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

$K$ is the global number field defined by \( x^{2} + 21 \)

$\times$ \(\chi_{ 84 } ( 1, ·)\) \(\chi_{ 84 } ( 83, ·)\)
\(\chi_{ 84 }(1, ·)\) \(\chi_{ 84 } ( 1, ·)\) \(\chi_{ 84 } ( 83, ·)\)
\(\chi_{ 84 }(83, ·)\) \(\chi_{ 84 } ( 83, ·)\) \(\chi_{ 84 } ( 1, ·)\)