# Fungrim entry: ec0054

Table of $\chi_{7 \, . \, \ell}$
$\ell$ \ $n$ 0123456
10111111
201$-{e}^{\pi i / 3}$ ${e}^{2 \pi i / 3}$ ${e}^{2 \pi i / 3}$ $-{e}^{\pi i / 3}$ 1
301${e}^{2 \pi i / 3}$ ${e}^{\pi i / 3}$ $-{e}^{\pi i / 3}$ $-{e}^{2 \pi i / 3}$ -1
401${e}^{2 \pi i / 3}$ $-{e}^{\pi i / 3}$ $-{e}^{\pi i / 3}$ ${e}^{2 \pi i / 3}$ 1
501$-{e}^{\pi i / 3}$ $-{e}^{2 \pi i / 3}$ ${e}^{2 \pi i / 3}$ ${e}^{\pi i / 3}$ -1
6011-11-1-1
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

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2021-03-15 19:12:00.328586 UTC