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

$K$ is the global number field defined by \( x^{2} - x - 87 \)

$\times$ \(\chi_{ 349 } ( 1, ·)\) \(\chi_{ 349 } ( 348, ·)\)
\(\chi_{ 349 }(1, ·)\) \(\chi_{ 349 } ( 1, ·)\) \(\chi_{ 349 } ( 348, ·)\)
\(\chi_{ 349 }(348, ·)\) \(\chi_{ 349 } ( 348, ·)\) \(\chi_{ 349 } ( 1, ·)\)