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

$K$ is the global number field defined by \( x^{2} - x + 641 \)

$\times$ \(\chi_{ 2563 } ( 1, ·)\) \(\chi_{ 2563 } ( 2562, ·)\)
\(\chi_{ 2563 }(1, ·)\) \(\chi_{ 2563 } ( 1, ·)\) \(\chi_{ 2563 } ( 2562, ·)\)
\(\chi_{ 2563 }(2562, ·)\) \(\chi_{ 2563 } ( 2562, ·)\) \(\chi_{ 2563 } ( 1, ·)\)