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

$R= 9.95201540908$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.423900207
4 0.5
5 -0.447213595
6 0.299742711
7 0.516637334
8 -0.353553390
9 -0.820308613
10 0.316227766
11 -0.550388015
12 -0.211950103
13 -1.866956592
14 -0.365317762
15 0.189573936
16 0.250000000
17 0.745487806
18 0.580045783
19 1.100316447
20 -0.223606797
21 -0.219002673
22 0.389183097
23 0.493389701
24 0.149871355
25 0.200000000
26 1.320137666
27 0.771629199
28 0.258318667
29 -0.607809823
30 -0.134049015
31 0.776882572
32 -0.176776695
33 0.233309593
34 -0.527139483
35 -0.231047240
36 -0.410154306
37 1.248489895
38 -0.778041221
39 0.791403287
40 0.158113883
41 -0.802269549
42 0.154858275
43 1.071628846
44 -0.275194007
45 0.366853164
46 -0.348879203
47 0.503198781
48 -0.105975051
49 -0.733085864
50 -0.141421356
51 -0.316012436
52 -0.933478296
53 1.297445148
54 -0.545624239
55 0.246141003
56 -0.182658881
57 -0.466424370
58 0.429786447
59 0.174573425
60 0.0947869680
61 1.616898194
62 -0.549338935
63 -0.423802056
64 0.125000000
65 0.834928370
66 -0.164974796
67 -0.486731595
68 0.372743903
69 -0.209147996
70 0.163375070
71 -1.813984176
72 0.290022891
73 -0.194381912
74 -0.882815671
75 -0.0847800415
76 0.550158223
77 -0.284350997
78 -0.559606631
79 1.437636099
80 -0.111803398
81 0.493214835
82 0.567290239
83 1.759715059
84 -0.109501336
85 -0.333392282
86 -0.757756023
87 0.257650710
88 0.194591548
89 -0.468639790
90 -0.259404360
91 -0.964539478
92 0.246694850
93 -0.329320684
94 -0.355815270
95 -0.492076474
96 0.0749356778
97 0.761515900
98 0.518369985
99 0.451488029
100 0.100000000
101 -1.873277999
102 0.223454536
103 -0.522953000
104 0.660068833
105 0.0979409730
106 -0.917432262
107 1.580006999
108 0.385814599
109 0.889337999
110 -0.174047972
111 -0.529235126
112 0.129159333
113 -0.714049999
114 0.329811835
115 -0.220650582
116 -0.303904911
117 1.531480574
118 -0.123442052
119 0.385146833
120 -0.0670245078
121 -0.697073032
122 -1.143319677
123 0.340082228
124 0.388441286
125 -0.0894427190
126 0.299673307
127 -0.0442999999
128 -0.0883883476
129 -0.454263690
130 -0.590383512
131 -1.258000000
132 0.116654796
133 0.568464556
134 0.344171211
135 -0.345083068
136 -0.263569741
137 0.704999999
138 0.147889966
139 -0.540000000
140 -0.115523620
141 -0.213306068
142 1.282680512
143 1.027550533
144 -0.205077153
145 0.271820816
146 0.137448768
147 0.310755250
148 0.624244947
149  0
150 0.0599485422