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

$R= 5.42416298033$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.905859327
4 0.499999999
5 -0.447213595
6 0.640539273
7 1.779314914
8 -0.353553390
9 -0.179418879
10 0.316227766
11 0.135545297
12 -0.452929663
13 1.113768838
14 -1.258165641
15 0.405112606
16 0.249999999
17 0.848420991
18 0.126868306
19 0.270004355
20 -0.223606797
21 -1.611809011
22 -0.0958449992
23 -0.177106924
24 0.320269636
25 0.200000000
26 -0.787553498
27 1.068387592
28 0.889657457
29 1.311458338
30 -0.286457871
31 -1.035372479
32 -0.176776695
33 -0.122784972
34 -0.599924236
35 -0.795733820
36 -0.0897094396
37 1.401442843
38 -0.190921910
39 -1.008917890
40 0.158113883
41 -0.811855878
42 1.139721081
43 1.039735548
44 0.0677726488
45 0.0802385621
46 0.125233507
47 -1.400637207
48 -0.226464831
49 2.165961564
50 -0.141421356
51 -0.768550068
52 0.556884419
53 -0.162334862
54 -0.755464111
55 -0.0606176999
56 -0.629082820
57 -0.244585963
58 -0.927341084
59 0.645789609
60 0.202556303
61 0.313877589
62 0.732118901
63 -0.319242687
64 0.124999999
65 -0.498092566
66 0.0868220865
67 -0.0864267999
68 0.424210495
69 0.160433959
70 0.562668780
71 0.271008499
72 0.0634341531
73 0.825589800
74 -0.990969738
75 -0.181171865
76 0.135002177
77 0.241177769
78 0.713412681
79 -1.286256999
80 -0.111803398
81 -0.788389986
82 0.574068797
83 -0.433910000
84 -0.805904505
85 -0.379425402
86 -0.735204057
87 -1.187996768
88 -0.0479224996
89 1.879453000
90 -0.0567372314
91 1.981745504
92 -0.0885534623
93 0.937901817
94 0.990400067
95 -0.120749618
96 0.160134818
97 0.310199999
98 -1.531566109
99 -0.0243193854
100 0.100000000
101 -0.938799999
102 0.543446965
103 -0.567999999
104 -0.393776749
105 0.720822903
106 0.114788082
107 -0.776900000
108 0.534193796
109 -0.367999999
110 0.0428631867
111 -1.269510071
112 0.444828728
113 -0.419999999
114 0.172948393
115 0.0792046245
116 0.655729169
117 -0.199831156
118 -0.456642211
119 1.509608124
120 -0.143228935
121 -0.981627472
122 -0.221944972
123 0.735427220
124 -0.517686239
125 -0.0894427190
126 0.225738669
127 1.100000000
128 -0.0883883476
129 -0.941854144
130 0.352204631