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

$R= 28.9257946349$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.607269779
4 0.5
5 -0.447213595
6 1.136511360
7 -1.552627695
8 0.353553390
9 1.583316145
10 -0.316227766
11 -0.195717154
12 0.803634889
13 1.382717513
14 -1.097873572
15 -0.718792897
16 0.250000000
17 -0.500571241
18 1.119573583
19 0.182629361
20 -0.223606797
21 -2.495491574
22 -0.138392927
23 -1.493752104
24 0.568255680
25 0.200000000
26 0.977728929
27 0.937546412
28 -0.776313847
29 1.337572685
30 -0.508263331
31 -1.612602617
32 0.176776695
33 -0.314570267
34 -0.353957319
35 0.694356214
36 0.791658072
37 -1.002438736
38 0.129138459
39 2.222400072
40 -0.158113883
41 -0.893083802
42 -1.764579014
43 0.394279378
44 -0.0978585772
45 -0.708080506
46 -1.056242242
47 1.637248061
48 0.401817444
49 1.410652760
50 0.141421356
51 -0.804553029
52 0.691358756
53 -1.325773544
54 0.662945426
55 0.0875273723
56 -0.548936786
57 0.293534653
58 0.945806716
59 -1.652548230
60 -0.359396448
61 0.108841119
62 -1.140282246
63 -2.458300498
64 0.125000000
65 -0.618370070
66 -0.222434769
67 0.255691556
68 -0.250285620
69 -2.400862616
70 0.490983987
71 -0.958783754
72 0.559786791
73 -0.562692880
74 -0.708831228
75 0.321453955
76 0.0913146805
77 0.303875874
78 1.571474162
79 -0.812207749
80 -0.111803398
81 -0.0764261287
82 -0.631505612
83 0.953672371
84 -1.247745787
85 0.223862264
86 0.278797622
87 2.149840155
88 -0.0691964635
89 -1.597107667
90 -0.500688527
91 -2.146845505
92 -0.746876052
93 -2.591887454
94 1.157709206
95 -0.0816743332
96 0.284127840
97 -0.754183892
98 0.997482132
99 -0.309882130
100 0.100000000
101 0.138043530
102 -0.568904902
103 0.0147002676
104 0.488864464
105 1.116017759
106 -0.937463463
107 -1.075893865
108 0.468773206
109 0.786987314
110 0.0618911985
111 -1.611189487
112 -0.388156923
113 -1.238065688
114 0.207560343
115 0.668026249
116 0.668786342
117 2.189278963
118 -1.168528059
119 0.777200772
120 -0.254131665
121 -0.961694795
122 0.0769622938
123 -1.435426606
124 -0.806301308
125 -0.0894427190
126 -1.738280952
127 -0.733165247
128 0.0883883476
129 0.633713329
130 -0.437253670
131 1.510057726
132 -0.157285133
133 -0.283555403
134 0.180801233
135 -0.419283502
136 -0.176978659
137 0.876259158
138 -1.697666237
139 -0.0620189344
140 0.347178107
141 2.631499332
142 -0.677962494
143 -0.270621536
144 0.395829036
145 -0.598180689
146 -0.397883951
147 2.267299551
148 -0.501219368
149 1.045895403
150 0.227302272
151 0.603093267
152 0.0645692298
153 -0.792562526
154 0.214872691
155 0.721177814
156 1.111200036
157 0.0695734104
158 -0.574317607
159 -2.130875745
160 -0.0790569415
161 2.319240912
162 -0.0540414338
163 -0.228696202
164 -0.446541901
165 0.140680100
166 0.674348201
167 -1.167241205
168 -0.882289507
169 0.911907658
170 0.158294525
171 0.289159856
172 0.197139689
173 1.032158842
174 1.520166552
175 -0.310525539
176 -0.0489292886
177 -2.656090501
178 -1.129325661
179 -1.028564926
180 -0.354040253
181 -0.0918230947
182 -1.518049015
183 0.174936750
184 -0.528121121
185 0.448304231
186 -1.832741195
187 0.0979696396
188 0.818624030
189 -1.455665712
190 -0.0577524748
191 0.845105273
192 0.200908722
193 -1.327591826
194 -0.533288544
195 -0.993887527
196 0.705326380
197 1.297960407
198 -0.219119755
199 -1.157452299
200 0.0707106781
201 0.411021073
202 0.0976115168
203 -2.076724975
204 -0.402276514
205 0.399399218
206 0.0103946589
207 -2.364836060
208 0.345679378
209 -0.0355877072
210 0.789143725
211 -1.482044518
212 -0.662886772
213 -1.541639950
214 -0.760771848
215 -0.176327098
216 0.331472713
217 2.502798632
218 0.556484066
219 -0.904019841
220 0.0437636861
221 -0.688861687
222 -1.139283012
223 -0.449747038
224 -0.274468393
225 0.316663229
226 -0.875444643
227 -0.368667938
228 0.146767326
229 0.111430534
230 0.472365891
231 0.494477044
232 0.472903358