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

$R= 28.869142831$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.308683305
4 0.5
5 -0.447213595
6 0.218272058
7 -0.00915103409
8 -0.353553390
9 -0.904714616
10 0.316227766
11 0.274532080
12 -0.154341652
13 0.304822841
14 0.00647075826
15 0.138047371
16 0.250000000
17 -1.556714141
18 0.639729840
19 0.0732014868
20 -0.223606797
21 0.00282477145
22 -0.194123496
23 1.323334243
24 0.109136029
25 0.200000000
26 -0.215542298
27 0.587953604
28 -0.00457551704
29 0.742119452
30 -0.0976142322
31 -1.721514515
32 -0.176776695
33 -0.0847434702
34 1.100763126
35 0.00409246685
36 -0.452357308
37 1.090609505
38 -0.0517612677
39 -0.0940937224
40 0.158113883
41 -0.113816017
42 -0.00199741505
43 0.230838289
44 0.137266040
45 0.404600676
46 -0.935738617
47 0.886583800
48 -0.0771708264
49 -0.999916258
50 -0.141421356
51 0.480531667
52 0.152411420
53 -1.715548477
54 -0.415745980
55 -0.122774478
56 0.00323537913
57 -0.0225960769
58 -0.524757697
59 0.430605219
60 0.0690236855
61 1.512602469
62 1.217294587
63 0.00827907429
64 0.125000000
65 -0.136320918
66 0.0599226824
67 -0.188448415
68 -0.778357070
69 -0.408491189
70 -0.00289381106
71 -0.147647700
72 0.319864920
73 0.194870637
74 -0.771177377
75 -0.0617366611
76 0.0366007434
77 -0.00251225241
78 0.0665343091
79 0.795665018
80 -0.111803398
81 0.723223154
82 0.0804800777
83 -1.065476137
84 0.00141238572
85 0.696183728
86 -0.163227319
87 -0.229079886
88 -0.0970617480
89 0.610489773
90 -0.286095882
91 -0.00278944421
92 0.661667121
93 0.531402791
94 -0.626909417
95 -0.0327367001
96 0.0545680147
97 0.374962701
98 0.707047567
99 -0.248373186
100 0.100000000
101 1.338314708
102 -0.339787200
103 0.292490546
104 -0.107771149
105 -0.00126327619
106 1.213075961
107 1.149502633
108 0.293976802
109 0.240863546
110 0.0868146666
111 -0.336652947
112 -0.00228775852
113 1.594904205
114 0.0159778392
115 -0.591813065
116 0.371059726
117 -0.275777680
118 -0.304483870
119 0.0142455441
120 -0.0488071161
121 -0.924632136
122 -1.069571463
123 0.0351331045
124 -0.860757257
125 -0.0894427190
126 -0.00585418957
127 0.394374618
128 -0.0883883476
129 -0.0712559263
130 0.0963934462
131 0.629715750
132 -0.0423717351
133 -0.000669869357
134 0.133253152
135 -0.262940845
136 0.550381563
137 -0.0418211902
138 0.288846889
139 -0.317309544
140 0.00204623342
141 -0.273673618
142 0.104402690
143 0.0836836490
144 -0.226178654
145 -0.331885908
146 -0.137794349
147 0.308657456
148 0.545304752
149 1.706403576
150 0.0436544117
151 0.763879590
152 -0.0258806338
153 1.408382037
154 0.00177643072
155 0.769884696
156 -0.0470468612
157 0.491889575
158 -0.562620129
159 0.529561180
160 0.0790569415
161 -0.0121098817
162 -0.511395996
163 -1.162333639
164 -0.0569080086
165 0.0378984320
166 0.753405402
167 -0.733026069
168 -0.000998707526
169 -0.907083020
170 -0.492276235
171 -0.0662264800
172 0.115419144
173 0.428427928
174 0.161983940
175 -0.00183020681
176 0.0686330202
177 -0.132920656
178 -0.431681458
179 -1.256050225
180 0.202300338
181 -0.0760736253
182 0.00197243492
183 -0.466915358
184 -0.467869308
185 -0.487735398
186 -0.375758517
187 -0.427368326
188 0.443291900
189 -0.00538047803
190 0.0231483426
191 -1.816322138
192 -0.0385854132
193 -1.490225892
194 -0.265138668
195 0.0420799919
196 -0.499958129
197 -0.438825028
198 0.175626364
199 -1.407563706
200 -0.0707106781
201 0.0581847209
202 -0.946331405
203 -0.00680516032
204 0.240265833
205 0.0509000703
206 -0.206822048
207 -1.197248907
208 0.0762057103
209 0.0201135772
210 0.000893271167
211 1.106539476
212 -0.857774238
213 0.0454786587
214 -0.812821107
215 -0.103234021
216 -0.207872990
217 0.0160610014
218 -0.170316246
219 -0.0601992061
220 -0.0613872394
221 -0.473122378
222 0.238049582
223 -1.410098846
224 0.00161768956
225 -0.180942923
226 -1.127767579
227 0.638034172
228 -0.0112980384
229 0.686616024
230 0.418475031
231 0.0131736783
232 -0.262378848
233 -1.702957397
234 0.195004267
235 -0.396492329
236 0.215302609
237 -0.225009985
238 -0.0100731208
239 -0.158347615
240 0.0345118427