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

$K$ is the global number field defined by x^2 - x 125

$\times$ \(\chi_{ 499 } ( 1, ·)\) \(\chi_{ 499 } ( 498, ·)\)
\(\chi_{ 499 }(1, ·)\) \(\chi_{ 499 } ( 1, ·)\) \(\chi_{ 499 } ( 498, ·)\)
\(\chi_{ 499 }(498, ·)\) \(\chi_{ 499 } ( 498, ·)\) \(\chi_{ 499 } ( 1, ·)\)