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

$R= 26.3524008204$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.411244700
4 0.5
5 0.447213595
6 -0.290793916
7 -0.703642669
8 0.353553390
9 -0.830877796
10 0.316227766
11 0.203409644
12 -0.205622350
13 0.339570871
14 -0.497550503
15 -0.183914220
16 0.250000000
17 0.776667699
18 -0.587519324
19 -0.421631161
20 0.223606797
21 0.289369318
22 0.143832339
23 0.771187765
24 -0.145396958
25 0.200000000
26 0.240112865
27 0.752938790
28 -0.351821334
29 -0.146712838
30 -0.130046992
31 0.316899118
32 0.176776695
33 -0.0836511383
34 0.549186997
35 -0.314678568
36 -0.415438898
37 -0.880440501
38 -0.298138253
39 -0.139646721
40 0.158113883
41 -0.552590284
42 0.204615007
43 -0.881361138
44 0.101704822
45 -0.371579846
46 0.545312098
47 0.680364069
48 -0.102811175
49 -0.504886993
50 0.141421356
51 -0.319400475
52 0.169785435
53 -0.970105073
54 0.532408124
55 0.0909675585
56 -0.248775251
57 0.173393580
58 -0.103741642
59 1.325231501
60 -0.0919571104
61 1.244749642
62 0.224081515
63 0.584641070
64 0.125000000
65 0.151860710
66 -0.0591502871
67 -0.0918497452
68 0.388333849
69 -0.317146881
70 -0.222511349
71 -1.518815402
72 -0.293759662
73 -0.169881045
74 -0.622565449
75 -0.0822489400
76 -0.210815580
77 -0.143127705
78 -0.0987451434
79 0.543020943
80 0.111803398
81 0.521235709
82 -0.390740337
83 -1.517548764
84 0.144684659
85 0.347336354
86 -0.623216437
87 0.0603348772
88 0.0719161695
89 0.212078769
90 -0.262746629
91 -0.238936554
92 0.385593882
93 -0.130323082
94 0.481090047
95 -0.188559187
96 -0.0726984790
97 -1.295959529
98 -0.357009016
99 -0.169008557
100 0.100000000
101 -0.952309254
102 -0.225850242
103 -1.538608232
104 0.120056432
105 0.129409893
106 -0.685967875
107 -0.514271032
108 0.376469395
109 1.053480929
110 0.0643237774
111 0.362076490
112 -0.175910667
113 1.519857403
114 0.122607776
115 0.344885653
116 -0.0733564191
117 -0.282141897
118 0.937080181
119 -0.546496533
120 -0.0650234964
121 -0.958624516
122 0.880170912
123 0.227249825
124 0.158449559
125 0.0894427190
126 0.413403665
127 0.299958835
128 0.0883883476
129 0.362455097
130 0.107381737
131 1.159709150
132 -0.0418255691
133 0.296677675
134 -0.0649475777
135 0.336724463
136 0.274593498
137 -1.284202994
138 -0.224256710
139 0.274098140
140 -0.157339284
141 -0.279796119
142 -1.073964670
143 0.0690719853
144 -0.207719449
145 -0.0656119759
146 -0.120124039
147 0.207632110
148 -0.440220250
149 -1.148411256
150 -0.0581587832
151 -1.784655217
152 -0.149069126
153 -0.645315933
154 -0.101206571
155 0.141721594
156 -0.0698233605
157 -0.593963885
158 0.383973791
159 0.398950572
160 0.0790569415
161 -0.542640571
162 0.368569304
163 -1.422566991
164 -0.276295142
165 -0.0374099263
166 -1.073069022
167 -1.046181162
168 0.102307503
169 -0.884690619
170 0.245603891
171 0.350325352
172 -0.440680569
173 -1.174954260
174 0.0426632008
175 -0.140728533
176 0.0508524111
177 -0.544995135
178 0.149962335
179 -1.823245937
180 -0.185789923
181 1.000070360
182 -0.168953657
183 -0.511889102
184 0.272656049
185 -0.393744962
186 -0.0921523356
187 0.158009078
188 0.340182034
189 -0.529817810
190 -0.133331480
191 -0.400971230
192 -0.0514055875
193 0.512138343
194 -0.916381771
195 -0.0624519122
196 -0.252443496
197 0.616435544
198 -0.119507096
199 1.059997745
200 0.0707106781
201 0.0379313273
202 -0.673384331
203 0.103355414
204 -0.159700237
205 -0.247125887
206 -1.087960314
207 -0.640951774
208 0.0848927177
209 -0.0852391671
210 0.0915066131
211 -0.754496813
212 -0.485052536
213 0.628146758
214 -0.363644534
215 -0.394156683
216 0.266204062
217 -0.206846489
218 0.744923509
219 0.0518984693
220 0.0454837792
221 0.228565778
222 0.256026741