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

$R= 31.6329465687$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.791478894
4 0.5
5 0.447213595
6 -0.559660093
7 -1.544537226
8 0.353553390
9 -0.373561159
10 0.316227766
11 -0.797593804
12 -0.395739447
13 -0.951467772
14 -1.092152746
15 -0.353960122
16 0.250000000
17 1.256696948
18 -0.264147628
19 1.019652917
20 0.223606797
21 1.222468617
22 -0.563983988
23 1.302198800
24 -0.279830046
25 0.200000000
26 -0.672789314
27 1.087144668
28 -0.772268613
29 -1.042648146
30 -0.250287602
31 1.568470126
32 0.176776695
33 0.631278662
34 0.888618934
35 -0.690738046
36 -0.186780579
37 1.570932295
38 0.721003492
39 0.753066661
40 0.158113883
41 0.540267524
42 0.864415848
43 -1.801550387
44 -0.398796902
45 -0.167061629
46 0.920793602
47 -0.473923386
48 -0.197869723
49 1.385595245
50 0.141421356
51 -0.994649111
52 -0.475733886
53 0.948048602
54 0.768727366
55 -0.356694793
56 -0.546076373
57 -0.807033764
58 -0.737263574
59 -1.500355903
60 -0.176980061
61 -1.092327579
62 1.109075862
63 0.576979117
64 0.125000000
65 -0.425509323
66 0.446381423
67 -0.253388276
68 0.628348474
69 -1.030662867
70 -0.488425556
71 1.180242282
72 -0.132073814
73 -1.823843914
74 1.110816878
75 -0.158295778
76 0.509826458
77 1.231913323
78 0.532498542
79 0.396038495
80 0.111803398
81 -0.486890900
82 0.382026830
83 -0.216785093
84 0.611234308
85 0.562011960
86 -1.273888495
87 0.825234002
88 -0.281991994
89 0.540906850
90 -0.118130410
91 1.469577395
92 0.651099400
93 -1.241411002
94 -0.335114440
95 0.456002647
96 -0.139915023
97 0.722069811
98 0.979763793
99 0.297950066
100 0.100000000
101 0.232911853
102 -0.703323131
103 -0.174153237
104 -0.336394657
105 0.546704585
106 0.670371595
107 -0.739080923
108 0.543572334
109 -0.437707485
110 -0.252221307
111 -1.243359756
112 -0.386134306
113 -0.194082050
114 -0.570659047
115 0.582361007
116 -0.521324073
117 0.355431404
118 -1.060911833
119 -1.941015219
120 -0.125143801
121 -0.363844122
122 -0.772392239
123 -0.427610342
124 0.784235063
125 0.0894427190
126 0.407985846
127 -0.755044155
128 0.0883883476
129 1.425889109
130 -0.300880528
131 1.384714585
132 0.315639331
133 -1.574891889
134 -0.179172568
135 0.486185875
136 0.444309467
137 -0.430259982
138 -0.728788702
139 -0.0166821340
140 -0.345369023
141 0.375100358
142 0.834557321
143 0.758884801
144 -0.0933902898
145 -0.466286426
146 -1.289652399
147 -1.096669393
148 0.785466147
149 -0.490554727
150 -0.111932018
151 -1.449800981
152 0.360501746
153 -0.469453169
154 0.871094264
155 0.701441164
156 0.376533330
157 -0.785598403
158 0.280041505
159 -0.750360461
160 0.0790569415
161 -2.011294523
162 -0.344283857
163 0.818665474
164 0.270133762
165 0.282316400
166 -0.153290209
167 -1.486395006
168 0.432207924
169 -0.0947090631
170 0.397402468
171 -0.380902704
172 -0.900775193
173 1.814812796
174 0.583528559
175 -0.308907445
176 -0.199398451
177 1.187500004
178 0.382478902
179 0.706420543
180 -0.0835308146
181 1.315073466
182 1.039148141
183 0.864554320
184 0.460396801
185 0.702542280
186 -0.877810138
187 -1.002333465
188 -0.236961693
189 -1.679135944
190 0.322442564
191 -0.172809070
192 -0.0989348618
193 0.764190010
194 0.510580460
195 0.336781649
196 0.692797622
197 -0.625974669
198 0.210682512
199 -0.284850810
200 0.0707106781
201 0.200557408
202 0.164693551
203 1.610400925
204 -0.497324555
205 0.241614982
206 -0.123144935
207 -0.486459848
208 -0.237866943
209 -0.813258856
210 0.386578519
211 0.0896317305
212 0.474024301
213 -0.934156673
214 -0.522609133
215 -0.805677826
216 0.384363683
217 -2.422591421
218 -0.309505931
219 1.443335436
220 -0.178347396
221 -1.195878237
222 -0.879188115
223 -1.499603889
224 -0.273038186
225 -0.0747122318
226 -0.137236734
227 0.587357248
228 -0.403516882
229 -0.132544488
230 0.411791417
231 -0.978146622
232 -0.368631787
233 0.708980784
234 0.251327956
235 -0.211944981
236 -0.750177951
237 -0.318148042
238 -1.372505024
239 -1.250891134
240 -0.0884900305
241 0.566594671
242 -0.257276646
243 -0.715339079
244 -0.546163789
245 0.619657031
246 -0.302366173
247 -0.971206586
248 0.554537931
249 0.352322972
250 0.0632455532