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

$R= 26.4098588141$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.611223823
4 0.5
5 0.447213595
6 1.139307291
7 0.0824202305
8 -0.353553390
9 1.596042210
10 -0.316227766
11 0.617568532
12 -0.805611911
13 -1.896360034
14 -0.0582799039
15 -0.720561199
16 0.250000000
17 1.706995149
18 -1.128572270
19 1.017429057
20 0.223606797
21 -0.132797439
22 -0.436686897
23 -0.179344271
24 0.569653645
25 0.200000000
26 1.340929039
27 -0.960357410
28 0.0412101152
29 1.484286985
30 0.509513710
31 1.478376138
32 -0.176776695
33 -0.995041133
34 -1.207027845
35 0.0368594476
36 0.798021105
37 0.220576829
38 -0.719430985
39 3.055460465
40 -0.158113883
41 0.469221700
42 0.0939019696
43 1.192453467
44 0.308784266
45 0.713771775
46 0.126815550
47 -0.948439691
48 -0.402805955
49 -0.993206905
50 -0.141421356
51 -2.750351252
52 -0.948180017
53 0.973504569
54 0.679075237
55 0.276185044
56 -0.0291399519
57 -1.639305935
58 -1.049549392
59 0.374975125
60 -0.360280599
61 -0.149647461
62 -1.045369792
63 0.131546167
64 0.125000000
65 -0.848077989
66 0.703600332
67 -1.090583532
68 0.853497574
69 0.288963763
70 -0.0260635653
71 0.339768181
72 -0.564286135
73 0.187658560
74 -0.155971371
75 -0.322244764
76 0.508714528
77 0.0509001408
78 -2.160536815
79 -0.692919240
80 0.111803398
81 -0.0486914718
82 -0.331789846
83 -0.390440371
84 -0.0663987195
85 0.763391438
86 -0.843191933
87 -2.391518551
88 -0.218343448
89 1.651531611
90 -0.504712862
91 -0.156298431
92 -0.0896721358
93 -2.381994854
94 0.670648137
95 0.455008106
96 0.284826822
97 -0.482384656
98 0.702303338
99 0.985665446
100 0.100000000
101 -0.744240000
102 1.944792021
103 0.181410576
104 0.670464519
105 -0.0593888201
106 -0.688371682
107 0.387992671
108 -0.480178705
109 -1.149886242
110 -0.195292317
111 -0.355398642
112 0.0206050576
113 0.251103121
114 1.159164343
115 -0.0802051966
116 0.742143492
117 -3.026670661
118 -0.265147453
119 0.140690933
120 0.254756855
121 -0.618609107
122 0.105816734
123 -0.756021182
124 0.739188069
125 0.0894427190
126 -0.0930171867
127 -1.351904909
128 -0.0883883476
129 -1.921309435
130 0.599681697
131 1.557067729
132 -0.497520566
133 0.0838567374
134 0.771159011
135 -0.429484890
136 -0.603513922
137 0.853101420
138 -0.204328236
139 -1.702379425
140 0.0184297238
141 1.528148626
142 -0.240252385
143 -1.171132292
144 0.399010552
145 0.663793319
146 -0.132694640
147 1.600278606
148 0.110288414
149 1.069430342
150 0.227861458
151 0.993918458
152 -0.359715492
153 2.724436345
154 -0.0359918347
155 0.661149908
156 1.527730232
157 -1.754706854
158 0.489967893
159 -1.568533841
160 -0.0790569415
161 -0.0147818873
162 0.0344300699
163 0.235126667
164 0.234610850
165 -0.444995922
166 0.276083034
167 0.354458575
168 0.0469509848
169 2.596182513
170 -0.539799262
171 1.623859115
172 0.596226733
173 1.622019413
174 1.691058985
175 0.0164840461
176 0.154392133
177 -0.604170142
178 -1.167809202
179 -0.203992707
180 0.356885887
181 -0.763991817
182 0.110519680
183 0.241130252
184 0.0634077753
185 0.0986449568
186 1.684324714
187 1.054213898
188 -0.474219845
189 -0.0792182471
190 -0.321739317
191 -1.822554986
192 -0.201402977
193 0.137662097
194 0.341097461
195 1.366443460
196 -0.496603452
197 1.510848222
198 -0.696970721
199 -0.138847125
200 -0.0707106781
201 1.757602454
202 0.526257151
203 0.124053549
204 -1.375175626
205 0.209842323
206 -0.128276648
207 -0.287295332
208 -0.474090008
209 0.630889841
210 0.0419942374
211 1.032614118
212 0.486752284
213 -0.555962496
214 -0.274352249
215 0.533281402
216 0.339537618
217 0.0910333206
218 0.813092359
219 -0.261041644
220 0.138092522
221 -3.261768538
222 0.251304789