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

$R= 10.2763012571$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0729766391
4 0.5
5 -0.447213595
6 0.0516022764
7 0.223535808
8 -0.353553390
9 -0.994674410
10 0.316227766
11 1.793114431
12 -0.0364883195
13 0.998220851
14 -0.158063685
15 0.0326361451
16 0.250000000
17 -0.0439405130
18 0.703341020
19 -0.906611329
20 -0.223606797
21 -0.0163128920
22 -1.267923373
23 -1.699421613
24 0.0258011382
25 0.200000000
26 -0.705848732
27 0.145564634
28 0.111767904
29 -0.0103926887
30 -0.0230772395
31 -0.925532349
32 -0.176776695
33 -0.130855464
34 0.0310706347
35 -0.0999682524
36 -0.497337205
37 -0.663585881
38 0.641071019
39 -0.0728468028
40 0.158113883
41 0.351693017
42 0.0115349565
43 -1.463691161
44 0.896557215
45 0.444831919
46 1.201672547
47 -0.490899419
48 -0.0182441597
49 -0.950031742
50 -0.141421356
51 0.00320663098
52 0.499110425
53 -0.562264720
54 -0.102929740
55 -0.801905151
56 -0.0790318428
57 0.0661614478
58 0.00734874068
59 0.752724198
60 0.0163180725
61 0.571787049
62 0.654450200
63 -0.222345348
64 0.125000000
65 -0.446417935
66 0.0925287865
67 0.744312754
68 -0.0219702565
69 0.124018078
70 0.0706882292
71 -1.474046058
72 0.351670510
73 -1.946976426
74 0.469226076
75 -0.0145953278
76 -0.453305664
77 0.400825286
78 0.0515104682
79 0.245073052
80 -0.111803398
81 0.984051598
82 -0.248684517
83 1.249826340
84 -0.00815644600
85 0.0196507948
86 1.034985945
87 0.000758408508
88 -0.633961686
89 -0.712987160
90 -0.314543666
91 0.223138095
92 -0.849710806
93 0.0675421588
94 0.347118308
95 0.405448912
96 0.0129005691
97 -1.034909589
98 0.671773887
99 -1.783565138
100 0.100000000
101 1.820913121
102 -0.00226743051
103 -1.053624841
104 -0.352924366
105 0.00729534708
106 0.397581196
107 -0.248241606
108 0.0727823173
109 1.035895591
110 0.567032570
111 0.0484245464
112 0.0558839520
113 -0.359221368
114 -0.0467832084
115 0.760004450
116 -0.00519634437
117 -0.992908713
118 -0.532256385
119 -0.00988991375
120 -0.0115386197
121 2.215218570
122 -0.404314500
123 -0.0256875633
124 -0.462766174
125 -0.0894427190
126 0.157221903
127 -1.687003693
128 -0.0883883476
129 0.106274251
130 0.315665149
131 0.349581499
132 -0.0654277323
133 -0.203549791
134 -0.526308596
135 -0.0650984836
136 0.0155353173
137 -1.080880183
138 -0.0876940240
139 0.00715429955
140 -0.0499841262
141 0.0261051141
142 1.042307963
143 1.799315617
144 -0.248668602
145 0.00464775170
146 1.376720233
147 0.0380610955
148 -0.331792940
149 -1.454549897
150 0.0103204552