Properties

Level 10
Symmetry odd
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

$R= 22.2244552093$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.515513973
4 0.5
5 -0.447213595
6 0.364523426
7 0.464791793
8 0.353553390
9 -0.734245343
10 -0.316227766
11 -1.266056211
12 0.257756986
13 -1.565078532
14 0.328657428
15 -0.230544857
16 0.250000000
17 1.852956134
18 -0.519189861
19 -0.366003924
20 -0.223606797
21 0.239606664
22 -0.895236932
23 1.496962896
24 0.182261713
25 0.200000000
26 -1.106677643
27 -0.894027707
28 0.232395896
29 0.212689548
30 -0.163019832
31 1.545811060
32 0.176776695
33 -0.652669668
34 1.310237847
35 -0.207861209
36 -0.367122671
37 1.641302973
38 -0.258803857
39 -0.806819852
40 -0.158113883
41 0.197985578
42 0.169427497
43 -0.698803371
44 -0.633028105
45 0.328364499
46 1.058512615
47 1.780599054
48 0.128878493
49 -0.783968588
50 0.141421356
51 0.955224779
52 -0.782539266
53 -0.373704058
54 -0.632173054
55 0.566197550
56 0.164328714
57 -0.188680137
58 0.150394222
59 1.181524182
60 -0.115272428
61 0.981770779
62 1.093053483
63 -0.341271209
64 0.125000000
65 0.699924397
66 -0.461507148
67 -0.634324605
68 0.926478067
69 0.771705290
70 -0.146980070
71 1.210225151
72 -0.259594930
73 -0.772045106
74 1.160576462
75 0.103102794
76 -0.183001962
77 -0.588452536
78 -0.570507789
79 -0.801526241
80 -0.111803398
81 0.273361567
82 0.139996944
83 -0.540242559
84 0.119803332
85 -0.828667174
86 -0.494128602
87 0.109644434
88 -0.447618466
89 -1.256035722
90 0.232188764
91 -0.727435657
92 0.748481448
93 0.796887202
94 1.259073666
95 0.163681931
96 0.0911308566
97 -0.671793634
98 -0.554349505
99 0.929595877
100 0.100000000
101 0.944308941
102 0.675445919
103 0.359606012
104 -0.553338821
105 -0.107155357
106 -0.264248674
107 0.470313439
108 -0.447013853
109 1.765933285
110 0.400362127
111 0.846114617
112 0.116197948
113 1.081191715
114 -0.133417004
115 -0.669462159
116 0.106344774
117 1.149151624
118 0.835463761
119 0.861238804
120 -0.0815099160
121 0.602898327
122 0.694216775
123 0.102064330
124 0.772905530
125 -0.0894427190
126 -0.241315186
127 -0.00229907588
128 0.0883883476
129 -0.360242896
130 0.494921287
131 0.0702435731
132 -0.326334834
133 -0.170115627
134 -0.448535230
135 0.399821345
136 0.655118923
137 0.566616564
138 0.545678044
139 -1.230127397
140 -0.103930604
141 0.917923627
142 0.855758411
143 1.981477359
144 -0.183561335
145 -0.0951176578
146 -0.545918330
147 -0.404147188
148 0.820651486
149 0.439495817
150 0.0729046852
151 0.331928808
152 -0.129401928
153 -1.360523084
154 -0.416098779
155 -0.691307722
156 -0.403409926
157 0.468908805
158 -0.566764640
159 -0.192654424
160 -0.0790569415
161 0.695784629
162 0.193295817
163 0.280736773
164 0.0989927890
165 0.291882748
166 -0.382009177
167 0.536301751
168 0.0847137485
169 1.449427567
170 -0.585956178
171 0.268735083
172 -0.349401685
173 0.565412130
174 0.0775303231
175 0.0929583586
176 -0.316514052
177 0.608897694
178 -0.888151376
179 -0.977793105
180 0.164182249
181 0.461166215
182 -0.514374686
183 0.506790139
184 0.529256307
185 -0.734013004
186 0.563484344
187 -2.346164501
188 0.890299527
189 -0.415616692
190 0.115740603
191 0.920158629
192 0.0644392466
193 0.0817970688
194 -0.475029834
195 0.360820807
196 -0.391984294
197 -0.800413508
198 0.657323548
199 0.631311885
200 0.0707106781
201 -0.349874451
202 0.667727256
203 0.0512872756
204 0.477612389
205 -0.0885418422
206 0.254279850
207 -0.940961009
208 -0.391269633
209 0.665533248
210 -0.0757702801