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

$K$ is the global number field defined by \( x^{2} - x + 15 \)

$\times$ \(\chi_{ 59 } ( 1, ·)\) \(\chi_{ 59 } ( 58, ·)\)
\(\chi_{ 59 }(1, ·)\) \(\chi_{ 59 } ( 1, ·)\) \(\chi_{ 59 } ( 58, ·)\)
\(\chi_{ 59 }(58, ·)\) \(\chi_{ 59 } ( 58, ·)\) \(\chi_{ 59 } ( 1, ·)\)