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

$R= 27.0752071997$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.821457999
4 0.5
5 0.447213595
6 1.287965303
7 0.213684096
8 0.353553390
9 2.317709243
10 0.316227766
11 1.080746279
12 0.910728999
13 0.601058147
14 0.151097473
15 0.814580781
16 0.250000000
17 0.680950010
18 1.638867923
19 1.739982562
20 0.223606797
21 0.389216607
22 0.764203023
23 -0.928998096
24 0.643982651
25 0.200000000
26 0.425012291
27 2.400152043
28 0.106842048
29 -0.389189410
30 0.575995594
31 -1.539244463
32 0.176776695
33 1.968533956
34 0.481504369
35 0.0955624331
36 1.158854621
37 -1.045146829
38 1.230353468
39 1.094802170
40 0.158113883
41 -1.449332383
42 0.275217702
43 -1.531323143
44 0.540373139
45 1.036511084
46 -0.656900853
47 -0.282762481
48 0.455364499
49 -0.954339106
50 0.141421356
51 1.240321843
52 0.300529073
53 0.698068502
54 1.697163785
55 0.483324429
56 0.0755487368
57 3.169305156
58 -0.275198471
59 1.185974857
60 0.407290390
61 -0.580133725
62 -1.088410198
63 0.495257605
64 0.125000000
65 0.268801375
66 1.391963709
67 0.189497420
68 0.340475005
69 -1.692131014
70 0.0675728444
71 -1.334835646
72 0.819433961
73 1.455269244
74 -0.739030410
75 0.364291599
76 0.869991281
77 0.230938292
78 0.774142038
79 0.921232832
80 0.111803398
81 2.054066895
82 -1.024832756
83 0.0307022766
84 0.194608303
85 0.304530102
86 -1.082808978
87 -0.708892164
88 0.382101511
89 1.620319561
90 0.732924016
91 0.128436567
92 -0.464499048
93 -2.803669141
94 -0.199943268
95 0.778143857
96 0.321991325
97 1.139553352
98 -0.674819654
99 2.504855643
100 0.100000000
101 -0.513761508
102 0.877039986
103 -0.514770884
104 0.212506145
105 0.174062958
106 0.493608971
107 -0.602896676
108 1.200076021
109 0.0600228743
110 0.341761981
111 -1.903691053
112 0.0534210241
113 -0.305376982
114 2.241037168
115 -0.415460578
116 -0.194594705
117 1.393078024
118 0.838610864
119 0.145508187
120 0.287997797
121 0.168012521
122 -0.410216491
123 -2.639898064
124 -0.769622231
125 0.0894427190
126 0.350200011
127 -1.581330536
128 0.0883883476
129 -2.789240788
130 0.190071275
131 0.231652041
132 0.984266978
133 0.371806601
134 0.133994911
135 1.073380625
136 0.240752184
137 -0.913406116
138 -1.196517314
139 0.792416466
140 0.0477812165
141 -0.515039985
142 -0.943871337
143 0.649591359
144 0.579427310
145 -0.174050795
146 1.029030750
147 -1.738288594
148 -0.522573414
149 -0.439165650
150 0.257593060
151 1.643922470
152 0.615176734
153 1.578244124
154 0.163298032
155 -0.688371050
156 0.547401085
157 -1.534810164
158 0.651409983
159 1.271502437
160 0.0790569415
161 -0.198512076
162 1.452444630
163 0.688907982
164 -0.724666191
165 0.880355148
166 0.0217097880
167 0.859210151
168 0.137608851
169 -0.638729358
170 0.215335300
171 4.032773677
172 -0.765661571
173 -1.093261842
174 -0.501262456
175 0.0427368193
176 0.270186569
177 2.160203288
178 1.145738949
179 0.871082369
180 0.518255542
181 -0.197894826
182 0.0908183676
183 -1.056694612
184 -0.328450426
185 -0.467403871
186 -1.982493462
187 0.735934513
188 -0.141381240
189 0.512852561
190 0.550230798
191 1.044677556
192 0.227682249
193 1.380440373
194 0.805785902
195 0.489610415
196 -0.477169553
197 0.786795194
198 1.771200411
199 -0.521540687
200 0.0707106781
201 0.344926775
202 -0.363284246
203 -0.0830639654
204 0.620160921
205 -0.648161146
206 -0.363997983
207 -2.153328213
208 0.150264536
209 1.880511470
210 0.123081098
211 0.756030093
212 0.349034251
213 -2.433132754
214 -0.426312327
215 -0.684828528
216 0.848581892
217 -0.334933968
218 0.0424425815
219 2.642680235
220 0.241662214
221 0.406404031
222 -1.346112852
223 0.0742050612
224 0.0377743684
225 0.463541848
226 -0.215934135