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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut -\mathstrut 11 \)

$\times$ \(\chi_{ 44 } ( 1, ·)\) \(\chi_{ 44 } ( 43, ·)\)
\(\chi_{ 44 }(1, ·)\) \(\chi_{ 44 } ( 1, ·)\) \(\chi_{ 44 } ( 43, ·)\)
\(\chi_{ 44 }(43, ·)\) \(\chi_{ 44 } ( 43, ·)\) \(\chi_{ 44 } ( 1, ·)\)