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

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

$\times$ \(\chi_{ 20 } ( 1, ·)\) \(\chi_{ 20 } ( 11, ·)\) \(\chi_{ 20 } ( 19, ·)\) \(\chi_{ 20 } ( 9, ·)\)
\(\chi_{ 20 }(1, ·)\) \(\chi_{ 20 } ( 1, ·)\) \(\chi_{ 20 } ( 11, ·)\) \(\chi_{ 20 } ( 19, ·)\) \(\chi_{ 20 } ( 9, ·)\)
\(\chi_{ 20 }(11, ·)\) \(\chi_{ 20 } ( 11, ·)\) \(\chi_{ 20 } ( 1, ·)\) \(\chi_{ 20 } ( 9, ·)\) \(\chi_{ 20 } ( 19, ·)\)
\(\chi_{ 20 }(19, ·)\) \(\chi_{ 20 } ( 19, ·)\) \(\chi_{ 20 } ( 9, ·)\) \(\chi_{ 20 } ( 1, ·)\) \(\chi_{ 20 } ( 11, ·)\)
\(\chi_{ 20 }(9, ·)\) \(\chi_{ 20 } ( 9, ·)\) \(\chi_{ 20 } ( 19, ·)\) \(\chi_{ 20 } ( 11, ·)\) \(\chi_{ 20 } ( 1, ·)\)