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

$R= 6.67376039246$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.288826446
4 0.499999999
5 -0.447213595
6 0.911337920
7 1.198128216
8 0.353553390
9 0.661073610
10 -0.316227766
11 0.178577677
12 0.644413223
13 1.223833478
14 0.847204586
15 -0.576380709
16 0.249999999
17 -1.638928339
18 0.467449632
19 0.303324089
20 -0.223606797
21 1.544179332
22 0.126273486
23 -1.891271380
24 0.455668960
25 0.200000000
26 0.865380951
27 -0.436817294
28 0.599064108
29 0.396206980
30 -0.407562708
31 -1.119329095
32 0.176776695
33 0.230155633
34 -1.158897342
35 -0.535819227
36 0.330536805
37 0.677443778
38 0.214482520
39 1.577308953
40 -0.158113883
41 -0.175219011
42 1.091899677
43 -1.174580736
44 0.0892888387
45 -0.295641106
46 -1.337330818
47 0.530510712
48 0.322206611
49 0.435511223
50 0.141421356
51 -2.112294187
52 0.611916739
53 -0.0408190909
54 -0.308876471
55 -0.0798623652
56 0.423602293
57 0.390932107
58 0.280160642
59 1.744273205
60 -0.288190354
61 -0.0848195006
62 -0.791485194
63 0.792050945
64 0.124999999
65 -0.547314970
66 0.162744609
67 1.399580625
68 -0.819464169
69 -2.437520573
70 -0.378881409
71 -0.450207316
72 0.233724816
73 0.0212123199
74 0.479025089
75 0.257765289
76 0.151662044
77 0.213958954
78 1.115325857
79 0.291414879
80 -0.111803398
81 -1.224055292
82 -0.123898551
83 -0.226413900
84 0.772089666
85 0.732951035
86 -0.830554003
87 0.510642034
88 0.0631367433
89 0.138120999
90 -0.209049830
91 1.466309423
92 -0.945635690
93 -1.442620941
94 0.375127722
95 -0.135650656
96 0.227834480
97 1.136900000
98 0.307952939
99 0.118052989
100 0.100000000
101 -1.338009999
102 -1.493617544
103 -0.784800000
104 0.432690475
105 -0.690577991
106 -0.0288634559
107 0.373900000
108 -0.218408647
109 0.236999999
110 -0.0564712200
111 0.873107457
112 0.299532054
113 1.387899999
114 0.276430744
115 0.845802274
116 0.198103490
117 0.809044015
118 1.233387412
119 -1.963646288
120 -0.203781354
121 -0.968110013
122 -0.0599764440
123 -0.225826896
124 -0.559664547
125 -0.0894427190
126 0.560064594
127 -0.320000000
128 0.0883883476
129 -1.513830717
130 -0.387010126