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

$R= 4.18409504645$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.582122857
4 0.499999999
5 -0.447213595
6 1.118729801
7 -1.045758593
8 0.353553390
9 1.503112735
10 -0.316227766
11 -0.612319495
12 0.791061428
13 -0.829857446
14 -0.739462992
15 -0.707546851
16 0.249999999
17 1.141791909
18 1.062861208
19 0.862748095
20 -0.223606797
21 -1.654518573
22 -0.432975267
23 -0.179135738
24 0.559364900
25 0.200000000
26 -0.586797828
27 0.795986158
28 -0.522879296
29 0.164220373
30 -0.500311176
31 0.164618885
32 0.176776695
33 -0.968764670
34 0.807368801
35 0.467677460
36 0.751556367
37 1.106021146
38 0.610055029
39 -1.312936435
40 -0.158113883
41 -1.704759291
42 -1.169921303
43 1.641899638
44 -0.306159747
45 -0.672212450
46 -0.126668095
47 0.0631873641
48 0.395530714
49 0.0936110358
50 0.141421356
51 1.806455078
52 -0.414928723
53 -1.281399723
54 0.562847210
55 0.273837603
56 -0.369731496
57 1.364973482
58 0.116121339
59 0.0956069499
60 -0.353773425
61 -0.277998640
62 0.116403129
63 -1.571893060
64 0.124999999
65 0.371123532
66 -0.685020067
67 -1.249280629
68 0.570895954
69 -0.283414746
70 0.330697903
71 -0.811554299
72 0.531430604
73 1.104174400
74 0.782075052
75 0.316424571
76 0.431374047
77 0.640338374
78 -0.928386256
79 0.890167000
80 -0.111803398
81 -0.243764839
82 -1.205446855
83 0.546876999
84 -0.827259286
85 -0.510624865
86 1.160998368
87 0.259816806
88 -0.216487633
89 -0.849316999
90 -0.475325982
91 0.867830556
92 -0.0895678692
93 0.260447300
94 0.0446802136
95 -0.385832677
96 0.279682450
97 -0.184669999
98 0.0661929982
99 -0.920385232
100 0.100000000
101 -1.690560999
102 1.277356635
103 0.320599999
104 -0.293398914
105 0.739923200
106 -0.906086434
107 0.301999999
108 0.397993079
109 0.336000000
110 0.193632426
111 1.749861336
112 -0.261439648
113 0.951200000
114 0.965182005
115 0.0801119377
116 0.0821101866
117 -1.247369297
118 0.0676043226
119 -1.194038701
120 -0.250155588
121 -0.625064834
122 -0.196574723
123 -2.697138641
124 0.0823094425
125 -0.0894427190
126 -1.111496242
127 1.300000000
128 0.0883883476
129 2.597686947
130 0.262423966