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

$R= 31.9896349188$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.495455784
4 0.5
5 -0.447213595
6 1.057446926
7 1.331067783
8 0.353553390
9 1.236388004
10 -0.316227766
11 -0.221217441
12 0.747727892
13 -1.660338508
14 0.941207055
15 -0.668788158
16 0.250000000
17 -0.117370667
18 0.874258342
19 -0.872658301
20 -0.223606797
21 1.990553017
22 -0.156424352
23 -1.011388709
24 0.528723463
25 0.200000000
26 -1.174036618
27 0.353507809
28 0.665533891
29 -1.340141994
30 -0.472904642
31 -0.529871853
32 0.176776695
33 -0.330820902
34 -0.0829935948
35 -0.595271609
36 0.618194002
37 -1.875028640
38 -0.617062602
39 -2.482962828
40 -0.158113883
41 -1.276576388
42 1.407533536
43 0.536600781
44 -0.110608720
45 -0.552929525
46 -0.715159814
47 0.552919791
48 0.373863946
49 0.771741444
50 0.141421356
51 -0.175522643
52 -0.830169254
53 -0.0881985865
54 0.249967769
55 0.0989314473
56 0.470603527
57 -1.305021905
58 -0.947623491
59 -0.725299046
60 -0.334394079
61 1.674936825
62 -0.374675980
63 1.645716241
64 0.125000000
65 0.742525954
66 -0.233925703
67 0.507512874
68 -0.0586853337
69 -1.512487096
70 -0.420920591
71 0.620064363
72 0.437129171
73 -0.798042885
74 -1.325845466
75 0.299091156
76 -0.436329150
77 -0.294455409
78 -1.755719853
79 -1.419381793
80 -0.111803398
81 -0.707732706
82 -0.902675821
83 -0.240266585
84 0.995276508
85 0.0524897581
86 0.379434051
87 -2.004123097
88 -0.0782121764
89 1.822858394
90 -0.390980216
91 -2.210023099
92 -0.505694354
93 -0.792399928
94 0.390973334
95 0.390264656
96 0.264361731
97 -0.704797113
98 0.545703608
99 -0.273510590
100 0.100000000
101 1.637887129
102 -0.124113251
103 1.122357563
104 -0.587018309
105 -0.890202371
106 -0.0623658186
107 -0.996530698
108 0.176753904
109 1.708728314
110 0.0699550972
111 -2.804022427
112 0.332766945
113 1.264659976
114 -0.922789839
115 0.452306781
116 -0.670070997
117 -2.052822616
118 -0.512863874
119 -0.156228314
120 -0.236452321
121 -0.951062843
122 1.184359187
123 -1.909063545
124 -0.264935926
125 -0.0894427190
126 1.163697114
127 -1.026973342
128 0.0883883476
129 0.802462742
130 0.525045137
131 -0.231663692
132 -0.165410451
133 -1.161567351
134 0.358865795
135 -0.158093498
136 -0.0414967974
137 -0.526554004
138 -1.069489882
139 1.560461039
140 -0.297635804
141 0.826867101
142 0.438451716
143 0.367295836
144 0.309097001
145 0.599329719
146 -0.564301536
147 1.154105207
148 -0.937514320
149 -0.814801356
150 0.211489385
151 -1.040582286
152 -0.308531301
153 -0.145115685
154 -0.208211416
155 0.236965896
156 -1.241481414
157 -0.151939080
158 -1.003654491
159 -0.131897087
160 -0.0790569415
161 -1.346226929
162 -0.500442595
163 1.626618861
164 -0.638288194
165 0.147947605
166 -0.169894131
167 0.721578942
168 0.703766768
169 1.756723965
170 0.0371158639
171 -1.078944253
172 0.268300390
173 -0.723861961
174 -1.417129032
175 0.266213556
176 -0.0553043603
177 -1.084652660
178 1.288955532
179 0.732488814
180 -0.276464762
181 0.879781525
182 -1.562722319
183 2.504793952
184 -0.357579907
185 0.838538300
186 -0.560311363
187 0.0259646422
188 0.276459895
189 0.470543176
190 0.275958785
191 1.022524761
192 0.186931973
193 0.0501665960
194 -0.498366818
195 1.110414733
196 0.385870722
197 0.372578003
198 -0.193401193
199 -0.125707812
200 0.0707106781
201 0.758965547
202 1.158161096
203 -1.783819220
204 -0.0877613218
205 0.570902316
206 0.793626643
207 -1.250462934
208 -0.415084627
209 0.193044350
210 -0.629468133
211 -1.511081724
212 -0.0440992932
213 0.927277038
214 -0.704653614
215 -0.239975164
216 0.124983884
217 -0.705295523
218 1.208253378
219 -1.193473570
220 0.0494657236
221 0.194813561
222 -1.982743273
223 0.118940577
224 0.235301763
225 0.247277600
226 0.894249645
227 -0.889000217
228 -0.652510952
229 1.143003550
230 0.319829192
231 -0.440541458
232 -0.473811745
233 -0.214184914
234 -1.451564792
235 -0.247273248
236 -0.362649523
237 -2.123276440
238 -0.110470100
239 -1.672323141
240 -0.167197039
241 -0.0818516943
242 -0.672502986
243 -1.410816935
244 0.837468412
245 -0.345133266
246 -1.349911778
247 1.457236200
248 -0.187337990
249 -0.301800878
250 -0.0632455532