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

$R= 28.6669629702$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.384840760
4 0.5
5 0.447213595
6 -0.979230292
7 0.377846805
8 -0.353553390
9 0.917783931
10 -0.316227766
11 0.594522497
12 0.692420380
13 -0.370933265
14 -0.267178038
15 0.619319615
16 0.250000000
17 -1.049706856
18 -0.648971241
19 -0.0213445758
20 0.223606797
21 0.523257657
22 -0.420390889
23 -1.130286016
24 -0.489615146
25 0.200000000
26 0.262289427
27 -0.113856162
28 0.188923402
29 0.107467284
30 -0.437925100
31 0.249310168
32 -0.176776695
33 0.823318988
34 0.742254836
35 0.168978228
36 0.458891965
37 0.514335303
38 0.0150928943
39 -0.513683504
40 -0.158113883
41 -1.615076427
42 -0.369999038
43 -0.893277950
44 0.297261248
45 0.410445452
46 0.799232906
47 1.344613619
48 0.346210190
49 -0.857231791
50 -0.141421356
51 -1.453676841
52 -0.185466632
53 0.138110709
54 0.0805084643
55 0.265878543
56 -0.133589019
57 -0.0295588387
58 -0.0759908458
59 -0.809379759
60 0.309659807
61 -1.787853385
62 -0.176288910
63 0.346781727
64 0.125000000
65 -0.165886399
66 -0.582174439
67 -0.996681221
68 -0.524853428
69 -1.565266146
70 -0.119485651
71 -0.0989944342
72 -0.324485620
73 -1.526874956
74 -0.363689981
75 0.276968152
76 -0.0106722879
77 0.224638426
78 0.363229089
79 0.377156311
80 0.111803398
81 -1.075456586
82 1.142031494
83 -1.272820552
84 0.261628828
85 -0.469443177
86 0.631642895
87 0.148825076
88 -0.210195444
89 1.182966505
90 -0.290228762
91 -0.140155949
92 -0.565143008
93 0.345254882
94 -0.950785408
95 -0.00954558453
96 -0.244807573
97 1.296378072
98 0.606154412
99 0.545643195
100 0.100000000
101 1.422229243
102 1.027904752
103 0.922761864
104 0.131144713
105 0.234007938
106 -0.0976590195
107 -0.406712272
108 -0.0569280810
109 -1.130532644
110 -0.188004521
111 0.712272493
112 0.0944617014
113 1.671062776
114 0.0209012553
115 -0.505479273
116 0.0537336424
117 -0.340436590
118 0.572317916
119 -0.396628382
120 -0.218962550
121 -0.646542999
122 1.264203252
123 -2.236623668
124 0.124655084
125 0.0894427190
126 -0.245211710
127 0.580266011
128 -0.0883883476
129 -1.237047715
130 0.117299397
131 -1.413524536
132 0.411659494
133 -0.00806497937
134 0.704760050
135 -0.0509180236
136 0.371127418
137 0.351128587
138 1.106810306
139 -0.588240701
140 0.0844891142
141 1.862075747
142 0.0699996357
143 -0.220528173
144 0.229445982
145 0.0480608308
146 1.079663635
147 -1.187129525
148 0.257167651
149 0.923001727
150 -0.195846058
151 1.725134792
152 0.00754644717
153 -0.963404088
154 -0.158843354
155 0.111494896
156 -0.256841752
157 -0.176462556
158 -0.266689785
159 0.191261315
160 -0.0790569415
161 -0.427074898
162 0.760462644
163 1.820684060
164 -0.807538213
165 0.368199444
166 0.900020043
167 -0.594331043
168 -0.184999519
169 -0.862408424
170 0.331946454
171 -0.0195890202
172 -0.446638975
173 -0.809558018
174 -0.105235220
175 0.0755693611
176 0.148630624
177 -1.120860964
178 -0.836483638
179 -1.781130964
180 0.205222726
181 -0.426287287
182 0.0991052221
183 -2.475889140
184 0.399616453
185 0.230017740
186 -0.244132068
187 -0.624069389
188 0.672306809
189 -0.0430231083
190 0.00674974755
191 0.769122689
192 0.173105095
193 -0.592494729
194 -0.916677726
195 -0.229726247
196 -0.428615895
197 -1.504127059
198 -0.385828003
199 1.762560693
200 -0.0707106781
201 -1.380223728
202 -1.005667942
203 0.0408120009
204 -0.726838420
205 -0.722284136
206 -0.652491171
207 -1.037545736
208 -0.0927333162
209 -0.0119545557
210 -0.165468600
211 0.749106997
212 0.0690553549
213 -0.135589626
214 0.287589005
215 -0.399486043
216 0.0402542321
217 0.0936459036
218 0.799407299
219 -2.108070445
220 0.132939271
221 0.375350411
222 -0.503652709
223 -0.793836555
224 -0.0667945096
225 0.183556786
226 -1.181619821