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

$R= 29.2867591963$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.941148685
4 0.5
5 0.447213595
6 -0.665492617
7 1.385586559
8 0.353553390
9 -0.114239151
10 0.316227766
11 1.091940943
12 -0.470574342
13 1.397785264
14 0.979757652
15 -0.420894487
16 0.250000000
17 1.665694746
18 -0.0807792788
19 1.356875560
20 0.223606797
21 -1.304042969
22 0.772118846
23 -0.109655468
24 -0.332746308
25 0.200000000
26 0.988383439
27 1.048664712
28 0.692793279
29 0.812676635
30 -0.297617346
31 -0.706899098
32 0.176776695
33 -1.027678784
34 1.177824050
35 0.619653147
36 -0.0571195758
37 -0.228881977
38 0.959455909
39 -1.315523764
40 0.158113883
41 -0.0849746051
42 -0.922097626
43 0.385881660
44 0.545970471
45 -0.0510893017
46 -0.0775381252
47 1.499114762
48 -0.235287171
49 0.919850113
50 0.141421356
51 -1.567666420
52 0.698892632
53 1.090658380
54 0.741517929
55 0.488330835
56 0.489878826
57 -1.277021649
58 0.574649159
59 0.289128189
60 -0.210447243
61 -1.428006346
62 -0.499853146
63 -0.158288233
64 0.125000000
65 0.625108573
66 -0.726678637
67 -0.613260373
68 0.832847373
69 0.103202099
70 0.438160942
71 -1.747817714
72 -0.0403896394
73 -1.637560811
74 -0.161843998
75 -0.188229737
76 0.678437780
77 1.512978695
78 -0.930215774
79 -0.867019901
80 0.111803398
81 -0.872710264
82 -0.0600861195
83 -1.713868181
84 -0.652021484
85 0.744921336
86 0.272859539
87 -0.764849547
88 0.386059423
89 -0.454485975
90 -0.0361255917
91 1.936752475
92 -0.0548277341
93 0.665297157
94 1.060034213
95 0.606813197
96 -0.166373154
97 0.769166587
98 0.650432252
99 -0.124742407
100 0.100000000
101 0.796518506
102 -1.108507556
103 -1.016754021
104 0.494191719
105 -0.583185744
106 0.771211937
107 1.442024546
108 0.524332356
109 -1.074202426
110 0.345302045
111 0.215411972
112 0.346396639
113 -1.215540279
114 -0.902990668
115 -0.0490394162
116 0.406338317
117 -0.159681802
118 0.204444503
119 2.307964252
120 -0.148808673
121 0.192335025
122 -1.009752971
123 0.0799737379
124 -0.353449549
125 0.0894427190
126 -0.111926683
127 1.718662763
128 0.0883883476
129 -0.363172017
130 0.442018511
131 0.590197067
132 -0.513839392
133 1.880068538
134 -0.433640568
135 0.468977116
136 0.588912025
137 0.789236852
138 0.0729749046
139 -1.296939045
140 0.309826573
141 -1.410889887
142 -1.235893758
143 1.526298960
144 -0.0285597879
145 0.363440040
146 -1.157930354
147 -0.865715725
148 -0.114440988
149 0.147086275
150 -0.133098523
151 -1.428363511
152 0.479727954
153 -0.190287556
154 1.069837495
155 -0.316134887
156 -0.657761882
157 0.368174383
158 -0.613075651
159 -1.026471712
160 0.0790569415
161 -0.151937156
162 -0.617099346
163 1.328586529
164 -0.0424873025
165 -0.459591924
166 -1.211887813
167 -0.325955595
168 -0.461048813
169 0.953803607
170 0.526738928
171 -0.155008412
172 0.192940830
173 0.685513467
174 -0.540830301
175 0.277117311
176 0.272985235
177 -0.272112600
178 -0.321370115
179 -0.265884562
180 -0.0255446508
181 -0.998999007
182 1.369490808
183 1.343966313
184 -0.0387690626
185 -0.102359132
186 0.470436131
187 1.818837341
188 0.749557381
189 1.453013088
190 0.429081727
191 0.0964622336
192 -0.117643585
193 0.0940015066
194 0.543882909
195 -0.588320112
196 0.459925056
197 0.734151104
198 -0.0882062019
199 -0.869123631
200 0.0707106781
201 0.577160096
202 0.563223637
203 1.126091848
204 -0.783833210
205 -0.0380017987
206 -0.718953663
207 0.0123924530
208 0.349446316
209 1.481451451
210 -0.412374594
211 1.235498284
212 0.545329190
213 1.645778412
214 1.019665335
215 0.172571524
216 0.370758964
217 -0.979403507
218 -0.759575820
219 1.541462084
220 0.244165417
221 2.332089738
222 0.152319266
223 -0.570226103
224 0.244939413
225 -0.0228478303
226 -0.859516774
227 -0.825193264
228 -0.638510824
229 0.554665590
230 -0.0346761037
231 -1.387806173
232 0.287324579