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

$R= 18.9864206642$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.789904027
4 0.5
5 0.447213595
6 -0.558546494
7 -1.077845434
8 -0.353553390
9 -0.376051627
10 -0.316227766
11 1.619405358
12 0.394952013
13 0.169246627
14 0.762151815
15 0.353255820
16 0.250000000
17 -1.233250428
18 0.265908655
19 0.385238572
20 0.223606797
21 -0.851394450
22 -1.145092510
23 1.300211261
24 -0.279273247
25 0.200000000
26 -0.119675438
27 -1.086948722
28 -0.538922717
29 -1.661101237
30 -0.249789586
31 -1.115443262
32 -0.176776695
33 1.279174815
34 0.872039741
35 -0.482027132
36 -0.188025813
37 1.339009980
38 -0.272404807
39 0.133688592
40 -0.158113883
41 0.374527123
42 0.602026789
43 -0.589843508
44 0.809702679
45 -0.168175400
46 -0.919388200
47 0.661371897
48 0.197476006
49 0.161750780
50 -0.141421356
51 -0.974149481
52 0.0846233138
53 0.633196602
54 0.768588812
55 0.724220093
56 0.381075907
57 0.304301500
58 1.174575949
59 -1.266053932
60 0.176627910
61 0.897900663
62 0.788737494
63 0.405325529
64 0.125000000
65 0.0756893928
66 -0.904513186
67 -1.532770018
68 -0.616625214
69 1.027042112
70 0.340844653
71 -1.002137608
72 0.132954327
73 0.420331623
74 -0.946823037
75 0.157980805
76 0.192619286
77 -1.745468672
78 -0.0945321106
79 -0.515833412
80 0.111803398
81 -0.482533546
82 -0.264830669
83 -0.642679758
84 -0.425697225
85 -0.551526358
86 0.417082344
87 -1.312110557
88 -0.572546255
89 -1.007005286
90 0.118917965
91 -0.182421705
92 0.650105630
93 -0.881093125
94 -0.467660553
95 0.172283927
96 -0.139636623
97 0.896277290
98 -0.114375074
99 -0.608980019
100 0.100000000
101 -1.139426318
102 0.688827703
103 1.227211935
104 -0.0598377190
105 -0.380755173
106 -0.447737611
107 -1.269199829
108 -0.543474361
109 -1.572622702
110 -0.512100938
111 1.057689376
112 -0.269461358
113 0.481389046
114 -0.215173654
115 0.581472153
116 -0.830550618
117 -0.0636454715
118 0.895235321
119 1.329253386
120 -0.124894793
121 1.622473744
122 -0.634911648
123 0.295840461
124 -0.557721631
125 0.0894427190
126 -0.286608430
127 -1.585080586
128 -0.0883883476
129 -0.465919712
130 -0.0535204829
131 -0.825851987
132 0.639587407
133 -0.415226980
134 1.083832073
135 -0.486098246
136 0.436019870
137 -0.793546092
138 -0.726228442
139 1.272835998
140 -0.241013566
141 0.522418667
142 0.708618298
143 0.274076490
144 -0.0940129067
145 -0.742867056
146 -0.297219341
147 0.127760462
148 0.669504990
149 -0.993751913
150 -0.111709298
151 0.901623800
152 -0.136202403
153 0.463798537
154 1.234232734
155 -0.498841391
156 0.0668442964
157 -1.342154774
158 0.364749304
159 0.499996719
160 -0.0790569415
161 -1.401593640
162 0.341202743
163 -1.439171573
164 0.187263561
165 0.572064368
166 0.454443215
167 0.328382755
168 0.301013394
169 -0.969466125
170 0.389988028
171 -0.143565534
172 -0.294921754
173 -0.440638531
174 0.927802273
175 -0.215569086
176 0.404851339
177 -0.999842842
178 0.712060266
179 -0.0763470292
180 -0.0840877001
181 0.918643899
182 0.128991624
183 0.729992035
184 -0.459694100
185 0.598823467
186 0.623026923
187 -1.947099848
188 0.330685948
189 1.371756929
190 -0.121823133
191 -0.739384035
192 0.0987380034