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

$R= 18.2714714374$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.544818787
4 0.5
5 0.447213595
6 -0.385245059
7 1.316924380
8 0.353553390
9 -0.703172488
10 0.316227766
11 -0.743157544
12 -0.272409393
13 -0.594275197
14 0.931206159
15 -0.243650369
16 0.250000000
17 -1.543480682
18 -0.497218034
19 0.0479396351
20 0.223606797
21 -0.717485144
22 -0.525491738
23 1.386346641
24 -0.192622529
25 0.200000000
26 -0.420216022
27 0.927920370
28 0.658462190
29 -0.729376869
30 -0.172286828
31 1.003138646
32 0.176776695
33 0.404886192
34 -1.091405656
35 0.588946487
36 -0.351586244
37 -1.239418245
38 0.0338984411
39 0.323772292
40 0.158113883
41 -1.632664181
42 -0.507338611
43 -1.334186531
44 -0.371578772
45 -0.314468296
46 0.980295110
47 0.393743335
48 -0.136204696
49 0.734289823
50 0.141421356
51 0.840917274
52 -0.297137598
53 -0.331646297
54 0.656138786
55 -0.332350157
56 0.465603079
57 -0.0261184139
58 -0.515747330
59 0.0819616972
60 -0.121825184
61 0.804271453
62 0.709326139
63 -0.926024993
64 0.125000000
65 -0.265767947
66 0.286297772
67 -0.805660637
68 -0.771740341
69 -0.755307696
70 0.416448054
71 -0.707245372
72 -0.248609017
73 -1.805500128
74 -0.876401045
75 -0.108963757
76 0.0239698175
77 -0.978682288
78 0.228941583
79 0.341476929
80 0.111803398
81 0.197624036
82 -1.154467913
83 1.037569396
84 -0.358742572
85 -0.690265545
86 -0.943412344
87 0.397378221
88 -0.262745869
89 -1.698958813
90 -0.222362665
91 -0.782615496
92 0.693173320
93 -0.546528781
94 0.278418582
95 0.0214392566
96 -0.0963112648
97 -1.627162105
98 0.519221313
99 0.522567940
100 0.100000000
101 1.850484072
102 0.594618307
103 -1.187906881
104 -0.210108011
105 -0.320869111
106 -0.234509345
107 -0.485057037
108 0.463960185
109 -1.230842684
110 -0.235007049
111 0.675258341
112 0.329231095
113 -0.242904535
114 -0.0184685076
115 0.619993065
116 -0.364688434
117 0.417877921
118 0.0579556719
119 -2.032647257
120 -0.0861434140
121 -0.447716802
122 0.568705798
123 0.889505944
124 0.501569323
125 0.0894427190
126 -0.654798552
127 0.212503206
128 0.0883883476
129 0.726889426
130 -0.187926318
131 -0.291352457
132 0.202443096
133 0.0631352755
134 -0.569688100
135 0.414978605
136 -0.545702828
137 1.202339338
138 -0.534083194
139 0.476984232
140 0.294473243
141 -0.214509530
142 -0.500097999
143 0.441624925
144 -0.175793122
145 -0.326187252
146 -1.276681384
147 -0.400012368
148 -0.619709122
149 -0.700079720
150 -0.0770490118
151 1.117458305
152 0.0169492205
153 1.085390118
154 -0.692032882
155 0.448617240
156 0.161886146
157 0.474279711
158 0.241460652
159 0.181014618
160 0.0790569415
161 1.825905786
162 0.139741296
163 -1.037871658
164 -0.816332090
165 0.181070609
166 0.733672356
167 0.216575030
168 -0.253669305
169 -0.648500172
170 -0.488091447
171 -0.0376280189
172 -0.667093265
173 -0.715876024
174 0.280988835
175 0.263384876
176 -0.185789386
177 -0.0671500117
178 -1.201345297
179 1.277995882
180 -0.157234148