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

$R= 19.7788534901$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.073397522
4 0.5
5 0.447213595
6 -0.759006666
7 0.529490152
8 0.353553390
9 0.152182241
10 0.316227766
11 -0.934861798
12 -0.536698761
13 0.382560699
14 0.374406077
15 -0.480037965
16 0.250000000
17 0.532679672
18 0.107609094
19 -0.533430567
20 0.223606797
21 -0.568353418
22 -0.661047117
23 -1.165883010
24 -0.379503333
25 0.200000000
26 0.270511264
27 0.910045481
28 0.264745076
29 0.914051599
30 -0.339438100
31 0.406820534
32 0.176776695
33 1.003478338
34 0.376661408
35 0.236795195
36 0.0760911205
37 -0.233164340
38 -0.377192371
39 -0.410639707
40 0.158113883
41 1.105221046
42 -0.401886556
43 0.850765822
44 -0.467430899
45 0.0680579672
46 -0.824403782
47 -1.881634076
48 -0.268349380
49 -0.719640178
50 0.141421356
51 -0.571777040
52 0.191280349
53 -1.032786143
54 0.643499331
55 -0.418082906
56 0.187203038
57 0.572583049
58 0.646332084
59 -0.572102727
60 -0.240018982
61 0.630634198
62 0.287665558
63 0.0805789981
64 0.125000000
65 0.171086345
66 0.709566338
67 -1.566592076
68 0.266339836
69 1.251455935
70 0.167439488
71 1.426421606
72 0.0538045473
73 -0.589953644
74 -0.164872086
75 -0.214679504
76 -0.266715283
77 -0.495000116
78 -0.290366121
79 -1.695548106
80 0.111803398
81 -1.129022806
82 0.781509296
83 -1.675995982
84 -0.284176709
85 0.238221591
86 0.601582282
87 -0.981140721
88 -0.330523558
89 0.301826766
90 0.0481242501
91 0.202562123
92 -0.582941505
93 -0.436680153
94 -1.330516214
95 -0.238557402
96 -0.189751666
97 -1.534682419
98 -0.508862449
99 -0.142269363
100 0.100000000
101 -0.504404083
102 -0.404307422
103 1.368796619
104 0.135255632
105 -0.254175375
106 -0.730290085
107 -0.650143780
108 0.455022740
109 -1.233256277
110 -0.295629258
111 0.250278028
112 0.132372538
113 0.190525989
114 0.404877357
115 -0.521398733
116 0.457025799
117 0.0582189494
118 -0.404537718
119 0.282048647
120 -0.169719050
121 -0.126033437
122 0.445925717
123 -1.186341543
124 0.203410267
125 0.0894427190
126 0.0569779559
127 -0.480005638
128 0.0883883476
129 -0.913209843
130 0.120976315
131 -0.165644343
132 0.501739169
133 -0.282446228
134 -1.107747880
135 0.406984712
136 0.188330704
137 0.268219626
138 0.884912978
139 -1.201986135
140 0.118397597
141 2.019740689
142 1.008632390
143 -0.357640552
144 0.0380455602
145 0.408776302
146 -0.417160222
147 0.772467204
148 -0.116582170
149 -1.729712346
150 -0.151801333
151 -1.674316589
152 -0.188596185
153 0.0810593979
154 -0.350017939
155 0.181935673
156 -0.205319853
157 1.049174792
158 -1.198933563
159 1.108609228
160 0.0790569415
161 -0.617304031
162 -0.798339682
163 1.602565221
164 0.552610523
165 0.448769155
166 -1.185108124
167 1.871610057
168 -0.200943278
169 -0.853761423
170 0.168448102
171 -0.0817679280
172 0.425382911
173 0.358790541
174 -0.693771257
175 0.105898030
176 -0.233715449
177 0.613799548
178 0.213423753
179 -0.825263442
180 0.0340289836
181 0.727998652
182 0.143233051
183 -0.688916010
184 -0.412201891
185 -0.104274263
186 -0.308779497
187 -0.522887300
188 -0.940817038
189 0.435871136
190 -0.168685556