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Fungrim entry: ec0054

Table of χ7.\chi_{7 \, . \, \ell}
\ell \ nn 0123456
10111111
201eπi/3-{e}^{\pi i / 3} e2πi/3{e}^{2 \pi i / 3} e2πi/3{e}^{2 \pi i / 3} eπi/3-{e}^{\pi i / 3} 1
301e2πi/3{e}^{2 \pi i / 3} eπi/3{e}^{\pi i / 3} eπi/3-{e}^{\pi i / 3} e2πi/3-{e}^{2 \pi i / 3} -1
401e2πi/3{e}^{2 \pi i / 3} eπi/3-{e}^{\pi i / 3} eπi/3-{e}^{\pi i / 3} e2πi/3{e}^{2 \pi i / 3} 1
501eπi/3-{e}^{\pi i / 3} e2πi/3-{e}^{2 \pi i / 3} e2πi/3{e}^{2 \pi i / 3} eπi/3{e}^{\pi i / 3} -1
6011-11-1-1
Table data: (,n,y)\left(\ell, n, y\right) such that χ(n)=y   where χ=χ7.\chi(n) = y\; \text{ where } \chi = \chi_{7 \, . \, \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("ec0054"),
    Description("Table of", DirichletCharacter(7, ell)),
    Table(TableRelation(Tuple(ell, n, y), Where(Equal(chi(n), y), Equal(chi, DirichletCharacter(7, ell)))), TableHeadings(Description(ell, "\", n), 0, 1, 2, 3, 4, 5, 6), TableColumnHeadings(1, 2, 3, 4, 5, 6), List(Tuple(0, 1, 1, 1, 1, 1, 1), Tuple(0, 1, Neg(Exp(Div(Mul(Pi, ConstI), 3))), Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Neg(Exp(Div(Mul(Pi, ConstI), 3))), 1), Tuple(0, 1, Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Exp(Div(Mul(Pi, ConstI), 3)), Neg(Exp(Div(Mul(Pi, ConstI), 3))), Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), -1), Tuple(0, 1, Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Neg(Exp(Div(Mul(Pi, ConstI), 3))), Neg(Exp(Div(Mul(Pi, ConstI), 3))), Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), 1), Tuple(0, 1, Neg(Exp(Div(Mul(Pi, ConstI), 3))), Neg(Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), Exp(Div(Mul(Mul(2, Pi), ConstI), 3)), Exp(Div(Mul(Pi, ConstI), 3)), -1), Tuple(0, 1, 1, -1, 1, -1, -1))))

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2021-03-15 19:12:00.328586 UTC