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

$R= 9.46193719273$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.106378715
4 0.5
5 0.447213595
6 -0.0752211109
7 1.332746900
8 -0.353553390
9 -0.988683568
10 -0.316227766
11 -1.605483566
12 0.0531893576
13 1.442939524
14 -0.942394370
15 0.0475740077
16 0.250000000
17 -0.256744243
18 0.699104856
19 1.592329055
20 0.223606797
21 0.141775902
22 1.135248317
23 0.341091737
24 -0.0376105554
25 0.200000000
26 -1.020312322
27 -0.211553603
28 0.666373450
29 0.518897891
30 -0.0336399034
31 1.117147212
32 -0.176776695
33 -0.170789279
34 0.181545595
35 0.596022533
36 -0.494341784
37 -0.0210745633
38 -1.125946672
39 0.153498052
40 -0.158113883
41 1.356648233
42 -0.100250702
43 -0.215277374
44 -0.802741783
45 -0.442152733
46 -0.241188280
47 1.050945430
48 0.0265946788
49 0.776214299
50 -0.141421356
51 -0.0273121228
52 0.721469762
53 -0.227201499
54 0.149590987
55 -0.717994078
56 -0.471197185
57 0.169389919
58 -0.366916218
59 0.465395736
60 0.0237870038
61 -0.107251416
62 -0.789942369
63 -1.317664961
64 0.125000000
65 0.645302173
66 0.120766257
67 1.782242731
68 -0.128372121
69 0.0362849008
70 -0.421451574
71 0.354755847
72 0.349552428
73 0.773365038
74 0.0149019666
75 0.0212757430
76 0.796164527
77 -2.139703246
78 -0.108539514
79 -1.151449320
80 0.111803398
81 0.966178768
82 -0.959295165
83 -0.451680020
84 0.0708879514
85 -0.114819516
86 0.152224091
87 0.0551996910
88 0.567624158
89 -0.750827330
90 0.312649196
91 1.923073178
92 0.170545868
93 0.118840685
94 -0.743130640
95 0.712111202
96 -0.0188052777
97 -1.254113299
98 -0.548866395
99 1.587315222
100 0.100000000
101 0.803543000
102 0.0193125872
103 -1.365591900
104 -0.510156161
105 0.0634041113
106 0.160655720
107 -0.909533000
108 -0.105776801
109 -0.572080000
110 0.507698481
111 -0.00224188497
112 0.333186725
113 0.654590000
114 -0.119776760
115 0.152540862
116 0.259448945
117 -1.426610599
118 -0.329084481
119 -0.342175095
120 -0.0168199517
121 1.577577482
122 0.0758382035
123 0.144318496
124 0.558573606
125 0.0894427190
126 0.931729829
127 -0.956999999
128 -0.0883883476
129 -0.0229009304
130 -0.456297542
131 -0.265000000
132 -0.0853946395
133 2.122171612
134 -1.260235921
135 -0.0946096474
136 0.0907727979
137 0.911000000
138 -0.0256572994
139 -0.611999999
140 0.298011266
141 0.111798224
142 -0.250850265
143 -2.316615694
144 -0.247170892
145 0.232058191
146 -0.546851663
147 0.0825726799
148 -0.0105372816