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

$K$ is the global number field defined by \( x^{2} - x - 19 \)

$\times$ \(\chi_{ 77 } ( 1, ·)\) \(\chi_{ 77 } ( 76, ·)\)
\(\chi_{ 77 }(1, ·)\) \(\chi_{ 77 } ( 1, ·)\) \(\chi_{ 77 } ( 76, ·)\)
\(\chi_{ 77 }(76, ·)\) \(\chi_{ 77 } ( 76, ·)\) \(\chi_{ 77 } ( 1, ·)\)