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

$R= 31.0175516329$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.015013389
4 0.5
5 0.447213595
6 -0.717722850
7 -0.433182522
8 0.353553390
9 0.0302521816
10 0.316227766
11 0.616946289
12 -0.507506694
13 0.579741223
14 -0.306306299
15 -0.453927787
16 0.250000000
17 -0.349390875
18 0.0213915228
19 -0.175097471
20 0.223606797
21 0.439686060
22 0.436246904
23 -0.213020058
24 -0.358861425
25 0.200000000
26 0.409938950
27 0.984307020
28 -0.216591261
29 -0.128298657
30 -0.320975416
31 0.848903083
32 0.176776695
33 -0.626208744
34 -0.247056657
35 -0.193725113
36 0.0151260908
37 -1.488519242
38 -0.123812609
39 -0.588445104
40 0.158113883
41 0.0854029280
42 0.310904994
43 0.869889302
44 0.308473144
45 0.0135291869
46 -0.150627927
47 -1.411257181
48 -0.253753347
49 -0.812352902
50 0.141421356
51 0.354636417
52 0.289870611
53 1.719830935
54 0.696010168
55 0.275906768
56 -0.153153149
57 0.177726278
58 -0.0907208509
59 -0.112980913
60 -0.226963893
61 1.386029343
62 0.600265127
63 -0.0131047163
64 0.125000000
65 0.259268157
66 -0.442796449
67 -1.185983615
68 -0.174695437
69 0.216218211
70 -0.136984341
71 0.216678765
72 0.0106957614
73 0.0421748238
74 -1.052542050
75 -0.203002677
76 -0.0875487358
77 -0.267250349
78 -0.416093524
79 -0.597033665
80 0.111803398
81 -1.029336987
82 0.0603889895
83 -0.726915161
84 0.219843030
85 -0.156252349
86 0.615104624
87 0.130224855
88 0.218123452
89 -1.042580936
90 0.00956657982
91 -0.251133765
92 -0.106510029
93 -0.861647996
94 -0.997909522
95 -0.0783059698
96 -0.179430712
97 0.134789005
98 -0.574420245
99 0.0186639712
100 0.100000000
101 0.641647893
102 0.250765815
103 -0.157878821
104 0.204969475
105 0.196633583
106 1.216104116
107 -0.245396836
108 0.492153510
109 0.717855597
110 0.195095546
111 1.510866962
112 -0.108295630
113 0.697238084
114 0.125671456
115 -0.0952654661
116 -0.0641493288
117 0.0175384368
118 -0.0798895703
119 0.151350020
120 -0.160487708
121 -0.619377275
122 0.980070747
123 -0.0866851155
124 0.424451541
125 0.0894427190
126 -0.00926643380
127 0.460361453
128 0.0883883476
129 -0.882949289
130 0.183330272
131 -0.389834754
132 -0.313104372
133 0.0758491644
134 -0.838617057
135 0.440195481
136 -0.123528328
137 -0.741003840
138 0.152889363
139 1.263250776
140 -0.0968625566
141 1.432444935
142 0.153215024
143 0.357669197
144 0.00756304541
145 -0.0573769040
146 0.0298221039
147 0.824549073
148 -0.744259621
149 0.906615304
150 -0.143544570
151 1.315848543
152 -0.0619063048
153 -0.0105698361
154 -0.188974534
155 0.379641000
156 -0.294222552
157 1.868985490
158 -0.422166553
159 -1.745651427
160 0.0790569415
161 0.0922765675
162 -0.727851163
163 0.367007131
164 0.0427014640
165 -0.280049064
166 -0.514006639
167 -0.775133820
168 0.155452497
169 -0.663900116
170 -0.110487096
171 -0.00529708240
172 0.434944651
173 -0.644266295
174 0.0920828784
175 -0.0866365044
176 0.154236572
177 0.114677139
178 -0.737216050
179 1.664879586
180 0.00676459346
181 -1.266311007
182 -0.177578388
183 -1.406838363
184 -0.0753139638
185 -0.665686042
186 -0.609277141
187 -0.215555579
188 -0.705628590
189 -0.426384446
190 -0.0553706823
191 -0.629628905
192 -0.126876673
193 1.969348056
194 0.0953102201
195 -0.263160651
196 -0.406176451
197 1.822435153
198 0.0131974206
199 0.731230570
200 0.0707106781
201 1.203789227
202 0.453713576
203 0.0555768050
204 0.177318208
205 0.0381933505
206 -0.111637185
207 -0.00643399242
208 0.144935305
209 -0.108030983
210 0.139040940
211 0.226775731
212 0.859915467
213 -0.219926023
214 -0.173521766
215 0.389026322
216 0.348005084
217 -0.367741573
218 0.507600560
219 -0.0429089132
220 0.137953384
221 -0.202412549
222 1.068344274
223 1.811316439
224 -0.0765765747
225 0.00605043633
226 0.493021777
227 1.705090576
228 0.0888631391
229 1.333055196
230 -0.0673628571
231 0.271554072
232 -0.0453604254
233 0.676511514
234 0.0124015476
235 -0.631133398
236 -0.0564904569
237 0.603617964
238 0.107020626
239 0.737417631
240 -0.113481946
241 1.044873059
242 -0.437965871
243 0.0638076761
244 0.693014671
245 -0.363295262
246 -0.0612956330
247 -0.0668800362
248 0.300132563
249 0.727197367
250 0.0632455532