Fungrim entry: ec0054

Table of

\chi_{7 \, . \, \ell}

$\ell$ \ $n$	1	2	3	4	5	6
1	1	1	1	1	1	1
2	1	$-{e}^{\pi i / 3}$	${e}^{2 \pi i / 3}$	${e}^{2 \pi i / 3}$	$-{e}^{\pi i / 3}$	1
3	1	${e}^{2 \pi i / 3}$	${e}^{\pi i / 3}$	$-{e}^{\pi i / 3}$	$-{e}^{2 \pi i / 3}$	-1
4	1	${e}^{2 \pi i / 3}$	$-{e}^{\pi i / 3}$	$-{e}^{\pi i / 3}$	${e}^{2 \pi i / 3}$	1
5	1	$-{e}^{\pi i / 3}$	$-{e}^{2 \pi i / 3}$	${e}^{2 \pi i / 3}$	${e}^{\pi i / 3}$	-1
6	1	1	-1	1	-1	-1

Table data:

\left(\ell, n, y\right)

such that

\chi(n) = y\; \text{ where } \chi = \chi_{7 \, . \, \ell}

Definitions:

Fungrim symbol	Notation	Short description
`DirichletCharacter`	$\chi_{q \, . \, \ell}$	Dirichlet character
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	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))))

Topics using this entry

Dirichlet characters