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

$K$ is the global number field defined by \( x^{2} + 41 \)

$\times$ \(\chi_{ 164 } ( 1, ·)\) \(\chi_{ 164 } ( 163, ·)\)
\(\chi_{ 164 }(1, ·)\) \(\chi_{ 164 } ( 1, ·)\) \(\chi_{ 164 } ( 163, ·)\)
\(\chi_{ 164 }(163, ·)\) \(\chi_{ 164 } ( 163, ·)\) \(\chi_{ 164 } ( 1, ·)\)