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

$R= 14.4354503421$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.555194553
4 0.5
5 0.447213595
6 0.392581833
7 0.283360393
8 -0.353553390
9 -0.691759007
10 -0.316227766
11 0.0151965767
12 -0.277597276
13 -0.354935384
14 -0.200366056
15 -0.248290552
16 0.250000000
17 0.453974471
18 0.489147485
19 0.397805739
20 0.223606797
21 -0.157320147
22 -0.0107456024
23 -0.158607526
24 0.196290916
25 0.200000000
26 0.250977217
27 0.939255387
28 0.141680196
29 1.079601760
30 0.175567933
31 0.645029753
32 -0.176776695
33 -0.00843705662
34 -0.321008427
35 0.126722620
36 -0.345879503
37 1.069811906
38 -0.281291136
39 0.197058192
40 -0.158113883
41 -1.267528157
42 0.111242143
43 -1.695119029
44 0.00759828835
45 -0.309364033
46 0.112152457
47 -1.592096400
48 -0.138798638
49 -0.919706887
50 -0.141421356
51 -0.252044153
52 -0.177467692
53 1.461544420
54 -0.664153853
55 0.00679611570
56 -0.100183028
57 -0.220859580
58 -0.763393725
59 -0.665649384
60 -0.124145276
61 -1.076699372
62 -0.456104912
63 -0.196017104
64 0.125000000
65 -0.158731929
66 0.00596589995
67 1.303756659
68 0.226987235
69 0.0880580347
70 -0.0896064243
71 0.369162601
72 0.244573742
73 -0.352103972
74 -0.756471253
75 -0.111038910
76 0.198902869
77 0.00430610779
78 -0.139341184
79 -1.393188202
80 0.111803398
81 0.170289532
82 0.896277755
83 -0.720323586
84 -0.0786600736
85 0.203023555
86 1.198630160
87 -0.599389017
88 -0.00537280121
89 -0.583892241
90 0.218753405
91 -0.100574629
92 -0.0793037632
93 -0.358117006
94 1.125782161
95 0.177904135
96 0.0981454584
97 -0.0979016436
98 0.650330976
99 -0.0105123653
100 0.100000000
101 -1.600027000
102 0.178222130
103 0.456486759
104 0.125488608
105 -0.0703557087
106 -1.033467971
107 0.730543797
108 0.469627693
109 -1.641908963
110 -0.00480557950
111 -0.593953807
112 0.0708400984
113 0.682431999
114 0.156171306
115 -0.0709314421
116 0.539800880
117 0.245529727
118 0.470685193
119 0.128637970
120 0.0877839666
121 -0.999767560
122 0.761341427
123 0.703725506
124 0.322514876
125 0.0894427190
126 0.138605024
127 -1.024257619
128 -0.0883883476
129 0.941124976
130 0.112240423
131 -1.449324811
132 -0.00421852831
133 0.112727778
134 -0.921895174
135 0.420047778
136 -0.160504213
137 -1.622615864
138 -0.0622664335
139 0.439504067
140 0.0633613102
141 0.883932465
142 -0.261037379
143 -0.00561060006
144 -0.172939751
145 0.482812585
146 0.248975106
147 0.510296517
148 0.534905953
149 -0.631564329
150 0.0785163667
151 1.444526122
152 -0.140645568
153 -0.317213302
154 -0.00304487802
155 0.288466075
156 0.0985290962
157 -0.581207282
158 0.985132825
159 -0.812761540
160 -0.0790569415
161 -0.0525231893
162 -0.120412883
163 -0.613583415
164 -0.633764078
165 -0.00377316642
166 0.509345692