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

$R= 8.42338862095$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.149114123
4 0.5
5 0.447213595
6 0.105439607
7 -1.326421961
8 -0.353553390
9 -0.977764978
10 -0.316227766
11 1.676059340
12 -0.0745570615
13 -0.575060667
14 0.937921963
15 -0.0666858631
16 0.250000000
17 1.377595705
18 0.691384246
19 0.528604624
20 0.223606797
21 0.197788247
22 -1.185152924
23 0.0441053409
24 0.0527198037
25 0.200000000
26 0.406629297
27 0.294912690
28 -0.663210980
29 1.307099680
30 0.0471540260
31 0.610190728
32 -0.176776695
33 -0.249924118
34 -0.974107265
35 -0.593193934
36 -0.488882489
37 1.432141805
38 -0.373779914
39 0.0857496670
40 -0.158113883
41 0.230826198
42 -0.139857411
43 -0.187406776
44 0.838029670
45 -0.437269791
46 -0.0311871856
47 0.513203200
48 -0.0372785307
49 0.759395218
50 -0.141421356
51 -0.205418975
52 -0.287530333
53 -1.144537578
54 -0.208534763
55 0.749556523
56 0.468960981
57 -0.0788224149
58 -0.924259047
59 -1.250664590
60 -0.0333429315
61 1.435261915
62 -0.431470001
63 1.296928939
64 0.125000000
65 -0.257174948
66 0.176723039
67 -0.857066486
68 0.688797852
69 -0.00657672923
70 0.419451453
71 1.599390520
72 0.345692123
73 -1.085886316
74 -1.012677182
75 -0.0298228246
76 0.264302312
77 -2.223161916
78 -0.0606341710
79 -0.504495262
80 0.111803398
81 0.933789331
82 -0.163218770
83 0.0706178100
84 0.0988941237
85 0.616079528
86 0.132516602
87 -0.194907022
88 -0.592576462
89 1.498002779
90 0.309196434
91 0.762773097
92 0.0220526704
93 -0.0909880553
94 -0.362889463
95 0.236399174
96 0.0263599018
97 0.0203559999
98 -0.536973508
99 -1.638792124
100 0.100000000
101 -0.0116293000
102 0.145253150
103 0.0655180000
104 0.203314648
105 0.0884535933
106 0.809310283
107 -1.692390000
108 0.147456345
109 0.589860999
110 -0.530016500
111 -0.213552569
112 -0.331605490
113 0.550030000
114 0.0557358641
115 0.0197245080
116 0.653549840
117 0.562274180
118 0.884353413
119 -1.827273197
120 0.0235770130
121 1.809174911
122 -1.014883433
123 -0.0344194461
124 0.305095364
125 0.0894427190
126 -0.917067248
127 1.443000000
128 -0.0883883476
129 0.0279449970
130 0.181850150
131 -0.612999999
132 -0.124962059
133 -0.701152782
134 0.606037524
135 0.131888964
136 -0.487053632