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

$R= 30.4874572847$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.710006193
4 0.5
5 -0.447213595
6 -1.209156975
7 1.943633898
8 -0.353553390
9 1.924121182
10 0.316227766
11 1.221568842
12 0.855003096
13 -0.670613703
14 -1.374356709
15 -0.764738018
16 0.250000000
17 -1.298587493
18 -1.360559135
19 1.251854116
20 -0.223606797
21 3.323626004
22 -0.863779612
23 0.785068011
24 -0.604578487
25 0.200000000
26 0.474195497
27 1.580252945
28 0.971816949
29 0.679237690
30 0.540751438
31 -0.712705663
32 -0.176776695
33 2.088890286
34 0.918240022
35 -0.869219504
36 0.962060591
37 -0.255802464
38 -0.885194534
39 -1.146753585
40 0.158113883
41 0.689011830
42 -2.350158486
43 -0.728547274
44 0.610784421
45 -0.860493152
46 -0.555126914
47 1.461823720
48 0.427501548
49 2.777712731
50 -0.141421356
51 -2.220592656
52 -0.335306851
53 0.495412832
54 -1.117407573
55 -0.546302194
56 -0.687178354
57 2.140678292
58 -0.480293576
59 -1.657850553
60 -0.382369009
61 -0.534485081
62 0.503959007
63 3.739787154
64 0.125000000
65 0.299907565
66 -1.477068486
67 1.212275286
68 -0.649293746
69 1.342471161
70 0.614631005
71 0.260635279
72 -0.680279567
73 0.505315287
74 0.180879657
75 0.342001238
76 0.625927058
77 2.374282611
78 0.810877236
79 -0.149109575
80 -0.111803398
81 0.778121141
82 -0.487204937
83 0.0471032880
84 1.661813002
85 0.580745981
86 0.515160718
87 1.161500657
88 -0.431889806
89 0.747051096
90 0.608460542
91 -1.303427526
92 0.392534005
93 -1.218731098
94 -1.033665465
95 -0.559846180
96 -0.302289243
97 0.834971212
98 -1.964139508
99 2.350446485
100 0.100000000
101 -0.291815887
102 1.570196125
103 -0.0804813623
104 0.237097748
105 -1.486370735
106 -0.350309773
107 -0.872474355
108 0.790126472
109 -0.546688197
110 0.386293986
111 -0.437423799
112 0.485908474
113 -0.321045428
114 -1.513688136
115 -0.351093088
116 0.339618845
117 -1.290342031
118 1.172277368
119 -2.523978672
120 0.270375719
121 0.492230436
122 0.377938025
123 1.178214497
124 -0.356352831
125 -0.0894427190
126 -2.644428857
127 -0.248405708
128 -0.0883883476
129 -1.245820352
130 -0.212066673
131 0.247008722
132 1.044445143
133 2.433146096
134 -0.857208075
135 -0.706710601
136 0.459120011
137 -0.798184734
138 -0.949270462
139 1.034257547
140 -0.434609752
141 2.499727615
142 -0.184296973
143 -0.819200805
144 0.481030295
145 -0.303764329
146 -0.357311866
147 4.749905975
148 -0.127901232
149 -0.601137904
150 -0.241831395
151 0.353180470
152 -0.442597267
153 -2.498639702
154 -1.678871335
155 0.318731662
156 -0.573376792
157 -0.161205250
158 0.105436391
159 0.847159011
160 0.0790569415
161 1.525884800
162 -0.550214735
163 -0.902959389
164 0.344505915
165 -0.934180135
166 -0.0333070544
167 0.225676066
168 -1.175079243
169 -0.550277274
170 -0.410649421
171 2.408719019
172 -0.364273637
173 -0.672163224
174 -0.821304991
175 0.388726779
176 0.305392210
177 -2.834934751
178 -0.528244895
179 -1.516924061
180 -0.430246576
181 1.975677071
182 0.921662442
183 -0.913972764
184 -0.277563457
185 0.114398340
186 0.861773024
187 -1.586314076
188 0.730911860
189 3.071433334
190 0.395871030
191 -1.876312518
192 0.213750774
193 0.362000133
194 -0.590413806
195 0.512843794
196 1.388856365
197 1.797023341
198 -1.662016648
199 -1.746598020
200 -0.0707106781
201 2.072993881
202 0.206344992
203 1.320180581
204 -1.110296328
205 -0.308135458
206 0.0569089170
207 1.510579784
208 -0.167653425
209 1.529201503
210 1.051022826
211 0.295159652
212 0.247706416
213 0.445710584
214 0.616932533
215 0.325816246
216 -0.558703786
217 -1.385275896
218 0.386566931
219 0.864025777
220 -0.273151097
221 0.870654219
222 0.309305334
223 -0.529812822
224 -0.343589177
225 0.384824236
226 0.227013399
227 0.123290254
228 1.070339146
229 1.559565184
230 0.248260303
231 4.059901225
232 -0.240146788
233 -1.053181128
234 0.912409600
235 -0.653747441
236 -0.828925276
237 -0.244799137
238 1.784722434
239 0.891522570
240 -0.191184504
241 0.00822627976
242 -0.348059479
243 -0.264598177
244 -0.267242540
245 -1.242230897
246 -0.833123461
247 -0.862876323
248 0.251979503
249 0.175504786
250 0.0632455532