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

$R= 30.9373388598$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.618422771
4 0.5
5 -0.447213595
6 0.437290935
7 -1.250716296
8 -0.353553390
9 -0.617553276
10 0.316227766
11 1.248280959
12 -0.309211385
13 0.824960884
14 0.884389974
15 0.276567071
16 0.250000000
17 0.168174659
18 0.436676109
19 1.624442023
20 -0.223606797
21 0.773471438
22 -0.882667931
23 1.359895076
24 0.218645467
25 0.200000000
26 -0.583335435
27 1.000331779
28 -0.625358148
29 -1.537757691
30 -0.195562451
31 -0.768370444
32 -0.176776695
33 -0.771965370
34 -0.118917441
35 0.559337331
36 -0.308776638
37 1.064543507
38 -1.148653970
39 -0.510174596
40 0.158113883
41 1.578969233
42 -0.546926898
43 -1.396934060
44 0.624140479
45 0.276178220
46 -0.961591030
47 -0.870825033
48 -0.154605692
49 0.564291254
50 -0.141421356
51 -0.104003038
52 0.412480442
53 1.366140726
54 -0.707341384
55 -0.558248216
56 0.442194987
57 -1.004591938
58 1.087358891
59 0.598702248
60 0.138283535
61 -0.174336911
62 0.543319952
63 0.772383946
64 0.125000000
65 -0.368933723
66 0.545861948
67 0.691019783
68 0.0840873295
69 -0.840990081
70 -0.395511220
71 -1.319640249
72 0.218338054
73 -0.671979151
74 -0.752745933
75 -0.123684554
76 0.812221011
77 -1.561245338
78 0.360747916
79 -0.506489490
80 -0.111803398
81 -0.00107467519
82 -1.116499852
83 1.401042200
84 0.386735719
85 -0.0752099939
86 0.987781547
87 0.950984373
88 -0.441333965
89 -0.126964292
90 -0.195287492
91 -1.031792022
92 0.679947538
93 0.475177779
94 0.615766286
95 -0.726472558
96 0.109322733
97 -1.377037905
98 -0.399014172
99 -0.770879996
100 0.100000000
101 -1.352737027
102 0.0735412539
103 1.884086201
104 -0.291667717
105 -0.345906942
106 -0.966007371
107 0.935068400
108 0.500165889
109 0.565236717
110 0.394741099
111 -0.658337946
112 -0.312679074
113 -1.565456835
114 0.710353771
115 -0.608163566
116 -0.768878845
117 -0.509457296
118 -0.423346419
119 -0.210338786
120 -0.0977812256
121 0.558205354
122 0.123274812
123 -0.976470529
124 -0.384185222
125 -0.0894427190
126 -0.546157926
127 0.206142121
128 -0.0883883476
129 0.863895833
130 0.260875537
131 -1.182885493
132 -0.385982685
133 -2.031716111
134 -0.488624774
135 -0.447361971
136 -0.0594587209
137 0.448999567
138 0.594669789
139 -0.0712655290
140 0.279668665
141 0.538538030
142 0.933126569
143 1.029782964
144 -0.154388319
145 0.687706146
146 0.475161014
147 -0.348970561
148 0.532271753
149 -0.256131873
150 0.0874581870
151 -0.139502455
152 -0.574326985
153 -0.103856811
154 1.103967166
155 0.343625709
156 -0.255087298
157 -0.273296562
158 0.358142153
159 -0.844852533
160 0.0790569415
161 -1.700842933
162 0.000759910119
163 0.971914543
164 0.789484616
165 0.345233408
166 -0.990686440
167 -0.172043603
168 -0.273463449
169 -0.319439534
170 0.0531814967
171 -1.003179482
172 -0.698467030
173 0.950872604
174 -0.672447499
175 -0.250143259
176 0.312070239
177 -0.370251105
178 0.0897773121
179 -0.711097010
180 0.138089110
181 -1.473005008
182 0.729587135
183 0.107813927
184 -0.480795515
185 -0.476078329
186 -0.336001430
187 0.209929043
188 -0.435412516
189 -1.251131150
190 0.513693672
191 0.743870918
192 -0.0773028464
193 -0.770315235
194 0.973712841
195 0.228157015
196 0.282145627
197 -0.144725032
198 0.545094472
199 1.244887852
200 -0.0707106781
201 -0.427342427
202 0.956529525
203 1.923300873
204 -0.0520015193
205 -0.706136508
206 -1.332250129
207 -0.839812181
208 0.206240221
209 2.027760064
210 0.244593144
211 0.706574859
212 0.683070363
213 0.816098384
214 -0.661193206
215 0.624727903
216 -0.353670692
217 0.960993639
218 -0.399682715
219 0.415589733
220 -0.279124108
221 0.138712674
222 0.465515226
223 0.859754230
224 0.221097493
225 -0.123510655
226 1.106945144
227 -0.0385415586
228 -0.502295969
229 0.881150988
230 0.430036582
231 0.964842964
232 0.543679445
233 0.532075181
234 0.360240709
235 0.389444794
236 0.299351124
237 0.305737253
238 0.148731982
239 1.292387509
240 0.0691417677
241 0.722764820
242 -0.394710791
243 -0.993698480
244 -0.0871684556
245 -0.252358720
246 0.690468932
247 1.371193110
248 0.271659976
249 -0.891828125
250 0.0632455532
251 -1.749738659
252 0.386191973
253 1.638706563
254 -0.145764492