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

$R= 15.5673897311$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.526492831
4 0.5
5 -0.447213595
6 -0.372286651
7 1.151886129
8 0.353553390
9 -0.722805298
10 -0.316227766
11 0.888263699
12 -0.263246415
13 -0.569876292
14 0.814506493
15 0.235454752
16 0.250000000
17 -0.163204921
18 -0.511100527
19 -1.151121293
20 -0.223606797
21 -0.606459790
22 0.628097285
23 0.627237615
24 -0.186143325
25 0.200000000
26 -0.402963390
27 0.907044639
28 0.575943064
29 1.538291447
30 0.166491651
31 -0.124436535
32 0.176776695
33 -0.467664470
34 -0.115403306
35 -0.515139137
36 -0.361402649
37 -0.284818886
38 -0.813965672
39 0.300035782
40 -0.158113883
41 1.685367415
42 -0.428831830
43 -1.253200432
44 0.444131849
45 0.323248356
46 0.443523971
47 1.362778727
48 -0.131623207
49 0.326841655
50 0.141421356
51 0.0859262213
52 -0.284938146
53 1.334339986
54 0.641377415
55 -0.397243602
56 0.407253246
57 0.606057109
58 1.087736313
59 0.392610083
60 0.117727376
61 1.891436422
62 -0.0879899177
63 -0.832589397
64 0.125000000
65 0.254856425
66 -0.330688718
67 0.102914973
68 -0.0816024608
69 -0.330236108
70 -0.364258377
71 1.376931773
72 -0.255550263
73 1.266177861
74 -0.201397365
75 -0.105298566
76 -0.575560646
77 1.023178634
78 0.212157336
79 -0.136589092
80 -0.111803398
81 0.245252797
82 1.191734728
83 -0.169724376
84 -0.303229895
85 0.0729874598
86 -0.886146523
87 -0.809899420
88 0.314048642
89 -1.078348565
90 0.228571104
91 -0.656432596
92 0.313618807
93 0.0655149444
94 0.963630079
95 0.514797092
96 -0.0930716628
97 1.046836154
98 0.231111951
99 -0.642041714
100 0.100000000
101 0.513329898
102 0.0607590138
103 -0.126563592
104 -0.201481695
105 0.271217063
106 0.943520852
107 -1.817513751
108 0.453522319
109 -1.349121256
110 -0.280893645
111 0.149955005
112 0.287971532
113 -1.036638633
114 0.428547091
115 -0.280509189
116 0.769145723
117 0.411909667
118 0.277617252
119 -0.187993650
120 0.0832458259
121 -0.210987624
122 1.337447520
123 -0.887334331
124 -0.0622182675
125 -0.0894427190
126 -0.588729608
127 1.026558976
128 0.0883883476
129 0.659799831
130 0.180210706
131 0.186685022
132 -0.233832235
133 -1.325964200
134 0.0727718759
135 -0.405642694
136 -0.0577016534
137 -0.151068701
138 -0.233512191
139 1.540776497
140 -0.257569568
141 -0.717478971
142 0.973637794
143 -0.506203644
144 -0.180701324
145 -0.687944849
146 0.895322952
147 -0.171955735
148 -0.142409443
149 -1.621960171
150 -0.0744573303
151 0.469541174
152 -0.406982836
153 0.118434239
154 0.723496550
155 0.0556497102
156 0.150017891
157 1.657952289
158 -0.0965830735
159 -0.703173732
160 -0.0790569415
161 0.719067926
162 0.173419916
163 0.345547039
164 0.842683707
165 0.209145909
166 -0.120013257
167 -1.164810351
168 -0.214415915
169 -0.689980331
170 0.0516099278
171 0.783298545
172 -0.626600216