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

$R= 9.44243727649$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.950600519
4 0.5
5 -0.447213595
6 0.672176073
7 1.651226409
8 0.353553390
9 -0.0963586519
10 -0.316227766
11 0.725122105
12 0.475300259
13 -0.977539159
14 1.167593391
15 -0.425121476
16 0.250000000
17 1.925369999
18 -0.0681358562
19 0.00120081783
20 -0.223606797
21 1.569656683
22 0.512738757
23 0.777016467
24 0.336088036
25 0.200000000
26 -0.691224568
27 -1.042199104
28 0.825613204
29 0.301591395
30 -0.300606278
31 0.483969645
32 0.176776695
33 0.689301450
34 1.361442182
35 -0.738450899
36 -0.0481793259
37 -0.575121022
38 0.000849106431
39 -0.929249233
40 -0.158113883
41 -0.0916844472
42 1.109914884
43 -0.926878974
44 0.362561052
45 0.0430928992
46 0.549433613
47 -1.482400169
48 0.237650129
49 1.726548656
50 0.141421356
51 1.830257721
52 -0.488769579
53 -1.578952741
54 -0.736946054
55 -0.324284463
56 0.583796695
57 0.00114149805
58 0.213257320
59 -1.375605356
60 -0.212560738
61 0.143321015
62 0.342218217
63 -0.159109950
64 0.125000000
65 0.437168802
66 0.487409729
67 -0.0408130687
68 0.962684999
69 0.738632257
70 -0.522163638
71 -0.651437538
72 -0.0340679281
73 -0.618907819
74 -0.406671974
75 0.190120103
76 0.000600408915
77 1.197340770
78 -0.657078434
79 0.731247117
80 -0.111803398
81 -0.894356358
82 -0.0648306943
83 -0.698656896
84 0.784828341
85 -0.861051640
86 -0.655402408
87 0.286692937
88 0.256369378
89 1.542260090
90 0.0304712812
91 -1.614138477
92 0.388508233
93 0.460061796
94 -1.048215212
95 -0.000537022059
96 0.168044018
97 1.525308600
98 1.220854263
99 -0.0698717885
100 0.100000000
101 -0.268540999
102 1.294187646
103 -0.221746999
104 -0.345612284
105 -0.701971809
106 -1.116488190
107 -0.573077999
108 -0.521099552
109 -1.032704999
110 -0.229303743
111 -0.546710342
112 0.412806602
113 1.048710000
114 0.000807161014
115 -0.347492328
116 0.150795697
117 0.0941943556
118 -0.972699875
119 3.179221791
120 -0.150303139
121 -0.474197932
122 0.101343262
123 -0.0871552832
124 0.241984822
125 -0.0894427190
126 -0.112507725
127 1.304999999
128 0.0883883476
129 -0.881091634
130 0.309125024
131 -1.324699999
132 0.344650725
133 0.00198282211
134 -0.0288591976
135 0.466085608
136 0.680721091
137 -1.530999999
138 0.522291878
139 0.955699999
140 -0.369225449
141 -1.409170371
142 -0.460635901
143 -0.708835253
144 -0.0240896629
145 -0.134875772
146 -0.437633916
147 1.641258050
148 -0.287560511