Properties

Level 10
Symmetry odd
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

$R= 31.0251790778$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.971471977
4 0.5
5 -0.447213595
6 -0.686934422
7 0.0370074694
8 0.353553390
9 -0.0562421974
10 -0.316227766
11 -1.466463625
12 -0.485735988
13 -0.733878211
14 0.0261682325
15 0.434455475
16 0.250000000
17 -0.160011738
18 -0.0397692392
19 -1.567548267
20 -0.223606797
21 -0.0359517194
22 -1.036946373
23 -0.960182167
24 -0.343467211
25 0.200000000
26 -0.518930260
27 1.026109696
28 0.0185037347
29 -0.342897425
30 0.307206413
31 -0.778542018
32 0.176776695
33 1.424628317
34 -0.113145385
35 -0.0165502434
36 -0.0281210987
37 -1.416288279
38 -1.108424009
39 0.712942117
40 -0.158113883
41 1.071943575
42 -0.0254217046
43 -0.723524381
44 -0.733231812
45 0.0251522753
46 -0.678951322
47 -0.320100114
48 -0.242867994
49 -0.998630447
50 0.141421356
51 0.155446920
52 -0.366939105
53 0.0682132954
54 0.725569124
55 0.655822470
56 0.0130841162
57 1.522829215
58 -0.242465094
59 1.084307724
60 0.217227737
61 -1.304006895
62 -0.550512340
63 -0.00208138140
64 0.125000000
65 0.328200313
66 1.007364343
67 -0.677985434
68 -0.0800058693
69 0.932790069
70 -0.0117027893
71 -0.689675713
72 -0.0198846196
73 -1.211021611
74 -1.001467046
75 -0.194294395
76 -0.783774133
77 -0.0542701077
78 0.504126205
79 0.244640072
80 -0.111803398
81 -0.940594617
82 0.757978571
83 -0.742955244
84 -0.0179758597
85 0.0715594249
86 -0.511608996
87 0.333115239
88 -0.518473186
89 -1.643647304
90 0.0177853444
91 -0.0271589754
92 -0.480091083
93 0.756331753
94 -0.226344961
95 0.701028896
96 -0.171733605
97 -1.940759427
98 -0.706138361
99 0.0824771367
100 0.100000000
101 1.483752302
102 0.109917571
103 0.306942382
104 -0.259465130
105 0.0160780977
106 0.0482340837
107 1.259460534
108 0.513054848
109 -0.839530479
110 0.463736516
111 1.375884375
112 0.00925186735
113 0.411623009
114 1.076802864
115 0.429406519
116 -0.171448712
117 0.0412749233
118 0.766721344
119 -0.00592162952
120 0.153603206
121 1.150515563
122 -0.922072118
123 -1.041363144
124 -0.389271009
125 -0.0894427190
126 -0.00147175890
127 -1.357059553
128 0.0883883476
129 0.702883661
130 0.232072667
131 0.153683723
132 0.712314158
133 -0.0580109945
134 -0.479408097
135 -0.458890206
136 -0.0565726927
137 0.877865326
138 0.659582183
139 0.131030003
140 -0.00827512172
141 0.310968291
142 -0.487674373
143 1.076205702
144 -0.0140605493
145 0.153348390
146 -0.856321593
147 0.970141495
148 -0.708144139
149 1.646769732
150 -0.137386884
151 0.721860152
152 -0.554212004
153 0.00899941171
154 -0.0383747612
155 0.348174575
156 0.356471058
157 0.132692090
158 0.172986654
159 -0.0662673045
160 -0.0790569415
161 -0.0355339128
162 -0.665100832
163 0.683792186
164 0.535971787
165 -0.637113152
166 -0.525348691
167 0.0335614667
168 -0.0127108523
169 -0.461422767
170 0.0506001546
171 0.0881623527
172 -0.361762190
173 -1.682157641
174 0.235548045
175 0.00740149388
176 -0.366615906
177 -1.053374554
178 -1.162234155
179 -1.702560362
180 0.0125761376
181 0.391826716
182 -0.0192042957
183 1.266806125
184 -0.339475661
185 0.633383373
186 0.534807311
187 0.234651336
188 -0.160050057
189 0.0379738977
190 0.495702286
191 0.764592398
192 -0.121433997
193 0.646637929
194 -1.372324151
195 -0.318837407
196 -0.499315223
197 -1.777144924
198 0.0583201427
199 0.197639274
200 0.0707106781
201 0.658643336
202 1.049171314
203 -0.0126883602
204 0.0777234600
205 -0.479387740
206 0.217041040
207 0.0539969410
208 -0.183469552
209 2.298745004
210 0.0113689319
211 1.377892865
212 0.0341066477
213 0.670024643
214 0.890573084
215 0.323569939
216 0.362784562
217 -0.0288478068
218 -0.593637694
219 1.176394455
220 0.327911235
221 0.117491947
222 0.972897171
223 0.212532035
224 0.00654205814
225 -0.0112484394
226 0.291061421
227 0.0632786869
228 0.761414607
229 -0.867590817
230 0.303636261
231 0.0541971729
232 -0.121232547
233 1.155951717
234 0.0291857781
235 0.143153123
236 0.542153862
237 -0.240258718
238 -0.00418722439
239 1.004397693
240 0.108613868
241 1.706531784
242 0.813537357
243 -0.0906731615
244 -0.652003447
245 0.446601112
246 -0.736354941
247 1.120625015
248 -0.275256170
249 0.683382940
250 -0.0632455532