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

$R= 21.3799613173$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.882094499
4 0.5
5 0.447213595
6 -1.330841783
7 0.237223920
8 0.353553390
9 2.542279706
10 0.316227766
11 -1.271719770
12 -0.941047249
13 -1.066818031
14 0.167742642
15 -0.841698248
16 0.250000000
17 -0.624263638
18 1.797663219
19 0.700775163
20 0.223606797
21 -0.446477835
22 -0.899241673
23 1.262741326
24 -0.665420891
25 0.200000000
26 -0.754354264
27 -2.902716152
28 0.118611960
29 1.388665567
30 -0.595170539
31 0.215487140
32 0.176776695
33 2.393496785
34 -0.441421051
35 0.106089762
36 1.271139853
37 1.543012340
38 0.495522870
39 2.007852349
40 0.158113883
41 -1.414178042
42 -0.315707505
43 0.210300979
44 -0.635859885
45 1.136942048
46 0.892892955
47 0.0437860792
48 -0.470523624
49 -0.943724811
50 0.141421356
51 1.174923159
52 -0.533409015
53 1.502402397
54 -2.052530275
55 -0.568730371
56 0.0838713213
57 -1.318925080
58 0.981934839
59 -1.589223500
60 -0.420849124
61 -1.333968581
62 0.152372417
63 0.603089558
64 0.125000000
65 -0.477095527
66 1.692457807
67 0.358680746
68 -0.312131819
69 -2.376598506
70 0.0750167903
71 -0.605989851
72 0.898831609
73 0.709825894
74 1.091074489
75 -0.376418899
76 0.350387581
77 -0.301682349
78 1.419766011
79 -0.119869825
80 0.111803398
81 2.920906398
82 -0.999974883
83 -0.360398211
84 -0.223238917
85 -0.279179186
86 0.148705248
87 -2.613599826
88 -0.449620836
89 0.345009541
90 0.803939432
91 -0.253074755
92 0.631370663
93 -0.405567161
94 0.0309614335
95 0.313396180
96 -0.332710445
97 -0.646856530
98 -0.667314213
99 -3.233067365
100 0.100000000
101 0.651990556
102 0.830796133
103 -1.211126982
104 -0.377177132
105 -0.199670958
106 1.062358923
107 -0.349369380
108 -1.451358076
109 0.813457356
110 -0.402153102
111 -2.904095039
112 0.0593059800
113 0.877465711
114 -0.932620868
115 0.564715089
116 0.694332783
117 -2.712149832
118 -1.123750714
119 -0.148090269
120 -0.297585269
121 0.617271174
122 -0.943258229
123 2.661616709
124 0.107743570
125 0.0894427190
126 0.426448716
127 -1.327740474
128 0.0883883476
129 -0.395806316
130 -0.337357482
131 -0.222711215
132 1.196748392
133 0.166240622
134 0.253625587
135 -1.298134127
136 -0.220710525
137 -1.658184467
138 -1.680508919
139 -0.507568699
140 0.0530448811
141 -0.0824094750
142 -0.428499533
143 1.356693502
144 0.635569926
145 0.621030121
146 0.501922703
147 1.776178851
148 0.771506170
149 -0.116806227
150 -0.266168356
151 -1.625899023
152 0.247761435
153 -1.587051950
154 -0.213321634
155 0.0963687786
156 1.003926174
157 1.447048293
158 -0.0847607667
159 -2.827666108
160 0.0790569415
161 0.299551136
162 2.065392721
163 -1.316885306
164 -0.707089021
165 1.070404303
166 -0.254840018
167 -1.127757822
168 -0.157853752
169 0.138084079
170 -0.197409495
171 1.781574898
172 0.105150489
173 -0.956336106
174 -1.848094160
175 0.0474447840
176 -0.317929942
177 2.991025484
178 0.243958586
179 -1.825588612
180 0.568471024
181 -1.358352031
182 -0.178950875
183 2.513014118
184 0.446446477
185 0.690056096
186 -0.286779289
187 0.795267555
188 0.0218930396
189 -0.682694254
190 0.221604564
191 -0.581602885
192 -0.235261812
193 -0.958337580
194 -0.457396638
195 0.897938868
196 -0.471862405
197 0.723545516
198 -2.286123857
199 -0.411375260
200 0.0707106781
201 -0.678184209
202 0.461026944
203 0.350427526
204 0.587461579
205 -0.632439646
206 -0.856396101
207 2.825610738