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

$R= 21.617168802$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.0782551000
4 0.5
5 0.447213595
6 -0.0553347119
7 -1.124354170
8 0.353553390
9 -0.993876139
10 0.316227766
11 0.158336619
12 -0.0391275500
13 -0.326090603
14 -0.795038458
15 -0.0349967446
16 0.250000000
17 -1.100568810
18 -0.702776557
19 0.227943487
20 0.223606797
21 0.0879864481
22 0.111960897
23 0.565297717
24 -0.0276673559
25 0.200000000
26 -0.230580877
27 0.156030976
28 -0.562177085
29 1.343084765
30 -0.0247464354
31 1.492547522
32 0.176776695
33 -0.0123906479
34 -0.778219669
35 -0.502826471
36 -0.496938069
37 -0.564824058
38 0.161180386
39 0.0255182528
40 0.158113883
41 0.804056398
42 0.0622158141
43 -0.395025120
44 0.0791683095
45 -0.444474921
46 0.399725849
47 -0.0636561544
48 -0.0195637750
49 0.264172300
50 0.141421356
51 0.0861251224
52 -0.163045301
53 1.137427011
54 0.110330561
55 0.0708102887
56 -0.397519229
57 -0.0178377404
58 0.949704345
59 -1.120426281
60 -0.0174983723
61 1.847099875
62 1.055390474
63 1.117468781
64 0.125000000
65 -0.145832151
66 -0.00876151120
67 0.833163197
68 -0.550284405
69 -0.0442374294
70 -0.355552007
71 0.137626237
72 -0.351388278
73 -1.068204382
74 -0.399390921
75 -0.0156510200
76 0.113971743
77 -0.178026438
78 0.0180441296
79 -1.012301707
80 0.111803398
81 0.981665919
82 0.568553731
83 -1.668802400
84 0.0439932240
85 -0.492189335
86 -0.279324941
87 -0.105103232
88 0.0559804485
89 0.919842351
90 -0.314291231
91 0.366641330
92 0.282648858
93 -0.116799455
94 -0.0450116984
95 0.101939426
96 -0.0138336779
97 1.455536052
98 0.186798024
99 -0.157366987
100 0.100000000
101 1.223803351
102 0.0608996581
103 1.833010048
104 -0.115290438
105 0.0393487358
106 0.804282352
107 0.0404615401
108 0.0780154884
109 1.002046302
110 0.0500704353
111 0.0442003632
112 -0.281088542
113 0.593683976
114 -0.0126131872
115 0.252808824
116 0.671542382
117 0.324093670
118 -0.792261021
119 1.237429132
120 -0.0123732177
121 -0.974929513
122 1.306096847
123 -0.0629215146
124 0.746273761
125 0.0894427190
126 0.790169753
127 0.854261713
128 0.0883883476
129 0.0309127278
130 -0.103118903
131 0.550969445
132 -0.00619532398
133 -0.256289215
134 0.589135346
135 0.0697791741
136 -0.389109834
137 -0.583054849
138 -0.0312805863
139 -0.466540204
140 -0.251413235
141 0.00498144905
142 0.0973164457
143 -0.0516321141
144 -0.248469034
145 0.600645766
146 -0.755334562
147 -0.0206726108
148 -0.282412029
149 1.732730870
150 -0.0110669423
151 1.492151488
152 0.0805901930
153 1.093829096
154 -0.125883701
155 0.667487544
156 0.0127591264
157 -1.989378328
158 -0.715805402
159 -0.0890059650
160 0.0790569415
161 -0.635596576
162 0.694142628
163 -0.0323215866
164 0.402028199
165 -0.00554126623
166 -1.180021493
167 1.273379863
168 0.0311079070
169 -0.893698483
170 -0.348030416
171 -0.226542092
172 -0.197512560
173 0.0226891935
174 -0.0743192085
175 -0.224870834
176 0.0395841547
177 0.0876728307
178 0.650426764
179 1.146351453
180 -0.222237460
181 0.893631512
182 0.259254570
183 -0.144806415
184 0.199862924
185 -0.252596997
186 -0.0825896872
187 -0.173166983
188 -0.0318280772
189 -0.175571085
190 0.0720820599
191 -0.0886508820
192 -0.00978188751
193 -1.112279025
194 1.029219412
195 0.0114121096
196 0.132086150
197 -0.415999728
198 -0.111275264
199 -1.038398044
200 0.0707106781
201 -0.0684306403
202 0.865359649
203 -1.476854345
204 0.0430625612
205 0.359584952
206 1.296133835
207 -0.634017544
208 -0.0815226509