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

$K$ is the global number field defined by \( x^{2} - 3 \)

$\times$ \(\chi_{ 12 } ( 1, ·)\) \(\chi_{ 12 } ( 11, ·)\)
\(\chi_{ 12 }(1, ·)\) \(\chi_{ 12 } ( 1, ·)\) \(\chi_{ 12 } ( 11, ·)\)
\(\chi_{ 12 }(11, ·)\) \(\chi_{ 12 } ( 11, ·)\) \(\chi_{ 12 } ( 1, ·)\)