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

$R= 23.6526399392$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.698118604
4 0.5
5 -0.447213595
6 -0.493644399
7 1.595820524
8 -0.353553390
9 -0.512648432
10 0.316227766
11 1.553711127
12 0.349059302
13 1.022537692
14 -1.128415514
15 -0.312208131
16 0.250000000
17 0.989002727
18 0.362497183
19 0.557250579
20 -0.223606797
21 1.114058226
22 -1.098639673
23 0.259244586
24 -0.246822199
25 0.200000000
26 -0.723043336
27 -1.055995148
28 0.797910262
29 0.584732786
30 0.220764486
31 -0.649009203
32 -0.176776695
33 1.084681169
34 -0.699330534
35 -0.713672634
36 -0.256324216
37 1.502122068
38 -0.394035663
39 0.713835979
40 0.158113883
41 1.071173256
42 -0.787758126
43 -0.0839177540
44 0.776855563
45 0.229263348
46 -0.183313604
47 -0.128745935
48 0.174529651
49 1.546593293
50 -0.141421356
51 0.690438307
52 0.511268846
53 -0.171951559
54 0.746701330
55 -0.694840739
56 -0.564207757
57 0.389026755
58 -0.413468518
59 0.496411764
60 -0.156104065
61 -1.391571592
62 0.458918808
63 -0.818055823
64 0.125000000
65 -0.457292758
66 -0.766985410
67 -1.883876446
68 0.494501363
69 0.180964591
70 0.504642759
71 -1.487533202
72 0.181248591
73 0.537824133
74 -1.062160701
75 0.139623720
76 0.278625289
77 2.479441383
78 -0.504758262
79 1.749767375
80 -0.111803398
81 -0.224536105
82 -0.757433873
83 -1.959617087
84 0.557029113
85 -0.442295465
86 0.0593388129
87 0.408224294
88 -0.549319836
89 -1.262234346
90 -0.162113668
91 1.631770685
92 0.129622293
93 -0.453077364
94 0.0910371243
95 -0.249210035
96 -0.123411099
97 -0.483199316
98 -1.093606605
99 -0.796493757
100 0.100000000
101 0.425230487
102 -0.488213608
103 -1.081179177
104 -0.361521668
105 -0.498221984
106 0.121588113
107 1.249137899
108 -0.527997574
109 0.670663042
110 0.491326598
111 1.048685787
112 0.398955131
113 0.0996362563
114 -0.275083456
115 -0.115937703
116 0.292366393
117 -0.524204469
118 -0.351016124
119 1.577939754
120 0.110382243
121 1.413363884
122 0.983989709
123 0.747236200
124 -0.324504601
125 -0.0894427190
126 0.578452820
127 -0.880916547
128 -0.0883883476
129 -0.0610948186
130 0.323354810
131 0.885503688
132 0.542340584
133 0.890813794
134 1.332101810
135 0.472255387
136 -0.349665267
137 -0.592831703
138 -0.127961290
139 1.488775126
140 -0.356836317
141 -0.0742602174
142 1.051844814
143 1.546742373
144 -0.128162108
145 -0.261500451
146 -0.380299091
147 1.113231594
148 0.751061034
149 -0.851002283
150 -0.0987288799