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

$K$ is the global number field defined by \( x^{2} - x + 1710 \)

$\times$ \(\chi_{ 6839 } ( 1, ·)\) \(\chi_{ 6839 } ( 6838, ·)\)
\(\chi_{ 6839 }(1, ·)\) \(\chi_{ 6839 } ( 1, ·)\) \(\chi_{ 6839 } ( 6838, ·)\)
\(\chi_{ 6839 }(6838, ·)\) \(\chi_{ 6839 } ( 6838, ·)\) \(\chi_{ 6839 } ( 1, ·)\)