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

$K$ is the global number field defined by \( x^{2} + 562 \)

$\times$ \(\chi_{ 2248 } ( 1, ·)\) \(\chi_{ 2248 } ( 1123, ·)\)
\(\chi_{ 2248 }(1, ·)\) \(\chi_{ 2248 } ( 1, ·)\) \(\chi_{ 2248 } ( 1123, ·)\)
\(\chi_{ 2248 }(1123, ·)\) \(\chi_{ 2248 } ( 1123, ·)\) \(\chi_{ 2248 } ( 1, ·)\)