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

$K$ is the global number field defined by \( x^{2} - x + 38 \)

$\times$ \(\chi_{ 151 } ( 1, ·)\) \(\chi_{ 151 } ( 150, ·)\)
\(\chi_{ 151 }(1, ·)\) \(\chi_{ 151 } ( 1, ·)\) \(\chi_{ 151 } ( 150, ·)\)
\(\chi_{ 151 }(150, ·)\) \(\chi_{ 151 } ( 150, ·)\) \(\chi_{ 151 } ( 1, ·)\)