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

$R= 8.45261564535$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.271088353
4 0.5
5 0.447213595
6 0.191688413
7 0.673628223
8 0.353553390
9 -0.926511104
10 0.316227766
11 0.398373199
12 0.135544176
13 1.654677484
14 0.476327085
15 0.121234397
16 0.250000000
17 0.863960266
18 -0.655142284
19 0.947785757
20 0.223606797
21 0.182612766
22 0.281692391
23 -0.0384592541
24 0.0958442065
25 0.200000000
26 1.170033670
27 -0.522254723
28 0.336814111
29 -0.887427571
30 0.0857256644
31 -1.115168567
32 0.176776695
33 0.107994334
34 0.610912163
35 0.301255700
36 -0.463255552
37 0.827010203
38 0.670185735
39 0.448563795
40 0.158113883
41 -1.822146033
42 0.129126725
43 0.308511524
44 0.199186599
45 -0.414348362
46 -0.0271947993
47 -1.099820495
48 0.0677720884
49 -0.546225016
50 0.141421356
51 0.234209566
52 0.827338742
53 1.551575033
54 -0.369289856
55 0.178157911
56 0.238163542
57 0.256933680
58 -0.627506053
59 -0.443946703
60 0.0606171986
61 0.303210776
62 -0.788543256
63 -0.624124029
64 0.125000000
65 0.739994267
66 0.0763635265
67 -1.916311188
68 0.431980133
69 -0.0104258558
70 0.213019948
71 1.545393674
72 -0.327571142
73 -1.033714669
74 0.584784522
75 0.0542176707
76 0.473892878
77 0.268355431
78 0.317182501
79 -0.718510960
80 0.111803398
81 0.784933931
82 -1.288451816
83 0.651158679
84 0.0913063830
85 0.386374777
86 0.218150591
87 -0.240571279
88 0.140846195
89 -1.671277899
90 -0.292988536
91 1.114637455
92 -0.0192296270
93 -0.302309211
94 -0.777690530
95 0.423862676
96 0.0479221032
97 -0.478436199
98 -0.386239412
99 -0.369097193
100 0.100000000
101 0.168119999
102 0.165611172
103 0.948690000
104 0.585016835
105 0.0816669117
106 1.097129227
107 -0.622619999
108 -0.261127361
109 1.033940000
110 0.125976667
111 0.224192834
112 0.168407055
113 -0.822869999
114 0.181679547
115 -0.0171995013
116 -0.443713785
117 -1.533077064
118 -0.313917724
119 0.581988020
120 0.0428628322
121 -0.841298793
122 0.214402396
123 -0.493962568
124 -0.557584283
125 0.0894427190
126 -0.441322333
127 0.457000000
128 0.0883883476
129 0.0836338813
130 0.523254964
131 1.981999999
132 0.0539971674
133 0.638455236
134 -1.355036636
135 -0.233559412
136 0.305456081
137 -0.550000000
138 -0.00737219339
139 0.910000000
140 0.150627850
141 -0.298148527
142 1.092758347
143 0.659179164
144 -0.231627776
145 -0.396869674
146 -0.730946652
147 -0.148075240
148 0.413505101
149 -1.699999999
150 0.0383376826