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

$R= 28.5712269238$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.412725756
4 0.5
5 0.447213595
6 0.998947962
7 0.0751260434
8 -0.353553390
9 0.995794062
10 -0.316227766
11 1.060285880
12 -0.706362878
13 0.695278661
14 -0.0531221347
15 -0.631790164
16 0.250000000
17 0.864687450
18 -0.704132734
19 -1.206199270
20 0.223606797
21 -0.106132496
22 -0.749735335
23 0.100604941
24 0.499473981
25 0.200000000
26 -0.491636256
27 0.00594183646
28 0.0375630217
29 -0.0552910430
30 0.446743109
31 -0.668666939
32 -0.176776695
33 -1.497893171
34 -0.611426359
35 0.0335973880
36 0.497897031
37 -0.637786482
38 0.852911683
39 -0.982238073
40 -0.158113883
41 -0.515349899
42 0.0750470080
43 0.189454510
44 0.530142940
45 0.445332642
46 -0.0711384365
47 -1.698456817
48 -0.353181439
49 -0.994356077
50 -0.141421356
51 -1.221566232
52 0.347639330
53 -1.708315142
54 -0.00420151286
55 0.474174260
56 -0.0265610673
57 1.704028777
58 0.0390966714
59 1.552533634
60 -0.315895082
61 1.337259221
62 0.472818927
63 0.0748100680
64 0.125000000
65 0.310938070
66 1.059170419
67 0.00929940457
68 0.432343725
69 -0.142127192
70 -0.0237569409
71 0.0329391566
72 -0.352066367
73 0.259471930
74 0.450983146
75 -0.282545151
76 -0.603099635
77 0.0796550831
78 0.694547202
79 1.852443066
80 0.111803398
81 -1.004188247
82 0.364407408
83 0.441677506
84 -0.0530662483
85 0.386699983
86 -0.133964568
87 0.0781110806
88 -0.374867667
89 -0.673964543
90 -0.314897731
91 0.0522335349
92 0.0503024708
93 0.944643007
94 1.200990333
95 -0.539428712
96 0.249736990
97 0.606065554
98 0.703115925
99 1.055826383
100 0.100000000
101 -1.669428827
102 0.863777766
103 1.851984340
104 -0.245818128
105 -0.0474638954
106 1.207961221
107 0.911540039
108 0.00297091823
109 -1.248248746
110 -0.335291835
111 0.901017390
112 0.0187815108
113 0.506067865
114 -1.204930303
115 0.0449918977
116 -0.0276455215
117 0.692354363
118 -1.097807060
119 0.0649605470
120 0.223371554
121 0.124206147
122 -0.945585063
123 0.728048076
124 -0.334333469
125 0.0894427190
126 -0.0528987064
127 -0.561413643
128 -0.0883883476
129 -0.267647266
130 -0.219866417
131 -0.510205181
132 -0.748946585
133 -0.0906169790
134 -0.00657567203
135 0.00265727005
136 -0.305713179
137 1.629233575
138 0.100499101
139 0.906436677
140 0.0167986940
141 2.399453692
142 -0.0232915010
143 0.737194148
144 0.248948515
145 -0.0247269061
146 -0.183474361
147 1.404752441
148 -0.318893241
149 -1.657932276
150 0.199789592
151 -1.745085576
152 0.426455841
153 0.861050624
154 -0.0563246494
155 -0.299036946
156 -0.491119036
157 1.883444076
158 -1.309875053
159 2.413380795
160 -0.0790569415
161 0.00755805860
162 0.710068319
163 1.251574867
164 -0.257674949
165 -0.669878191
166 -0.312313159
167 -1.606491806
168 0.0375235040
169 -0.516587529
170 -0.273438180
171 -1.201125948
172 0.0947272551
173 0.129673051
174 -0.0552328747
175 0.0150252086
176 0.265071470
177 -2.193304058
178 0.476564898
179 0.329048649
180 0.222666321
181 -1.628671315
182 -0.0369346867
183 -1.889179790
184 -0.0355692182
185 -0.285226785
186 -0.667963476
187 0.916815363
188 -0.849228408
189 0.000445530073
190 0.381433700
191 0.284453836
192 -0.176590719
193 -1.123924514
194 -0.428553063
195 -0.439270220
196 -0.497178038
197 0.117590438
198 -0.746581995
199 -0.788607346
200 -0.0707106781
201 -0.0131122457
202 1.180464444
203 -0.00432344748
204 -0.610783116
205 -0.230471481
206 -1.309550685
207 0.100405118
208 0.173819665
209 -1.278770738
210 0.0335620423
211 -1.101648039
212 -0.854157571
213 -0.0469279262
214 -0.644556143
215 0.0847266327
216 -0.00210075643
217 -0.0500917015
218 0.882645153
219 -0.364177150
220 0.237087130
221 0.604512232
222 -0.637115506
223 -0.843468766
224 -0.0132805336
225 0.199158812
226 -0.357844019
227 0.394107805
228 0.852014388
229 0.726571251
230 -0.0318140759
231 -0.126854766
232 0.0195483357