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

$R= 15.6281191067$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.739669760
4 0.5
5 0.447213595
6 1.230132284
7 0.0615990835
8 0.353553390
9 2.026450874
10 0.316227766
11 -0.698193210
12 0.869834880
13 -0.0836609383
14 0.0435571297
15 0.778003968
16 0.250000000
17 1.538321743
18 1.432917155
19 -0.347323741
20 0.223606797
21 0.107162062
22 -0.493697153
23 1.421168565
24 0.615066142
25 0.200000000
26 -0.0591572168
27 1.785685546
28 0.0307995417
29 1.933741495
30 0.550131881
31 -1.810051728
32 0.176776695
33 -1.214625614
34 1.087757736
35 0.0275479476
36 1.013225437
37 -1.017280645
38 -0.245594972
39 -0.145542404
40 0.158113883
41 -1.160248328
42 0.0757750213
43 -0.188879644
44 -0.349096605
45 0.906256381
46 1.004917930
47 0.703645608
48 0.434917440
49 -0.996205552
50 0.141421356
51 2.676171818
52 -0.0418304691
53 -0.466029182
54 1.262670359
55 -0.312241495
56 0.0217785648
57 -0.604228610
58 1.367361724
59 1.324851021
60 0.389001984
61 0.793453420
62 -1.279899851
63 0.124827516
64 0.125000000
65 -0.0374143090
66 -0.858870008
67 0.846186363
68 0.769160871
69 2.472363978
70 0.0194793405
71 0.120773154
72 0.716458577
73 -1.125710106
74 -0.719326042
75 0.347933952
76 -0.173661870
77 -0.0430080618
78 -0.102914021
79 -1.797416058
80 0.111803398
81 1.080052272
82 -0.820419460
83 0.433314920
84 0.0535810314
85 0.687958397
86 -0.133558077
87 3.364071604
88 -0.246848576
89 -1.113134788
90 0.640820032
91 -0.00515343569
92 0.710584282
93 -3.148892254
94 0.497552581
95 -0.155327899
96 0.307533071
97 0.313340346
98 -0.704423701
99 -1.414854251
100 0.100000000
101 -0.325476260
102 1.892339240
103 0.194621503
104 -0.0295786084
105 0.0479243314
106 -0.329532395
107 0.899030308
108 0.892842773
109 -0.638384599
110 -0.220788079
111 -1.769732449
112 0.0153997708
113 0.755116521
114 -0.427254147
115 0.635565904
116 0.966870747
117 -0.169534928
118 0.936811141
119 0.0947594409
120 0.275065940
121 -0.512526315
122 0.561056293
123 -2.018448466
124 -0.905025864
125 0.0894427190
126 0.0882663835
127 0.575913832
128 0.0883883476
129 -0.328588593
130 -0.0264559116
131 -0.832168673
132 -0.607312807
133 -0.0213866616
134 0.598344115
135 0.798582853
136 0.543878868
137 -1.131011485
138 1.748225334
139 -0.625103370
140 0.0137739738
141 1.224058201
142 0.0853995166
143 0.0583074291
144 0.506612718
145 0.864795487
146 -0.795997249
147 -1.733271860
148 -0.508640322
149 -0.494827044
150 0.246026456
151 -1.270170587
152 -0.122797486
153 3.118130900
154 -0.0304112922
155 -0.809479741
156 -0.0727712022
157 1.370781259
158 -1.270965083
159 -0.809596140
160 0.0790569415
161 0.0858715894
162 0.763712285
163 -0.000117191488
164 -0.580124164
165 -0.543197088
166 0.306399918
167 -0.821249431
168 0.0378875106
169 -1.033636005
170 0.486460048
171 -0.731860251
172 -0.0944398222