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

$R= 24.2793539858$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.311419861
4 0.5
5 0.447213595
6 -0.220207096
7 -0.796783009
8 0.353553390
9 -0.903017669
10 0.316227766
11 -1.737613143
12 -0.155709930
13 -1.279613608
14 -0.563410668
15 -0.139271196
16 0.250000000
17 -0.117240806
18 -0.638529917
19 -0.829892462
20 0.223606797
21 0.248134054
22 -1.228678036
23 0.397688031
24 -0.110103548
25 0.200000000
26 -0.904823460
27 0.592637499
28 -0.398391504
29 0.172552248
30 -0.0984796071
31 1.508177542
32 0.176776695
33 0.541127244
34 -0.0829017692
35 -0.356332194
36 -0.451508834
37 0.574631832
38 -0.586822587
39 0.398497093
40 0.158113883
41 1.265176964
42 0.175457272
43 0.983977775
44 -0.868806571
45 -0.403841778
46 0.281207904
47 -1.775283798
48 -0.0778549654
49 -0.365136836
50 0.141421356
51 0.0365111157
52 -0.639806804
53 -0.0397142365
54 0.419057994
55 -0.777084221
56 -0.281705334
57 0.258444995
58 0.122012865
59 1.741269361
60 -0.0696355980
61 -1.007225726
62 1.066442567
63 0.719509136
64 0.125000000
65 -0.572260602
66 0.382634744
67 0.354353012
68 -0.0586204032
69 -0.123847951
70 -0.251964910
71 -0.881183484
72 -0.319264958
73 1.626697898
74 0.406326065
75 -0.0622839723
76 -0.414946231
77 1.384500629
78 0.281779996
79 -0.610543174
80 0.111803398
81 0.718458581
82 0.894615211
83 1.062387331
84 0.124067027
85 -0.0524316825
86 0.695777357
87 -0.0537361974
88 -0.614339018
89 -0.512103444
90 -0.285559260
91 1.019574381
92 0.198844015
93 -0.469676441
94 -1.255315212
95 -0.371139191
96 -0.0550517740
97 0.128654211
98 -0.258190732
99 1.569095371
100 0.100000000
101 -1.060951686
102 0.0258172575
103 -1.568999054
104 -0.452411730
105 0.110968922
106 -0.0280822059
107 0.0954923775
108 0.296318749
109 -0.908026590
110 -0.549481522
111 -0.178951765
112 -0.199195752
113 -0.777897494
114 0.182748209
115 0.177851494
116 0.0862761243
117 1.155513699
118 1.231263373
119 0.0934154823
120 -0.0492398035
121 2.019299435
122 -0.712216141
123 -0.394001235
124 0.754088771
125 0.0894427190
126 0.508769789
127 1.291775926
128 0.0883883476
129 -0.306430223
130 -0.404649352
131 -0.917155539
132 0.270563622
133 0.661244213
134 0.250565417
135 0.265035547
136 -0.0414508846
137 1.585777235
138 -0.0875737266
139 1.988068515
140 -0.178166097
141 0.552858622
142 -0.623090817
143 2.223473404
144 -0.225754417
145 0.0771677115
146 1.150249114
147 0.113710837
148 0.287315916
149 -0.532804237
150 -0.0440414192
151 -0.230421332
152 -0.293411293
153 0.105870673
154 0.978989783
155 0.674477501
156 0.199248546
157 0.304388960
158 -0.431719218
159 0.0123677185
160 0.0790569415
161 -0.316871943
162 0.508026934
163 -1.828923919
164 0.632588482
165 0.241999460
166 0.751221286
167 0.559492477
168 0.0877286363
169 0.637409750
170 -0.0370747983
171 0.749413425
172 0.491988887
173 0.641229471
174 -0.0379972296
175 -0.159356601
176 -0.434403285
177 -0.542251641
178 -0.362111817
179 0.779828771
180 -0.201920889
181 -0.928298971
182 0.720947959
183 0.313597799
184 0.140603952
185 0.256983167
186 -0.332111396
187 0.203708053
188 -0.887641899
189 -0.472221216
190 -0.262435039
191 0.567714486
192 -0.0389274827
193 -0.0596755710
194 0.0909722656
195 0.178213317
196 -0.182568418
197 0.0922880450
198 1.109517977
199 0.243682480
200 0.0707106781
201 -0.113934440
202 -0.750206131
203 -0.143368865
204 0.0182555578
205 0.565804339
206 -1.109449871
207 -0.360977742
208 -0.319903402
209 1.435142924
210 0.0784668777