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

$R= 12.9729966293$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.511027952
4 0.5
5 0.447213595
6 1.068458111
7 -0.726788452
8 0.353553390
9 1.283205473
10 0.316227766
11 -0.115581979
12 0.755513976
13 1.330254151
14 -0.513917043
15 0.675752243
16 0.250000000
17 1.431904352
18 0.907363291
19 1.148602374
20 0.223606797
21 -1.098197667
22 -0.0817288011
23 -1.421795009
24 0.534229055
25 0.200000000
26 0.940631730
27 0.427931386
28 -0.363394226
29 -1.406564862
30 0.477828993
31 1.501103982
32 0.176776695
33 -0.174647601
34 1.012509277
35 -0.325029677
36 0.641602736
37 -0.122923530
38 0.812184527
39 2.010051206
40 0.158113883
41 0.996748626
42 -0.776543018
43 0.299132151
44 -0.0577909895
45 0.573866933
46 -1.005360892
47 0.0948045177
48 0.377756988
49 -0.471778544
50 0.141421356
51 2.163647502
52 0.665127075
53 -1.086734823
54 0.302593185
55 -0.0516898324
56 -0.256958521
57 1.735570294
58 -0.994591552
59 -0.308370340
60 0.337876121
61 -1.590908086
62 1.061440805
63 -0.932618920
64 0.125000000
65 0.594907741
66 -0.123494503
67 1.263279080
68 0.715952176
69 -2.148372002
70 -0.229830688
71 0.552176948
72 0.453681645
73 -0.961863361
74 -0.0869200622
75 0.302205590
76 0.574301187
77 0.0840036471
78 1.421320838
79 0.00209235211
80 0.111803398
81 -0.636589183
82 0.704807712
83 -1.127277720
84 -0.549098833
85 0.640367094
86 0.211518372
87 -2.125358814
88 -0.0408644005
89 -0.340855480
90 0.405785200
91 -0.966813325
92 -0.710897504
93 2.268210089
94 0.0670369174
95 0.513670597
96 0.267114527
97 1.556551883
98 -0.333597808
99 -0.148315469
100 0.100000000
101 -0.512976662
102 1.529929821
103 -0.723414188
104 0.470315865
105 -0.491128927
106 -0.768437562
107 -1.593468223
108 0.213965693
109 -1.257890571
110 -0.0365502310
111 -0.185738588
112 -0.181697113
113 1.619098790
114 1.227233524
115 -0.635846058
116 -0.703282431
117 1.707004222
118 -0.218050759
119 -1.040685834
120 0.238914496
121 -0.986624515
122 -1.124941896
123 1.506125564
124 0.750551991
125 0.0894427190
126 -0.659461163
127 1.144694961
128 0.0883883476
129 0.452032896
130 0.420663298
131 -0.656012582
132 -0.0873238005
133 -0.834573178
134 0.893273204
135 0.191376733
136 0.506254638
137 0.109398089
138 -1.519128411
139 -0.832346041
140 -0.162514838
141 0.143544154
142 0.390448064
143 -0.152798806
144 0.320801368
145 -0.629034929
146 -0.680140105
147 -0.700154195
148 -0.0614617654
149 -0.441724218
150 0.213691622
151 1.125806600
152 0.406092263
153 1.861490476
154 0.0593995485
155 0.671314109
156 1.005025603
157 -1.722918364
158 0.00147951636
159 -1.664020430
160 0.0790569415
161 1.000093224
162 -0.450136528
163 0.537700814
164 0.498374313
165 -0.0781047816