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

$R= 31.4294214363$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.413790635
4 0.5
5 0.447213595
6 0.292594164
7 1.456634462
8 -0.353553390
9 -0.828777310
10 -0.316227766
11 0.559858664
12 -0.206895317
13 -1.871911143
14 -1.029996106
15 -0.185052797
16 0.250000000
17 1.400401725
18 0.586034056
19 0.960183287
20 0.223606797
21 -0.602741699
22 -0.395879858
23 0.550588725
24 0.146297082
25 0.200000000
26 1.323641063
27 0.756730925
28 0.728317231
29 -1.086533276
30 0.130852088
31 -0.143068737
32 -0.176776695
33 -0.231664272
34 -0.990233556
35 0.651426735
36 -0.414388655
37 -1.069202881
38 -0.678952113
39 0.774579301
40 -0.158113883
41 -0.674817876
42 0.426202743
43 -1.021658406
44 0.279929332
45 -0.370640480
46 -0.389325021
47 0.0836600706
48 -0.103447658
49 1.121783956
50 -0.141421356
51 -0.579473120
52 -0.935955571
53 0.207274286
54 -0.535089568
55 0.250376406
56 -0.514998053
57 -0.397314852
58 0.768295047
59 -1.213948454
60 -0.0925263989
61 1.034413333
62 0.101164874
63 -1.207225591
64 0.125000000
65 -0.837144112
66 0.163811378
67 -1.304138065
68 0.700200862
69 -0.227828458
70 -0.460628261
71 0.455851092
72 0.293017028
73 0.158849759
74 0.756040608
75 -0.0827581270
76 0.480091643
77 0.815509424
78 -0.547710276
79 1.261751162
80 0.111803398
81 0.515649139
82 0.477168296
83 -1.836444823
84 -0.301370849
85 0.626278690
86 0.722421587
87 0.449597294
88 -0.197939929
89 -1.212869578
90 0.262082397
91 -2.726690281
92 0.275294362
93 0.0592005039
94 -0.0591566032
95 0.429407020
96 0.0731485410
97 1.882509163
98 -0.793221043
99 -0.463998157
100 0.100000000
101 0.726466686
102 0.409749372
103 1.043629594
104 0.661820531
105 -0.269554282
106 -0.146565053
107 0.0725030520
108 0.378365462
109 -0.975808248
110 -0.177042854
111 0.442426139
112 0.364158615
113 -1.713783943
114 0.280944026
115 0.246230763
116 -0.543266638
117 1.551397481
118 0.858391184
119 2.039873414
120 0.0654260441
121 -0.686558276
122 -0.731440682
123 0.279233317
124 -0.0715343689
125 0.0894427190
126 0.853637402
127 -0.111200719
128 -0.0883883476
129 0.422752681
130 0.591950279
131 -0.830693990
132 -0.115832136
133 1.398636067
134 0.922164869
135 0.338420357
136 -0.495116778
137 1.813009276
138 0.161099047
139 0.177075494
140 0.325713367
141 -0.0346177533
142 -0.322335398
143 -1.048005671
144 -0.207194327
145 -0.485912453
146 -0.112323741
147 -0.464183695
148 -0.534601440
149 -0.241357856
150 0.0585188328
151 0.563387159
152 -0.339476056
153 -1.160621173
154 -0.576652244
155 -0.0639822846
156 0.387289650
157 1.227721009
158 -0.892192803
159 -0.0857681604
160 -0.0790569415
161 0.802006508
162 -0.364619003
163 -1.631261608
164 -0.337408938
165 -0.103603412
166 1.298562588
167 0.786257618
168 0.213101371
169 2.504051352
170 -0.442845909
171 -0.795778169
172 -0.510829203
173 -0.928980374
174 -0.317913296
175 0.291326892
176 0.139964666
177 0.502320393
178 0.857628303
179 -0.141079186
180 -0.185320240
181 1.222657209
182 1.928061188
183 -0.428030560
184 -0.194662510
185 -0.478162065
186 -0.0418610778
187 0.784026112
188 0.0418300353
189 1.102279632
190 -0.303636616
191 0.890883616
192 -0.0517238294
193 -0.199662202
194 -1.331134995
195 0.346402394
196 0.560891978
197 0.365416439
198 0.328096243
199 0.313819713
200 -0.0707106781
201 0.539642420
202 -0.513689520
203 -1.582689337
204 -0.289736560
205 -0.301787728
206 -0.737957563
207 -0.456278211
208 -0.467977785
209 0.537548639
210 0.190603661
211 -0.877135473
212 0.103637143
213 -0.188555463
214 -0.0512673997
215 -0.456899529
216 -0.267544784
217 -0.208214816
218 0.690000629
219 -0.0655433976
220 0.125188203
221 -2.620961327
222 -0.312842523
223 -0.145475670
224 -0.257499026
225 -0.165755462
226 1.211828248
227 -1.081056746
228 -0.198657426
229 0.197613524
230 -0.174111442
231 -0.340445776
232 0.384147523
233 -1.110846823
234 -1.097003679
235 0.0374139210
236 -0.606974227
237 -0.528155980
238 -1.442408324
239 -1.357300948
240 -0.0462631994
241 -0.545119778
242 0.485470012
243 -0.964369901
244 0.517206666
245 0.501677036
246 -0.197447772
247 -1.916703769
248 0.0505824373
249 0.912219276
250 -0.0632455532