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

$R= 20.0135298126$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.266246526
4 0.5
5 -0.447213595
6 -0.895371505
7 0.643628021
8 0.353553390
9 0.603380266
10 -0.316227766
11 -0.0525944536
12 -0.633123263
13 -1.232480166
14 0.455113738
15 0.566282662
16 0.250000000
17 0.220281207
18 0.426654278
19 1.192467279
20 -0.223606797
21 -0.814991746
22 -0.0371898948
23 -0.718154695
24 -0.447685752
25 0.200000000
26 -0.871495083
27 0.502218360
28 0.321814010
29 1.734991444
30 0.400422310
31 1.028693143
32 0.176776695
33 0.0665975442
34 0.155762335
35 -0.287839201
36 0.301690133
37 -0.492524814
38 0.843201699
39 1.560623730
40 -0.158113883
41 0.352560719
42 -0.576286190
43 -1.202788319
44 -0.0262972268
45 -0.269839858
46 -0.507812054
47 0.544795189
48 -0.316561631
49 -0.585742970
50 0.141421356
51 -0.278930314
52 -0.616240083
53 -1.863883140
54 0.355122008
55 0.0235209547
56 0.227556869
57 -1.509957550
58 1.226824215
59 -0.218943801
60 0.283141331
61 -0.385591328
62 0.727395897
63 0.388352446
64 0.125000000
65 0.551181886
66 0.0470915751
67 1.653525256
68 0.110140603
69 0.909360888
70 -0.203533051
71 -1.814571533
72 0.213327139
73 -0.850179044
74 -0.348267636
75 -0.253249305
76 0.596233639
77 -0.0338512641
78 1.103527622
79 -0.332004544
80 -0.111803398
81 -1.239312520
82 0.249298075
83 0.581366850
84 -0.407495873
85 -0.0985127509
86 -0.850499777
87 -2.196926890
88 -0.0185949474
89 -0.400178801
90 -0.190805593
91 -0.793258770
92 -0.359077347
93 -1.302579120
94 0.385228372
95 -0.533287579
96 -0.223842876
97 1.096106211
98 -0.414182826
99 -0.0317344549
100 0.100000000
101 -0.819341884
102 -0.197233516
103 -1.089530267
104 -0.435747541
105 0.364475389
106 -1.317964407
107 0.906670619
108 0.251109180
109 -0.727846465
110 0.0166318265
111 0.623657839
112 0.160907005
113 -1.304728644
114 -1.067701223
115 0.321168543
116 0.867495722
117 -0.743654207
118 -0.154816646
119 0.141779145
120 0.200211155
121 -0.997233841
122 -0.272654243
123 -0.446428768
124 0.514346571
125 -0.0894427190
126 0.274606648
127 -0.273431234
128 0.0883883476
129 1.523026436
130 0.389744449
131 -1.352547325
132 0.0332987721
133 0.767505108
134 1.169218921
135 -0.224598878
136 0.0778811679
137 -1.056210516
138 0.643015250
139 -1.222016487
140 -0.143919600
141 -0.689845212
142 -1.283095836
143 0.0648194417
144 0.150845066
145 -0.775911761
146 -0.601167367
147 0.741692762
148 -0.246262407
149 1.490637376
150 -0.179074301
151 1.700378953
152 0.421600849
153 0.132911206
154 -0.0239364584
155 -0.460045559
156 0.780311865
157 -1.868163582
158 -0.234762664
159 2.360105997
160 -0.0790569415
161 -0.462277071
162 -0.876326287
163 -0.102053178
164 0.176280359
165 -0.0297833272
166 0.411088442
167 -1.286029459
168 -0.288143095
169 0.519375048
170 -0.0696590342
171 0.719062313
172 -0.601394159
173 -0.0742517606
174 -1.553461901
175 0.128725604
176 -0.0131486134
177 0.282182866
178 -0.282969144
179 1.259764522
180 -0.134919929
181 0.812650607
182 -0.560918656
183 0.495754059
184 -0.253906027
185 0.220263793
186 -0.921062528
187 0.000416763885
188 0.272397594
189 0.400551564
190 -0.377091263