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

$K$ is the global number field defined by \( x^{2} + 254 \)

$\times$ \(\chi_{ 1016 } ( 1, ·)\) \(\chi_{ 1016 } ( 253, ·)\)
\(\chi_{ 1016 }(1, ·)\) \(\chi_{ 1016 } ( 1, ·)\) \(\chi_{ 1016 } ( 253, ·)\)
\(\chi_{ 1016 }(253, ·)\) \(\chi_{ 1016 } ( 253, ·)\) \(\chi_{ 1016 } ( 1, ·)\)