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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut -\mathstrut 274 \)

$\times$ \(\chi_{ 1096 } ( 1, ·)\) \(\chi_{ 1096 } ( 821, ·)\)
\(\chi_{ 1096 }(1, ·)\) \(\chi_{ 1096 } ( 1, ·)\) \(\chi_{ 1096 } ( 821, ·)\)
\(\chi_{ 1096 }(821, ·)\) \(\chi_{ 1096 } ( 821, ·)\) \(\chi_{ 1096 } ( 1, ·)\)