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

$K$ is the global number field defined by \( x^{2} - 282 \)

$\times$ \(\chi_{ 1128 } ( 1, ·)\) \(\chi_{ 1128 } ( 845, ·)\)
\(\chi_{ 1128 }(1, ·)\) \(\chi_{ 1128 } ( 1, ·)\) \(\chi_{ 1128 } ( 845, ·)\)
\(\chi_{ 1128 }(845, ·)\) \(\chi_{ 1128 } ( 845, ·)\) \(\chi_{ 1128 } ( 1, ·)\)