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Fungrim entry: 7a56c2

Table of χ11.\chi_{11 \, . \, \ell}
\ell \ nn 012345678910
101111111111
201eπi/5{e}^{\pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} e4πi/5-{e}^{4 \pi i / 5} e2πi/5-{e}^{2 \pi i / 5} e3πi/5{e}^{3 \pi i / 5} eπi/5-{e}^{\pi i / 5} -1
301e3πi/5-{e}^{3 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} eπi/5-{e}^{\pi i / 5} e2πi/5{e}^{2 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} eπi/5-{e}^{\pi i / 5} e4πi/5{e}^{4 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} 1
401e2πi/5{e}^{2 \pi i / 5} eπi/5-{e}^{\pi i / 5} e4πi/5{e}^{4 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} eπi/5-{e}^{\pi i / 5} e2πi/5{e}^{2 \pi i / 5} 1
501e4πi/5{e}^{4 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} eπi/5-{e}^{\pi i / 5} eπi/5-{e}^{\pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} 1
601e4πi/5-{e}^{4 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} eπi/5-{e}^{\pi i / 5} eπi/5{e}^{\pi i / 5} e3πi/5{e}^{3 \pi i / 5} e2πi/5-{e}^{2 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} -1
701e2πi/5-{e}^{2 \pi i / 5} eπi/5-{e}^{\pi i / 5} e4πi/5{e}^{4 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e3πi/5{e}^{3 \pi i / 5} e4πi/5-{e}^{4 \pi i / 5} eπi/5{e}^{\pi i / 5} e2πi/5{e}^{2 \pi i / 5} -1
801e3πi/5{e}^{3 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} eπi/5-{e}^{\pi i / 5} e2πi/5{e}^{2 \pi i / 5} e2πi/5-{e}^{2 \pi i / 5} eπi/5{e}^{\pi i / 5} e4πi/5-{e}^{4 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} -1
901eπi/5-{e}^{\pi i / 5} e3πi/5-{e}^{3 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} e4πi/5{e}^{4 \pi i / 5} e2πi/5{e}^{2 \pi i / 5} e3πi/5-{e}^{3 \pi i / 5} eπi/5-{e}^{\pi i / 5} 1
1001-1111-1-1-11-1
Table data: (,n,y)\left(\ell, n, y\right) such that χ(n)=y   where χ=χ11.\chi(n) = y\; \text{ where } \chi = \chi_{11 \, . \, \ell}
Definitions:
Fungrim symbol Notation Short description
DirichletCharacterχq.\chi_{q \, . \, \ell} Dirichlet character
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("7a56c2"),
    Description("Table of", DirichletCharacter(11, ell)),
    Table(TableRelation(Tuple(ell, n, y), Where(Equal(chi(n), y), Equal(chi, DirichletCharacter(11, ell)))), TableHeadings(Description(ell, "\", n), 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), TableColumnHeadings(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), List(Tuple(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), Tuple(0, 1, Exp(Div(Mul(Pi, ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(4, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 5))), Exp(Div(Mul(Mul(3, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), -1), Tuple(0, 1, Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), 1), Tuple(0, 1, Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), 1), Tuple(0, 1, Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), 1), Tuple(0, 1, Neg(Exp(Div(Mul(Mul(4, Pi), ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Pi, ConstI), 5)), Exp(Div(Mul(Mul(3, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), -1), Tuple(0, 1, Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(3, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(4, Pi), ConstI), 5))), Exp(Div(Mul(Pi, ConstI), 5)), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), -1), Tuple(0, 1, Exp(Div(Mul(Mul(3, Pi), ConstI), 5)), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Pi, ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 5))), Exp(Div(Mul(Pi, ConstI), 5)), Neg(Exp(Div(Mul(Mul(4, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), -1), Tuple(0, 1, Neg(Exp(Div(Mul(Pi, ConstI), 5))), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Exp(Div(Mul(Mul(4, Pi), ConstI), 5)), Exp(Div(Mul(Mul(2, Pi), ConstI), 5)), Neg(Exp(Div(Mul(Mul(3, Pi), ConstI), 5))), Neg(Exp(Div(Mul(Pi, ConstI), 5))), 1), Tuple(0, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC