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

$K$ is the global number field defined by \( x^{2} - x - 174 \)

$\times$ \(\chi_{ 697 } ( 1, ·)\) \(\chi_{ 697 } ( 696, ·)\)
\(\chi_{ 697 }(1, ·)\) \(\chi_{ 697 } ( 1, ·)\) \(\chi_{ 697 } ( 696, ·)\)
\(\chi_{ 697 }(696, ·)\) \(\chi_{ 697 } ( 696, ·)\) \(\chi_{ 697 } ( 1, ·)\)