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

$R= 13.8221167093$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.461639467
4 0.5
5 -0.447213595
6 -0.326428397
7 -0.215020653
8 -0.353553390
9 -0.786889002
10 0.316227766
11 -0.124202659
12 0.230819733
13 1.363876038
14 0.152042562
15 -0.206451446
16 0.250000000
17 -1.124964084
18 0.556414549
19 0.842811280
20 -0.223606797
21 -0.0992620199
22 0.0878245429
23 -1.190663896
24 -0.163214198
25 0.200000000
26 -0.964405995
27 -0.824898487
28 -0.107510326
29 -0.604757462
30 0.145983217
31 0.213566517
32 -0.176776695
33 -0.0573368497
34 0.795469732
35 0.0961601595
36 -0.393444501
37 0.753576545
38 -0.595957571
39 0.629619008
40 0.158113883
41 1.529101041
42 0.0701888474
43 1.754380426
44 -0.0621013298
45 0.351907459
46 0.841926515
47 0.281474978
48 0.115409866
49 -0.953766118
50 -0.141421356
51 -0.519327820
52 0.681938019
53 0.758559699
54 0.583291314
55 0.0555451180
56 0.0760212810
57 0.389074950
58 0.427628102
59 0.627697312
60 -0.103225723
61 0.305090708
62 -0.151014332
63 0.169197387
64 0.125000000
65 -0.609943907
66 0.0405432752
67 -0.843445355
68 -0.562482042
69 -0.549657447
70 -0.0679955008
71 1.454710226
72 0.278207274
73 0.564005591
74 -0.532859085
75 0.0923278935
76 0.421405640
77 0.0267061369
78 -0.445207870
79 0.980754319
80 -0.111803398
81 0.406083302
82 -1.081237715
83 0.466283254
84 -0.0496310099
85 0.503099232
86 -1.240534296
87 -0.279179914
88 0.0439122714
89 0.777058231
90 -0.248836151
91 -0.293261518
92 -0.595331948
93 0.0985907334
94 -0.199032866
95 -0.376916663
96 -0.0816070994
97 1.239016666
98 0.674414490
99 0.0977337528
100 0.100000000
101 -1.577372853
102 0.367220223
103 1.977035430
104 -0.482202997
105 0.0443913248
106 -0.536382707
107 -0.0936955586
108 -0.412449243
109 -0.0135790773
110 -0.0392763296
111 0.347880665
112 -0.0537551633
113 0.643791735
114 -0.275117536
115 0.532481082
116 -0.302378731
117 -1.073219305
118 -0.443849026
119 0.241891637
120 0.0729916087
121 -0.984571893
122 -0.215731709
123 0.705894279
124 0.106783258
125 -0.0894427190
126 -0.119640620
127 -0.815824380
128 -0.0883883476
129 0.809878788
130 0.431295472
131 1.766561898
132 -0.0286684248
133 -0.181249955
134 0.596405930
135 0.368905818
136 0.397734866
137 0.109382071
138 0.388666508
139 -1.902239961
140 0.0480800797
141 0.130016715
142 -1.028635465
143 -0.169570964
144 -0.196722250
145 0.270455759
146 -0.398812178
147 -0.439791786
148 0.376788272
149 -1.503724854
150 -0.0652856795
151 0.403729477
152 -0.297978785
153 0.891170956
154 -0.0188840905
155 -0.0955098502
156 0.314809504
157 1.115781456
158 -0.693498029
159 0.326635927
160 0.0790569415
161 0.245612639
162 -0.287144257