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

$R= 3.59362788512$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.795237892
4 0.5
5 -0.447213595
6 0.562318106
7 -0.899804719
8 -0.353553390
9 -0.367596693
10 0.316227766
11 1.496840608
12 -0.397618946
13 -1.122252763
14 0.636258018
15 0.355641197
16 0.250000000
17 -0.665073354
18 0.259930115
19 -1.124694255
20 -0.223606797
21 0.715558808
22 -1.058426144
23 1.079808371
24 0.281159053
25 0.200000000
26 0.793552539
27 1.087564713
28 -0.449902359
29 -1.150055047
30 -0.251476302
31 -0.430292791
32 -0.176776695
33 -1.190344371
34 0.470277878
35 0.402404903
36 -0.183798346
37 -0.367025502
38 0.795278934
39 0.892457922
40 0.158113883
41 0.366062478
42 -0.505976485
43 -0.283147973
44 0.748420304
45 0.164394239
46 -0.763539821
47 0.242440106
48 -0.198809473
49 -0.190351467
50 -0.141421356
51 0.528891532
52 -0.561126381
53 -0.297510284
54 -0.769024383
55 -0.669407470
56 0.318129009
57 0.894399489
58 0.813211723
59 -0.926145769
60 0.177820598
61 -0.174208400
62 0.304262950
63 0.330765239
64 0.125000000
65 0.501886693
66 0.841700576
67 0.0700250679
68 -0.332536677
69 -0.858704533
70 -0.284543236
71 -0.360022999
72 0.129965057
73 1.470123999
74 0.259526222
75 -0.159047578
76 -0.562347127
77 -1.346864243
78 -0.631063049
79 0.814991000
80 -0.111803398
81 -0.497275976
82 -0.258845260
83 -1.372230000
84 0.357779404
85 0.297429846
86 0.200215852
87 0.914567352
88 -0.529213072
89 1.572799999
90 -0.116244281
91 1.009808332
92 0.539904185
93 0.342185132
94 -0.171431043
95 0.502978561
96 0.140579526
97 -0.914000000
98 0.134598813
99 -0.550233658
100 0.100000000
101 -1.633999999
102 -0.373982789
103 -0.826999999
104 0.396776269
105 -0.320007627
106 0.210371539
107 1.026999999
108 0.543782356
109 -1.520000000
110 0.473342561
111 0.291872587
112 -0.224951179