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

$K$ is the global number field defined by \( x^{2} - x + 81 \)

$\times$ \(\chi_{ 323 } ( 1, ·)\) \(\chi_{ 323 } ( 322, ·)\)
\(\chi_{ 323 }(1, ·)\) \(\chi_{ 323 } ( 1, ·)\) \(\chi_{ 323 } ( 322, ·)\)
\(\chi_{ 323 }(322, ·)\) \(\chi_{ 323 } ( 322, ·)\) \(\chi_{ 323 } ( 1, ·)\)