Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 15.9987139994$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.370920475
4 0.5
5 -0.447213595
6 0.969387164
7 -0.756361486
8 -0.353553390
9 0.879422950
10 0.316227766
11 -0.360267653
12 -0.685460237
13 -0.944252375
14 0.534828336
15 0.613094275
16 0.250000000
17 -0.666750944
18 -0.621845931
19 1.658655114
20 -0.223606797
21 1.036911448
22 0.254747700
23 0.325038395
24 0.484693582
25 0.200000000
26 0.667687258
27 0.165301546
28 -0.378180743
29 1.645532529
30 -0.433523119
31 -0.936099935
32 -0.176776695
33 0.493898302
34 0.471464114
35 0.338255139
36 0.439711475
37 1.363758647
38 -1.172846279
39 1.294494916
40 0.158113883
41 1.733449779
42 -0.733207116
43 0.0709107453
44 -0.180133826
45 -0.393289899
46 -0.229836853
47 -0.653027513
48 -0.342730118
49 -0.427917301
50 -0.141421356
51 0.914062521
52 -0.472126187
53 -0.198510946
54 -0.116885844
55 0.161116592
56 0.267414168
57 -2.273884258
58 -1.163567210
59 -1.587314088
60 0.306547137
61 -1.109267835
62 0.661922612
63 -0.665161649
64 0.125000000
65 0.422282500
66 -0.349238839
67 1.047569669
68 -0.333375472
69 -0.445601791
70 -0.239182503
71 -0.241537717
72 -0.310922965
73 -1.073197975
74 -0.964322987
75 -0.274184095
76 0.829327557
77 0.272492577
78 -0.915346133
79 1.983387070
80 -0.111803398
81 -1.106038224
82 -1.225734093
83 0.564964834
84 0.518455724
85 0.298180087
86 -0.0501414689
87 -2.255894236
88 0.127373850
89 0.667463577
90 0.278097955
91 0.714196129
92 0.162519197
93 1.283318564
94 0.461760183
95 -0.741773117
96 0.242346791
97 -1.424198442
98 0.302583225
99 -0.316827631
100 0.100000000
101 -0.370964188
102 -0.646339807
103 -0.142882343
104 0.333843629
105 -0.463720897
106 0.140368436
107 -0.298988166
108 0.0826507730
109 1.289312737
110 -0.113926635
111 -1.869604643
112 -0.189090371
113 1.128822372
114 1.607878979
115 -0.145361589
116 0.822766264
117 -0.830397683
118 1.122400555
119 0.504304398
120 -0.216761559
121 -0.870207079
122 0.784370808
123 -2.376420451
124 -0.468049967
125 -0.0894427190
126 0.470340313
127 -0.0560906902
128 -0.0883883476
129 -0.0972034524
130 -0.298598819
131 1.764995809
132 0.246949151
133 -1.254574747
134 -0.740743617
135 -0.0739250987
136 0.235732057
137 -1.220231804
138 0.315088048
139 0.685157004
140 0.169127569
141 0.895181054
142 0.170792957
143 0.339996716
144 0.219855737
145 -0.735904519
146 0.758865565
147 0.586785144
148 0.681879323
149 -0.647883977
150 0.193877432
151 0.453600230
152 -0.586423139
153 -0.584818682
154 -0.192681349
155 0.418636618
156 0.647247458
157 -1.971489942
158 -1.402466447
159 0.267118807
160 0.0790569415
161 -0.233209402
162 0.782087128
163 -1.115416670
164 0.866724889
165 -0.220878035
166 -0.399490465