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

$R= 11.0484521159$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.727958123
4 0.5
5 -0.447213595
6 -1.221850906
7 1.979290422
8 -0.353553390
9 1.985839276
10 0.316227766
11 -0.116772910
12 0.863979061
13 0.374262914
14 -1.399569679
15 -0.772766365
16 0.250000000
17 -0.356881387
18 -1.404200418
19 -0.332696604
20 -0.223606797
21 3.420130964
22 0.0825709166
23 -0.563583475
24 -0.610925453
25 0.200000000
26 -0.264643844
27 1.703488986
28 0.989645211
29 -0.142268350
30 0.546428337
31 1.422310111
32 -0.176776695
33 -0.201778698
34 0.252353248
35 -0.885165586
36 0.992919638
37 -0.250143499
38 0.235252025
39 0.646710643
40 0.158113883
41 0.751308339
42 -2.418397797
43 1.399326049
44 -0.0583864551
45 -0.888094322
46 0.398513697
47 -0.381837656
48 0.431989530
49 2.917590578
50 -0.141421356
51 -0.616676092
52 0.187131457
53 -0.861283475
54 -1.204548614
55 0.0522224330
56 -0.699784839
57 -0.574885800
58 0.100598915
59 1.370672755
60 -0.386383182
61 -0.909939883
62 -1.005725124
63 3.930552661
64 0.125000000
65 -0.167375463
66 0.142679086
67 -0.413454521
68 -0.178440693
69 -0.973848644
70 0.625906588
71 0.539087862
72 -0.702100209
73 -0.859809500
74 0.176878164
75 0.345591624
76 -0.166348302
77 -0.231127503
78 -0.457293481
79 -0.652037206
80 -0.111803398
81 0.957718353
82 -0.531255221
83 0.484594131
84 1.710065482
85 0.159602208
86 -0.989472939
87 -0.245833749
88 0.0412854583
89 -1.220907596
90 0.627977518
91 0.740774992
92 -0.281791737
93 2.457692336
94 0.269999996
95 0.148786444
96 -0.305462726
97 -1.077635517
98 -2.063048082
99 -0.231892135
100 0.100000000
101 -1.027062645
102 0.436055846
103 0.665020520
104 -0.132321922
105 -1.529529065
106 0.609019385
107 1.300830702
108 0.851744493
109 -0.00241825384
110 -0.0369268365
111 -0.432236161
112 0.494822605
113 -0.373546056
114 0.406505648
115 0.252042192
116 -0.0711341753
117 0.743232942
118 -0.969212000
119 -0.706374320
120 0.273214168
121 -0.986355918
122 0.643424662
123 1.298258066
124 0.711155055
125 -0.0894427190
126 -2.779320440
127 0.832562601
128 -0.0883883476
129 2.417922741
130 0.118352325
131 -0.655512710
132 -0.100889349
133 -0.658757503
134 0.292356495
135 -0.761823434
136 0.126176624
137 -1.625196051
138 0.688614980
139 -1.399320983
140 -0.442582793
141 -0.658275637
142 -0.381192683
143 -0.0440627101
144 0.496459819
145 0.0636243406
146 0.607977127
147 5.033125574
148 -0.125071749
149 1.088836414
150 -0.244370181
151 -1.049438967
152 0.117626012
153 -0.687687705
154 0.163431824
155 -0.636076418
156 0.323355321