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

$R= 10.4363421604$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.358604350
4 0.5
5 0.447213595
6 0.960678349
7 -1.517857988
8 -0.353553390
9 0.845805780
10 -0.316227766
11 -1.422822855
12 -0.679302175
13 -1.659263884
14 1.073287676
15 -0.607586336
16 0.250000000
17 -0.509665515
18 -0.598075003
19 -0.212122258
20 0.223606797
21 2.062168466
22 1.006087689
23 -0.472358723
24 0.480339174
25 0.200000000
26 1.173276744
27 0.209488936
28 -0.758928994
29 0.987238505
30 0.429628418
31 -1.130489963
32 -0.176776695
33 1.933053322
34 0.360387942
35 -0.678806728
36 0.422902890
37 -1.030951848
38 0.149993087
39 2.254283132
40 -0.158113883
41 0.405257392
42 -1.458173306
43 -0.598466277
44 -0.711411427
45 0.378255844
46 0.334008056
47 -0.285137600
48 -0.339651087
49 1.303892872
50 -0.141421356
51 0.692433786
52 -0.829631942
53 0.866780955
54 -0.148131047
55 -0.636305725
56 0.536643838
57 0.288190222
58 -0.698083041
59 0.141125512
60 -0.303793168
61 0.770282294
62 0.799377118
63 -1.283813061
64 0.125000000
65 -0.742045367
66 -1.366875112
67 0.0793326390
68 -0.254832757
69 0.641748616
70 0.479988840
71 0.165556354
72 -0.299037501
73 1.780711690
74 0.728993042
75 -0.271720870
76 -0.106061129
77 2.159643034
78 -1.594018889
79 -0.442401820
80 0.111803398
81 -1.130418361
82 -0.286560250
83 -1.551860306
84 1.031084233
85 -0.227929347
86 0.423179563
87 -1.341266549
88 0.503043844
89 -1.255093164
90 -0.267467272
91 2.518526930
92 -0.236179361
93 1.535888508
94 0.201622730
95 -0.0948639578
96 0.240169587
97 -0.0255910872
98 -0.921991492
99 -1.203432128
100 0.100000000
101 0.245393213
102 -0.489624626
103 0.812479395
104 0.586638372
105 0.922229774
106 -0.612906691
107 -0.137383410
108 0.104744468
109 -0.921396260
110 0.449936093
111 1.400659224
112 -0.379464497
113 -1.726332601
114 -0.203781260
115 -0.211245242
116 0.493619252
117 -1.403414329
118 -0.0997908071
119 0.773598336
120 0.214814209
121 1.024447644
122 -0.544671834
123 -0.550696269
124 -0.565244981
125 0.0894427190
126 0.907792921
127 -0.609897465
128 -0.0883883476
129 0.812848579
130 0.524705311
131 0.986023891
132 0.966526661
133 0.321373618
134 -0.0560966470
135 0.0936863006
136 0.180193971
137 -1.569543334
138 -0.453784798
139 -1.673592321
140 -0.339403364
141 0.400852259
142 -0.117066021
143 2.351718220
144 0.211451445
145 0.441506481
146 -1.259153311
147 -1.729325804
148 -0.515475924
149 0.0358270697
150 0.192135669