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

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

$\times$ \(\chi_{ 11 } ( 1, ·)\) \(\chi_{ 11 } ( 10, ·)\)
\(\chi_{ 11 }(1, ·)\) \(\chi_{ 11 } ( 1, ·)\) \(\chi_{ 11 } ( 10, ·)\)
\(\chi_{ 11 }(10, ·)\) \(\chi_{ 11 } ( 10, ·)\) \(\chi_{ 11 } ( 1, ·)\)