0.965321911
100 0.100000000
101 -1.676731316
102 -0.0924108136
103 -1.894278632
104 0.110529263
105 -0.0266485418
106 -0.961520267
107 -0.125288187
108 0.345458956
109 0.0271707382
110 0.353981036
111 0.143947534
112 -0.0401547839
113 -0.592336969
114 0.188562391
115 0.473916642
116 0.0748448036
117 0.269596617
118 -0.415052494
119 0.0565814300
120 -0.0586585295
121 0.253025737
122 -0.927798650
123 -0.712802251
124 0.0420967710
125 -0.0894427190
126 -0.0979432373
127 -0.468694992
128 -0.0883883476
129 -0.288704466
130 -0.0988603788
131 0.432642595
132 -0.207640070
133 -0.115453246
134 -0.375192020
135 -0.308987884
136 0.124546529
137 0.738814259
138 -0.277992533
139 1.703798555
140 0.0359155306
141 0.00775980482
142 0.320879688
143 -0.349946892
144 -0.215591769
145 -0.0669432275
146 -0.996139183
147 0.361419152
148 -0.194005066
149 0.938300579
150 0.0524657837
151 -1.120079109
152 -0.254134668
153 0.303786017
154 0.127134167
155 -0.0376524966
156 0.0579900444
157 -1.408265246
158 0.895701945
159 -0.504492859
160 0.0790569415
161 0.170184614
162 -0.428537858
163 0.0747559265
164 0.960678100
165 0.185718925
166 1.117582126
167 -0.936445927
168 -0.0210675221
169 -0.902351221
170 -0.111397802
171 -0.620478124
172 0.389101012
173 1.188572212
174 0.0392679128
175 -0.0321238271
176 0.279846580
177 -0.217249720
178 0.525218406
179 -0.540728382
180 0.192831140
181 0.501222879
182 -0.0355062296
183 -0.490330189
184 0.374664002
185 0.173523406
186 0.0220864008
187 -0.405622357
188 -0.0104587240
189 -0.120459734
190 0.227304957
191 -0.622582204
192 -0.0463736393
193 -1.739414089
194 0.465588321
195 -0.0518678725
196 -0.487100746
197 -1.290297124
198 0.682585669