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

$K$ is the global number field defined by \( x^{2} - x - 314 \)

$\times$ \(\chi_{ 1257 } ( 1, ·)\) \(\chi_{ 1257 } ( 1256, ·)\)
\(\chi_{ 1257 }(1, ·)\) \(\chi_{ 1257 } ( 1, ·)\) \(\chi_{ 1257 } ( 1256, ·)\)
\(\chi_{ 1257 }(1256, ·)\) \(\chi_{ 1257 } ( 1256, ·)\) \(\chi_{ 1257 } ( 1, ·)\)