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

$K$ is the global number field defined by \( x^{2} - x - 22 \)

$\times$ \(\chi_{ 89 } ( 1, ·)\) \(\chi_{ 89 } ( 88, ·)\)
\(\chi_{ 89 }(1, ·)\) \(\chi_{ 89 } ( 1, ·)\) \(\chi_{ 89 } ( 88, ·)\)
\(\chi_{ 89 }(88, ·)\) \(\chi_{ 89 } ( 88, ·)\) \(\chi_{ 89 } ( 1, ·)\)