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

$K$ is the global number field defined by \( x^{2} - 259 \)

$\times$ \(\chi_{ 1036 } ( 1, ·)\) \(\chi_{ 1036 } ( 1035, ·)\)
\(\chi_{ 1036 }(1, ·)\) \(\chi_{ 1036 } ( 1, ·)\) \(\chi_{ 1036 } ( 1035, ·)\)
\(\chi_{ 1036 }(1035, ·)\) \(\chi_{ 1036 } ( 1035, ·)\) \(\chi_{ 1036 } ( 1, ·)\)