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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 17 \)

$\times$ \(\chi_{ 69 } ( 1, ·)\) \(\chi_{ 69 } ( 68, ·)\)
\(\chi_{ 69 }(1, ·)\) \(\chi_{ 69 } ( 1, ·)\) \(\chi_{ 69 } ( 68, ·)\)
\(\chi_{ 69 }(68, ·)\) \(\chi_{ 69 } ( 68, ·)\) \(\chi_{ 69 } ( 1, ·)\)