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

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

$\times$ \(\chi_{ 28 } ( 1, ·)\) \(\chi_{ 28 } ( 27, ·)\)
\(\chi_{ 28 }(1, ·)\) \(\chi_{ 28 } ( 1, ·)\) \(\chi_{ 28 } ( 27, ·)\)
\(\chi_{ 28 }(27, ·)\) \(\chi_{ 28 } ( 27, ·)\) \(\chi_{ 28 } ( 1, ·)\)