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

$R= 24.1201522922$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.390128345
4 0.5
5 -0.447213595
6 0.982969180
7 1.223013618
8 -0.353553390
9 0.932456817
10 0.316227766
11 1.147513718
12 -0.695064172
13 -0.556862474
14 -0.864801223
15 0.621684295
16 0.250000000
17 -0.958102804
18 -0.659346539
19 0.459270964
20 -0.223606797
21 -1.700145898
22 -0.811414732
23 -1.407141040
24 0.491484590
25 0.200000000
26 0.393761232
27 0.0938936920
28 0.611506809
29 1.116834372
30 -0.439597181
31 -1.711524336
32 -0.176776695
33 -1.595191347
34 0.677480989
35 -0.546948317
36 0.466228408
37 -0.598756244
38 -0.324753613
39 0.774110311
40 0.158113883
41 -0.120504117
42 1.202184693
43 0.890928027
44 0.573756859
45 -0.417007366
46 0.994998971
47 0.220874611
48 -0.347532086
49 0.495762310
50 -0.141421356
51 1.331885866
52 -0.278431237
53 1.238383547
54 -0.0663928663
55 -0.513183736
56 -0.432400611
57 -0.638445585
58 -0.789721157
59 -1.025050879
60 0.310842147
61 1.911993174
62 1.210230464
63 1.140407386
64 0.125000000
65 0.249036469
66 1.127970619
67 -1.310036125
68 -0.479051402
69 1.956106647
70 0.386750864
71 1.197192227
72 -0.329673269
73 -1.225878725
74 0.423384600
75 -0.278025669
76 0.229635482
77 1.403424905
78 -0.547378650
79 0.206259341
80 -0.111803398
81 -1.062981100
82 0.0852092783
83 0.694630274
84 -0.850072949
85 0.428476599
86 -0.629981250
87 -1.552543118
88 -0.405707366
89 1.881952919
90 0.294868736
91 -0.681050390
92 -0.703570520
93 2.379238494
94 -0.156181935
95 -0.205392219
96 0.245742295
97 1.108770756
98 -0.350556891
99 1.070006990
100 0.100000000
101 0.731691781
102 -0.941785527
103 1.314227718
104 0.196880616
105 0.760328360
106 -0.875669404
107 -0.595869064
108 0.0469468460
109 -1.354278781
110 0.362875699
111 0.832348027
112 0.305753404
113 -1.020461806
114 0.451449203
115 0.629292604
116 0.558417186
117 -0.519250211
118 0.724820428
119 -1.171772777
120 -0.219798590
121 0.316787734
122 -1.351983339
123 0.167516189
124 -0.855762168
125 -0.0894427190
126 -0.806389796
127 -0.571300076
128 -0.0883883476
129 -1.238504304
130 -0.176095376
131 -1.148962563
132 -0.797595673
133 0.561694643
134 0.926335427
135 -0.0419905356
136 0.338740494
137 -0.857950489
138 -1.383176274
139 -0.251598133
140 -0.273474158
141 -0.307044060
142 -0.846542742
143 -0.639007317
144 0.233114204
145 -0.499463515
146 0.866827159
147 -0.689173243
148 -0.299378122
149 0.566816583
150 0.196593836
151 -0.489457691
152 -0.162376806
153 -0.893389508
154 -0.992371267
155 0.765416952
156 0.387055155
157 0.370453755
158 -0.145847378
159 -1.721512113
160 0.0790569415
161 -1.720953600
162 0.751641144
163 -0.913115065
164 -0.0602520585
165 0.713391258
166 -0.491177777
167 -0.723093890
168 0.601092346
169 -0.689903770
170 -0.302978709
171 0.428251980
172 0.445464013
173 1.283095884
174 1.097813766
175 0.244602723
176 0.286878429
177 1.424940317
178 -1.330741671
179 0.511497784
180 -0.208503683
181 -1.715941036
182 0.481575349
183 -2.657850477
184 0.497499485
185 0.267771933
186 -1.682375673
187 -1.099343583
188 0.110437305
189 0.114772310
190 0.145234231
191 1.713497423
192 -0.173766043
193 1.620785701
194 -0.784019320
195 -0.346192655
196 0.247881155
197 -0.560677320
198 -0.756609199
199 0.411940876
200 -0.0707106781
201 1.821739294
202 -0.517384220
203 1.365675524
204 0.665942933
205 0.0538910794
206 -0.929299331
207 -1.308541899
208 -0.139215618
209 0.531015961
210 -0.537633339