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

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

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