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

$R= 28.3445409049$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.858428956
4 0.5
5 -0.447213595
6 -1.314107717
7 -1.602168079
8 -0.353553390
9 2.453758186
10 0.316227766
11 1.700041883
12 0.929214478
13 -0.831642425
14 1.132903913
15 -0.831114695
16 0.250000000
17 -0.392434900
18 -1.735069053
19 -0.445400128
20 -0.223606797
21 -2.977515552
22 -1.202111144
23 0.483577291
24 -0.657053858
25 0.200000000
26 0.588059998
27 2.701706309
28 -0.801084039
29 -0.949400480
30 0.587686837
31 0.829710470
32 -0.176776695
33 3.159407064
34 0.277493379
35 0.716511347
36 1.226879093
37 -0.586024099
38 0.314945451
39 -1.545548364
40 0.158113883
41 -1.554742023
42 2.105421437
43 0.232063762
44 0.850020941
45 -1.097354021
46 -0.341940782
47 0.669853330
48 0.464607239
49 1.566942554
50 -0.141421356
51 -0.729312383
52 -0.415821212
53 0.253008918
54 -1.910394852
55 -0.760281843
56 0.566451956
57 -0.827744496
58 0.671327517
59 0.861961816
60 -0.415557347
61 0.0183384984
62 -0.586693899
63 -3.931333041
64 0.125000000
65 0.371921799
66 -2.234038159
67 -0.847652358
68 -0.196217450
69 0.898694041
70 -0.506650032
71 -1.573297964
72 -0.867534526
73 0.795999333
74 0.414381615
75 0.371685791
76 -0.222700064
77 -2.723752840
78 1.092867729
79 -1.109631553
80 -0.111803398
81 2.567171051
82 1.099368627
83 -0.479983683
84 -1.488757776
85 0.175502222
86 -0.164093860
87 -1.764393344
88 -0.601055572
89 0.888567576
90 0.775946469
91 1.332430947
92 0.241788645
93 1.541957963
94 -0.473657832
95 0.199188993
96 -0.328526929
97 -1.124660014
98 -1.107995706
99 4.171491690
100 0.100000000
101 -0.687531595
102 0.515701731
103 -0.730723160
104 0.294029999
105 1.331585435
106 -0.178904321
107 0.668618135
108 1.350853154
109 0.807252945
110 0.537600447
111 -1.089084156
112 -0.400542019
113 -1.572391009
114 0.585303746
115 -0.216262339
116 -0.474700240
117 -2.040649409
118 -0.609499045
119 0.628746671
120 0.293843418
121 1.890142407
122 -0.0129672765
123 -2.889377596
124 0.414855235
125 -0.0894427190
126 2.779872252
127 -1.363329884
128 -0.0883883476
129 0.431274015
130 -0.262988426
131 -1.622576706
132 1.579703532
133 0.713605868
134 0.599380730
135 -1.208239792
136 0.138746689
137 -0.0618943388
138 -0.635472651
139 0.473254787
140 0.358255673
141 1.244874828
142 1.112489659
143 -1.413826953
144 0.613439546
145 0.424584802
146 -0.562856526
147 2.912051421
148 -0.293012049
149 -0.609773591
150 -0.262821543
151 0.460480734
152 0.157472725
153 -0.962940343
154 1.925984103
155 -0.371057802
156 -0.772774182
157 1.335204488
158 0.784627996
159 0.470199082
160 0.0790569415
161 -0.774772040
162 -1.815264059
163 -0.387996879
164 -0.777371011
165 -1.412929792
166 0.339399717
167 -0.526691183
168 1.052710718
169 -0.308370894
170 -0.124098811
171 -1.092904083
172 0.116031881
173 -1.635234735
174 1.247614498
175 -0.320433615
176 0.425010470
177 1.601895350
178 -0.628312159
179 0.618013148
180 -0.548677010
181 -1.840211640
182 -0.942170958
183 0.0340800704
184 -0.170970391
185 0.262077944
186 -1.090328932
187 -0.667157054
188 0.334926665
189 -4.328580288
190 -0.140847887
191 -0.627689489
192 0.232303619
193 0.618518799
194 0.795254723
195 0.691190241
196 0.783471277
197 -0.380385703
198 -2.949690061
199 -0.710249336
200 -0.0707106781
201 -1.575216640
202 0.486158253
203 1.521038375
204 -0.364656191
205 0.695301770
206 0.516699301
207 1.186892555
208 -0.207910606
209 -0.757267712
210 -0.941573091
211 0.406194802
212 0.126504459
213 -2.926355849
214 -0.472784417
215 -0.103782069
216 -0.955197426
217 -1.330313178
218 -0.570814031
219 1.477679816
220 -0.380140921
221 0.335284606
222 0.770098792
223 1.416170841
224 0.283225978
225 0.490751637
226 1.111848345
227 -1.006923697
228 -0.413872248
229 0.508627562
230 0.152920566
231 -5.060585044
232 0.335663758