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

$R= 13.7422588437$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.550334059
4 0.5
5 -0.447213595
6 0.389144945
7 -0.880993645
8 0.353553390
9 -0.697132422
10 -0.316227766
11 1.664911728
12 0.275167029
13 -0.327949010
14 -0.622956580
15 -0.246116873
16 0.250000000
17 1.597636852
18 -0.492947063
19 1.664547309
20 -0.223606797
21 -0.484840809
22 1.177270373
23 0.459804834
24 0.194572472
25 0.200000000
26 -0.231894968
27 -0.933989776
28 -0.440496822
29 0.461960031
30 -0.174030910
31 -1.266909458
32 0.176776695
33 0.916257630
34 1.129699852
35 0.393992335
36 -0.348566211
37 0.790853318
38 1.177012690
39 -0.180481510
40 -0.158113883
41 0.756522784
42 -0.342834224
43 0.0940127953
44 0.832455864
45 0.311767097
46 0.325131116
47 1.745087957
48 0.137583514
49 -0.223850197
50 0.141421356
51 0.879233974
52 -0.163974505
53 0.877609165
54 -0.660430504
55 -0.744571160
56 -0.311478290
57 0.916057078
58 0.326655071
59 0.696835404
60 -0.123058436
61 -0.543097797
62 -0.895840269
63 0.614169234
64 0.125000000
65 0.146663255
66 0.647891983
67 -0.555203600
68 0.798818426
69 0.253046261
70 0.278594652
71 -0.475185029
72 -0.246473531
73 0.0155155004
74 0.559217744
75 0.110066811
76 0.832273654
77 -1.466776652
78 -0.127619699
79 -1.155410027
80 -0.111803398
81 0.183126036
82 0.534942391
83 0.121813848
84 -0.242420404
85 -0.714484920
86 0.0664770851
87 0.254232335
88 0.588635186
89 1.250836962
90 0.220452628
91 0.288920996
92 0.229902417
93 -0.697223434
94 1.233963528
95 -0.744408187
96 0.0972862363
97 -0.218507329
98 -0.158285992
99 -1.160663981
100 0.100000000
101 -1.345206145
102 0.621712305
103 -1.420708959
104 -0.115947484
105 0.216827401
106 0.620563391
107 1.217972500
108 -0.466994888
109 1.425380176
110 -0.526491316
111 0.435233945
112 -0.220248411
113 -0.602223821
114 0.647750172
115 -0.205630973
116 0.230980015
117 0.228625554
118 0.492737040
119 -1.407510483
120 -0.0870154551
121 1.771934621
122 -0.384028135
123 0.416334939
124 -0.633454729
125 -0.0894427190
126 0.434283230
127 -1.883216511
128 0.0883883476
129 0.0517424477
130 0.103706582
131 -0.0674155592
132 0.458128815
133 -1.466446899
134 -0.392588230
135 0.417692925
136 0.564849926
137 0.148787859
138 0.178930727
139 0.294259624
140 0.196996167
141 0.961186234
142 -0.336006556
143 -0.545958567
144 -0.174283105
145 -0.206594806
146 0.0109711155
147 -0.119870319
148 0.395426659
149 1.202927261
150 0.0778289891
151 0.596292998
152 0.588506345
153 -1.115470116
154 -1.037167717
155 0.566579134
156 -0.0902407550
157 -0.539389956
158 -0.816998265
159 0.514652366
160 -0.0790569415
161 -0.410016326
162 0.129489662