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

$R= 29.5726130963$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.334120238
4 0.5
5 -0.447213595
6 -0.943365467
7 0.481981975
8 -0.353553390
9 0.779876811
10 0.316227766
11 -0.0366657377
12 0.667060119
13 0.782866272
14 -0.340812722
15 -0.596636708
16 0.250000000
17 0.561650216
18 -0.551456182
19 -1.398226222
20 -0.223606797
21 0.643021907
22 0.0259265918
23 -0.693005320
24 -0.471682733
25 0.200000000
26 -0.553570050
27 -0.293670800
28 0.240990987
29 -0.102306176
30 0.421885862
31 -0.337148573
32 -0.176776695
33 -0.0489165028
34 -0.397146676
35 -0.215548892
36 0.389938405
37 1.618530384
38 0.988695243
39 1.044437738
40 0.158113883
41 -0.244624335
42 -0.454685151
43 -0.503490033
44 -0.0183328688
45 -0.348771512
46 0.490028761
47 -0.0990936183
48 0.333530059
49 -0.767693375
50 -0.141421356
51 0.749308921
52 0.391433136
53 1.308128236
54 0.207656614
55 0.0163974164
56 -0.170406361
57 -1.865401901
58 0.0723413913
59 -1.102580552
60 -0.298318354
61 -0.131247195
62 0.238400042
63 0.375886565
64 0.125000000
65 -0.350108440
66 0.0345891909
67 -1.246996828
68 0.280825108
69 -0.924552423
70 0.152416083
71 -0.341629688
72 -0.275728091
73 -1.414789183
74 -1.144473810
75 0.266824047
76 -0.699113111
77 -0.0176722247
78 -0.738529007
79 -0.953921411
80 -0.111803398
81 -1.171668970
82 0.172975526
83 1.843637817
84 0.321510953
85 -0.251177612
86 0.356021216
87 -0.136488741
88 0.0129632959
89 -1.176789440
90 0.246618701
91 0.377327432
92 -0.346502660
93 -0.449796735
94 0.0700697695
95 0.625305776
96 -0.235841366
97 1.234912963
98 0.542841191
99 -0.0285947586
100 0.100000000
101 -0.346295697
102 -0.529841419
103 0.994059841
104 -0.276785025
105 -0.287568139
106 -0.924986347
107 0.826295373
108 -0.146835400
109 1.887633318
110 -0.0115947243
111 2.159314143
112 0.120495493
113 -1.267443017
114 1.319038334
115 0.309921401
116 -0.0511530883
117 0.610539252
118 0.779642185
119 0.270705280
120 0.210942931
121 -0.998655623
122 0.0928057822
123 -0.326358277
124 -0.168574286
125 -0.0894427190
126 -0.265791939
127 -1.073912296
128 -0.0883883476
129 -0.671716243
130 0.247564052
131 0.651857965
132 -0.0244582514
133 -0.673919836
134 0.881759913
135 0.131333574
136 -0.198573338
137 -1.659014605
138 0.653757288
139 -0.0578813842
140 -0.107774446
141 -0.132202802
142 0.241568669
143 -0.0287043699
144 0.194969202
145 0.0457527131
146 1.000407025
147 -1.024195267
148 0.809265192
149 -0.0315620418
150 -0.188673093
151 -1.516533145
152 0.494347621
153 0.438017978
154 0.0124961499
155 0.150777425
156 0.522218869
157 1.532627432
158 0.674524298
159 1.745200364
160 0.0790569415
161 -0.334016070
162 0.828495074
163 0.226061027
164 -0.122312167
165 0.0218761251
166 -1.303648802
167 1.855491909
168 -0.227342575
169 -0.387120335
170 0.177609393
171 -1.090444285
172 -0.251745016
173 -0.397217307
174 0.0965121143
175 0.0963963950
176 -0.00916643444
177 -1.470974808
178 0.832115793
179 0.837403222
180 -0.174385756
181 -0.0238622163
182 -0.266810786
183 -0.175100166
184 0.245014380
185 -0.723828792
186 0.318054322
187 -0.0205925036
188 -0.0495468091
189 -0.141544649
190 -0.442157954
191 -0.573595872
192 0.166765029
193 -0.844662279
194 -0.873215330
195 -0.467086756
196 -0.383846687
197 -0.729150660
198 0.0202195477
199 -1.204802678
200 -0.0707106781
201 -1.663667090
202 0.244868035
203 -0.0492985583
204 0.374654460
205 0.109399328
206 -0.702906454
207 -0.540359037
208 0.195716568
209 0.0512482577
210 0.203341381
211 -1.828784983
212 0.654064118
213 -0.455676806
214 -0.584279062
215 0.225167588
216 0.103828307
217 -0.162190057
218 -1.334758320
219 -1.887350620
220 0.00819870821
221 0.439002104
222 -1.526865673
223 0.946078356
224 -0.0852031807
225 0.155975362
226 0.896217552
227 1.802534734
228 -0.932700950
229 -0.369538041
230 -0.219147524
231 -0.0249485811
232 0.0361706956