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

$R= 30.4710497659$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.561667441
4 0.5
5 0.447213595
6 -0.397158856
7 -0.729049734
8 -0.353553390
9 -0.684529684
10 -0.316227766
11 1.035074743
12 0.280833720
13 -1.163736565
14 0.515516011
15 0.251185316
16 0.250000000
17 -0.347614164
18 0.484035582
19 -1.052029670
20 0.223606797
21 -0.409483499
22 -0.731908370
23 1.384391614
24 -0.198579428
25 0.200000000
26 0.822886016
27 -0.946145478
28 -0.364524867
29 1.503338040
30 -0.177614840
31 1.337587396
32 -0.176776695
33 0.581367783
34 0.245800333
35 -0.326040953
36 -0.342264842
37 1.222612171
38 0.743897313
39 -0.653632939
40 -0.158113883
41 -0.499242713
42 0.289548559
43 1.227771471
44 0.517537371
45 -0.306130981
46 -0.978912698
47 -1.091545034
48 0.140416860
49 -0.468486484
50 -0.141421356
51 -0.195243558
52 -0.581868282
53 0.461081161
54 0.669025884
55 0.462899497
56 0.257758005
57 -0.590890813
58 -1.063020523
59 0.966305616
60 0.125592658
61 -1.261057314
62 -0.945817118
63 0.499056185
64 0.125000000
65 -0.520438813
66 -0.411089102
67 -0.383453461
68 -0.173807082
69 0.777567696
70 0.230545768
71 0.254029959
72 0.242017791
73 0.283808011
74 -0.864517357
75 0.112333488
76 -0.526014835
77 -0.754620967
78 0.462188283
79 -1.127328359
80 0.111803398
81 0.153110574
82 0.353017907
83 -1.799130019
84 -0.204741749
85 -0.155457780
86 -0.868165533
87 0.844376031
88 -0.365954185
89 -1.517400322
90 0.216467292
91 0.848421834
92 0.692195807
93 0.751279291
94 0.771838895
95 -0.470481971
96 -0.0992897142
97 1.255968729
98 0.331269969
99 -0.708539388
100 0.100000000
101 -1.692663389
102 0.138058044
103 0.483207674
104 0.411443008
105 -0.183126588
106 -0.326033616
107 0.563459991
108 -0.473072739
109 1.246838577
110 -0.327319373
111 0.686701450
112 -0.182262433
113 0.405734339
114 0.417822901
115 0.619118751
116 0.751669020
117 0.796612224
118 -0.683281254
119 0.253428014
120 -0.0888074201
121 0.0713797253
122 0.891702178
123 -0.280408377
124 0.668793698
125 0.0894427190
126 -0.352886012
127 0.395860956
128 -0.0883883476
129 0.689599261
130 0.368005814
131 -0.167193500
132 0.290683891
133 0.766981952
134 0.271142543
135 -0.423129121
136 0.122900166
137 -0.496823966
138 -0.549823391
139 -1.241186067
140 -0.163020476
141 -0.613085307
142 -0.179626307
143 -1.204554326
144 -0.171132421
145 0.672313210
146 -0.200682569
147 -0.263133605
148 0.611306085
149 0.115255137
150 -0.0794317713
151 -1.096800133
152 0.371948656
153 0.237952213
154 0.533597603
155 0.598187268
156 -0.326816469
157 1.011779346
158 0.797141527
159 0.258974276
160 -0.0790569415
161 -1.009290338
162 -0.108265525
163 0.635178765
164 -0.249621356
165 0.259995576
166 1.272177037
167 -1.364082565
168 0.144774279
169 0.354282790
170 0.109925250
171 0.720145542
172 0.613885735
173 0.739316869
174 -0.597064017
175 -0.145809946
176 0.258768685
177 0.542742443
178 1.072964057
179 0.526958255
180 -0.153065490
181 1.420166372
182 -0.599924832
183 -0.708295053
184 -0.489456349
185 0.546768785
186 -0.531234681
187 -0.359806474
188 -0.545772517
189 0.689786710
190 0.332680992
191 -1.006598167
192 0.0702084302
193 0.154443110
194 -0.888104005
195 -0.292313536
196 -0.234243242
197 -1.428547066
198 0.501013006
199 -0.348793178
200 -0.0707106781
201 -0.215367641
202 1.196893761
203 -1.096000595
204 -0.0976217793
205 -0.223268128
206 -0.341679423
207 -0.947672453
208 -0.290934141
209 -1.088967300
210 0.129490052
211 -1.484176628
212 0.230540580
213 0.142611621
214 -0.398426381
215 0.549076094
216 0.334512942
217 -0.974885043
218 -0.881648012
219 0.159403315
220 0.231449748
221 0.404807208
222 -0.485571252
223 -1.356300003
224 0.128879002
225 -0.136905936
226 -0.286897502
227 -1.309245398
228 -0.295445406
229 -0.494507672
230 -0.437783067
231 -0.430229528
232 -0.531510261
233 -0.824832873
234 -0.563289905
235 -0.488153779
236 0.483152808
237 -0.637519040
238 -0.179200667
239 1.204893433
240 0.0627963290
241 -0.795108242
242 -0.0504730878
243 1.052933471
244 -0.630528657
245 -0.209513525
246 0.198278665
247 1.278255280
248 -0.472908559
249 -1.009038180
250 -0.0632455532