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

$R= 10.7422023202$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.611704537
4 0.5
5 -0.447213595
6 0.432540426
7 -0.546838000
8 0.353553390
9 -0.625817559
10 -0.316227766
11 -1.834139533
12 0.305852268
13 0.367866626
14 -0.386672858
15 -0.273562585
16 0.250000000
17 1.189851313
18 -0.442519839
19 -1.004726038
20 -0.223606797
21 -0.334503285
22 -1.296932501
23 -0.660513622
24 0.216270213
25 0.200000000
26 0.260120986
27 -0.994519977
28 -0.273419000
29 -1.207363654
30 -0.193437959
31 -0.971870491
32 0.176776695
33 -1.121951474
34 0.841351932
35 0.244553388
36 -0.312908779
37 0.964072852
38 -0.710448595
39 0.225025684
40 -0.158113883
41 0.477314361
42 -0.236529541
43 -0.628051640
44 -0.917069766
45 0.279874120
46 -0.467053661
47 0.185239145
48 0.152926134
49 -0.700968201
50 0.141421356
51 0.727837447
52 0.183933313
53 1.336182695
54 -0.703231820
55 0.820252135
56 -0.193336429
57 -0.614595476
58 -0.853735027
59 1.076154205
60 -0.136781292
61 -0.889949478
62 -0.687216215
63 0.342220822
64 0.125000000
65 -0.164514956
66 -0.793339495
67 1.296152404
68 0.594925656
69 -0.404039179
70 0.172925359
71 -1.169566228
72 -0.221259919
73 0.850448038
74 0.681702451
75 0.122340907
76 -0.502363019
77 1.002977195
78 0.159117187
79 -1.151003787
80 -0.111803398
81 0.0174651760
82 0.337512221
83 1.240109551
84 -0.167251642
85 -0.532117683
86 -0.444099574
87 -0.738549828
88 -0.648466250
89 0.457378899
90 0.197900888
91 -0.201163450
92 -0.330256811
93 -0.594497585
94 0.130983856
95 0.449327144
96 0.108135106
97 -0.252835455
98 -0.495659368
99 1.147836725
100 0.100000000
101 0.435086617
102 0.514658794
103 1.594633084
104 0.130060493
105 0.149594417
106 0.944823845
107 -1.848910731
108 -0.497259988
109 -1.715611736
110 0.580005847
111 0.589726403
112 -0.136709500
113 -1.353753235
114 -0.434584629
115 0.295390671
116 -0.603681827
117 -0.230208337
118 0.760955935
119 -0.650656704
120 -0.0967189796
121 2.364089482
122 -0.629289311
123 0.291973692
124 -0.485935245
125 -0.0894427190
126 0.241986664
127 0.0554869393
128 0.0883883476
129 -0.384076870
130 -0.116329641
131 1.306449308
132 -0.560975737
133 0.549650747
134 0.916518155
135 0.444762854
136 0.420675966
137 -1.315054934
138 -0.285698843
139 -0.420519408
140 0.122276694
141 0.109728494
142 -0.827008211
143 -0.675879699
144 -0.156454389
145 0.539949441
146 0.601357574
147 -0.430700081
148 0.482036426
149 -1.006929812
150 0.0865080852