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

$R= 31.63446345$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.999740986
4 0.5
5 0.447213595
6 -0.706923631
7 0.124293464
8 -0.353553390
9 -0.000517959769
10 -0.316227766
11 0.353588895
12 0.499870493
13 1.677157153
14 -0.0878887514
15 0.447097761
16 0.250000000
17 1.387565457
18 0.000366252865
19 1.455604309
20 0.223606797
21 0.124261270
22 -0.250025105
23 1.791277311
24 -0.353461815
25 0.200000000
26 -1.185929196
27 -1.000258812
28 0.0621467321
29 1.853765374
30 -0.316145858
31 -0.131788408
32 -0.176776695
33 0.353497311
34 -0.981156943
35 0.0555857270
36 -0.000258979884
37 -0.515010060
38 -1.029267677
39 1.676722747
40 -0.158113883
41 -0.301918649
42 -0.0878659871
43 -1.258132968
44 0.176794447
45 -0.000231638650
46 -1.266624334
47 1.524849119
48 0.249935246
49 -0.984551134
50 -0.141421356
51 1.387206058
52 0.838578576
53 -0.506650833
54 0.707289789
55 0.158129761
56 -0.0439443757
57 1.455227288
58 -1.310810067
59 -0.381723585
60 0.223548880
61 -0.927094821
62 0.0931884769
63 -6.437901460e-5
64 0.125000000
65 0.750047480
66 -0.249960345
67 -1.078392850
68 0.693782728
69 1.790813346
70 -0.0393050445
71 -0.150794958
72 0.000183126432
73 1.439256293
74 0.364167106
75 0.199948197
76 0.727802154
77 0.0439487887
78 -1.185622024
79 -0.510403833
80 0.111803398
81 -0.999481771
82 0.213488724
83 1.566988945
84 0.0621306353
85 0.620538137
86 0.889634353
87 1.853285224
88 -0.125012552
89 0.177064280
90 0.000163793260
91 0.208459672
92 0.895638655
93 -0.131754273
94 -1.078231152
95 0.650966036
96 -0.176730907
97 0.930386363
98 0.696182783
99 -0.000183144811
100 0.100000000
101 -0.700403547
102 -0.980902811
103 0.0605720949
104 -0.592964598
105 0.0555713296
106 0.358256240
107 -0.0337958739
108 -0.500129406
109 -0.261993726
110 -0.111814626
111 -0.514876665
112 0.0310733660
113 -0.564672275
114 -1.029001083
115 0.801083567
116 0.926882687
117 -0.000868699936
118 0.269919336
119 0.172465317
120 -0.158072929
121 -0.874974893
122 0.655555035
123 -0.301840448
124 -0.0658942040
125 0.0894427190
126 4.552283779e-5
127 -1.701743201
128 -0.0883883476
129 -1.257807095
130 -0.530363659
131 -1.240129592
132 0.176748655
133 0.180922102
134 0.762538897
135 -0.447329339
136 -0.490578471
137 -0.131013137
138 -1.266296261
139 -0.188213922
140 0.0277928635
141 1.524454163
142 0.106628137
143 0.593024145
144 -0.000129489942
145 0.829029078
146 -1.017707884
147 -0.984296122
148 -0.257505030
149 0.616742856
150 -0.141384726
151 0.864189649
152 -0.514633838
153 -0.000718702867
154 -0.0310764865
155 -0.0589375677
156 0.838361373
157 0.842726178
158 0.360910011
159 -0.506519605
160 -0.0790569415
161 0.222644061
162 0.706740338
163 1.878714570
164 -0.150959324
165 0.158088803
166 -1.108028509
167 -1.125207864
168 -0.0439329935
169 1.812856122
170 -0.438786724
171 -0.000753936278
172 -0.629066484
173 -1.306625859
174 -1.310470549
175 0.0248586928
176 0.0883972238
177 -0.381624732
178 -0.125203353
179 0.459618796
180 -0.000115819325
181 -0.269237339
182 -0.147403248
183 -0.926854715
184 -0.633312167
185 -0.230319500
186 0.0931643399
187 0.490627921
188 0.762424559
189 -0.124325353
190 -0.460302498
191 -1.878140933
192 0.124967623
193 -0.474006550
194 -0.657882506
195 0.749853208
196 -0.492275567
197 1.079790882
198 0.000129502938
199 0.406474760
200 -0.0707106781
201 -1.078115895
202 0.495260097
203 0.230409051
204 0.693603029
205 -0.135022124
206 -0.0428309391
207 -0.000919066031
208 0.419289288
209 0.514692959
210 -0.0392948640
211 -0.419867492
212 -0.253325416
213 -0.150753346
214 0.0238972916
215 -0.562654168
216 0.353644894
217 -0.0164286422
218 0.185257540
219 1.438792604
220 0.0790648806
221 2.327113948
222 0.364072781
223 0.772666296
224 -0.0219721878
225 -0.000103591953
226 0.399283595
227 1.738989803
228 0.727613644
229 0.340559751
230 -0.566451622
231 0.0451147625
232 -0.655405033
233 1.499499548
234 0.000614263615
235 0.681933257
236 -0.190861792
237 -0.509421438
238 -0.121951395
239 -0.427620253
240 0.111774440
241 0.510255147
242 0.618700680
243 -0.00496224567
244 -0.463547410
245 -0.440304652
246 0.213433427
247 2.492562464
248 0.0465942384
249 1.633515884
250 -0.0632455532