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

$K$ is the global number field defined by \( x^{2} - x - 279 \)

$\times$ \(\chi_{ 1117 } ( 1, ·)\) \(\chi_{ 1117 } ( 1116, ·)\)
\(\chi_{ 1117 }(1, ·)\) \(\chi_{ 1117 } ( 1, ·)\) \(\chi_{ 1117 } ( 1116, ·)\)
\(\chi_{ 1117 }(1116, ·)\) \(\chi_{ 1117 } ( 1116, ·)\) \(\chi_{ 1117 } ( 1, ·)\)