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

$R= 7.56348983462$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.339300156
4 0.5
5 -0.447213595
6 -0.239921441
7 0.139947613
8 0.353553390
9 -0.884875403
10 -0.316227766
11 -1.354417235
12 -0.169650078
13 -1.151271487
14 0.0989579066
15 0.151739643
16 0.250000000
17 -0.631270843
18 -0.625701398
19 0.0283025593
20 -0.223606797
21 -0.0474842472
22 -0.957717611
23 0.918653885
24 -0.119960720
25 0.200000000
26 -0.814071875
27 0.639538519
28 0.0699738068
29 1.101272764
30 0.107296130
31 -1.534506155
32 0.176776695
33 0.459553980
34 -0.446375894
35 -0.0625864755
36 -0.442437701
37 -0.544979648
38 0.0200129316
39 0.390626596
40 -0.158113883
41 0.587445229
42 -0.0335764332
43 1.653581446
44 -0.677208617
45 0.395728310
46 0.649586392
47 -0.781004251
48 -0.0848250391
49 -0.980414665
50 0.141421356
51 0.214190296
52 -0.575635743
53 -1.840894207
54 0.452222024
55 0.605713801
56 0.0494789533
57 -0.00960306281
58 0.778717439
59 0.119196637
60 0.0758698215
61 1.875984822
62 -1.085059708
63 -0.123836201
64 0.125000000
65 0.514864261
66 0.324953735
67 -1.212148666
68 -0.315635421
69 -0.311699407
70 -0.0442553212
71 0.460179575
72 -0.312850699
73 0.519610781
74 -0.385358804
75 -0.0678600313
76 0.0141512796
77 -0.189547460
78 0.276214714
79 -1.576740100
80 -0.111803398
81 0.667879883
82 0.415386505
83 0.123591989
84 -0.0237421236
85 0.282312903
86 1.169258653
87 -0.373662021
88 -0.478858805
89 0.341120299
90 0.279822172
91 -0.161117697
92 0.459326942
93 0.520658178
94 -0.552253402
95 -0.0126572893
96 -0.0599803604
97 -1.000588999
98 -0.693257858
99 1.198490498
100 0.100000000
101 0.405191999
102 0.151455410
103 -0.901773000
104 -0.407035937
105 0.0212356009
106 -1.301708777
107 -1.501851999
108 0.319769259
109 1.260369999
110 0.428304336
111 0.184911680
112 0.0349869034
113 0.382599999
114 -0.00679039083
115 -0.410834507
116 0.550636382
117 1.018731822
118 0.0842847507
119 -0.0883448481
120 0.0536480652
121 0.834446048
122 1.326521589
123 -0.199320258
124 -0.767253077
125 -0.0894427190
126 -0.0875654176
127 -1.753499999
128 0.0883883476
129 -0.561060443
130 0.364064010
131 -0.102999999
132 0.229776990
133 0.00396087563
134 -0.857118541
135 -0.286010320
136 -0.223187947