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

$K$ is the global number field defined by \( x^{2} - x - 16 \)

$\times$ \(\chi_{ 65 } ( 1, ·)\) \(\chi_{ 65 } ( 64, ·)\)
\(\chi_{ 65 }(1, ·)\) \(\chi_{ 65 } ( 1, ·)\) \(\chi_{ 65 } ( 64, ·)\)
\(\chi_{ 65 }(64, ·)\) \(\chi_{ 65 } ( 64, ·)\) \(\chi_{ 65 } ( 1, ·)\)