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

$R= 30.8419511661$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.570999284
4 0.5
5 -0.447213595
6 1.110864247
7 1.041040118
8 -0.353553390
9 1.468038753
10 0.316227766
11 -1.038463424
12 -0.785499642
13 -0.991488164
14 -0.736126526
15 0.702572238
16 0.250000000
17 -1.346470187
18 -1.038060157
19 -0.881462158
20 -0.223606797
21 -1.635473281
22 0.734304529
23 0.381007172
24 0.555432123
25 0.200000000
26 0.701088004
27 -0.735288546
28 0.520520059
29 -0.352912167
30 -0.496793594
31 1.011477640
32 -0.176776695
33 1.631425297
34 0.952098200
35 -0.465567294
36 0.734019376
37 -0.0478378724
38 0.623287869
39 1.557627197
40 0.158113883
41 -1.707187860
42 1.156454247
43 1.587566031
44 -0.519231712
45 -0.656526889
46 -0.269412755
47 -1.561741197
48 -0.392749821
49 0.0837645274
50 -0.141421356
51 2.115303701
52 -0.495744082
53 -1.038144883
54 0.519927517
55 0.464414961
56 -0.368063263
57 1.384776420
58 0.249546586
59 -0.282624495
60 0.351286119
61 1.651007527
62 -0.715222698
63 1.528287237
64 0.125000000
65 0.443406986
66 -1.153591890
67 -0.121684340
68 -0.673235093
69 -0.598561996
70 0.329205790
71 -1.862738358
72 -0.519030078
73 -1.419561803
74 0.0338264839
75 -0.314199856
76 -0.440731079
77 -1.081082085
78 -1.101408753
79 -0.810390536
80 -0.111803398
81 -0.312900971
82 1.207164113
83 1.030887096
84 -0.817736640
85 0.602159773
86 -1.122578706
87 0.554424762
88 0.367152264
89 -0.0702537665
90 0.464234615
91 -1.032178955
92 0.190503586
93 -1.589030649
94 1.104317791
95 0.394201861
96 0.277716061
97 -1.461424981
98 -0.0592304653
99 -1.524504550
100 0.100000000
101 0.229565720
102 -1.495745591
103 0.156683320
104 0.350544002
105 0.731405886
106 0.734079286
107 0.927740424
108 -0.367644273
109 -0.646420638
110 -0.328390968
111 0.0751532633
112 0.260260029
113 -0.422576352
114 -0.979184797
115 -0.170391587
116 -0.176456083
117 -1.455543049
118 0.199845697
119 -1.401729483
120 -0.248396797
121 0.0784062835
122 -1.167438618
123 2.681990908
124 0.505738820
125 -0.0894427190
126 -1.080662269
127 0.474128840
128 -0.0883883476
129 -2.494065101
130 -0.313536087
131 -1.040894778
132 0.815712648
133 -0.917637469
134 0.0860438222
135 0.328831034
136 0.476049100
137 -0.783581311
138 0.423247246
139 -1.623648422
140 -0.232783647
141 2.453494304
142 1.317154924
143 1.029624194
144 0.367009688
145 0.157827119
146 1.003781777
147 -0.131594013
148 -0.0239189362
149 -1.298105560
150 0.222172849
151 0.0936796661
152 0.311643934
153 -1.976670416
154 0.764440473
155 -0.452346552
156 0.778813598
157 -0.840655797
158 0.573032643
159 1.630924874
160 0.0790569415
161 0.396643756
162 0.221254399
163 -1.776802280
164 -0.853593930
165 -0.729595572
166 -0.728947256
167 0.116413948
168 0.578227123
169 -0.0169512268
170 -0.425791259
171 -1.294020610
172 0.793783015
173 0.0668234642
174 -0.392037509
175 0.208208023
176 -0.259615856
177 0.444003024
178 0.0496769147
179 -1.365299167
180 -0.328263444
181 -0.219817332
182 0.729860739
183 -2.593731300
184 -0.134706377
185 0.0213937469
186 1.123614347
187 1.398259648
188 -0.780870598
189 -0.765465084
190 -0.278742809
191 -1.518885049
192 -0.196374910
193 1.277504400
194 1.033383514
195 -0.696592059
196 0.0418822637
197 0.589691622
198 1.077987505
199 1.584114753
200 -0.0707106781
201 0.191163805
202 -0.162327477
203 -0.367386104
204 1.057651850
205 0.763477621
206 -0.110791838
207 0.559332872
208 -0.247872041
209 0.915379684
210 -0.517182062
211 -1.679358197
212 -0.519072441
213 2.926220129
214 -0.656011545
215 -0.709981113
216 0.259963758
217 1.052974684
218 0.457088417
219 2.229833023
220 0.232207480
221 1.335021212
222 -0.0531413821
223 -1.653392865
224 -0.184031631
225 0.293607750
226 0.298806604
227 1.393793774
228 0.692388210
229 -0.153221025
230 0.120485047
231 1.702588334
232 0.124773293
233 -1.802858122
234 1.029224360
235 0.698431896
236 -0.141312247
237 1.268467980
238 0.991172422
239 -0.459332807
240 0.175643059
241 0.510141055
242 -0.0554416147
243 1.367802361
244 0.825503763
245 -0.0374606355
246 -1.896453958
247 0.907322747
248 -0.357611349
249 -1.467738187
250 0.0632455532
251 1.028729590
252 0.764143618
253 -1.146899943
254 -0.335259717