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

$R= 11.5198192086$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.604138285
4 0.5
5 0.447213595
6 0.427190278
7 1.381000738
8 -0.353553390
9 -0.635016931
10 -0.316227766
11 1.266202546
12 -0.302069142
13 -0.650177156
14 -0.976514986
15 -0.270178854
16 0.250000000
17 -1.480686229
18 0.449024778
19 -0.803110596
20 0.223606797
21 -0.834315418
22 -0.895340406
23 1.595947646
24 0.213595139
25 0.200000000
26 0.459744676
27 0.987776326
28 0.690500369
29 0.0258481445
30 0.191045300
31 1.236145979
32 -0.176776695
33 -0.764961435
34 1.047003273
35 0.617602305
36 -0.317508465
37 0.0111550072
38 0.567884948
39 0.392796912
40 -0.158113883
41 -0.0351277977
42 0.589950090
43 1.079777016
44 0.633101273
45 -0.283988205
46 -1.128505403
47 -1.261633311
48 -0.151034571
49 0.907163039
50 -0.141421356
51 0.894539240
52 -0.325088578
53 -0.0270986714
54 -0.698463338
55 0.566262993
56 -0.488257493
57 0.485189858
58 -0.0182773983
59 1.269389060
60 -0.135089427
61 1.390329383
62 -0.874087204
63 -0.876958851
64 0.125000000
65 -0.290768063
66 0.540909418
67 -0.941792524
68 -0.740343114
69 -0.964173074
70 -0.436710778
71 1.016745089
72 0.224512389
73 0.668821295
74 -0.00788778130
75 -0.120827657
76 -0.401555298
77 1.748626652
78 -0.277749360
79 1.058447941
80 0.111803398
81 0.0382634354
82 0.0248391039
83 -0.724710686
84 -0.417157709
85 -0.662183012
86 -0.763517650
87 -0.0156158508
88 -0.447670203
89 0.897556970
90 0.200809985
91 -0.897895129
92 0.797973823
93 -0.746803092
94 0.892109470
95 -0.359161977
96 0.106797569
97 0.750756029
98 -0.641461136
99 -0.804060079
100 0.100000000
101 1.008448861
102 -0.632534762
103 1.232121583
104 0.229872338
105 -0.373117198
106 0.0191616543
107 -0.548846700
108 0.493888163
109 0.235981468
110 -0.400408402
111 -0.00673905875
112 0.345250184
113 0.0856340138
114 -0.343081039
115 0.713729485
116 0.0129240722
117 0.412866789
118 -0.897593612
119 -2.044826834
120 0.0955226502
121 0.603265786
122 -0.983111334
123 0.0212014824
124 0.618072989
125 0.0894427190
126 0.620103550
127 -0.235550926
128 -0.0883883476
129 -0.652324234
130 0.205604069
131 1.672993080
132 -0.382480717
133 -1.109258457
134 0.665947880
135 0.441747002
136 0.523501636
137 -1.303411146
138 0.681773319
139 1.798698336
140 0.308801152
141 0.762303903
142 -0.718947347
143 -0.825047714
144 -0.158754232
145 0.0115596416
146 -0.472928073
147 -0.554663468
148 0.00557750364
149 -1.613433488
150 0.0854380556
151 0.351639193
152 0.283942474
153 0.924647510
154 -1.236465763
155 0.552821287
156 0.196398456