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

$R= 23.5240326785$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.574187165
4 0.5
5 0.447213595
6 1.113118419
7 -0.102639145
8 0.353553390
9 1.478065231
10 0.316227766
11 -0.963101465
12 0.787093582
13 1.193470716
14 -0.0725768360
15 0.703997902
16 0.250000000
17 -0.724895091
18 1.045149948
19 0.879568072
20 0.223606797
21 -0.161573226
22 -0.681015577
23 1.136306152
24 0.556559209
25 0.200000000
26 0.843911236
27 0.752564151
28 -0.0513195729
29 0.210817053
30 0.497801690
31 -0.696299778
32 0.176776695
33 -1.516101966
34 -0.512578234
35 -0.0459016214
36 0.739032615
37 1.727690370
38 0.621948548
39 1.878746283
40 0.158113883
41 1.371808455
42 -0.114249523
43 -1.056254729
44 -0.481550732
45 0.661010866
46 0.803489785
47 1.642101496
48 0.393546791
49 -0.989465205
50 0.141421356
51 -1.141120549
52 0.596735358
53 1.696342982
54 0.532143214
55 -0.430712069
56 -0.0362884180
57 1.384604770
58 0.149070168
59 -0.0897290642
60 0.351998951
61 0.241456078
62 -0.492358294
63 -0.151707352
64 0.125000000
65 0.533736330
66 -1.072045981
67 0.844041916
68 -0.362447545
69 1.788758560
70 -0.0324573478
71 -0.512564298
72 0.522574974
73 -0.582618136
74 1.221661576
75 0.314837433
76 0.439784036
77 0.0988519118
78 1.328474237
79 0.663508623
80 0.111803398
81 -0.293388403
82 0.970015061
83 -1.328583075
84 -0.0807866130
85 -0.324182940
86 -0.746884881
87 0.331865499
88 -0.340507788
89 -0.947987451
90 0.467405266
91 -0.122496815
92 0.568153076
93 -1.096106173
94 1.161141103
95 0.393354800
96 0.278279604
97 -1.452153096
98 -0.699657556
99 -1.423526790
100 0.100000000
101 -0.575735436
102 -0.806894078
103 1.301418938
104 0.421955618
105 -0.0722577433
106 1.199495626
107 -1.881494756
108 0.376282075
109 -0.385047455
110 -0.304559424
111 2.719708006
112 -0.0256597864
113 -1.423692695
114 0.979063422
115 0.508171559
116 0.105408526
117 1.764027570
118 -0.0634480297
119 0.0744026122
120 0.248900845
121 -0.0724355657
122 0.170735230
123 2.159483262
124 -0.348149889
125 0.0894427190
126 -0.107273298
127 1.365456791
128 0.0883883476
129 -1.662742642
130 0.377408578
131 1.114685509
132 -0.758050983
133 -0.0902781118
134 0.596827762
135 0.336556919
136 -0.256289117
137 1.558318345
138 1.264843307
139 1.625489992
140 -0.0229508107
141 2.584975101
142 -0.362437691
143 -1.149433448
144 0.369516307
145 0.0942802524
146 -0.411973234
147 -1.557603457
148 0.863845185
149 0.321030070
150 0.222623683
151 -0.974749429
152 0.310974274
153 -1.071442053
154 0.0698988572
155 -0.311394727
156 0.939373141
157 -0.482150877
158 0.469171446
159 2.670361557
160 0.0790569415
161 -0.116628335
162 -0.207456929
163 0.640811352
164 0.685904227
165 -0.678021411
166 -0.939450102
167 0.561191252
168 -0.0571247619
169 0.424343821
170 -0.229231955
171 1.300060358
172 -0.528127364
173 -0.466363391
174 0.234664345
175 -0.0205278291
176 -0.240775366
177 -0.141342920
178 -0.670328355
179 -1.346655026
180 0.330505433
181 0.514786525
182 -0.0866183285
183 0.380296877
184 0.401744892
185 0.772646622
186 -0.775064108
187 0.699102312
188 0.821050748
189 -0.0770611506
190 0.278143846
191 -1.372900741
192 0.196773395
193 -0.567050189
194 -1.026827301
195 0.840200880
196 -0.494732602
197 1.124447458
198 -1.006585446
199 0.0767147422
200 0.0707106781
201 1.320299139
202 -0.407106431
203 -0.0225363174
204 -0.570560274
205 0.613491391
206 0.920242156
207 1.697522566
208 0.298367679
209 -0.944564501
210 -0.0510939403