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

$K$ is the global number field defined by \( x^{2} + 77 \)

$\times$ \(\chi_{ 308 } ( 1, ·)\) \(\chi_{ 308 } ( 307, ·)\)
\(\chi_{ 308 }(1, ·)\) \(\chi_{ 308 } ( 1, ·)\) \(\chi_{ 308 } ( 307, ·)\)
\(\chi_{ 308 }(307, ·)\) \(\chi_{ 308 } ( 307, ·)\) \(\chi_{ 308 } ( 1, ·)\)