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

$K$ is the global number field defined by \( x^{2} - x + 431 \)

$\times$ \(\chi_{ 1723 } ( 1, ·)\) \(\chi_{ 1723 } ( 1722, ·)\)
\(\chi_{ 1723 }(1, ·)\) \(\chi_{ 1723 } ( 1, ·)\) \(\chi_{ 1723 } ( 1722, ·)\)
\(\chi_{ 1723 }(1722, ·)\) \(\chi_{ 1723 } ( 1722, ·)\) \(\chi_{ 1723 } ( 1, ·)\)