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

$K$ is the global number field defined by \( x^{6} - x^{3} + 1 \)

$\times$ \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 8, ·)\)
\(\chi_{ 9 }(1, ·)\) \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 8, ·)\)
\(\chi_{ 9 }(2, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 8, ·)\) \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 7, ·)\)
\(\chi_{ 9 }(4, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 8, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 5, ·)\)
\(\chi_{ 9 }(5, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 8, ·)\) \(\chi_{ 9 } ( 4, ·)\)
\(\chi_{ 9 }(7, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 1, ·)\) \(\chi_{ 9 } ( 8, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 2, ·)\)
\(\chi_{ 9 }(8, ·)\) \(\chi_{ 9 } ( 8, ·)\) \(\chi_{ 9 } ( 7, ·)\) \(\chi_{ 9 } ( 5, ·)\) \(\chi_{ 9 } ( 4, ·)\) \(\chi_{ 9 } ( 2, ·)\) \(\chi_{ 9 } ( 1, ·)\)