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

$R= 10.2641383944$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.949911716
4 0.5
5 0.447213595
6 -0.671689015
7 -1.170229306
8 -0.353553390
9 -0.0976677317
10 -0.316227766
11 0.0804208005
12 0.474955858
13 0.856648240
14 0.827477078
15 0.424813433
16 0.250000000
17 -0.809348682
18 0.0690615154
19 -1.322186045
20 0.223606797
21 -1.111614528
22 -0.0568660934
23 0.183706176
24 -0.335844507
25 0.200000000
26 -0.605741780
27 -1.042687438
28 -0.585114653
29 -1.521978498
30 -0.300388459
31 1.574309325
32 -0.176776695
33 0.0763926606
34 0.572295942
35 -0.523342455
36 -0.0488338658
37 -1.710014159
38 0.934926718
39 0.813740200
40 -0.158113883
41 -0.966216708
42 0.786030171
43 -0.492739271
44 0.0402104002
45 -0.0436783374
46 -0.129899883
47 -0.831729083
48 0.237477929
49 0.369436629
50 -0.141421356
51 -0.768809796
52 0.428324120
53 1.421048112
54 0.737291358
55 0.0359652753
56 0.413738539
57 -1.255960015
58 1.076201317
59 -1.700552830
60 0.212406716
61 -0.236859644
62 -1.113204799
63 0.114293641
64 0.125000000
65 0.383104739
66 -0.0540177683
67 -0.364358190
68 -0.404674341
69 0.174504649
70 0.370058999
71 1.391805966
72 0.0345307577
73 0.110379640
74 1.209162608
75 0.189982343
76 -0.661093022
77 -0.0941107786
78 -0.575401213
79 -1.014692423
80 0.111803398
81 -0.892793276
82 0.683218386
83 1.139842181
84 -0.555807264
85 -0.361951734
86 0.348419280
87 -1.445745216
88 -0.0284330467
89 0.387069764
90 0.0308852486
91 -1.002474877
92 0.0918530884
93 1.495454884
94 0.588121274
95 -0.591299575
96 -0.167922253
97 1.627782527
98 -0.261231146
99 -0.00785466051
100 0.100000000
101 0.0105473000
102 0.543630620
103 -0.518205937
104 -0.302870890
105 -0.497129130
106 -1.004832756
107 1.812047576
108 -0.521343719
109 0.168712735
110 -0.0254312900
111 -1.624366001
112 -0.292557326
113 -0.300817565
114 0.888097843
115 0.0821558998
116 -0.760989249
117 -0.0836674389
118 1.202472438
119 0.947119149
120 -0.150194229
121 -0.993547520
122 0.167485061
123 -0.917896247
124 0.787154662
125 0.0894427190
126 -0.0808178093
127 0.746655439
128 -0.0883883476
129 -0.467973972
130 -0.270895959
131 -0.483028766
132 0.0381963303
133 1.547227777
134 0.257640147
135 -0.466303998
136 0.286147971
137 1.801624934
138 -0.123393421
139 0.0637089738
140 -0.261671227
141 -0.786897568
142 -0.984155436
143 0.0686870938
144 -0.0244169329
145 -0.680649476
146 -0.0780501924
147 0.345368114
148 -0.855007079
149 -1.581156863
150 -0.134337803