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

$R= 25.1400643416$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.530898050
4 0.5
5 0.447213595
6 -1.082508392
7 0.357741970
8 0.353553390
9 1.343648841
10 0.316227766
11 0.00415722550
12 -0.765449025
13 0.411297429
14 0.252961773
15 -0.684638421
16 0.250000000
17 1.606268001
18 0.950103207
19 0.496567556
20 0.223606797
21 -0.547666485
22 0.00293960234
23 0.0714504828
24 -0.541254196
25 0.200000000
26 0.290831201
27 -0.526091342
28 0.178870985
29 -1.322400709
30 -0.484112470
31 0.378715821
32 0.176776695
33 -0.00636428842
34 1.135802996
35 0.159987072
36 0.671824420
37 1.585449674
38 0.351126286
39 -0.629654432
40 0.158113883
41 -1.382695236
42 -0.387258685
43 1.058789911
44 0.00207861275
45 0.600898029
46 0.0505231209
47 -0.991885299
48 -0.382724512
49 -0.872020682
50 0.141421356
51 -2.459032553
52 0.205648714
53 -1.134376571
54 -0.372002755
55 0.00185916776
56 0.126480886
57 -0.760194304
58 -0.935078509
59 -1.133146158
60 -0.342319210
61 1.104747549
62 0.267792525
63 0.480679584
64 0.125000000
65 0.183937802
66 -0.00450023149
67 0.648416572
68 0.803134000
69 -0.109383404
70 0.113127944
71 -0.0793322243
72 0.475051603
73 -1.716771503
74 1.121082215
75 -0.306179610
76 0.248283778
77 0.00148721404
78 -0.445232919
79 1.746764887
80 0.111803398
81 -0.538256631
82 -0.977713177
83 0.0263920127
84 -0.273833242
85 0.718344888
86 0.748677526
87 2.024460668
88 0.00146980117
89 1.152648516
90 0.424899071
91 0.147138352
92 0.0357252414
93 -0.579775312
94 -0.701368821
95 0.222071762
96 -0.270627098
97 0.196288917
98 -0.616611737
99 0.00558585123
100 0.100000000
101 1.229791302
102 -1.738798593
103 1.369089710
104 0.145415600
105 -0.244923898
106 -0.802125366
107 0.228027197
108 -0.263045671
109 0.810002267
110 0.00131463013
111 -2.427161815
112 0.0894354926
113 -1.312984576
114 -0.537538547
115 0.0319536273
116 -0.661200354
117 0.552639314
118 -0.801255332
119 0.574629480
120 -0.242056235
121 -0.999982717
122 0.781174483
123 2.116765441
124 0.189357910
125 0.0894427190
126 0.339891793
127 1.646785222
128 0.0883883476
129 -1.620899410
130 0.130063667
131 -0.419235082
132 -0.00318214421
133 0.177643059
134 0.458499755
135 -0.235275200
136 0.567901498
137 0.570465342
138 -0.0773457473
139 1.629111354
140 0.0799935364
141 1.518475276
142 -0.0560963538
143 0.00170986734
144 0.335912210
145 -0.591395575
146 -1.213940772
147 1.334974758
148 0.792724837
149 1.542996876
150 -0.216501678
151 0.410873342
152 0.175563143
153 2.158260241
154 0.00105161913
155 0.169366864
156 -0.314827216
157 -1.065898364
158 1.235149296
159 1.736615420
160 0.0790569415
161 0.0255609674
162 -0.380604914
163 -0.647431755
164 -0.691347618
165 -0.00284619630
166 0.0186619711
167 1.201017592
168 -0.193629342
169 -0.830832277
170 0.507946541
171 0.667209708
172 0.529394955
173 -1.361788588
174 1.431509866
175 0.0715483941
176 0.00103930637
177 1.734737726
178 0.815045582
179 -0.617045666
180 0.300449014
181 1.059343233
182 0.104042527
183 -1.691277272
184 0.0252615604
185 0.709034649
186 -0.409963055
187 0.00684696113
188 -0.495942649
189 -0.188272408
190 0.157028449
191 -0.303990453
192 -0.191362256
193 0.456688619
194 0.138797224
195 -0.281590022
196 -0.436010341
197 1.075279991
198 0.00394979328
199 1.211773396
200 0.0707106781
201 -0.992614593
202 0.869593769
203 -0.472098860
204 -1.229516276
205 -0.618360108
206 0.968092618
207 0.0913983081
208 0.102824357
209 -0.00852927610
210 -0.173187349
211 -0.269335273
212 -0.567188285
213 0.134215407
214 0.161239577
215 0.473505243
216 -0.186001377
217 0.104155579
218 0.572758096
219 2.663773358
220 0.000929583883
221 0.557720693
222 -1.716262578