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

$R= 26.7592831751$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.102073070
4 0.5
5 -0.447213595
6 0.0721765601
7 -1.152636143
8 0.353553390
9 -0.989581088
10 -0.316227766
11 1.640849566
12 0.0510365351
13 -0.127317103
14 -0.815036833
15 -0.0456484647
16 0.250000000
17 -0.365084651
18 -0.699739498
19 0.849228180
20 -0.223606797
21 -0.117653110
22 1.160255855
23 0.604588038
24 0.0360882800
25 0.200000000
26 -0.0900267874
27 -0.203082650
28 -0.576318071
29 1.451638408
30 -0.0322783389
31 0.586992039
32 0.176776695
33 0.167486553
34 -0.258153833
35 0.515474554
36 -0.494790544
37 0.173633682
38 0.600495004
39 -0.0129956476
40 -0.158113883
41 -1.212923205
42 -0.0831933120
43 -0.573644453
44 0.820424783
45 0.442554116
46 0.427508301
47 -1.103827630
48 0.0255182675
49 0.328570080
50 0.141421356
51 -0.0372653113
52 -0.0636585518
53 -1.156963898
54 -0.143601119
55 -0.733810234
56 -0.407518416
57 0.0866833277
58 1.026463362
59 -0.595470048
60 -0.0228242323
61 0.323622166
62 0.415066051
63 1.140626929
64 0.125000000
65 0.0569379397
66 0.118430877
67 -0.361890639
68 -0.182542325
69 0.0617121573
70 0.364495552
71 1.061240916
72 -0.349869749
73 -1.682703151
74 0.122777554
75 0.0204146140
76 0.424614090
77 -1.891302516
78 -0.00918931059
79 -1.924245585
80 -0.111803398
81 0.968851818
82 -0.857666223
83 0.748665462
84 -0.0588265550
85 0.163270819
86 -0.405627883
87 0.148173189
88 0.580127927
89 -0.389725274
90 0.312933016
91 0.146750295
92 0.302294019
93 0.0599160796
94 -0.780524002
95 -0.379786387
96 0.0180441400
97 -1.586052745
98 0.232334131
99 -1.623753699
100 0.100000000
101 0.691846288
102 -0.0263505543
103 -0.236290069
104 -0.0450133937
105 0.0526160704
106 -0.818097018
107 1.414315485
108 -0.101541325
109 -0.981502215
110 -0.518882192
111 0.0177233231
112 -0.288159035
113 -1.034747026
114 0.0612943688
115 -0.270379990
116 0.725819204
117 0.125990598
118 -0.421060909
119 0.420809765
120 -0.0161391694
121 1.692387299
122 0.228835428
123 -0.123806795
124 0.293496019
125 -0.0894427190
126 0.806545036
127 1.856399312
128 0.0883883476
129 -0.0585536504
130 0.0402612032
131 0.490676132
132 0.0837432765
133 -0.978851094
134 -0.255895325
135 0.0908213222
136 -0.129076916
137 -1.315117815
138 0.0436370849
139 1.569289066
140 0.257737277
141 -0.112671075
142 0.750410648
143 -0.208908214
144 -0.247395272
145 -0.649192431
146 -1.189850809
147 0.0335381564
148 0.0868168414
149 -0.847170841
150 0.0144353120
151 1.171257650
152 0.300247502
153 0.361280862
154 -1.337352834
155 -0.262510820
156 -0.00649782383
157 -1.706637106
158 -1.360647102
159 -0.118094852
160 -0.0790569415
161 -0.696870030
162 0.685081690
163 -0.839846974
164 -0.606461602
165 -0.0749022636
166 0.529386425
167 -1.317989492
168 -0.0415966560
169 -0.983790296
170 0.115449903
171 -0.840380202
172 -0.286822226
173 -0.717898590
174 0.104774266
175 -0.230527228
176 0.410212391
177 -0.0607820339
178 -0.275577384
179 0.0393895659
180 0.221277058
181 -1.582307933
182 0.103768129
183 0.0330311894
184 0.213754150
185 -0.0776513436
186 0.0423670662
187 -0.599048388
188 -0.551913815
189 0.234075172
190 -0.268549530
191 -1.741365447
192 0.0127591337
193 1.681324481
194 -1.121508651
195 0.00581183032
196 0.164285040
197 -0.348196784
198 -1.148167251
199 -0.277400725
200 0.0707106781
201 -0.0368585543
202 0.489209202
203 -1.673207666
204 -0.0186326556
205 0.542435747
206 -0.167082310
207 -0.598146705
208 -0.0318292759
209 1.393767746
210 0.0372051801
211 1.481277253
212 -0.578481949
213 0.110459042
214 1.000072070
215 0.256541598
216 -0.0718005595
217 -0.680027418
218 -0.694026872
219 -0.173869564
220 -0.366905117
221 0.0596730888
222 0.0125322819
223 -0.678555541
224 -0.203759208
225 -0.197916217
226 -0.731676639
227 0.102179916
228 0.0433416638
229 -0.108751216
230 -0.191187524
231 -0.167934314
232 0.513231681