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

$K$ is the global number field defined by \( x^{4} - x^{3} + 4 x^{2} + 3 x + 9 \)

$\times$ \(\chi_{ 39 } ( 1, ·)\) \(\chi_{ 39 } ( 14, ·)\) \(\chi_{ 39 } ( 38, ·)\) \(\chi_{ 39 } ( 25, ·)\)
\(\chi_{ 39 }(1, ·)\) \(\chi_{ 39 } ( 1, ·)\) \(\chi_{ 39 } ( 14, ·)\) \(\chi_{ 39 } ( 38, ·)\) \(\chi_{ 39 } ( 25, ·)\)
\(\chi_{ 39 }(14, ·)\) \(\chi_{ 39 } ( 14, ·)\) \(\chi_{ 39 } ( 1, ·)\) \(\chi_{ 39 } ( 25, ·)\) \(\chi_{ 39 } ( 38, ·)\)
\(\chi_{ 39 }(38, ·)\) \(\chi_{ 39 } ( 38, ·)\) \(\chi_{ 39 } ( 25, ·)\) \(\chi_{ 39 } ( 1, ·)\) \(\chi_{ 39 } ( 14, ·)\)
\(\chi_{ 39 }(25, ·)\) \(\chi_{ 39 } ( 25, ·)\) \(\chi_{ 39 } ( 38, ·)\) \(\chi_{ 39 } ( 14, ·)\) \(\chi_{ 39 } ( 1, ·)\)