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

$K$ is the global number field defined by \( x^{2} - 39 \)

$\times$ \(\chi_{ 156 } ( 1, ·)\) \(\chi_{ 156 } ( 155, ·)\)
\(\chi_{ 156 }(1, ·)\) \(\chi_{ 156 } ( 1, ·)\) \(\chi_{ 156 } ( 155, ·)\)
\(\chi_{ 156 }(155, ·)\) \(\chi_{ 156 } ( 155, ·)\) \(\chi_{ 156 } ( 1, ·)\)