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

$R= 12.9582818801$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.885765320
4 0.5
5 0.447213595
6 0.626330664
7 -0.890160208
8 -0.353553390
9 -0.215419797
10 -0.316227766
11 0.0254015799
12 -0.442882660
13 1.364018809
14 0.629438320
15 -0.396126293
16 0.250000000
17 -0.169867128
18 0.152324799
19 0.550229074
20 0.223606797
21 0.788473042
22 -0.0179616294
23 1.633451940
24 0.313165332
25 0.200000000
26 -0.964506950
27 1.076576706
28 -0.445080104
29 -0.112110883
30 0.280103588
31 -1.206332683
32 -0.176776695
33 -0.0224998385
34 0.120114198
35 -0.398091747
36 -0.107709898
37 -1.361417949
38 -0.389070710
39 -1.208200557
40 -0.158113883
41 -0.843747463
42 -0.557534635
43 1.098334586
44 0.0127007899
45 -0.0963386622
46 -1.155024944
47 0.585830340
48 -0.221441330
49 -0.207614802
50 -0.141421356
51 0.150462411
52 0.682009404
53 -1.189873058
54 -0.761254689
55 0.0113599318
56 0.314719160
57 -0.487373832
58 0.0792743656
59 -1.546185773
60 -0.198063146
61 1.372244328
62 0.853006021
63 0.191758132
64 0.125000000
65 0.610007756
66 0.0159097884
67 0.806931781
68 -0.0849335641
69 -1.446855081
70 0.281493374
71 -1.182509947
72 0.0761623998
73 -1.791934076
74 0.962667863
75 -0.177153064
76 0.275114537
77 -0.0226114761
78 0.854326807
79 -0.207074054
80 0.111803398
81 -0.738174511
82 0.596619553
83 1.576722176
84 0.394236521
85 -0.0759668892
86 -0.776639834
87 0.0993039305
88 -0.00898081471
89 -0.949192115
90 0.0681217213
91 -1.214195279
92 0.816725970
93 1.068527660
94 -0.414244606
95 0.246069922
96 0.156582666
97 -0.572152539
98 0.146805834
99 -0.00547204799
100 0.100000000
101 -0.867639043
102 -0.106392991
103 -0.302434603
104 -0.482253475
105 0.352615864
106 0.841367308
107 -0.965442267
108 0.538288353
109 0.665100813
110 -0.00803268487
111 1.205897684
112 -0.222540052
113 -1.167103922
114 0.344625342
115 0.730501915
116 -0.0560554415
117 -0.293834400
118 1.093318445
119 0.151213013
120 0.140051794
121 -0.999354523
122 -0.970323269
123 0.747364554
124 -0.603166341
125 0.0894427190
126 -0.135593475
127 -0.675403985
128 -0.0883883476
129 -0.972877383
130 -0.431340621
131 1.551797311
132 -0.0112499192
133 -0.489669787
134 -0.570586934
135 0.481459739
136 0.0600570991
137 0.783677688
138 1.023081039
139 -0.408441504
140 -0.199045873
141 -0.519179864
142 0.836160802
143 0.0346479268
144 -0.0538549494
145 -0.0501375111
146 1.267088737
147 0.184656619
148 -0.680708974
149 1.522396984
150 0.125266132
151 -1.772872517
152 -0.194535355
153 0.0412108868
154 0.0159887281
155 -0.539488376
156 -0.604100278