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

$K$ is the global number field defined by \( x^{2} + 69 \)

$\times$ \(\chi_{ 276 } ( 1, ·)\) \(\chi_{ 276 } ( 275, ·)\)
\(\chi_{ 276 }(1, ·)\) \(\chi_{ 276 } ( 1, ·)\) \(\chi_{ 276 } ( 275, ·)\)
\(\chi_{ 276 }(275, ·)\) \(\chi_{ 276 } ( 275, ·)\) \(\chi_{ 276 } ( 1, ·)\)