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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut -\mathstrut 7 \)

$\times$ \(\chi_{ 29 } ( 1, ·)\) \(\chi_{ 29 } ( 28, ·)\)
\(\chi_{ 29 }(1, ·)\) \(\chi_{ 29 } ( 1, ·)\) \(\chi_{ 29 } ( 28, ·)\)
\(\chi_{ 29 }(28, ·)\) \(\chi_{ 29 } ( 28, ·)\) \(\chi_{ 29 } ( 1, ·)\)