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

$K$ is the global number field defined by \( x^{2} - x - 1222 \)

$\times$ \(\chi_{ 4889 } ( 1, ·)\) \(\chi_{ 4889 } ( 4888, ·)\)
\(\chi_{ 4889 }(1, ·)\) \(\chi_{ 4889 } ( 1, ·)\) \(\chi_{ 4889 } ( 4888, ·)\)
\(\chi_{ 4889 }(4888, ·)\) \(\chi_{ 4889 } ( 4888, ·)\) \(\chi_{ 4889 } ( 1, ·)\)