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

$R= 22.5860946319$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.366805618
4 0.5
5 -0.447213595
6 -0.966477521
7 -0.559621680
8 0.353553390
9 0.868157598
10 -0.316227766
11 1.175296893
12 -0.683402809
13 -1.266671271
14 -0.395712284
15 0.611254054
16 0.250000000
17 -1.262494063
18 0.613880125
19 0.830491494
20 -0.223606797
21 0.764894056
22 0.831060403
23 1.716489460
24 -0.483238760
25 0.200000000
26 -0.895671845
27 0.180202934
28 -0.279810840
29 -0.628890627
30 0.432221887
31 0.330621864
32 0.176776695
33 -1.606402397
34 -0.892718113
35 0.250270423
36 0.434078799
37 1.089838600
38 0.587246167
39 1.731293410
40 -0.158113883
41 0.715033976
42 0.540861774
43 0.757488993
44 0.587648446
45 -0.388251881
46 1.213741337
47 -0.827488998
48 -0.341701404
49 -0.686823575
50 0.141421356
51 1.725583978
52 -0.633335635
53 -0.0258456369
54 0.127422717
55 -0.525608749
56 -0.197856142
57 -1.135120440
58 -0.444692827
59 1.066557249
60 0.305627027
61 -0.132090433
62 0.233784962
63 -0.485839813
64 0.125000000
65 0.566472613
66 -1.135898028
67 -1.265726426
68 -0.631247031
69 -2.346107438
70 0.176967913
71 1.452482836
72 0.306940062
73 -1.978102650
74 0.770632265
75 -0.273361123
76 0.415245747
77 -0.657721622
78 1.224209310
79 1.300095744
80 -0.111803398
81 -1.114459982
82 0.505605373
83 -0.952709933
84 0.382447028
85 0.564604509
86 0.535625603
87 0.859571243
88 0.415530201
89 -0.126716283
90 -0.274535537
91 0.708856704
92 0.858244730
93 -0.451895821
94 -0.585123081
95 -0.371407087
96 -0.241619380
97 0.770287021
98 -0.485657607
99 1.020342928
100 0.100000000
101 -1.597370301
102 1.220172133
103 -0.461211742
104 -0.447835922
105 -0.342071021
106 -0.0182756251
107 -1.211831922
108 0.0901014674
109 -0.435673364
110 -0.371661511
111 -1.489597522
112 -0.139905420
113 -0.373103959
114 -0.802651360
115 -0.767637423
116 -0.314445313
117 -1.099670289
118 0.754169863
119 0.706519046
120 0.216110943
121 0.381322789
122 -0.0934020413
123 -0.977312456
124 0.165310932
125 -0.0894427190
126 -0.343540626
127 -1.246765347
128 0.0883883476
129 -1.035340208
130 0.400556626
131 -1.598597084
132 -0.803201198
133 -0.464761040
134 -0.895003739
135 -0.0805892024
136 -0.446359056
137 1.733846564
138 -1.658948479
139 0.856440119
140 0.125135211
141 1.131016764
142 1.027060463
143 -1.488714765
144 0.217039399
145 0.281248438
146 -1.398729797
147 0.938754197
148 0.544919300
149 -0.805595510
150 -0.193295504
151 -0.328579159
152 0.293623083
153 -1.096043214
154 -0.465079419
155 -0.147858592
156 0.865646705
157 -0.567078016
158 0.919306517
159 0.0353237345
160 -0.0790569415
161 -0.960581229
162 -0.788042211
163 -0.114607896
164 0.357516988
165 0.718404992
166 -0.673667654
167 -1.314643345
168 0.270430887
169 0.604502038
170 0.399235677
171 0.720973165
172 0.378744496
173 -0.128606544
174 0.607808655
175 -0.111924336
176 0.293824223
177 -1.457700488
178 -0.0896019433
179 0.894904392
180 -0.194125940
181 0.558880414
182 0.501237382
183 0.180087660
184 0.606870668
185 -0.487390639
186 -0.319538599
187 -1.483025099
188 -0.413744499
189 -0.0986387415
190 -0.262624469
191 -1.357410160
192 -0.170850702
193 1.869759624
194 0.544675176
195 -0.774257950
196 -0.343411787
197 -1.673834842
198 0.721491404
199 0.928282667
200 0.0707106781
201 1.788867461
202 -1.129511372
203 0.325193660
204 0.862791989
205 -0.319772915
206 -0.326125950
207 1.484335155
208 -0.316667817
209 0.904028649
210 -0.241880738