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

$R= 13.5062656949$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.165203532
4 0.5
5 0.447213595
6 0.116816538
7 -0.195467517
8 0.353553390
9 -0.972707792
10 0.316227766
11 -1.689083460
12 0.0826017662
13 1.354802699
14 -0.138216407
15 0.0738812657
16 0.250000000
17 -1.782147248
18 -0.687808276
19 0.0563655238
20 0.223606797
21 -0.0322919244
22 -1.194362368
23 -0.334297852
24 0.0584082690
25 0.200000000
26 0.957990175
27 -0.325898295
28 -0.0977337589
29 1.579992809
30 0.0522419440
31 -1.230986142
32 0.176776695
33 -0.279042554
34 -1.260168404
35 -0.0874157314
36 -0.486353896
37 -1.332231534
38 0.0398564441
39 0.223818191
40 0.158113883
41 -0.0732773055
42 -0.0228338387
43 -1.224796838
44 -0.844541730
45 -0.435008149
46 -0.236384278
47 -0.583373001
48 0.0413008831
49 -0.961792449
50 0.141421356
51 -0.294417020
52 0.677401349
53 -0.111515129
54 -0.230444894
55 -0.755381087
56 -0.0691082037
57 0.00931178364
58 1.117223630
59 -0.0630444312
60 0.0369406328
61 -0.500910273
62 -0.870438648
63 0.190132777
64 0.125000000
65 0.605886186
66 -0.197312882
67 -0.587898458
68 -0.891073624
69 -0.0552271862
70 -0.0618122565
71 0.681303736
72 -0.343904138
73 1.107096061
74 -0.942029952
75 0.0330407064
76 0.0281827619
77 0.330160951
78 0.158263361
79 0.414830626
80 0.111803398
81 0.918868243
82 -0.0518148796
83 -0.198748578
84 -0.0161459622
85 -0.797000478
86 -0.866062149
87 0.261020395
88 -0.597181184
89 0.398292127
90 -0.307597212
91 -0.264819921
92 -0.167148926
93 -0.203363264
94 -0.412507005
95 0.0252074285
96 0.0292041345
97 1.537430896
98 -0.680089963
99 1.642984660
100 0.100000000
101 0.719955705
102 -0.208184271
103 -0.901344031
104 0.478995087
105 -0.0144413876
106 -0.0788531045
107 0.950514649
108 -0.162949147
109 -1.577364894
110 -0.534135089
111 -0.220088579
112 -0.0488668794
113 -0.299101022
114 0.00658442535
115 -0.149502544
116 0.789996404
117 -1.317827236
118 -0.0445791448
119 0.348354619
120 0.0261209720
121 1.853003292
122 -0.354197050
123 -0.0121036065
124 -0.615493071
125 0.0894427190
126 0.134444176
127 0.0132935722
128 0.0883883476
129 -0.202361862
130 0.428426230
131 1.547798725
132 -0.139521277
133 -0.0110850528
134 -0.415706986
135 -0.145746148
136 -0.630084202
137 -0.546343958
138 -0.0390515178
139 0.947936208
140 -0.0437078657
141 -0.0957764185
142 0.481754492
143 -2.289226183
144 -0.243176948
145 0.706594265
146 0.782835132
147 -0.159973152
148 -0.666115767
149 -0.135948320
150 0.0233633076
151 -0.616139673
152 0.0199282220
153 1.734952318
154 0.233459047
155 -0.550513738
156 0.111909095
157 -0.766891720
158 0.293329549
159 -0.0550844707
160 0.0790569415
161 0.000608137223
162 0.649737965