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

$R= 27.3228024652$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.802893720
4 0.5
5 -0.447213595
6 1.274838375
7 0.00418371124
8 -0.353553390
9 2.250425768
10 0.316227766
11 1.321328506
12 -0.901446860
13 0.374053934
14 -0.00295833059
15 0.806278583
16 0.250000000
17 -1.697104709
18 -1.591291321
19 -0.761862513
20 -0.223606797
21 -0.00754278672
22 -0.934320347
23 0.201761214
24 0.637419187
25 0.200000000
26 -0.264496073
27 -2.254384766
28 0.00209185562
29 0.0855458921
30 -0.570125053
31 0.407913247
32 -0.176776695
33 -2.382214867
34 1.200034248
35 -0.00187101254
36 1.125212884
37 0.988836996
38 0.538718149
39 -0.674379490
40 0.158113883
41 -0.655828582
42 0.00533355564
43 -1.817289012
44 0.660664253
45 -1.006420999
46 -0.142666722
47 -1.684077979
48 -0.450723430
49 -0.999982496
50 -0.141421356
51 3.059699424
52 0.187026967
53 1.073860647
54 1.594090755
55 -0.590916072
56 -0.00147916529
57 1.373557141
58 -0.0604900804
59 1.516538589
60 0.403139291
61 -0.296697004
62 -0.288438223
63 0.00941513160
64 0.125000000
65 -0.167282005
66 1.684480287
67 1.627800234
68 -0.848552354
69 -0.363754026
70 0.00132300566
71 1.537224333
72 -0.795645660
73 0.886330136
74 -0.699213346
75 -0.360578744
76 -0.380931256
77 0.00552805692
78 0.476858310
79 -0.358982465
80 -0.111803398
81 1.813990371
82 0.463740837
83 -1.262356292
84 -0.00377139336
85 0.758968299
86 1.285017384
87 -0.154230151
88 -0.467160173
89 1.008575931
90 0.711647113
91 0.00156493367
92 0.100880607
93 -0.735424233
94 1.190822959
95 0.340715273
96 0.318709593
97 0.0535339524
98 0.707094404
99 2.973551719
100 0.100000000
101 0.146849788
102 -2.163534211
103 -1.777819996
104 -0.132248036
105 0.00337323677
106 -0.759334145
107 1.209917603
108 -1.127192383
109 1.478643486
110 0.417840761
111 -1.782768012
112 0.00104592781
113 0.501838416
114 -0.971251568
115 -0.0902303581
116 0.0427729460
117 0.841780613
118 -1.072354720
119 -0.00710019602
120 -0.285062526
121 0.745909022
122 0.209796463
123 1.182389232
124 0.203956623
125 -0.0894427190
126 -0.00665750340
127 -0.683828505
128 -0.0883883476
129 3.276378950
130 0.118286240
131 0.122568269
132 -1.191107433
133 -0.00318741283
134 -1.151028584
135 1.008191517
136 0.600017124
137 -0.912913789
138 0.257212939
139 -0.123351303
140 -0.000935506274
141 3.036213614
142 -1.086981750
143 0.494248126
144 0.562606442
145 -0.0382572860
146 -0.626730049
147 1.802862162
148 0.494418498
149 -1.417630462
150 0.254967675
151 0.334695968
152 0.269359074
153 -3.819208176
154 -0.00390892653
155 -0.182424350
156 -0.337189745
157 -1.108246565
158 0.253838935
159 -1.936056604
160 0.0790569415
161 0.000844112466
162 -1.282684892
163 1.777916202
164 -0.327914291
165 1.065358876
166 0.892620694
167 0.595472918
168 0.00266677782
169 -0.860083568
170 -0.536671630
171 -1.714514951
172 -0.908644506
173 -1.038702439
174 0.109057186
175 0.000836742249
176 0.330332126
177 -2.734157737
178 -0.713170880
179 -0.0557264652
180 -0.503210499
181 0.440920791
182 -0.00110657521
183 0.534914691
184 -0.0713333614
185 -0.442221348
186 0.520023462
187 -2.242426680
188 -0.842038989
189 -0.00942771553
190 -0.240922080
191 -0.0359999595
192 -0.225361715
193 1.326793863
194 -0.0378542207
195 0.301591676
196 -0.499991248
197 1.313706444
198 -2.102618585
199 0.123107465
200 -0.0707106781
201 -2.934630233
202 -0.103838481
203 0.000458531786
204 1.529849712
205 0.293295458
206 1.257108574
207 0.454133625
208 0.0935134836
209 -1.006990045
210 -0.00238523859
211 -0.183652760
212 0.536930323
213 -2.770973553
214 -0.855540942
215 0.812716353
216 0.797045377
217 0.00496507122
218 -1.045558836
219 -1.589043371
220 -0.295458036
221 -0.622056838
222 1.260607351
223 1.251656566
224 -0.000739582648
225 0.450085153
226 -0.354853347
227 -0.728666840
228 0.686778570
229 0.428502228
230 0.0638024981
231 -0.0785074224
232 -0.0302450402
233 0.210555518
234 -0.595228780
235 0.753142568
236 0.758269294
237 0.986461999