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

$R= 11.5070658355$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.920617422
4 0.5
5 0.447213595
6 -1.358081603
7 -0.286223952
8 0.353553390
9 2.688771282
10 0.316227766
11 -0.239799522
12 -0.960308711
13 1.375875168
14 -0.202390897
15 -0.858926222
16 0.250000000
17 -0.165991617
18 1.901248406
19 -1.755384022
20 0.223606797
21 0.549726710
22 -0.169563868
23 -0.433282186
24 -0.679040801
25 0.200000000
26 0.972890661
27 -3.243483547
28 -0.143111976
29 -0.182073571
30 -0.607352556
31 -1.127084522
32 0.176776695
33 0.460563141
34 -0.117373798
35 -0.128003242
36 1.344385641
37 -0.198006399
38 -1.241243945
39 -2.642529819
40 0.158113883
41 -0.977251822
42 0.388715484
43 1.006498052
44 -0.119899761
45 1.202455072
46 -0.306376772
47 0.936622365
48 -0.480154355
49 -0.918075848
50 0.141421356
51 0.318806392
52 0.687937584
53 -0.863115439
54 -2.293489210
55 -0.107241606
56 -0.101195448
57 3.371421136
58 -0.128745456
59 -0.207210153
60 -0.429463111
61 -0.630939422
62 -0.796969109
63 -0.769590744
64 0.125000000
65 0.615310081
66 0.325667320
67 0.605983948
68 -0.0829958086
69 0.832169316
70 -0.0905119611
71 0.0755723695
72 0.950624203
73 -0.226608256
74 -0.140011668
75 -0.384123484
76 -0.877692011
77 0.0686363691
78 -1.868550755
79 -1.271383387
80 0.111803398
81 3.540719728
82 -0.691021390
83 -0.887924562
84 0.274863355
85 -0.0742337080
86 0.711701597
87 0.349693685
88 -0.0847819343
89 -1.202443651
90 0.850264135
91 -0.393808411
92 -0.216641093
93 2.164698197
94 0.662292026
95 -0.785031600
96 -0.339520400
97 -0.568421488
98 -0.649177658
99 -0.644765977
100 0.100000000
101 1.233074656
102 0.225430161
103 -0.0997958364
104 0.486445330
105 0.245845258
106 -0.610314779
107 -1.170970299
108 -1.621741773
109 -0.481052164
110 -0.0758312673
111 0.380296371
112 -0.0715559881
113 -1.113778407
114 2.383954747
115 -0.193769684
116 -0.0910367856
117 3.699435817
118 -0.146519704
119 0.0475194636
120 -0.303676278
121 -0.942464011
122 -0.446141544
123 1.876958900
124 -0.563542261
125 0.0894427190
126 -0.544182833
127 -0.555927630
128 0.0883883476
129 -1.933160238
130 0.435089930
131 -1.485225380
132 0.230281570
133 0.502812736
134 0.428495359
135 -1.450529939
136 -0.0586868991
137 0.997820666
138 0.588432567
139 1.889813481
140 -0.0640016214
141 -1.798476642
142 0.0534377349
143 -0.330015147
144 0.672192820
145 -0.0814257764
146 -0.160236234
147 1.775863928
148 -0.0990031999
149 -1.091524063
150 -0.271616320
151 1.783863419
152 -0.620621972
153 -0.455216092
154 0.0485332420
155 -0.504047521
156 -1.321264909