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

$K$ is the global number field defined by \( x^{2} - x - 544 \)

$\times$ \(\chi_{ 2177 } ( 1, ·)\) \(\chi_{ 2177 } ( 2176, ·)\)
\(\chi_{ 2177 }(1, ·)\) \(\chi_{ 2177 } ( 1, ·)\) \(\chi_{ 2177 } ( 2176, ·)\)
\(\chi_{ 2177 }(2176, ·)\) \(\chi_{ 2177 } ( 2176, ·)\) \(\chi_{ 2177 } ( 1, ·)\)