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

$K$ is the global number field defined by \( x^{2} - x - 57 \)

$\times$ \(\chi_{ 229 } ( 1, ·)\) \(\chi_{ 229 } ( 228, ·)\)
\(\chi_{ 229 }(1, ·)\) \(\chi_{ 229 } ( 1, ·)\) \(\chi_{ 229 } ( 228, ·)\)
\(\chi_{ 229 }(228, ·)\) \(\chi_{ 229 } ( 228, ·)\) \(\chi_{ 229 } ( 1, ·)\)