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

$R= 12.3624041926$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.772786699
4 0.5
5 0.447213595
6 -1.253549496
7 -0.377572230
8 -0.353553390
9 2.142772682
10 -0.316227766
11 1.091063548
12 0.886393349
13 0.692464939
14 0.266983884
15 0.792814314
16 0.250000000
17 -1.441547817
18 -1.515169094
19 1.410356242
20 0.223606797
21 -0.669355027
22 -0.771498433
23 -0.950211028
24 -0.626774748
25 0.200000000
26 -0.489646654
27 2.025892212
28 -0.188786115
29 1.813793865
30 -0.560604377
31 -0.748569240
32 -0.176776695
33 1.934222947
34 1.019328237
35 -0.168855434
36 1.071386341
37 -0.0455484490
38 -0.997272462
39 1.227592634
40 -0.158113883
41 0.0510988463
42 0.473305479
43 -0.522225066
44 0.545531774
45 0.958277075
46 0.671900661
47 1.231489069
48 0.443196674
49 -0.857439211
50 -0.141421356
51 -2.555556797
52 0.346232469
53 0.822795161
54 -1.432522121
55 0.487938452
56 0.133491942
57 2.500260787
58 -1.282545941
59 -0.0702788538
60 0.396407157
61 1.029618398
62 0.529318386
63 -0.809051460
64 0.125000000
65 0.309679735
66 -1.367702162
67 1.237837199
68 -0.720773908
69 -1.684521472
70 0.119398822
71 0.965218231
72 -0.757584547
73 0.372942216
74 0.0322076171
75 0.354557339
76 0.705178121
77 -0.411955296
78 -0.868039076
79 0.0478705818
80 0.111803398
81 1.448702084
82 -0.0361323407
83 -0.529530898
84 -0.334677513
85 -0.644679782
86 0.369268885
87 3.215469633
88 -0.385749216
89 -0.582601172
90 -0.677604218
91 -0.261455503
92 -0.475105514
93 -1.327053572
94 -0.870794271
95 0.630730486
96 -0.313387374
97 -1.272598073
98 0.606301080
99 2.337901200
100 0.100000000
101 -1.063712802
102 1.807051541
103 -0.753479933
104 -0.244823327
105 -0.299344668
106 -0.581804038
107 0.157740028
108 1.012946106
109 1.715257112
110 -0.345024588
111 -0.0807462960
112 -0.0943930575
113 -1.244781029
114 -1.767951357
115 -0.424947290
116 0.906896932
117 1.483771827
118 0.0496946541
119 0.544279577
120 -0.280302188
121 0.190451357
122 -0.728050151
123 0.0905412754
124 -0.374284620
125 0.0894427190
126 0.572085773
127 -0.330287641
128 -0.0883883476
129 -0.925912581
130 -0.218976640
131 -1.568065683
132 0.967111473
133 -0.531746061
134 -0.875283077
135 0.906006540
136 0.509664118
137 -0.646027124
138 1.191136556
139 1.459377202
140 -0.0844277172
141 2.188301744
142 -0.682512356
143 0.750016883
144 0.535693170
145 0.811153275
146 -0.263709970
147 -1.504699879
148 -0.0227742245
149 -1.736629126
150 -0.250709899