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

$R= 20.8896134485$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.557028040
4 0.5
5 -0.447213595
6 0.393878304
7 -0.158247851
8 0.353553390
9 -0.689719761
10 -0.316227766
11 0.975923394
12 0.278514020
13 -0.585915330
14 -0.111898129
15 -0.249110512
16 0.250000000
17 0.581182712
18 -0.487705520
19 -0.133886472
20 -0.223606797
21 -0.0881484909
22 0.690082050
23 0.324524378
24 0.196939152
25 0.200000000
26 -0.414304703
27 -0.941221288
28 -0.0791239259
29 -0.706512982
30 -0.176147732
31 -0.441327096
32 0.176776695
33 0.543616696
34 0.410958237
35 0.0707705908
36 -0.344859880
37 -1.186102550
38 -0.0946720328
39 -0.326371268
40 -0.158113883
41 0.253706330
42 -0.0623303956
43 -0.0532887743
44 0.487961697
45 0.308452054
46 0.229473388
47 -1.748446177
48 0.139257010
49 -0.974957617
50 0.141421356
51 0.323735067
52 -0.292957665
53 0.118127070
54 -0.665543955
55 -0.436446210
56 -0.0559490646
57 -0.0745785196
58 -0.499580120
59 -1.411033303
60 -0.124555256
61 -0.916945939
62 -0.312065382
63 0.109146670
64 0.125000000
65 0.262029301
66 0.384395052
67 1.158459826
68 0.290591356
69 0.180769178
70 0.0500423646
71 1.238855566
72 -0.243852760
73 0.293329926
74 -0.838701156
75 0.111405608
76 -0.0669432363
77 -0.154437780
78 -0.230779337
79 1.503058696
80 -0.111803398
81 0.165433111
82 0.179397466
83 -0.582735424
84 -0.0440742454
85 -0.259912810
86 -0.0376808537
87 -0.393547542
88 0.345041025
89 -1.739484216
90 0.218108539
91 0.0927198425
92 0.162262189
93 -0.245831568
94 -1.236338148
95 0.0598758508
96 0.0984695762
97 -1.806097815
98 -0.689399142
99 -0.673113651
100 0.100000000
101 -1.207273739
102 0.228915261
103 -0.0707951322
104 -0.207152351
105 0.0394212035
106 0.0835284527
107 -0.761074770
108 -0.470610644
109 1.031727138
110 -0.308614075
111 -0.660692378
112 -0.0395619629
113 -1.035224104
114 -0.0527349769
115 -0.145131714
116 -0.353256491
117 0.404117382
118 -0.997751217
119 -0.0919709107
120 -0.0880738664
121 -0.0475735165
122 -0.648378692
123 0.141321551
124 -0.220663548
125 -0.0894427190
126 0.0771783510
127 -1.154745011
128 0.0883883476
129 -0.0296833025
130 0.185282696
131 0.127166464
132 0.271808348
133 0.0211873116
134 0.819154799
135 0.420926956
136 0.205479118
137 -1.142769879
138 0.127823112
139 0.545559993
140 0.0353852954
141 -0.973932994
142 0.876003171
143 -0.571808083
144 -0.172429940
145 0.315962211
146 0.207415580
147 -0.543078331
148 -0.593051275
149 -0.877951350
150 0.0787756609
151 -0.859757445
152 -0.0473360164
153 -0.400849391
154 -0.109204002
155 0.197367477
156 -0.163185634
157 1.894235700
158 1.062822997
159 0.0658188421
160 -0.0790569415
161 -0.0513186247
162 0.116978874
163 0.339694022
164 0.126853165
165 -0.243112777
166 -0.412056170
167 1.225910205
168 -0.0311651978
169 -0.656549955
170 -0.183786110
171 0.0925467084
172 -0.0266443871
173 -1.240775682
174 -0.278280135
175 -0.0316495703
176 0.243980848
177 -0.785618214
178 -1.230001084
179 0.486744260
180 0.154226027
181 1.025174296
182 0.0655628293
183 -0.510473027
184 0.114736694
185 0.530441186
186 -0.173829168
187 0.568639975
188 -0.874223088
189 0.155662121
190 0.0423386201
191 1.318574283
192 0.0696285051
193 1.071457000
194 -1.277104012
195 0.145957668
196 -0.487478808
197 1.011928978
198 -0.475963227
199 -0.226320281
200 0.0707106781
201 0.686830978
202 -0.853671448
203 0.0981665639
204 0.161867533
205 -0.113460920