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

$R= 29.9472580173$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.293975681
4 0.5
5 -0.447213595
6 -0.914978978
7 1.034965912
8 0.353553390
9 0.674373063
10 -0.316227766
11 0.144678295
12 -0.646987840
13 -0.0257067561
14 0.731831415
15 0.578683516
16 0.250000000
17 -1.286829476
18 0.476853766
19 0.747927899
20 -0.223606797
21 -1.339220722
22 0.102303004
23 1.095049274
24 -0.457489489
25 0.200000000
26 -0.0181774216
27 0.421353336
28 0.517482956
29 1.452671633
30 0.409191038
31 0.191957724
32 0.176776695
33 -0.187210196
34 -0.909925848
35 -0.462850827
36 0.337186531
37 0.258823569
38 0.528864889
39 0.0332639173
40 -0.158113883
41 -1.081325303
42 -0.946972054
43 -0.910621855
44 0.0723391478
45 -0.301588802
46 0.774316767
47 -0.958233924
48 -0.323493920
49 0.0711544405
50 0.141421356
51 1.665126048
52 -0.0128533780
53 0.918811417
54 0.297941801
55 -0.0647021008
56 0.365915707
57 -0.967800513
58 1.027193963
59 0.000447802111
60 0.289341758
61 -0.995426634
62 0.135734608
63 0.697953133
64 0.125000000
65 0.0114964108
66 -0.132377599
67 -1.551671839
68 -0.643414738
69 -1.416967131
70 -0.327284958
71 -0.837322542
72 0.238426883
73 0.517542177
74 0.183015900
75 -0.258795136
76 0.373963949
77 0.149737104
78 0.0235211415
79 -1.899239040
80 -0.111803398
81 -1.219594034
82 -0.764612454
83 0.610795884
84 -0.669610361
85 0.575487636
86 -0.643906889
87 -1.879721766
88 0.0511515020
89 1.511193551
90 -0.213255487
91 -0.0266056164
92 0.547524637
93 -0.248388627
94 -0.677573705
95 -0.334483525
96 -0.228744744
97 1.821146144
98 0.0503137874
99 0.0975671455
100 0.100000000
101 0.410549165
102 1.177421920
103 1.352352539
104 -0.00908871080
105 0.598917714
106 0.649697784
107 -1.676431251
108 0.210676668
109 1.000250604
110 -0.0457512942
111 -0.334911404
112 0.258741478
113 0.696204253
114 -0.684338305
115 -0.489720923
116 0.726335816
117 -0.0173359439
118 0.000316643909
119 -1.331824643
120 0.204595519
121 -0.979068190
122 -0.703872923
123 1.399208646
124 0.0959788624
125 -0.0894427190
126 0.493527393
127 1.022358508
128 0.0883883476
129 1.178322536
130 0.00812919007
131 0.433485754
132 -0.0936050981
133 0.774079881
134 -1.097197679
135 -0.188434940
136 -0.454962924
137 1.435111091
138 -1.001947067
139 1.352847338
140 -0.231425413
141 1.239931395
142 -0.592076447
143 -0.00371920888
144 0.168593265
145 -0.649654504
146 0.365957583
147 -0.0920721154
148 0.129411784
149 0.921547931
150 -0.182995795
151 -0.181424400
152 0.264432444
153 -0.867803132
154 0.105880121
155 -0.0858461043
156 0.0166319586
157 -0.406859132
158 -1.342964804
159 -1.188919613
160 -0.0790569415
161 1.133338697
162 -0.862383212
163 -0.492555312
164 -0.540662651
165 0.0837229449
166 0.431897911
167 0.0168779704
168 -0.473486027
169 -0.999339046
170 0.406931210
171 0.504382608
172 -0.455310927
173 -0.993924310
174 -1.329164008
175 0.206993182
176 0.0361695739
177 -0.000579254715
178 1.068575208
179 0.397022975
180 -0.150794401
181 1.329441243
182 -0.0188130117
183 1.288058423
184 0.387158383
185 -0.115749419
186 -0.175637283
187 -0.186175103
188 -0.479116962
189 0.436090326
190 -0.236515568
191 0.722833521
192 -0.161746960
193 -1.841024365
194 1.287744788
195 -0.0148760760
196 0.0355772202
197 -0.869246144
198 0.0689903902
199 1.216865781
200 0.0707106781
201 2.007864753
202 0.290302098
203 1.503478606
204 0.832563024
205 0.483583376
206 0.956257651
207 0.738556214
208 -0.00642668904
209 0.108393817
210 0.423498777
211 -0.168363879
212 0.459405708
213 1.083503752
214 -1.185415905
215 0.407242474
216 0.148970900
217 0.199411202
218 0.707283985
219 -0.668103990
220 -0.0323510504
221 0.0342836559
222 -0.236818125
223 -0.176807729
224 0.182957853
225 0.134874612
226 0.492290748
227 1.133500384
228 -0.483900256
229 1.977616218
230 -0.346284985
231 -0.188219951
232 0.513596981
233 0.680692330
234 -0.0122583635
235 0.428535238
236 0.000223901055
237 2.493899026
238 -0.941742236
239 -0.577100557
240 0.144670879
241 0.428071720
242 -0.692305756
243 1.103602362
244 -0.497713317
245 -0.0318212331
246 0.989389922
247 0.233852242
248 0.0678673044
249 -0.487750275