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

$R= 31.5042508761$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.753046962
4 0.5
5 0.447213595
6 0.532484613
7 -1.035528296
8 -0.353553390
9 -0.432920271
10 -0.316227766
11 -1.538427533
12 -0.376523481
13 0.650763591
14 0.732229080
15 -0.336772839
16 0.250000000
17 -1.347704040
18 0.306120859
19 -0.326143529
20 0.223606797
21 0.779801438
22 1.087832541
23 0.212599111
24 0.266242306
25 0.200000000
26 -0.460159348
27 1.079056258
28 -0.517764148
29 0.808616783
30 0.238134358
31 0.639535536
32 -0.176776695
33 1.158508181
34 0.952970665
35 -0.463102332
36 -0.216460135
37 0.532610496
38 0.230618301
39 -0.490055546
40 -0.158113883
41 0.633404719
42 -0.551402885
43 -0.0665450412
44 -0.769213766
45 -0.193607831
46 -0.150330273
47 0.268053541
48 -0.188261740
49 0.0723188530
50 -0.141421356
51 1.014884434
52 0.325381795
53 -1.382365920
54 -0.763007997
55 -0.688005708
56 0.366114540
57 0.245601394
58 -0.571778410
59 0.738510092
60 -0.168386419
61 -1.519039725
62 -0.452219914
63 0.448301191
64 0.125000000
65 0.291030325
66 -0.819188991
67 -0.886601649
68 -0.673852020
69 -0.160097115
70 0.327462799
71 0.488086898
72 0.153060429
73 1.641594796
74 -0.376612494
75 -0.150609392
76 -0.163071764
77 1.593085243
78 0.346521599
79 1.291035731
80 0.111803398
81 -0.379659766
82 -0.447884772
83 1.336129965
84 0.389900719
85 -0.602711569
86 0.0470544499
87 -0.608926412
88 0.543916270
89 -0.971942674
90 0.136901410
91 -0.673884113
92 0.106299555
93 -0.481600293
94 -0.189542476
95 -0.145855820
96 0.133121153
97 -0.140827704
98 -0.0511371514
99 0.666016465
100 0.100000000
101 1.956422179
102 -0.717631665
103 1.418747923
104 -0.230079674
105 0.348737805
106 0.977480316
107 -1.519004532
108 0.539528129
109 -0.979408311
110 0.486493502
111 -0.401080717
112 -0.258882074
113 0.682454333
114 -0.173666411
115 0.0950772130
116 0.404308391
117 -0.281728750
118 -0.522205494
119 1.395585668
120 0.119067179
121 1.366759275
122 1.074123290
123 -0.476983500
124 0.319767768
125 0.0894427190
126 -0.316996812
127 -1.060534245
128 -0.0883883476
129 0.0501115412
130 -0.205789516
131 1.318519343
132 0.579254090
133 0.337730853
134 0.626922038
135 0.482568629
136 0.476485332
137 1.327445130
138 0.113205755
139 0.619189294
140 -0.231551166
141 -0.201856905
142 -0.345129555
143 -1.001152626
144 -0.108230067
145 0.361624418
146 -1.160782812
147 -0.0544594926
148 0.266305248
149 -1.456039435
150 0.106496922
151 0.563071753
152 0.115309150
153 0.583448399
154 -1.126481378
155 0.286008986
156 -0.245027773
157 -1.663316631
158 -0.912900120
159 1.040986457
160 -0.0790569415
161 -0.220152396
162 0.268459995
163 1.126396335
164 0.316702359
165 0.518100609
166 -0.944786559
167 0.216980880
168 -0.275701442
169 -0.576506745
170 0.426181437
171 0.141194152
172 -0.0332725206
173 1.334499825
174 0.430575995
175 -0.207105659
176 -0.384606883
177 -0.556132761
178 0.687267256
179 1.526451630
180 -0.0968039156
181 -1.632592470
182 0.476508026
183 1.143908231
184 -0.0751651367
185 0.238190655
186 0.340542833
187 2.073344991
188 0.134026770
189 -1.117393104
190 0.103135639
191 0.547091551
192 -0.0941308703
193 0.853915682
194 0.0995802244
195 -0.219159502
196 0.0361594265
197 1.271843600
198 -0.470944759
199 -0.921668693
200 -0.0707106781
201 0.667654037
202 -1.383399390
203 -0.837344637
204 0.507442217
205 0.283267202
206 -1.003206277
207 -0.0920403555
208 0.162690897
209 0.501749646
210 -0.246594866
211 -1.603892246
212 -0.691182960
213 -0.367535203
214 1.074098405
215 -0.0297598471
216 -0.381503998
217 -0.662267863
218 0.692546258
219 -1.236262623
220 -0.344002854
221 -0.877132915
222 0.283606894
223 -0.0380923283
224 0.183057270
225 -0.0865840543
226 -0.482568086
227 0.104497010
228 0.122800697
229 -0.967136689
230 -0.0672297420
231 -1.199862824
232 -0.285889205
233 -1.446410009
234 0.199212310
235 0.119877187
236 0.369255046
237 -0.969576846
238 -0.986828090
239 0.113169850
240 -0.0841932099
241 -0.622348171
242 -0.966444751
243 -0.796334304
244 -0.759519862
245 0.0323419743
246 0.337278267
247 -0.195379737
248 -0.226109957
249 -1.006569217
250 -0.0632455532
251 -0.211084326
252 0.224150595
253 -0.434358776
254 0.749910956
255 0.453870116
256 0.0625000000