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

$R= 9.78345165027$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.833725766
4 0.5
5 0.447213595
6 1.296639924
7 0.860362392
8 0.353553390
9 2.362550188
10 0.316227766
11 -1.295956425
12 0.916862883
13 -0.841264560
14 0.608368081
15 0.820067093
16 0.250000000
17 -1.123057161
18 1.670575258
19 1.059662302
20 0.223606797
21 1.577668687
22 -0.916379576
23 -0.467215212
24 0.648319962
25 0.200000000
26 -0.594863875
27 2.498543388
28 0.430181196
29 -0.122080035
30 0.579875002
31 0.0540614594
32 0.176776695
33 -2.376428690
34 -0.794121334
35 0.384765758
36 1.181275094
37 1.156702918
38 0.749294399
39 -1.542648500
40 0.158113883
41 -0.469035044
42 1.115580227
43 0.206837693
44 -0.647978212
45 1.056564564
46 -0.330371045
47 -0.373301187
48 0.458431441
49 -0.259776554
50 0.141421356
51 -2.059378854
52 -0.420632280
53 -0.441144834
54 1.766736973
55 -0.579569332
56 0.304184040
57 1.943130068
58 -0.0863236206
59 -1.350114562
60 0.410033546
61 -0.0482388865
62 0.0382272245
63 2.032649331
64 0.125000000
65 -0.376224948
66 -1.680388842
67 -0.481277086
68 -0.561528580
69 -0.856744573
70 0.272070477
71 -0.843937118
72 0.835287629
73 1.357615943
74 0.817912477
75 0.366745153
76 0.529831151
77 -1.114992170
78 -1.090817215
79 -1.408586196
80 0.111803398
81 2.219093203
82 -0.331657860
83 -0.348212069
84 0.788834343
85 -0.502246430
86 0.146256335
87 -0.223861305
88 -0.458189788
89 1.818351400
90 0.747103968
91 -0.723792389
92 -0.233607606
93 0.0991338911
94 -0.263963801
95 0.473895388
96 0.324159981
97 -1.706391599
98 -0.183689763
99 -3.061762097
100 0.100000000
101 1.926530999
102 -1.456200752
103 0.857974000
104 -0.297431937
105 0.705554886
106 -0.311936504
107 1.633320000
108 1.249271694
109 -0.743900000
110 -0.409817405
111 2.121075945
112 0.215090598
113 -0.713749999
114 1.374000447
115 -0.208944995
116 -0.0610400175
117 -1.987529744
118 -0.954675162
119 -0.966236145
120 0.289937501
121 0.679503057
122 -0.0341100437
123 -0.860081647
124 0.0270307297
125 0.0894427190
126 1.437300126
127 -0.599999999
128 0.0883883476
129 0.379283608
130 -0.266031212
131 -0.910000000
132 -1.188214345
133 0.911693593
134 -0.340314291
135 1.117382572
136 -0.397060667
137 0.859999999
138 -0.605809898
139 0.284700000
140 0.192382879
141 -0.684532007
142 -0.596753659
143 1.090242212
144 0.590637547
145 -0.0545958514
146 0.959979440
147 -0.476358960
148 0.578351459