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

$R= 18.2615112082$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.322936496
4 0.5
5 -0.447213595
6 0.935457367
7 -0.0716390544
8 0.353553390
9 0.750160972
10 -0.316227766
11 0.245063034
12 0.661468248
13 0.888726585
14 -0.0506564611
15 -0.591635187
16 0.250000000
17 -0.777583962
18 0.530443910
19 0.300389457
20 -0.223606797
21 -0.0947739196
22 0.173285733
23 1.718464713
24 0.467728683
25 0.200000000
26 0.628424594
27 -0.330521167
28 -0.0358195272
29 1.734057032
30 -0.418349252
31 0.0902042493
32 0.176776695
33 0.324202832
34 -0.549834893
35 0.0320379591
36 0.375080486
37 1.054974157
38 0.212407422
39 1.175728834
40 -0.158113883
41 0.843227270
42 -0.0670152812
43 1.189140875
44 0.122531517
45 -0.335482185
46 1.215138051
47 -0.987216414
48 0.330734124
49 -0.994867845
50 0.141421356
51 -1.028694203
52 0.444363292
53 -0.987731436
54 -0.233713758
55 -0.109595520
56 -0.0253282305
57 0.397396176
58 1.226163486
59 0.333680520
60 -0.295817593
61 -1.520477443
62 0.0637840364
63 -0.0537408227
64 0.125000000
65 -0.397450611
66 0.229246021
67 0.792038419
68 -0.388791981
69 2.273419686
70 0.0226542581
71 1.152613151
72 0.265221955
73 0.872914085
74 0.745979380
75 0.264587299
76 0.150194728
77 -0.0175560840
78 0.831365831
79 -0.728991050
80 -0.111803398
81 -1.187419487
82 0.596251721
83 1.035335459
84 -0.0473869598
85 0.347746119
86 0.840849576
87 2.294047334
88 0.0866428668
89 -0.306359351
90 -0.237221728
91 -0.0636675322
92 0.859232356
93 0.119334493
94 -0.698067421
95 -0.134338249
96 0.233864341
97 0.657099325
98 -0.703477800
99 0.183836725
100 0.100000000
101 1.126182387
102 -0.727396646
103 0.733524316
104 0.314212297
105 0.0423841853
106 -0.698431596
107 -1.804591736
108 -0.165260583
109 0.176541876
110 -0.0774957360
111 1.395663824
112 -0.0179097636
113 0.899636746
114 0.281001530
115 -0.768520783
116 0.867028516
117 0.666687983
118 0.235947758
119 0.0557053405
120 -0.209174626
121 -0.939944121
122 -1.075139910
123 1.115536182
124 0.0451021246
125 -0.0894427190
126 -0.0380005002
127 -1.541788821
128 0.0883883476
129 1.573157673
130 -0.281040022
131 -1.163593823
132 0.162101416
133 -0.0215194215
134 0.560055737
135 0.147813559
136 -0.274917446
137 -1.742664512
138 1.607550476
139 1.393102016
140 0.0160189795
141 -1.306024935
142 0.815020575
143 0.217792779
144 0.187540243
145 -0.775493880
146 0.617243469
147 -1.316151286
148 0.527487078
149 -0.183705820
150 0.187091473
151 1.706740284
152 0.106203711
153 -0.583313499
154 -0.0124140260
155 -0.0403405667
156 0.587864417
157 0.0764847091
158 -0.515474514
159 -1.306916210
160 -0.0790569415
161 -0.123201703
162 -0.839632371
163 -0.528326137
164 0.421613635
165 -0.144987914
166 0.732092724
167 -1.431320463
168 -0.0335076406
169 -0.212413702
170 0.245893639
171 0.226901523
172 0.594570437
173 1.330741790
174 1.622136426
175 -0.0143278108
176 0.0612657587
177 0.431192467
178 -0.216628774
179 -0.201239853
180 -0.167741092