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

$R= 13.2036691317$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.120084054
4 0.5
5 -0.447213595
6 0.0849122493
7 0.364894062
8 0.353553390
9 -0.985579819
10 -0.316227766
11 0.502834786
12 0.0600420272
13 -0.0816264894
14 0.258019065
15 -0.0537032218
16 0.250000000
17 -0.994651781
18 -0.696910174
19 -1.353216184
20 -0.223606797
21 0.0438179585
22 0.355557887
23 0.870925052
24 0.0424561246
25 0.200000000
26 -0.0577186441
27 -0.238436475
28 0.182447031
29 -1.101926243
30 -0.0379739123
31 0.320578233
32 0.176776695
33 0.0603824399
34 -0.703325019
35 -0.163185585
36 -0.492789909
37 -1.055333998
38 -0.956868340
39 -0.00980203982
40 -0.158113883
41 -1.943484713
42 0.0309839755
43 -0.282040870
44 0.251417393
45 0.440764694
46 0.615837010
47 -1.061162262
48 0.0300210136
49 -0.866852323
50 0.141421356
51 -0.119441818
52 -0.0408132447
53 -0.654916348
54 -0.168600048
55 -0.224874552
56 0.129009532
57 -0.162499686
58 -0.779179519
59 1.167357148
60 -0.0268516109
61 -0.594876401
62 0.226683042
63 -0.359632224
64 0.125000000
65 0.0365044758
66 0.0426968327
67 1.343225978
68 -0.497325890
69 0.104584211
70 -0.115389634
71 -0.110043224
72 -0.348455087
73 0.370182913
74 -0.746233826
75 0.0240168109
76 -0.676608092
77 0.183481428
78 -0.00693108883
79 -0.365849938
80 -0.111803398
81 0.956947398
82 -1.374251220
83 1.089062391
84 0.0219089792
85 0.444821799
86 -0.199433012
87 -0.132323779
88 0.177778943
89 0.949944155
90 0.311667704
91 -0.0297850020
92 0.435462526
93 0.0384963050
94 -0.750355031
95 0.605176675
96 0.0212280623
97 -1.699299213
98 -0.612957156
99 -0.495583649
100 0.100000000
101 -1.026193096
102 -0.0844581200
103 1.317400179
104 -0.0288593220
105 -0.0195959867
106 -0.463095791
107 1.418763995
108 -0.119218237
109 0.644016421
110 -0.159010321
111 -0.126728555
112 0.0912235156
113 1.309342313
114 -0.114904630
115 -0.389489524
116 -0.550963121
117 0.0804523451
118 0.825446155
119 -0.362940983
120 -0.0189869561
121 -0.747160135
122 -0.420641137
123 -0.233378324
124 0.160289116
125 -0.0894427190
126 -0.254298384
127 0.251467919
128 0.0883883476
129 -0.0338740627
130 0.0258125623
131 -1.336952797
132 0.0301912199
133 -0.493666640
134 0.949804197
135 0.106632033
136 -0.351662509
137 1.538111629
138 0.0739522053
139 0.364130402
140 -0.0815927928
141 -0.126859345
142 -0.0778123105
143 -0.0432922929
144 -0.246394954
145 0.492796397
146 0.261758848
147 -0.108093298
148 -0.527666999
149 -0.139922733
150 0.0169824498
151 0.603832739
152 -0.478434170
153 1.009929404
154 0.129740962
155 -0.143366944
156 -0.00490101991