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

$R= 21.2395974784$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.674305845
4 0.5
5 -0.447213595
6 -1.183913017
7 -1.689117430
8 0.353553390
9 1.803300063
10 -0.316227766
11 -1.248361619
12 -0.837152922
13 1.378748742
14 -1.194386389
15 0.748772337
16 0.250000000
17 1.214302494
18 1.275125703
19 0.370205175
20 -0.223606797
21 2.828099186
22 -0.882724966
23 -0.815952323
24 -0.591956508
25 0.200000000
26 0.974922585
27 -1.344969992
28 -0.844558715
29 -0.738262301
30 0.529461997
31 0.265722619
32 0.176776695
33 2.090139157
34 0.858641528
35 0.755396279
36 0.901650031
37 1.295824086
38 0.261774589
39 -2.308447079
40 -0.158113883
41 1.582600279
42 1.999768112
43 0.189487142
44 -0.624180809
45 -0.806460305
46 -0.576965421
47 0.351340973
48 -0.418576461
49 1.853117693
50 0.141421356
51 -2.033113764
52 0.689374371
53 -0.413492270
54 -0.951037402
55 0.558284288
56 -0.597193194
57 -0.619836688
58 -0.522030279
59 0.601409482
60 0.374386168
61 -1.018484606
62 0.187894266
63 -3.045985569
64 0.125000000
65 -0.616595182
66 1.477951571
67 -0.819264024
68 0.607151247
69 1.366153744
70 0.534145831
71 0.337844842
72 0.637562851
73 -0.886938751
74 0.916285999
75 -0.334861169
76 0.185102587
77 2.108629371
78 -1.632318583
79 -1.370757570
80 -0.111803398
81 0.448591056
82 1.119067389
83 -0.708454989
84 1.414049593
85 -0.543052584
86 0.133987643
87 1.236076887
88 -0.441362483
89 0.191741515
90 -0.570253550
91 -2.328868533
92 -0.407976161
93 -0.444900934
94 0.248435585
95 -0.165560787
96 -0.295978254
97 -0.725378182
98 1.310352087
99 -2.251170588
100 0.100000000
101 0.796240934
102 -1.437628529
103 -1.145981677
104 0.487461292
105 -1.264764405
106 -0.292383188
107 -0.367215947
108 -0.672484996
109 1.682203746
110 0.394766606
111 -2.169605842
112 -0.422279357
113 -0.782364304
114 -0.438290725
115 0.364904972
116 -0.369131150
117 2.486297695
118 0.425260723
119 -2.051099507
120 0.264730998
121 0.558406732
122 -0.720177371
123 -2.649756898
124 0.132861309
125 -0.0894427190
126 -2.153837051
127 0.772016262
128 0.0883883476
129 -0.317259429
130 -0.435998634
131 1.491824599
132 1.045069578
133 -0.625320036
134 -0.579307147
135 0.601488866
136 0.429320764
137 -0.599233700
138 0.966016577
139 0.919766670
140 0.377698139
141 -0.588252306
142 0.238892378
143 -1.721176970
144 0.450825015
145 0.330160938
146 -0.627160405
147 -3.102686068
148 0.647912043
149 -0.560013019
150 -0.236782603
151 -0.126429064
152 0.130887294
153 2.189751478
154 1.491026127
155 -0.118834768
156 -1.154223539
157 -0.723530431
158 -0.969271973
159 0.692312072
160 -0.0790569415
161 1.378245828
162 0.317201778
163 -0.153766025
164 0.791300139
165 -0.934738647
166 -0.500953327
167 -1.167240172
168 0.999884056
169 0.900955862
170 -0.383996165
171 0.667565009
172 0.0947435711
173 -0.575060192
174 0.874038349
175 -0.337823486
176 -0.312090404
177 -1.006825994
178 0.135581726
179 0.685693648
180 -0.403230152
181 -0.521328185
182 -1.646758732
183 1.705454565
184 -0.288482710
185 -0.579510149
186 -0.314592468
187 -1.516854114
188 0.175670486
189 2.271928778
190 -0.117069155
191 1.564780958
192 -0.209288230
193 -1.890411977
194 -0.512919832
195 1.032368918
196 0.926558846
197 0.103841660
198 -1.591817988