Group of Dirichlet characters

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

$K$ is the global number field defined by \(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 4 x^{3} \) \(\mathstrut +\mathstrut 3 x^{2} \) \(\mathstrut +\mathstrut 3 x \) \(\mathstrut -\mathstrut 1 \)

$\times$	\(\chi_{ 11 } ( 1, ·)\)	\(\chi_{ 11 } ( 3, ·)\)	\(\chi_{ 11 } ( 4, ·)\)	\(\chi_{ 11 } ( 5, ·)\)	\(\chi_{ 11 } ( 9, ·)\)
\(\chi_{ 11 }(1, ·)\)	\(\chi_{ 11 } ( 1, ·)\)	\(\chi_{ 11 } ( 3, ·)\)	\(\chi_{ 11 } ( 4, ·)\)	\(\chi_{ 11 } ( 5, ·)\)	\(\chi_{ 11 } ( 9, ·)\)
\(\chi_{ 11 }(3, ·)\)	\(\chi_{ 11 } ( 3, ·)\)	\(\chi_{ 11 } ( 9, ·)\)	\(\chi_{ 11 } ( 1, ·)\)	\(\chi_{ 11 } ( 4, ·)\)	\(\chi_{ 11 } ( 5, ·)\)
\(\chi_{ 11 }(4, ·)\)	\(\chi_{ 11 } ( 4, ·)\)	\(\chi_{ 11 } ( 1, ·)\)	\(\chi_{ 11 } ( 5, ·)\)	\(\chi_{ 11 } ( 9, ·)\)	\(\chi_{ 11 } ( 3, ·)\)
\(\chi_{ 11 }(5, ·)\)	\(\chi_{ 11 } ( 5, ·)\)	\(\chi_{ 11 } ( 4, ·)\)	\(\chi_{ 11 } ( 9, ·)\)	\(\chi_{ 11 } ( 3, ·)\)	\(\chi_{ 11 } ( 1, ·)\)
\(\chi_{ 11 }(9, ·)\)	\(\chi_{ 11 } ( 9, ·)\)	\(\chi_{ 11 } ( 5, ·)\)	\(\chi_{ 11 } ( 3, ·)\)	\(\chi_{ 11 } ( 1, ·)\)	\(\chi_{ 11 } ( 4, ·)\)