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

$R= 21.738972733$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.193491071
4 0.5
5 0.447213595
6 -0.136818848
7 1.567745783
8 -0.353553390
9 -0.962561205
10 -0.316227766
11 0.958167774
12 0.0967455357
13 0.901049347
14 -1.108563674
15 0.0865318377
16 0.250000000
17 -1.578850567
18 0.680633555
19 -0.532825120
20 0.223606797
21 0.303344811
22 -0.677526930
23 -0.637724730
24 -0.0684094243
25 0.200000000
26 -0.637138103
27 -0.379738070
28 0.783872891
29 -0.569526991
30 -0.0611872492
31 -1.189313411
32 -0.176776695
33 0.185396909
34 1.116415942
35 0.701117228
36 -0.481280602
37 -1.531700123
38 0.376764255
39 0.174345003
40 -0.158113883
41 -1.138279543
42 -0.214497173
43 -0.828740265
44 0.479083887
45 -0.430470457
46 0.450939481
47 0.265205167
48 0.0483727678
49 1.457826841
50 -0.141421356
51 -0.305493488
52 0.450524673
53 1.372355423
54 0.268515364
55 0.428505655
56 -0.554281837
57 -0.103096903
58 0.402716397
59 1.313864291
60 0.0432659188
61 -1.129614809
62 0.840971578
63 -1.509051270
64 0.125000000
65 0.402961518
66 -0.131095411
67 -0.322527971
68 -0.789425283
69 -0.123394041
70 -0.495764746
71 1.956178516
72 0.340316777
73 -0.179123210
74 1.083075544
75 0.0386982143
76 -0.266412560
77 1.502163488
78 -0.123280534
79 -0.114120143
80 0.111803398
81 0.889085279
82 0.804885184
83 -1.430493834
84 0.151672405
85 -0.706083439
86 0.586007861
87 -0.110198387
88 -0.338763465
89 0.368697715
90 0.304388579
91 1.412616315
92 -0.318862365
93 -0.230121526
94 -0.187528372
95 -0.238286637
96 -0.0342047121
97 -0.408563046
98 -1.030839245
99 -0.922295127
100 0.100000000
101 -1.192063493
102 0.216016517
103 -1.267662311
104 -0.318569051
105 0.135659923
106 -0.970401826
107 -1.514410014
108 -0.189869035
109 0.987432595
110 -0.302999254
111 -0.296370297
112 0.391936445
113 0.814133595
114 0.0729005195
115 -0.285199169
116 -0.284763495
117 -0.867315145
118 -0.929042350
119 -2.475236315
120 -0.0305936246
121 -0.0819145064
122 0.798758292
123 -0.220246921
124 -0.594656705
125 0.0894427190
126 1.067060386
127 -1.466615947
128 -0.0883883476
129 -0.160353821
130 -0.284936822
131 -0.624146765
132 0.0926984546
133 -0.835334301
134 0.228061715
135 -0.169824027
136 0.558207971
137 1.360433167
138 0.0872527634
139 -0.788038006
140 0.350558614
141 0.0513147757
142 -1.383227094
143 0.863356569
144 -0.240640301
145 -0.254700213
146 0.126659236
147 0.282076183
148 -0.765850061
149 0.527284839
150 -0.0273637697
151 -1.636974553
152 0.188382127
153 1.519739088
154 -1.062189988
155 -0.531877126
156 0.0871725018
157 0.415669362
158 0.0806951271
159 0.265537505
160 -0.0790569415
161 -0.999786728
162 -0.628678229
163 1.058034481
164 -0.569139771
165 0.0829120184
166 1.011511891
167 0.273954988
168 -0.107248586
169 -0.188126113
170 0.499276387
171 0.512933237
172 -0.414370132
173 -0.711882698
174 0.0779220272
175 0.313549156
176 0.239541943
177 0.254145961
178 -0.260708655
179 0.950002502
180 -0.215235228
181 0.261501945
182 -0.998870575
183 -0.216915474
184 0.225469740
185 -0.684997119
186 0.162720491
187 -1.514316897
188 0.132602583
189 -0.592211748
190 0.168494097
191 0.00803234870
192 0.0241863839
193 -0.491831276
194 0.288897700
195 0.0779694559
196 0.728913420
197 1.401279828
198 0.652161139
199 -0.333898371
200 -0.0707106781
201 -0.0243671570
202 0.842916180
203 -0.874082727
204 -0.152746744
205 -0.509054087
206 0.896372616
207 0.892687118
208 0.225262336
209 -0.610666388