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

$K$ is the global number field defined by \( x^{2} - 170 \)

$\times$ \(\chi_{ 680 } ( 1, ·)\) \(\chi_{ 680 } ( 509, ·)\)
\(\chi_{ 680 }(1, ·)\) \(\chi_{ 680 } ( 1, ·)\) \(\chi_{ 680 } ( 509, ·)\)
\(\chi_{ 680 }(509, ·)\) \(\chi_{ 680 } ( 509, ·)\) \(\chi_{ 680 } ( 1, ·)\)