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

$R= 19.9265889222$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.914236134
4 0.5
5 0.447213595
6 1.353569351
7 -1.498127020
8 -0.353553390
9 2.664299977
10 -0.316227766
11 0.314084348
12 -0.957118067
13 0.377109798
14 1.059335775
15 -0.856072424
16 0.250000000
17 1.007182884
18 -1.883944580
19 1.032422695
20 0.223606797
21 2.867768876
22 -0.222091172
23 0.508951509
24 0.676784675
25 0.200000000
26 -0.266656895
27 -3.185863154
28 -0.749063510
29 0.887588836
30 0.605334616
31 -1.600120679
32 -0.176776695
33 -0.601231609
34 -0.712185847
35 -0.669982771
36 1.332149988
37 0.342885963
38 -0.730033089
39 -0.721877202
40 -0.158113883
41 -0.544140888
42 -2.027818819
43 -1.910789558
44 0.157042174
45 1.191511172
46 -0.359883063
47 0.765212055
48 -0.478559033
49 1.244384569
50 -0.141421356
51 -1.927985870
52 0.188554899
53 -1.035591821
54 2.252745440
55 0.140462790
56 0.529667887
57 -1.976300829
58 -0.627620085
59 0.881338667
60 -0.428036212
61 0.148457705
62 1.131456183
63 -3.991459786
64 0.125000000
65 0.168648628
66 0.425134947
67 0.0570829424
68 0.503591442
69 -0.974253369
70 0.473749360
71 0.649536279
72 -0.941972290
73 -0.944376761
74 -0.242456990
75 -0.382847226
76 0.516211347
77 -0.470538249
78 0.510444265
79 0.180315179
80 0.111803398
81 3.434194391
82 0.384765712
83 -0.853155173
84 1.433884438
85 0.450425878
86 1.351132253
87 -1.699054623
88 -0.111045586
89 0.543451275
90 -0.842525629
91 -0.564958379
92 0.254475754
93 3.063008823
94 -0.541086633
95 0.461713465
96 0.338392337
97 1.089535403
98 -0.879912767
99 0.836814922
100 0.100000000
101 0.234251934
102 1.363291883
103 -0.120150581
104 -0.133328447
105 1.282505230
106 0.732273999
107 0.943509818
108 -1.592931577
109 -0.739040766
110 -0.0993221918
111 -0.656364701
112 -0.374531755
113 0.483829197
114 1.397455718
115 0.227610034
116 0.443794418
117 1.004733625
118 -0.623200548
119 -1.508887875
120 0.302667308
121 -0.901351017
122 -0.104975450
123 1.041614165
124 -0.800060339
125 0.0894427190
126 2.822388281
127 -1.319958608
128 -0.0883883476
129 3.657702524
130 -0.119252589
131 -0.590023519
132 -0.300615804
133 -1.546700236
134 -0.0403637356
135 -1.424761315
136 -0.356092923
137 0.390181476
138 0.688901163
139 0.708603242
140 -0.334991385
141 -1.464796851
142 -0.459291508
143 0.118444843
144 0.666074994
145 0.396941795
146 0.667775212
147 -2.382047494
148 0.171442981
149 1.830324429
150 0.270713870
151 0.149428874
152 -0.365016544
153 2.683439233
154 0.332720786
155 -0.715595722
156 -0.360938601
157 -1.893329400
158 -0.127502086
159 1.982355610
160 -0.0790569415
161 -0.762418201
162 -2.428342141
163 1.151058853
164 -0.272070444
165 -0.268878949
166 0.603271808
167 0.700303221
168 -1.013909409
169 -0.857973134
170 -0.318499193
171 2.751184848
172 -0.955394779
173 1.365240902
174 1.201413046
175 -0.299625404
176 0.0785210871
177 -1.686008174
178 -0.384278081
179 -1.194336113
180 0.595755586
181 -1.386386554
182 0.399485900
183 -0.280505127
184 -0.179941531
185 0.153343264
186 -2.165874309
187 0.345815901
188 0.382606027
189 4.790391928
190 -0.326480722
191 1.284652429
192 -0.239279516
193 1.198982118
194 -0.770417872
195 -0.322833299
196 0.622192284