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

$R= 24.9063465366$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0623058512
4 0.5
5 -0.447213595
6 0.0440568899
7 0.0897067766
8 -0.353553390
9 -0.996117980
10 0.316227766
11 -0.842286812
12 -0.0311529256
13 0.506504379
14 -0.0634322700
15 0.0278640237
16 0.250000000
17 1.251674182
18 0.704361779
19 -0.504350613
20 -0.223606797
21 -0.00558925708
22 0.595586716
23 -0.437311787
24 0.0220284449
25 0.200000000
26 -0.358152681
27 0.124369830
28 0.0448533883
29 1.507076764
30 -0.0197028401
31 0.0752394234
32 -0.176776695
33 0.0524793968
34 -0.885067302
35 -0.0401180901
36 -0.498058990
37 -0.137109171
38 0.356629738
39 -0.0315581865
40 0.158113883
41 -0.910341781
42 0.00395220158
43 0.976107421
44 -0.421143406
45 0.445477503
46 0.309226130
47 -0.405160440
48 -0.0155764628
49 -0.991952694
50 -0.141421356
51 -0.0779866254
52 0.253252189
53 0.681208420
54 -0.0879427501
55 0.376682113
56 -0.0317161350
57 0.0314239943
58 -1.065664200
59 0.302351787
60 0.0139320118
61 -1.189067823
62 -0.0532023065
63 -0.0893585332
64 0.125000000
65 -0.226515644
66 -0.0371085374
67 1.948611052
68 0.625837091
69 0.0272470832
70 0.0283677735
71 0.743907593
72 0.352180889
73 1.232092665
74 0.0969508246
75 -0.0124611702
76 -0.252175306
77 -0.0755588349
78 0.0223150077
79 0.200016372
80 -0.111803398
81 0.988369012
82 0.643708846
83 0.612896803
84 -0.00279462854
85 -0.559765711
86 -0.690212177
87 -0.0938997007
88 0.297793358
89 -1.676602842
90 -0.315000163
91 0.0454368752
92 -0.218655893
93 -0.00468785633
94 0.286491695
95 0.225552451
96 0.0110142224
97 -0.861840808
98 0.701416476
99 0.839017039
100 0.100000000
101 1.043123710
102 0.0551448717
103 0.618167093
104 -0.179076340
105 0.00249959175
106 -0.481687093
107 1.358939638
108 0.0621849150
109 0.726416966
110 -0.266354477
111 0.00854270361
112 0.0224266941
113 0.0430711241
114 -0.0222201194
115 0.195571776
116 0.753538382
117 -0.504538120
118 -0.213794999
119 0.112283656
120 -0.00985142007
121 -0.290552925
122 0.840797921
123 0.0567196197
124 0.0376197117
125 -0.0894427190
126 0.0631860248
127 -1.711452841
128 -0.0883883476
129 -0.0608172046
130 0.160170748
131 -0.603304321
132 0.0262396984
133 -0.0452436686
134 -1.377876089
135 -0.0556198788
136 -0.442533651
137 -0.482261615
138 -0.0192665973
139 -1.628959549
140 -0.0200590450
141 0.0252438609
142 -0.526022104
143 -0.426621954
144 -0.249029495
145 -0.673985218
146 -0.871221078
147 0.0618044544
148 -0.0685545855
149 0.879726697
150 0.00881137798
151 -0.668821464
152 0.178314869
153 -1.246815229
154 0.0534281645
155 -0.0336480930
156 -0.0157790932
157 -0.494654542
158 -0.141432933
159 -0.0424432863
160 0.0790569415
161 -0.0392299247
162 -0.698882431
163 -1.433041087
164 -0.455170890
165 -0.0234694997
166 -0.433383486
167 -0.919853499
168 0.00197610079
169 -0.743453365
170 0.395814130
171 0.502393698
172 0.488053710
173 -0.592388189
174 0.0663971151
175 0.0179413553
176 -0.210571703
177 -0.0188446911
178 1.185537239
179 0.454507346
180 0.222738751
181 -0.406659050
182 -0.0321287226
183 0.0740899151
184 0.154613065
185 0.0613170854
186 0.00331481500
187 -1.054279089
188 -0.202580220
189 0.0110907307
190 -0.159489667
191 -1.577895726
192 -0.00778823140
193 -0.988638292
194 0.609413480
195 0.0141132500
196 -0.495976347
197 1.278632092
198 -0.593274637
199 0.811587857
200 -0.0707106781
201 -0.122936340
202 -0.737599849
203 0.134927367
204 -0.0389933127
205 0.407117221
206 -0.437110143
207 0.438555927
208 0.126626094
209 0.421080147
210 -0.00176747828
211 1.696102641
212 0.340604210
213 -0.0556324772
214 -0.960915433
215 -0.436528509
216 -0.0439713750
217 -0.0108932062
218 -0.513654362
219 -0.00299632894
220 0.188341056
221 0.632835702
222 -0.00604060365
223 -0.731192058
224 -0.0158580675
225 -0.199223596