Dirichlet character table generator

This page generates a table of non-zero values for Dirichlet characters modulo k.

Select a value for k:    

Dirichlet characters modulo 24

k = 24, φ(k) = 8, (Z/kZ)* ≅ C2 x C2 x C2, generators = 5,7,13
G={1,5,7,11,13,17,19,23}, λ = 2
X(n) mod 24
n1571113171923
X1(n)11111111
X2(n)1-11-11-11-1
X3(n)11-1-111-1-1
X4(n)1-1-111-1-11
X5(n)1111-1-1-1-1
X6(n)1-11-1-11-11
X7(n)11-1-1-1-111
X8(n)1-1-11-111-1
X(n) mod 24
------------------------------
n       1  5  7 11 13 17 19 23 
------------------------------
X_1(n)  1  1  1  1  1  1  1  1 
X_2(n)  1 -1  1 -1  1 -1  1 -1 
X_3(n)  1  1 -1 -1  1  1 -1 -1 
X_4(n)  1 -1 -1  1  1 -1 -1  1 
X_5(n)  1  1  1  1 -1 -1 -1 -1 
X_6(n)  1 -1  1 -1 -1  1 -1  1 
X_7(n)  1  1 -1 -1 -1 -1  1  1 
X_8(n)  1 -1 -1  1 -1  1  1 -1 
------------------------------

$\chi(n)\pmod{24}$ \\
\begin{tabular}{c c c c c c c c c }
\hline
$n$ & $1$ & $5$ & $7$ & $11$ & $13$ & $17$ & $19$ & $23$ \\
\hline
$\chi_1(n)$ & $1$ & $1$ & $1$ & $1$ & $1$ & $1$ & $1$ & $1$ \\
$\chi_2(n)$ & $1$ & $-1$ & $1$ & $-1$ & $1$ & $-1$ & $1$ & $-1$ \\
$\chi_3(n)$ & $1$ & $1$ & $-1$ & $-1$ & $1$ & $1$ & $-1$ & $-1$ \\
$\chi_4(n)$ & $1$ & $-1$ & $-1$ & $1$ & $1$ & $-1$ & $-1$ & $1$ \\
$\chi_5(n)$ & $1$ & $1$ & $1$ & $1$ & $-1$ & $-1$ & $-1$ & $-1$ \\
$\chi_6(n)$ & $1$ & $-1$ & $1$ & $-1$ & $-1$ & $1$ & $-1$ & $1$ \\
$\chi_7(n)$ & $1$ & $1$ & $-1$ & $-1$ & $-1$ & $-1$ & $1$ & $1$ \\
$\chi_8(n)$ & $1$ & $-1$ & $-1$ & $1$ & $-1$ & $1$ & $1$ & $-1$ \\
\hline
\end{tabular}

Use the results from this page at your own risk. Note that ordering of the rows is arbitrary except the first. Other tables may have the rows in a different order.

How to cite this generator

David A. Ireland, A Dirichlet character table generator, D.I. Management Services Pty Ltd, <https://www.di-mgt.com.au/dirichlet-character-generator.html>, {date accessed}.

The code behind this page was written in Perl by David Ireland. Last updated 23 January 2019.

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