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

$K$ is the global number field defined by \( x^{2} - x - 372 \)

$\times$ \(\chi_{ 1489 } ( 1, ·)\) \(\chi_{ 1489 } ( 1488, ·)\)
\(\chi_{ 1489 }(1, ·)\) \(\chi_{ 1489 } ( 1, ·)\) \(\chi_{ 1489 } ( 1488, ·)\)
\(\chi_{ 1489 }(1488, ·)\) \(\chi_{ 1489 } ( 1488, ·)\) \(\chi_{ 1489 } ( 1, ·)\)