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

$R= 11.4177272153$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.935440518
4 0.5
5 0.447213595
6 0.661456333
7 0.504930465
8 0.353553390
9 -0.124951036
10 0.316227766
11 1.302129300
12 0.467720259
13 0.581158602
14 0.357039756
15 0.418341717
16 0.250000000
17 -0.514298997
18 -0.0883537252
19 -1.159742018
20 0.223606797
21 0.472332416
22 0.920744458
23 0.918436776
24 0.330728166
25 0.200000000
26 0.410941188
27 -1.052324780
28 0.252465232
29 1.401997949
30 0.295812265
31 1.190428166
32 0.176776695
33 1.218064508
34 -0.363664308
35 0.225811769
36 -0.0624755182
37 0.755986384
38 -0.820061445
39 0.543639303
40 0.158113883
41 -0.477738292
42 0.333989454
43 -1.248819864
44 0.651064650
45 -0.0558798023
46 0.649432872
47 1.844205083
48 0.233860129
49 -0.745045224
50 0.141421356
51 -0.481096120
52 0.290579301
53 -0.577654356
54 -0.744105988
55 0.582329926
56 0.178519878
57 -1.084869674
58 0.991362257
59 -1.166768114
60 0.209170858
61 0.139542987
62 0.841759828
63 -0.0630915851
64 0.125000000
65 0.259902027
66 0.861301673
67 -0.781761485
68 -0.257149498
69 0.859142974
70 0.159673033
71 -1.898137957
72 -0.0441768626
73 0.739473969
74 0.534563099
75 0.187088103
76 -0.579871009
77 0.657484754
78 0.384411038
79 -1.366024241
80 0.111803398
81 -0.859436202
82 -0.337811986
83 0.535031879
84 0.236166208
85 -0.230001503
86 -0.883048994
87 1.311485691
88 0.460372229
89 -0.790896340
90 -0.0395129871
91 0.293444685
92 0.459218388
93 1.113574724
94 1.304049920
95 -0.518652397
96 0.165364083
97 -0.328176227
98 -0.526826530
99 -0.162702403
100 0.100000000
101 -1.347284324
102 -0.340186329
103 -0.691612041
104 0.205470594
105 0.211233478
106 -0.408463312
107 -0.812924843
108 -0.526162390
109 0.478251321
110 0.411769439
111 0.707178861
112 0.126232616
113 1.843553275
114 -0.767118703
115 0.410737413
116 0.700998974
117 -0.0726162598
118 -0.825029645
119 -0.259690069
120 0.147906132
121 0.695533109
122 0.0986717930
123 -0.446889634
124 0.595214083
125 0.0894427190
126 -0.0446124876
127 -1.560633933
128 0.0883883476
129 -1.168263003
130 0.183778486
131 1.777989330
132 0.609032254
133 -0.585336942
134 -0.552788847
135 -0.470613948
136 -0.181832154
137 -0.951948558
138 0.607505823
139 -1.337405929
140 0.112905884
141 1.723708290
142 -1.342186221
143 0.758078045
144 -0.0312377591
145 0.626992543
146 0.522887058
147 -0.695031608
148 0.377993192
149 0.855531474
150 0.132291266
151 0.176610174
152 -0.410030722
153 0.0677674967
154 0.464911928
155 0.532375660
156 0.271819651