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

$R= 11.7496208831$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.430547550
4 0.5
5 0.447213595
6 -0.304443092
7 -0.0142644136
8 -0.353553390
9 -0.814628806
10 -0.316227766
11 0.0354434024
12 0.215273775
13 -0.662765162
14 0.0100864636
15 0.192546718
16 0.250000000
17 1.031468441
18 0.576029553
19 1.061415800
20 0.223606797
21 -0.00614150837
22 -0.0250622701
23 -1.236849444
24 -0.152221546
25 0.200000000
26 0.468645740
27 -0.781283988
28 -0.00713220683
29 -1.032431283
30 -0.136151090
31 -1.318004457
32 -0.176776695
33 0.0152600701
34 -0.729358329
35 -0.00637923972
36 -0.407314403
37 -0.161407390
38 -0.750534310
39 -0.285351917
40 -0.158113883
41 0.378202402
42 0.00434270221
43 0.514055141
44 0.0177217012
45 -0.364313077
46 0.874584629
47 -1.310737020
48 0.107636887
49 -0.999796526
50 -0.141421356
51 0.444096211
52 -0.331382581
53 -0.767058399
54 0.552451206
55 0.0158507714
56 0.00504323181
57 0.456989973
58 0.730039161
59 0.936521485
60 0.0962733591
61 -1.580378303
62 0.931969889
63 0.0116202022
64 0.125000000
65 -0.296397591
66 -0.0107904990
67 -1.646415113
68 0.515734220
69 -0.532522499
70 0.00451080366
71 -1.413150813
72 0.288014776
73 1.661191346
74 0.114132260
75 0.0861095101
76 0.530707900
77 -0.000505579566
78 0.201774275
79 -0.207984217
80 0.111803398
81 0.478248899
82 -0.267429483
83 0.0622382957
84 -0.00307075418
85 0.461286710
86 -0.363491876
87 -0.444510763
88 -0.0125311350
89 -1.005199370
90 0.257608247
91 0.00945396400
92 -0.618424722
93 -0.567463595
94 0.926831035
95 0.474679576
96 -0.0761107732
97 -1.140994458
98 0.706962903
99 -0.0288731999
100 0.100000000
101 0.653371613
102 -0.314023442
103 0.488906576
104 0.234322870
105 -0.00274656604
106 0.542392196
107 0.147020111
108 -0.390641994
109 -0.668575155
110 -0.0112081879
111 -0.0694933591
112 -0.00356610341
113 1.365172128
114 -0.323140709
115 -0.553135887
116 -0.516215641
117 0.539904855
118 -0.662220692
119 -0.0147143235
120 -0.0680755451
121 -0.998734457
122 1.117496215
123 0.162842444
124 -0.659002228
125 0.0894427190
126 -0.00821672383
127 -0.361874044
128 -0.0883883476
129 0.221282490
130 0.209584746
131 -0.963464670
132 0.00763003505
133 -0.0151350401
134 1.164191291
135 -0.349400821
136 -0.364679164
137 1.213810081
138 0.376550270
139 1.634885158
140 -0.00318961986
141 -0.564044819
142 0.999248523
143 -0.0237385179
144 -0.203657201
145 -0.461717306
146 -1.174639666
147 -0.431155075
148 -0.0807036951
149 0.697058968
150 -0.0608886185
151 -1.566675302
152 -0.375267155
153 -0.835070715
154 0.000357498740
155 -0.589429512
156 -0.142675958
157 1.660896807
158 0.147067050
159 -0.265498108
160 -0.0790569415
161 0.212630123
162 -0.338173039
163 0.780446123
164 0.189101201
165 0.00682451081
166 -0.0440091209