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

$R= 19.32930345$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.960672378
4 0.5
5 -0.447213595
6 -0.679297953
7 -0.642095721
8 -0.353553390
9 -0.0798866423
10 0.316227766
11 -0.507040338
12 0.480336189
13 1.172287771
14 0.454030238
15 -0.429625748
16 0.250000000
17 1.587227072
18 0.0564883865
19 -0.239508933
20 -0.223606797
21 -0.614136607
22 0.358531662
23 0.983377825
24 -0.339648976
25 0.200000000
26 -0.828932632
27 -1.035755998
28 -0.321047860
29 -0.808707834
30 0.303791279
31 -1.283069183
32 -0.176776695
33 -0.488366358
34 -1.122339026
35 0.287153936
36 -0.0399433211
37 1.367728634
38 0.169358390
39 1.123242006
40 0.158113883
41 -0.605673308
42 0.434260159
43 1.055928571
44 -0.253520169
45 0.0357263925
46 -0.695353128
47 -0.637560994
48 0.240168094
49 -0.590804885
50 -0.141421356
51 1.523651857
52 0.586143885
53 -0.920608286
54 0.732390090
55 0.226755333
56 0.227015119
57 -0.230431974
58 0.571842793
59 0.986956951
60 -0.214812874
61 -0.236365898
62 0.907266920
63 0.0492812860
64 0.125000000
65 -0.524263029
66 0.345327163
67 -0.0471721732
68 0.793613536
69 0.944348584
70 -0.203048495
71 -0.238716722
72 0.0282441932
73 -1.517828410
74 -0.967130191
75 0.192134475
76 -0.119754466
77 0.326554781
78 -0.794252039
79 -1.381780375
80 -0.111803398
81 -0.913332954
82 0.428275703
83 0.0256793111
84 -0.307068303
85 -0.709829525
86 -0.746654253
87 -0.774564368
88 0.179265831
89 0.224482192
90 -0.0252623744
91 -0.751877626
92 0.491688912
93 -1.230287459
94 0.450823702
95 0.107111651
96 -0.169824488
97 -1.911590638
98 0.417762140
99 0.0337951004
100 0.100000000
101 -1.536467020
102 -1.077384560
103 -0.413337359
104 -0.414466316
105 0.274650240
106 0.650968361
107 0.315928991
108 -0.517877999