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

$R= 29.178819528$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.390839392
4 0.5
5 0.447213595
6 0.276365184
7 -0.829623522
8 -0.353553390
9 -0.847244569
10 -0.316227766
11 -1.539713823
12 -0.195419696
13 -1.484850587
14 0.586632418
15 -0.174788689
16 0.250000000
17 1.043020486
18 0.599092380
19 0.918857294
20 0.223606797
21 0.324249553
22 1.088742085
23 -0.0962652434
24 0.138182592
25 0.200000000
26 1.049947919
27 0.721975944
28 -0.414811761
29 0.901082603
30 0.123594267
31 0.449668769
32 -0.176776695
33 0.601780815
34 -0.737526859
35 -0.371018918
36 -0.423622284
37 1.078779193
38 -0.649730223
39 0.580338101
40 -0.158113883
41 -0.136420470
42 -0.229279058
43 -0.500456228
44 -0.769856911
45 -0.378899290
46 0.0680698064
47 1.251776567
48 -0.0977098480
49 -0.311724810
50 -0.141421356
51 -0.407653493
52 -0.742425293
53 -0.555591098
54 -0.510514086
55 -0.688580955
56 0.293316209
57 -0.359125626
58 -0.637161619
59 0.661406908
60 -0.0873943449
61 1.815464549
62 -0.317963836
63 0.702894024
64 0.125000000
65 -0.664045370
66 -0.425523295
67 1.524780724
68 0.521510243
69 0.0376242492
70 0.262349993
71 -1.019828611
72 0.299546190
73 -1.069125477
74 -0.762812083
75 -0.0781678784
76 0.459428647
77 1.277382806
78 -0.410361006
79 -1.553219902
80 0.111803398
81 0.565067929
82 0.0964638400
83 0.752103277
84 0.162124776
85 0.466452942
86 0.353875992
87 -0.352178577
88 0.544371042
89 -1.368374971
90 0.267922257
91 1.231866974
92 -0.0481326217
93 -0.175748268
94 -0.885139699
95 0.410925474
96 0.0690912961
97 -1.174446082
98 0.220422727
99 1.304514175
100 0.100000000
101 1.357283788
102 0.288254549
103 -0.464556455
104 0.524973959
105 0.145008808
106 0.392862233
107 0.921582266
108 0.360987972
109 1.216531158
110 0.486900262
111 -0.421629404
112 -0.207405880
113 -0.719767092
114 0.253940165
115 -0.0430511256
116 0.450541301
117 1.258031596
118 -0.467685310
119 -0.865314330
120 0.0617971339
121 1.370718658
122 -1.283727293
123 0.0533184939
124 0.224834384
125 0.0894427190
126 -0.497021130
127 -0.0113219888
128 -0.0883883476
129 0.195598008
130 0.469550984
131 -1.849816090
132 0.300890407
133 -0.762305625
134 -1.078182790
135 0.322877458
136 -0.368763429
137 -1.017665039
138 -0.0266043617
139 1.508095099
140 -0.185509459
141 -0.489243592
142 0.721127727
143 2.286244975
144 -0.211811142
145 0.402976391
146 0.755985875
147 0.121834336
148 0.539389596
149 0.408062718
150 0.0552730369
151 -0.118111705
152 -0.324865111
153 -0.883693445
154 -0.903246044
155 0.201097987
156 0.290169050
157 1.194684422
158 1.098292325
159 0.217146885
160 -0.0790569415
161 0.0798639089
162 -0.399563365
163 0.473637321
164 -0.0682102354
165 0.269124562
166 -0.531817327
167 1.256264241
168 -0.114639529
169 1.204781275
170 -0.329832038
171 -0.778496861
172 -0.250228114
173 -0.208632113
174 0.249027860
175 -0.165924704
176 -0.384928455
177 -0.258503890
178 0.967587221
179 -1.664906949
180 -0.189449645
181 -0.832744684
182 -0.871061491
183 -0.709555229
184 0.0340349032
185 0.482444722
186 0.124272792
187 -1.605953835
188 0.625888283
189 -0.598968422
190 -0.290568189
191 -0.800679841
192 -0.0488549240
193 -1.994806149
194 0.830458788
195 0.259535088
196 -0.155862405
197 0.864131758
198 -0.922430819
199 -0.0440144622
200 -0.0707106781
201 -0.595976501
202 -0.959744570
203 -0.747550218
204 -0.203826746
205 -0.0610090893
206 0.328491020
207 0.0815728236
208 -0.371212646
209 -1.414664871
210 -0.102536711
211 -0.657303511
212 -0.277795549
213 0.398658554
214 -0.651657069
215 -0.223810829
216 -0.255257043
217 -0.373002434
218 -0.860217431
219 0.418675366
220 -0.344290477
221 -1.550832011
222 0.298137011
223 0.560759520
224 0.146658104
225 -0.169448913
226 0.508952192
227 0.0707300391
228 -0.179562813
229 -1.292659083
230 0.0304417428
231 -0.512558630
232 -0.318580809
233 0.923648388
234 -0.889562672
235 0.559811499
236 0.330703454
237 0.698153243
238 0.611869630