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

$K$ is the global number field defined by \( x^{2} - x - 522 \)

$\times$ \(\chi_{ 2089 } ( 1, ·)\) \(\chi_{ 2089 } ( 2088, ·)\)
\(\chi_{ 2089 }(1, ·)\) \(\chi_{ 2089 } ( 1, ·)\) \(\chi_{ 2089 } ( 2088, ·)\)
\(\chi_{ 2089 }(2088, ·)\) \(\chi_{ 2089 } ( 2088, ·)\) \(\chi_{ 2089 } ( 1, ·)\)