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

$R= 14.1093933296$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.990361882
4 0.5
5 -0.447213595
6 0.700291603
7 -0.161149651
8 -0.353553390
9 -0.0191833411
10 0.316227766
11 -0.576634756
12 -0.495180941
13 0.484844600
14 0.113950011
15 0.442903298
16 0.250000000
17 0.901292023
18 0.0135646706
19 0.285655031
20 -0.223606797
21 0.159596472
22 0.407742346
23 0.456302289
24 0.350145801
25 0.200000000
26 -0.342836904
27 1.009360332
28 -0.0805748259
29 1.170925984
30 -0.313179925
31 1.420821777
32 -0.176776695
33 0.571077083
34 -0.637309701
35 0.0720683152
36 -0.00959167058
37 -1.747754769
38 -0.201988609
39 -0.480171611
40 0.158113883
41 -0.126581897
42 -0.112851748
43 -1.065407340
44 -0.288317378
45 0.00857905097
46 -0.322654443
47 -0.134651703
48 -0.247590470
49 -0.974030789
50 -0.141421356
51 -0.892605265
52 0.242422300
53 -1.164431769
54 -0.713725535
55 0.257878902
56 0.0569750058
57 -0.282901854
58 -0.827969704
59 1.798171036
60 0.221451649
61 1.004263618
62 -1.004672713
63 0.00309138869
64 0.125000000
65 -0.216829096
66 -0.403812478
67 -1.825105262
68 0.450646011
69 -0.451904394
70 -0.0509599944
71 -1.179871005
72 0.00678233531
73 1.300843022
74 1.235849249
75 -0.198072376
76 0.142827515
77 0.0929244903
78 0.339532602
79 0.424887423
80 -0.111803398
81 -0.980448660
82 0.0895069183
83 -0.468147662
84 0.0797982363
85 -0.403070046
86 0.753356755
87 -1.159640453
88 0.203871173
89 1.382183208
90 -0.00606630512
91 -0.0781325530
92 0.228151144
93 -1.407127776
94 0.0952131325
95 -0.127748813
96 0.175072900
97 -1.387738714
98 0.688743776
99 0.0110618460
100 0.100000000
101 0.897201118
102 0.631167235
103 -0.322685549
104 -0.171418452
105 -0.0713737123
106 0.823377600
107 -0.0316657489
108 0.504680166
109 -1.166108680
110 -0.182347920
111 1.730908197
112 -0.0402874129
113 -1.387874024
114 0.200041819
115 -0.204064587
116 0.585462992
117 -0.00929793855
118 -1.271498933
119 -0.145246718
120 -0.156589962
121 -0.667500294
122 -0.710121614
123 0.125347830
124 0.710410888
125 -0.0894427190
126 -0.00218594190
127 0.931235774
128 -0.0883883476
129 1.055117601
130 0.153321324
131 -0.629911121
132 0.285538541
133 -0.0459588636
134 1.290544307
135 -0.451399663
136 -0.318654850
137 0.120884194
138 0.319544662
139 -0.814361462
140 0.0360341576
141 0.134181150
142 0.834294789
143 -0.279938440
144 -0.00479583529
145 -0.523654019
146 -0.919834922
147 0.965854981
148 -0.873877384
149 -1.180688484
150 0.140058320
151 0.416033217
152 -0.100994304
153 -0.0170942070
154 -0.0657075372
155 -0.635410815
156 -0.240085805