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

$R= 24.2298934341$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.761445972
4 0.5
5 -0.447213595
6 1.245530391
7 0.116152924
8 -0.353553390
9 2.102691912
10 0.316227766
11 -1.333466472
12 -0.880722986
13 1.167726317
14 -0.0821325206
15 0.787742586
16 0.250000000
17 0.412230980
18 -1.486827709
19 1.876472734
20 -0.223606797
21 -0.204597101
22 0.942903185
23 1.592568117
24 0.622765195
25 0.200000000
26 -0.825707197
27 -1.942332227
28 0.0580764622
29 0.510299232
30 -0.557018124
31 1.142835827
32 -0.176776695
33 2.348829146
34 -0.291491321
35 -0.0519451670
36 1.051345956
37 1.372621162
38 -1.326866595
39 -2.056886818
40 0.158113883
41 0.0271301819
42 0.144671997
43 -0.0993404957
44 -0.666733236
45 -0.940352410
46 -1.126115715
47 -0.781566605
48 -0.440361493
49 -0.986508498
50 -0.141421356
51 -0.726122600
52 0.583863158
53 0.229220829
54 1.373436289
55 0.596344335
56 -0.0410662603
57 -3.305305339
58 -0.360836047
59 0.111313381
60 0.393871293
61 1.346761564
62 -0.808106963
63 0.244233815
64 0.125000000
65 -0.522223085
66 -1.660873017
67 -0.0455471327
68 0.206115490
69 -2.805222695
70 0.0367307798
71 0.309262552
72 -0.743413854
73 0.385446572
74 -0.970589732
75 -0.352289194
76 0.938236367
77 -0.154886030
78 1.454438617
79 -1.268839810
80 -0.111803398
81 1.318621365
82 -0.0191839356
83 0.727659643
84 -0.102298550
85 -0.184355299
86 0.0702443382
87 -0.898864527
88 0.471451592
89 -1.093775744
90 0.664929566
91 0.135634826
92 0.796284058
93 -2.013043564
94 0.552651046
95 -0.839184118
96 0.311382597
97 0.995830186
98 0.697566848
99 -2.803869167
100 0.100000000
101 -0.963035223
102 0.513446214
103 0.928687271
104 -0.412853598
105 0.0914986052
106 -0.162083603
107 -1.559120447
108 -0.971166113
109 0.749260550
110 -0.421679123
111 -2.417798017
112 0.0290382311
113 0.931627444
114 2.337203819
115 -0.712218113
116 0.255149616
117 2.455368684
118 -0.0787104466
119 0.0478818344
120 -0.278509062
121 0.778132832
122 -0.952304234
123 -0.0477883498
124 0.571417913
125 -0.0894427190
126 -0.172699386
127 1.705573821
128 -0.0883883476
129 0.174982916
130 0.369267484
131 -0.563761265
132 1.174414573
133 0.217957810
134 0.0322066864
135 0.868637378
136 -0.145745660
137 1.062408275
138 1.983591991
139 -0.668559045
140 -0.0259725835
141 1.376687265
142 -0.218681648
143 -1.557123990
144 0.525672978
145 -0.228212754
146 -0.272551885
147 1.737681357
148 0.686310581
149 1.461942090
150 0.249106078
151 0.388341547
152 -0.663433297
153 0.866795334
154 0.109520962
155 -0.511091719
156 -1.028443409
157 1.344499881
158 0.897205234
159 -0.403758899
160 0.0790569415
161 0.184982688
162 -0.932406109
163 0.559075401
164 0.0135650909
165 -1.050428328
166 -0.514533068
167 -1.484242042
168 0.0723359988
169 0.363595346
170 0.130358882
171 3.945622805
172 -0.0496702478
173 1.223684961
174 0.635593202
175 0.0232305849
176 -0.333366618
177 -0.196215170
178 0.773416246
179 1.284917953
180 -0.470176205
181 -1.176345117
182 -0.0959083058
183 -2.372466504
184 -0.563057857
185 -0.613854845
186 1.423436755
187 -0.549188054
188 -0.390783302
189 -0.224330005
190 0.593392780
191 -0.433034593
192 -0.220180746
193 0.970926120
194 -0.704158277
195 0.919867749
196 -0.493254249
197 0.464686114
198 1.982634901
199 -1.037093406
200 -0.0707106781
201 0.0998160590
202 0.680968737
203 0.0618018721
204 -0.363061300
205 -0.0121329862
206 -0.656681067
207 3.328586324
208 0.291931579
209 -2.495321214
210 -0.0646992842