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

$R= 26.2369605037$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.0513593622
4 0.5
5 0.447213595
6 0.0363165533
7 1.675735128
8 0.353553390
9 -0.997362215
10 0.316227766
11 0.404968252
12 0.0256796811
13 1.668618647
14 1.184923672
15 0.0229686050
16 0.250000000
17 -1.141856111
18 -0.705241586
19 0.796413650
20 0.223606797
21 0.0860646875
22 0.286355797
23 1.239801189
24 0.0181582766
25 0.200000000
26 1.179891561
27 -0.102583249
28 0.837867564
29 -1.598082601
30 0.0162412564
31 1.591877609
32 0.176776695
33 0.0207989111
34 -0.807414199
35 0.749411531
36 -0.498681107
37 0.981229653
38 0.563149493
39 0.0856991896
40 0.158113883
41 0.621143814
42 0.0608569242
43 -0.796992802
44 0.202484126
45 -0.446033942
46 0.876671828
47 -1.149713316
48 0.0128398405
49 1.808088220
50 0.141421356
51 -0.0586450017
52 0.834309323
53 -0.432012914
54 -0.0725373114
55 0.181107308
56 0.592461836
57 0.0409032972
58 -1.130015044
59 -0.682584821
60 0.0114843025
61 -0.970928523
62 1.125627452
63 -1.671314901
64 0.125000000
65 0.746228944
66 0.0147070511
67 0.353281605
68 -0.570928055
69 0.0636753984
70 0.529913976
71 0.00744172255
72 -0.352620793
73 1.816680304
74 0.693834141
75 0.0102718724
76 0.398206825
77 0.678619525
78 0.0605984781
79 -1.017795556
80 0.111803398
81 0.992093605
82 0.439215003
83 -0.967461320
84 0.0430323437
85 -0.510653577
86 -0.563559015
87 -0.0820765033
88 0.143177898
89 -0.0621926690
90 -0.315393625
91 2.796162884
92 0.619900594
93 0.0817578189
94 -0.812970082
95 0.356167012
96 0.00907913833
97 0.843273897
98 1.278511441
99 -0.403900033
100 0.100000000
101 -1.375851683
102 -0.0414682784
103 1.432303245
104 0.589945780
105 0.0384892983
106 -0.305479261
107 -0.0642095971
108 -0.0512916248
109 -0.928840996
110 0.128062205
111 0.0503953292
112 0.418933782
113 1.897979464
114 0.0289229988
115 0.554455947
116 -0.799041300
117 -1.664217192
118 -0.482660356
119 -1.913448397
120 0.00812062820
121 -0.836000714
122 -0.686550142
123 0.0319015502
124 0.795938804
125 0.0894427190
126 -1.181798100
127 0.198068504
128 0.0883883476
129 -0.0409330420
130 0.527663547
131 -0.639632782
132 0.0103994555
133 1.334578332
134 0.249807819
135 -0.0458766239
136 -0.403707099
137 -0.0288469176
138 0.0450253060
139 0.0335565861
140 0.374705765
141 -0.0590485437
142 0.00526209247
143 0.675737575
144 -0.249340553
145 -0.714684266
146 1.284586962
147 0.0928622553
148 0.490614826
149 -0.0695172511
150 0.00726331067
151 0.596891667
152 0.281574746
153 1.138844137
154 0.479856468
155 0.711909309
156 0.0428495948
157 1.041074834
158 -0.719690139
159 -0.0221879064
160 0.0790569415
161 2.077578435
162 0.701516116
163 0.606831818
164 0.310571907
165 0.00930155584
166 -0.684098460
167 0.000532640025
168 0.0304284621
169 1.784287920
170 -0.361086607
171 -0.794313571
172 -0.398496401
173 1.826284046
174 -0.0580368520
175 0.335147025
176 0.101242063
177 -0.0350560338
178 -0.0439768580
179 -0.259767494
180 -0.223016971
181 0.273919398
182 1.977185736
183 -0.0498718208
184 0.438335914
185 0.438819241
186 0.0578115081
187 -0.462420085
188 -0.574856658
189 -0.171930417
190 0.251848109
191 -0.341473578
192 0.00641992028
193 1.370062947
194 0.596284691
195 0.0383258427
196 0.904044110
197 0.393449585
198 -0.285600452
199 1.406833383
200 0.0707106781
201 0.0175713210
202 -0.972874055
203 -2.677683745
204 -0.0293225008
205 0.277783958
206 1.012791337
207 -1.236829424
208 0.417154661
209 0.322443174
210 0.0272160438
211 -0.00299247180
212 -0.216006457
213 0.00274664580
214 -0.0454030415
215 -0.356426016
216 -0.0362686557
217 2.666176339
218 -0.656789767
219 0.104879792
220 0.0905536540
221 -1.918614205
222 0.0356348790