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

$R= 12.9433745145$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.424107352
4 0.5
5 -0.447213595
6 -1.006995965
7 -0.659730655
8 0.353553390
9 1.028081750
10 -0.316227766
11 -1.379756391
12 -0.712053676
13 -1.181514907
14 -0.466500020
15 0.636880169
16 0.250000000
17 0.424027550
18 0.726963577
19 -0.572099020
20 -0.223606797
21 0.939527277
22 -0.975635100
23 0.910339733
24 -0.503497982
25 0.200000000
26 -0.835457203
27 -0.0399914278
28 -0.329865327
29 -0.508591216
30 0.450342286
31 1.585752411
32 0.176776695
33 1.964921220
34 0.299832756
35 0.295040518
36 0.514040875
37 -1.782397877
38 -0.404535097
39 1.682604066
40 -0.158113883
41 1.232120904
42 0.664346109
43 1.358058346
44 -0.689878195
45 -0.459772136
46 0.643707398
47 1.590786783
48 -0.356026838
49 -0.564755461
50 0.141421356
51 -0.603860752
52 -0.590757453
53 1.257092682
54 -0.0282782098
55 0.617045816
56 -0.233250010
57 0.814730421
58 -0.359628298
59 -1.792294082
60 0.318440084
61 -0.0154341115
62 1.121296283
63 -0.678257047
64 0.125000000
65 0.528389529
66 1.389409119
67 0.521040716
68 0.212013775
69 -1.296421508
70 0.208625151
71 -0.695454934
72 0.363481788
73 -0.820935381
74 -1.260345625
75 -0.284821470
76 -0.286049510
77 0.910267589
78 1.189780745
79 0.544755598
80 -0.111803398
81 -0.971129662
82 0.871241046
83 -1.126419784
84 0.469763638
85 -0.189630885
86 0.960292265
87 0.724288484
88 -0.487817550
89 -0.00604944677
90 -0.325107995
91 0.779481622
92 0.455169866
93 -2.258281655
94 1.124856121
95 0.255850460
96 -0.251748991
97 0.444692195
98 -0.399342416
99 -1.418502352
100 0.100000000
101 -0.696802585
102 -0.426994033
103 0.989576267
104 -0.417728601
105 -0.420169371
106 0.888898760
107 0.112282963
108 -0.0199957139
109 -0.557237783
110 0.436317281
111 2.538326279
112 -0.164932663
113 0.982389933
114 0.576101406
115 -0.407116305
116 -0.254295608
117 -1.214696159
118 -1.267343299
119 -0.279750247
120 0.225171143
121 0.903739590
122 -0.0109135649
123 -1.754673177
124 0.792876205
125 -0.0894427190
126 -0.479600157
127 -0.504923706
128 0.0883883476
129 -1.934047766
130 0.373627819
131 1.683865606
132 0.982460610
133 0.377492329
134 0.368431423
135 0.0178847102
136 0.149916378
137 -0.0342191900
138 -0.916708439
139 1.486971538
140 0.147520259
141 -2.263265266
142 -0.491760900
143 1.631380126
144 0.257020437
145 0.227448906
146 -0.580488975
147 0.809376380
148 -0.891198938
149 -0.411412663
150 -0.201399193
151 0.435377251
152 -0.202267548
153 0.450440113
154 0.643656385
155 -0.709170037
156 0.841302033