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

$K$ is the global number field defined by \( x^{2} - 271 \)

$\times$ \(\chi_{ 1084 } ( 1, ·)\) \(\chi_{ 1084 } ( 1083, ·)\)
\(\chi_{ 1084 }(1, ·)\) \(\chi_{ 1084 } ( 1, ·)\) \(\chi_{ 1084 } ( 1083, ·)\)
\(\chi_{ 1084 }(1083, ·)\) \(\chi_{ 1084 } ( 1083, ·)\) \(\chi_{ 1084 } ( 1, ·)\)