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

$K$ is the global number field defined by \( x^{3} - x^{2} - 4 x - 1 \)

$\times$ \(\chi_{ 13 } ( 1, ·)\) \(\chi_{ 13 } ( 3, ·)\) \(\chi_{ 13 } ( 9, ·)\)
\(\chi_{ 13 }(1, ·)\) \(\chi_{ 13 } ( 1, ·)\) \(\chi_{ 13 } ( 3, ·)\) \(\chi_{ 13 } ( 9, ·)\)
\(\chi_{ 13 }(3, ·)\) \(\chi_{ 13 } ( 3, ·)\) \(\chi_{ 13 } ( 9, ·)\) \(\chi_{ 13 } ( 1, ·)\)
\(\chi_{ 13 }(9, ·)\) \(\chi_{ 13 } ( 9, ·)\) \(\chi_{ 13 } ( 1, ·)\) \(\chi_{ 13 } ( 3, ·)\)