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

$K$ is the global number field defined by \( x^{2} + 58 \)

$\times$ \(\chi_{ 232 } ( 1, ·)\) \(\chi_{ 232 } ( 115, ·)\)
\(\chi_{ 232 }(1, ·)\) \(\chi_{ 232 } ( 1, ·)\) \(\chi_{ 232 } ( 115, ·)\)
\(\chi_{ 232 }(115, ·)\) \(\chi_{ 232 } ( 115, ·)\) \(\chi_{ 232 } ( 1, ·)\)