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

$R= 22.9495013485$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.059292330
4 0.5
5 0.447213595
6 0.749032789
7 -0.342572397
8 -0.353553390
9 0.122100240
10 -0.316227766
11 1.623698325
12 -0.529646165
13 0.569443484
14 0.242235265
15 -0.473729931
16 0.250000000
17 -1.742476211
18 -0.0863379079
19 1.805768359
20 0.223606797
21 0.362884312
22 -1.148128096
23 0.302284916
24 0.374516394
25 0.200000000
26 -0.402657349
27 0.929952481
28 -0.171286198
29 1.275567521
30 0.334977647
31 1.551687678
32 -0.176776695
33 -1.719971182
34 1.232116745
35 -0.153203033
36 0.0610501202
37 0.172007610
38 -1.276871051
39 -0.603207115
40 -0.158113883
41 -0.398353627
42 -0.256597958
43 -1.120394535
44 0.811849162
45 0.0546048875
46 -0.213747714
47 0.389811119
48 -0.264823082
49 -0.882644152
50 -0.141421356
51 1.845791686
52 0.284721742
53 -0.975295118
54 -0.657575706
55 0.726139966
56 0.121117632
57 -1.912836572
58 -0.901962444
59 -1.008715298
60 -0.236864965
61 -0.240824379
62 -1.097208880
63 -0.0418281720
64 0.125000000
65 0.254662868
66 1.216203286
67 0.513438238
68 -0.871238105
69 -0.320208093
70 0.108330903
71 -1.007756214
72 -0.0431689539
73 0.714523007
74 -0.121627747
75 -0.211858466
76 0.902884179
77 -0.556234227
78 0.426531841
79 0.982535744
80 0.111803398
81 -1.107191771
82 0.281678551
83 -0.687703540
84 0.181442156
85 -0.779259051
86 0.792238573
87 -1.351198892
88 -0.574064048
89 -0.875603490
90 -0.0386114862
91 -0.195075619
92 0.151142458
93 -1.643690856
94 -0.275638086
95 0.807564160
96 0.187258197
97 -0.182309908
98 0.624123665
99 0.198253955
100 0.100000000
101 1.076759220
102 -1.305171817
103 0.0904726894
104 -0.201328674
105 0.162286798
106 0.689637792
107 1.458828228
108 0.464976240
109 -1.186598740
110 -0.513458494
111 -0.182206342
112 -0.0856430993
113 0.721083665
114 1.352579711
115 0.135185924
116 0.637783760
117 0.0695291869
118 0.713269427
119 0.596924253
120 0.167488823
121 1.636396252
122 0.170288551
123 0.421972942
124 0.775843839
125 0.0894427190
126 0.0295769841
127 -0.351298554
128 -0.0883883476
129 1.186825338
130 -0.180073841
131 1.249575857
132 -0.859985591
133 -0.618606397
134 -0.363055659
135 0.415887393
136 0.616058372
137 1.591744907
138 0.226421314
139 -0.583736872
140 -0.0766015167
141 -0.412923919
142 0.712591252
143 0.924604461
144 0.0305250601
145 0.570451137
146 -0.505244064
147 0.934978172
148 0.0860038053
149 0.405474052
150 0.149806557
151 -0.834278215
152 -0.638435525
153 -0.212756689
154 0.393316994
155 0.693935825
156 -0.301603557
157 1.140695459
158 -0.694757687
159 1.033123600
160 -0.0790569415
161 -0.103554459
162 0.782902809
163 -0.274952579
164 -0.199176813
165 -0.769194496
166 0.486279836
167 -1.451559717
168 -0.128298979
169 -0.675739132
170 0.551019359
171 0.220486732
172 -0.560197267
173 -0.906247994
174 0.955441899
175 -0.0685144794
176 0.405924581
177 1.068517038
178 0.619145165
179 0.741200389
180 0.0273024437
181 0.965603388
182 0.137939293
183 0.255243481
184 -0.106873857
185 0.0769241420
186 1.162264951
187 -2.829407992
188 0.194905559
189 -0.319298949
190 -0.571034094
191 -0.810234595
192 -0.132411541
193 -0.0972191314
194 0.128912572
195 -0.269762423
196 -0.441322076
197 0.128223125
198 -0.140186716
199 1.658023190
200 -0.0707106781
201 -0.547301178
202 -0.761383746
203 -0.436413995
204 0.922895843
205 -0.178149157
206 -0.0639738522
207 0.0435411256
208 0.142360871
209 2.942693675
210 -0.114754095