Fungrim entry: 7a56c2

Table of

\chi_{11 \, . \, \ell}

$\ell$ \ $n$	1	2	3	4	5	6	7	8	9	10
1	1	1	1	1	1	1	1	1	1	1
2	1	${e}^{\pi i / 5}$	$-{e}^{3 \pi i / 5}$	${e}^{2 \pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{4 \pi i / 5}$	$-{e}^{2 \pi i / 5}$	${e}^{3 \pi i / 5}$	$-{e}^{\pi i / 5}$	-1
3	1	$-{e}^{3 \pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{2 \pi i / 5}$	${e}^{2 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	1
4	1	${e}^{2 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{2 \pi i / 5}$	1
5	1	${e}^{4 \pi i / 5}$	${e}^{2 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	$-{e}^{\pi i / 5}$	$-{e}^{\pi i / 5}$	$-{e}^{3 \pi i / 5}$	${e}^{2 \pi i / 5}$	${e}^{4 \pi i / 5}$	1
6	1	$-{e}^{4 \pi i / 5}$	${e}^{2 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{\pi i / 5}$	${e}^{3 \pi i / 5}$	$-{e}^{2 \pi i / 5}$	${e}^{4 \pi i / 5}$	-1
7	1	$-{e}^{2 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	${e}^{3 \pi i / 5}$	$-{e}^{4 \pi i / 5}$	${e}^{\pi i / 5}$	${e}^{2 \pi i / 5}$	-1
8	1	${e}^{3 \pi i / 5}$	${e}^{4 \pi i / 5}$	$-{e}^{\pi i / 5}$	${e}^{2 \pi i / 5}$	$-{e}^{2 \pi i / 5}$	${e}^{\pi i / 5}$	$-{e}^{4 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	-1
9	1	$-{e}^{\pi i / 5}$	$-{e}^{3 \pi i / 5}$	${e}^{2 \pi i / 5}$	${e}^{4 \pi i / 5}$	${e}^{4 \pi i / 5}$	${e}^{2 \pi i / 5}$	$-{e}^{3 \pi i / 5}$	$-{e}^{\pi i / 5}$	1
10	1	-1	1	1	1	-1	-1	-1	1	-1

Table data:

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

such that

\chi(n) = y\; \text{ where } \chi = \chi_{11 \, . \, \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("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))))

Topics using this entry

Dirichlet characters