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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut +\mathstrut 130 \)

$\times$ \(\chi_{ 520 } ( 1, ·)\) \(\chi_{ 520 } ( 259, ·)\)
\(\chi_{ 520 }(1, ·)\) \(\chi_{ 520 } ( 1, ·)\) \(\chi_{ 520 } ( 259, ·)\)
\(\chi_{ 520 }(259, ·)\) \(\chi_{ 520 } ( 259, ·)\) \(\chi_{ 520 } ( 1, ·)\)