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

$R= 6.4845713681$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.595578528
4 0.499999999
5 0.447213595
6 -1.128244397
7 1.429328252
8 0.353553390
9 1.545870840
10 0.316227766
11 0.165764734
12 -0.797789264
13 0.577731306
14 1.010687699
15 -0.713564410
16 0.249999999
17 -0.964544706
18 1.093095754
19 1.762468762
20 0.223606797
21 -2.280605469
22 0.117213367
23 0.272053286
24 -0.564122198
25 0.200000000
26 0.408517724
27 -0.870979792
28 0.714664126
29 0.611671210
30 -0.504566233
31 0.589121985
32 0.176776695
33 -0.264490650
34 -0.682036102
35 0.639215026
36 0.772935420
37 -1.405112330
38 1.246253613
39 -0.921815667
40 0.158113883
41 0.288727058
42 -1.612631592
43 -0.780251746
44 0.0828823670
45 0.691334456
46 0.192370723
47 1.046107629
48 -0.398894632
49 1.042979253
50 0.141421356
51 1.539006823
52 0.288865653
53 -1.311551784
54 -0.615875717
55 0.0741322427
56 0.505343849
57 -2.812157315
58 0.432516860
59 -0.925550214
60 -0.356782205
61 0.122720204
62 0.416572150
63 2.209556867
64 0.124999999
65 0.258369294
66 -0.187023132
67 -0.343113806
68 -0.482272353
69 -0.434082382
70 0.451993280
71 0.444035479
72 0.546547877
73 0.0855293599
74 -0.993564457
75 -0.319115705
76 0.881234381
77 0.236932217
78 -0.651822109
79 1.295369599
80 0.111803398
81 -0.156154184
82 0.204160860
83 -0.924409799
84 -1.140302734
85 -0.431357506
86 -0.551721300
87 -0.975969449
88 0.0586066837
89 1.050753000
90 0.488847282
91 0.825767678
92 0.136026643
93 -0.939990390
94 0.739709798
95 0.788199992
96 -0.282061099
97 -0.900329999
98 0.737497702
99 0.256250868
100 0.100000000
101 -1.020350000
102 1.088242161
103 1.908741999
104 0.204258862
105 -1.019917772
106 -0.927407160
107 -1.314799999
108 -0.435489896
109 0.225399999
110 0.0524194115
111 2.241967064
112 0.357332063
113 -0.590670000
114 -1.988495507
115 0.121665928
116 0.305835605
117 0.893097980
118 -0.654462832
119 -1.378650999
120 -0.252283116
121 -0.972522052
122 0.0867762891
123 -0.460686695
124 0.294560992
125 0.0894427190
126 1.562392644
127 0.750000000
128 0.0883883476
129 1.244952932
130 0.182694680