Properties

Level 10
Symmetry odd
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

$R= 19.7518011761$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.176346587
4 0.5
5 -0.447213595
6 -0.124695867
7 -1.867394079
8 0.353553390
9 -0.968901881
10 -0.316227766
11 -0.638315825
12 -0.0881732937
13 -0.914754631
14 -1.320447016
15 0.0788645914
16 0.250000000
17 -0.923722899
18 -0.685117090
19 0.0674552659
20 -0.223606797
21 0.329308573
22 -0.451357448
23 1.688635832
24 -0.0623479339
25 0.200000000
26 -0.646829203
27 0.347209127
28 -0.933697039
29 0.745850485
30 0.0557656873
31 -0.868893034
32 0.176776695
33 0.112564817
34 -0.653170726
35 0.835124020
36 -0.484450940
37 0.120453236
38 0.0476980759
39 0.161313857
40 -0.158113883
41 0.584524155
42 0.232856325
43 -1.120776485
44 -0.319157912
45 0.433306093
46 1.194045848
47 0.691784457
48 -0.0440866468
49 2.487160649
50 0.141421356
51 0.162895381
52 -0.457377315
53 -0.106515966
54 0.245513928
55 0.285463515
56 -0.660223508
57 -0.0118955059
58 0.527395936
59 -0.518133520
60 0.0394322957
61 -1.621748987
62 -0.614400156
63 1.809321636
64 0.125000000
65 0.409090707
66 0.0795953458
67 -1.915750656
68 -0.461861449
69 -0.297785166
70 0.590521858
71 -1.550361909
72 -0.342558545
73 1.395070455
74 0.0851733003
75 -0.0352693174
76 0.0337276329
77 1.191987194
78 0.114066122
79 1.067313984
80 -0.111803398
81 0.907672736
82 0.413320994
83 0.886461432
84 0.164654286
85 0.413101439
86 -0.792508652
87 -0.131528187
88 -0.225678724
89 0.282673597
90 0.306393677
91 1.708207384
92 0.844317916
93 0.153226321
94 0.489165481
95 -0.0301669120
96 -0.0311739669
97 -0.936702776
98 1.758688160
99 0.618465404
100 0.100000000
101 0.433505072
102 0.115184428
103 0.839134502
104 -0.323414601
105 -0.147271271
106 -0.0753181622
107 1.624441216
108 0.173604563
109 -1.297192865
110 0.201853187
111 -0.0212415177
112 -0.466848519
113 0.497547067
114 -0.00841139292
115 -0.755180902
116 0.372925242
117 0.886307480
118 -0.366375726
119 1.724954674
120 0.0278828436
121 -0.592552907
122 -1.146749706
123 -0.103078843
124 -0.434446517
125 -0.0894427190
126 1.279383598
127 0.829149619
128 0.0883883476
129 0.197645029
130 0.289270813
131 0.825806280
132 0.0562824087
133 -0.125965616
134 -1.354640279
135 -0.155276642
136 -0.326585363
137 0.702337514
138 -0.210565910
139 -0.886433133
140 0.417562010
141 -0.121994215
142 -1.096271419
143 0.583902623
144 -0.242225470
145 -0.333554477
146 0.986463779
147 -0.438601691
148 0.0602266182
149 0.0965186277
150 -0.0249391735
151 -0.525338181
152 0.0238490379
153 0.894990815
154 0.842862227
155 0.388580778
156 0.0806569288
157 1.510808393
158 0.754704956
159 0.0188335685
160 -0.0790569415
161 -3.153349419
162 0.641821546
163 -1.178289942
164 0.292262077
165 -0.0503405168
166 0.626822890
167 -0.928090878
168 0.116428162
169 -0.163046803
170 0.292106829
171 -0.0650141587
172 -0.560388242
173 0.400086347
174 -0.0930044736
175 -0.373478815
176 -0.159578956
177 0.0899886466
178 0.199880417
179 -0.874126903
180 0.216653046
181 0.420449329
182 1.207885025
183 0.293538546
184 0.597022924
185 -0.0538683249
186 0.108347370
187 0.607136432
188 0.345892228
189 -0.648833986
190 -0.0213312280
191 0.555932141
192 -0.0220433234