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

$R= 31.8711232416$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.846103962
4 0.5
5 0.447213595
6 1.305392630
7 -1.234508999
8 0.353553390
9 2.408099838
10 0.316227766
11 -1.511158026
12 0.923051981
13 1.310846428
14 -0.872929685
15 0.825602790
16 0.250000000
17 -0.219365098
18 1.702783725
19 1.151650816
20 0.223606797
21 -2.279031955
22 -1.068550087
23 0.954495102
24 0.652696315
25 0.200000000
26 0.926908398
27 2.599498691
28 -0.617254499
29 0.638113643
30 0.583789331
31 0.963157851
32 0.176776695
33 -2.789754819
34 -0.155114548
35 -0.552089208
36 1.204049919
37 -1.328067920
38 0.814340102
39 2.419958784
40 0.158113883
41 -0.123713101
42 -1.611518950
43 1.472559769
44 -0.755579013
45 1.076934987
46 0.674929959
47 -1.182448197
48 0.461525990
49 0.524012470
50 0.141421356
51 -0.404970777
52 0.655423214
53 0.153075861
54 1.838123152
55 -0.675810414
56 -0.436464842
57 2.126067136
58 0.451214484
59 -0.947043179
60 0.412801395
61 -0.583971325
62 0.681055447
63 -2.972820922
64 0.125000000
65 0.586228344
66 -1.972654550
67 0.808398299
68 -0.109682549
69 1.762097190
70 -0.390386023
71 0.800293119
72 0.851391862
73 0.394174430
74 -0.939085832
75 0.369220792
76 0.575825408
77 1.865538183
78 1.711169266
79 0.945042520
80 0.111803398
81 2.390844994
82 -0.0874783731
83 -0.764290384
84 -1.139515977
85 -0.0981030545
86 1.041256998
87 1.178024126
88 -0.534275043
89 1.761165254
90 0.761508032
91 -1.618251712
92 0.477247551
93 1.778089525
94 -0.836117138
95 0.515033902
96 0.326348157
97 1.055919718
98 0.370532771
99 -3.639019399
100 0.100000000
101 -0.524542531
102 -0.286357583
103 0.869410857
104 0.463454199
105 -1.019214075
106 0.108240979
107 1.870819916
108 1.299749345
109 0.363602651
110 -0.477870126
111 -2.451751450
112 -0.308627249
113 0.485938892
114 1.503356489
115 0.426863186
116 0.319056821
117 3.156649071
118 -0.669660654
119 0.270808188
120 0.291894665
121 1.283598580
122 -0.412930084
123 -0.228387247
124 0.481578925
125 0.0894427190
126 -2.102101833
127 0.0744468549
128 0.0883883476
129 2.718498424
130 0.414526037
131 -0.0478960194
132 -1.394877409
133 -1.421723298
134 0.571623919
135 1.162531156
136 -0.0775572744
137 -0.676233453
138 1.245990872
139 0.652350393
140 -0.276044604
141 -2.182922302
142 0.565892691
143 -1.980896101
144 0.602024959
145 0.285373096
146 0.278723412
147 0.967381497
148 -0.664033960
149 0.300393776
150 0.261078526
151 -0.197573085
152 0.407170051
153 -0.528253059
154 1.319134700
155 0.430737285
156 1.209979392
157 1.604678940
158 0.668245974
159 0.282593954
160 0.0790569415
161 -1.178332794
162 1.690582708
163 -1.621088269
164 -0.0618565508
165 -1.247616283
166 -0.540434913
167 -0.855622934
168 -0.805759475
169 0.718318356
170 -0.0693693351
171 2.773290146
172 0.736279884
173 -1.142108236
174 0.832988847
175 -0.246901799
176 -0.377789506
177 -1.748340214
178 1.245331894
179 -0.917783597
180 0.538467493
181 0.102511335
182 -1.144276759
183 -1.078071777
184 0.337464979
185 -0.593930029
186 1.257299160
187 0.331495383
188 -0.591224098
189 -3.209104413
190 0.364183965
191 -0.107856855
192 0.230762995
193 -0.954374978
194 0.746647993
195 1.082238468
196 0.262006235
197 -1.264629110
198 -2.573175294
199 0.571476871
200 0.0707106781
201 1.492384290
202 -0.370907581
203 -0.787759945
204 -0.202485388
205 -0.0553261810
206 0.614766313
207 2.298515783
208 0.327711607
209 -1.740328400
210 -0.720693183
211 0.526349074
212 0.0765379308
213 1.477430210
214 1.322869449
215 0.658548749
216 0.919061576
217 -1.188965457
218 0.257105900
219 0.727677644
220 -0.337905207
221 -0.287540882
222 -1.733650076
223 1.444340849
224 -0.218232421
225 0.481619967
226 0.343610686
227 -1.897834635
228 1.063033568
229 0.00454830631
230 0.301837853
231 3.443055482
232 0.225607242
233 -1.290538179
234 2.232087964
235 -0.528806909
236 -0.473521589
237 1.744819179
238 0.191490306
239 0.0287800917
240 0.206400697
241 0.830103237
242 0.907641260
243 1.828327795
244 -0.291985662
245 0.234345500
246 -0.161494171
247 1.527503863
248 0.340527723
249 -1.369212181
250 0.0632455532
251 0.168842565
252 -1.486410461
253 -1.449008594
254 0.0526418759
255 -0.181108437
256 0.0625000000