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

$R= 4.64274919042$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.080839253
4 0.499999999
5 0.447213595
6 -0.764268765
7 1.531132989
8 -0.353553390
9 0.168213491
10 -0.316227766
11 0.915986377
12 0.540419626
13 -0.806179941
14 -1.082674519
15 0.483366008
16 0.249999999
17 -0.603903078
18 -0.118944900
19 0.890052229
20 0.223606797
21 1.654908637
22 -0.647700179
23 -1.219966174
24 -0.382134382
25 0.200000000
26 0.570055303
27 -0.899027508
28 0.765566494
29 -1.437404644
30 -0.341791382
31 0.592768703
32 -0.176776695
33 0.990034032
34 0.427023962
35 0.684743489
36 0.0841067459
37 0.980234057
38 -0.629361966
39 -0.871350926
40 -0.158113883
41 0.0873745959
42 -1.170197119
43 -1.137881900
44 0.457993188
45 0.0752273604
46 0.862646354
47 -0.324142822
48 0.270209813
49 1.344368230
50 -0.141421356
51 -0.652722152
52 -0.403089970
53 -0.550686644
54 0.635708447
55 0.409641561
56 -0.541337259
57 0.962003387
58 1.016398571
59 -1.437991095
60 0.241683004
61 0.645030732
62 -0.419150770
63 0.257557226
64 0.124999999
65 -0.360534630
66 -0.700059778
67 -0.159642106
68 -0.301951539
69 -1.318587329
70 -0.484186764
71 1.515932209
72 -0.0594724503
73 -0.331655629
74 -0.693130149
75 0.216167850
76 0.445026114
77 1.402496960
78 0.616138148
79 0.877903180
80 0.111803398
81 -1.139917712
82 -0.0617831693
83 0.333598999
84 0.827454318
85 -0.270073667
86 0.804604007
87 -1.553603363
88 -0.323850089
89 -0.0940857999
90 -0.0531937767
91 -1.234368704
92 -0.609983087
93 0.640687683
94 0.229203587
95 0.398043457
96 -0.191067191
97 0.101263000
98 -0.950611892
99 0.154081267
100 0.100000000
101 -0.103900000
102 0.461544260
103 -0.943119999
104 0.285027651
105 0.740097641
106 0.389394260
107 0.950099999
108 -0.449513754
109 1.005300000
110 -0.289660326
111 1.059475447
112 0.382783247
113 -0.213999999
114 -0.680239118
115 -0.545585459
116 -0.718702322
117 -0.135610343
118 1.016813255
119 -0.924655925
120 -0.170895691
121 -0.160968955
122 -0.456105605
123 0.0944378931
124 0.296384351
125 0.0894427190
126 -0.182120461
127 -0.479999999
128 -0.0883883476
129 -1.229867423
130 0.254936482