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

$R= 29.5432049025$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.617188221
4 0.5
5 0.447213595
6 1.143524757
7 0.338998679
8 0.353553390
9 1.615297743
10 0.316227766
11 0.945531784
12 0.808594110
13 -0.456707435
14 0.239708265
15 0.723228559
16 0.250000000
17 -0.914157394
18 1.142187988
19 0.521250057
20 0.223606797
21 0.548224671
22 0.668591936
23 1.480676180
24 0.571762378
25 0.200000000
26 -0.322940924
27 0.995052264
28 0.169499339
29 -1.219207609
30 0.511399818
31 1.395634199
32 0.176776695
33 1.529102865
34 -0.646406893
35 0.151604818
36 0.807648871
37 0.619375850
38 0.368579450
39 -0.738581885
40 0.158113883
41 -0.726800379
42 0.387653382
43 0.995975537
44 0.472765892
45 0.722383111
46 1.046996167
47 0.766916072
48 0.404297055
49 -0.885079895
50 0.141421356
51 -1.478364571
52 -0.228353717
53 -0.823190435
54 0.703608203
55 0.422854669
56 0.119854132
57 0.842959453
58 -0.862109968
59 -1.450921615
60 0.361614279
61 1.824655044
62 0.986862406
63 0.547583802
64 0.125000000
65 -0.204245774
66 1.081239005
67 1.112373481
68 -0.457078697
69 2.394532078
70 0.107200795
71 -0.267192308
72 0.571093994
73 0.827164511
74 0.437964863
75 0.323437644
76 0.260625028
77 0.320534026
78 -0.522256259
79 -0.121391538
80 0.111803398
81 -0.00611094232
82 -0.513925476
83 0.945434571
84 0.274112335
85 -0.408823615
86 0.704261056
87 -1.971688185
88 0.334295968
89 -1.656764569
90 0.510801997
91 -0.154823217
92 0.740338090
93 2.257003189
94 0.542291555
95 0.233110112
96 0.285881189
97 1.358780284
98 -0.625845995
99 1.527315358
100 0.100000000
101 1.377401311
102 -1.045361613
103 -0.511130411
104 -0.161470462
105 0.245173526
106 -0.582083538
107 -1.215799952
108 0.497526132
109 1.390836379
110 0.299003403
111 1.001647329
112 0.0847496698
113 -0.789199665
114 0.596062345
115 0.662178518
116 -0.609603804
117 -0.737718490
118 -1.025956513
119 -0.309898149
120 0.255699909
121 -0.105969644
122 1.290225955
123 -1.175373012
124 0.697817099
125 0.0894427190
126 0.387200219
127 1.401311168
128 0.0883883476
129 1.610679908
130 -0.144423572
131 -1.839708389
132 0.764551432
133 0.176703081
134 0.786566832
135 0.445000900
136 -0.323203446
137 -0.410563569
138 1.693189870
139 -1.192197727
140 0.0758024091
141 1.240247639
142 -0.188933493
143 -0.431831396
144 0.403824435
145 -0.545246218
146 0.584893635
147 -1.431340782
148 0.309687925
149 -0.0136902062
150 0.228704951
151 -1.938629763
152 0.184289725
153 -1.476636378
154 0.226651783
155 0.624146588
156 -0.369290942
157 -0.0369762180
158 -0.0858367799
159 -1.331253885
160 0.0790569415
161 0.501947276
162 -0.00432108875
163 -0.410777876
164 -0.363400189
165 0.683835590
166 0.668523196
167 -0.509861391
168 0.193826691
169 -0.791418314
170 -0.289081950
171 0.841974055
172 0.497987768
173 -0.908602593
174 -1.394194086
175 0.0677997359
176 0.236382946
177 -2.346413435
178 -1.171509462
179 1.939273948
180 0.361191555
181 0.643505165
182 -0.109476547
183 2.950810877
184 0.523498083
185 0.276993300
186 1.595942260
187 -0.864364666
188 0.383458036
189 0.337323541
190 0.164833741
191 -0.200425185
192 0.202148527
193 0.698589669
194 0.960802753
195 -0.330303860
196 -0.442539947
197 -0.378912340
198 1.079975047
199 -0.457462527
200 0.0707106781
201 1.798931376
202 0.973969807
203 -0.413274825
204 -0.739182285
205 -0.325035010
206 -0.361423780
207 2.391767254
208 -0.114176858
209 0.493023610
210 0.173363863
211 1.968609517
212 -0.411595217
213 -0.432141484
214 -0.859700390
215 0.445413801
216 0.351804101
217 0.473560342
218 0.983469835
219 1.337451360
220 0.211427334
221 0.417371325
222 0.708271618
223 -0.377601614
224 0.0599270662
225 0.323059548
226 -0.558048434
227 0.799351954
228 0.421479726
229 -0.345449634
230 0.468230920
231 0.506705655
232 -0.431054984
233 0.102092940
234 -0.521645747
235 0.342975294
236 -0.725460807
237 -0.207684538
238 -0.219131083
239 0.169068215
240 0.180807139
241 1.023568722
242 -0.0749318539
243 -1.082182789
244 0.912327522
245 -0.395819762
246 -0.831114227
247 -0.686462426