Group of Dirichlet characters

Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by \(x^{6} \) \(\mathstrut +\mathstrut 9 x^{4} \) \(\mathstrut -\mathstrut 5 x^{3} \) \(\mathstrut +\mathstrut 36 x^{2} \) \(\mathstrut -\mathstrut 12 x \) \(\mathstrut +\mathstrut 8 \)

$\times$	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)
\(\chi_{ 63 }(1, ·)\)	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)
\(\chi_{ 63 }(34, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)	\(\chi_{ 63 } ( 1, ·)\)
\(\chi_{ 63 }(22, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)
\(\chi_{ 63 }(55, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)
\(\chi_{ 63 }(43, ·)\)	\(\chi_{ 63 } ( 43, ·)\)	\(\chi_{ 63 } ( 13, ·)\)	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)
\(\chi_{ 63 }(13, ·)\)	\(\chi_{ 63 } ( 13, ·)\)	\(\chi_{ 63 } ( 1, ·)\)	\(\chi_{ 63 } ( 34, ·)\)	\(\chi_{ 63 } ( 22, ·)\)	\(\chi_{ 63 } ( 55, ·)\)	\(\chi_{ 63 } ( 43, ·)\)