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

$K$ is the global number field defined by \( x^{2} - 30 \)

$\times$ \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(1, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(59, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 1, ·)\)