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

$K$ is the global number field defined by \( x^{2} + 102 \)

$\times$ \(\chi_{ 408 } ( 1, ·)\) \(\chi_{ 408 } ( 101, ·)\)
\(\chi_{ 408 }(1, ·)\) \(\chi_{ 408 } ( 1, ·)\) \(\chi_{ 408 } ( 101, ·)\)
\(\chi_{ 408 }(101, ·)\) \(\chi_{ 408 } ( 101, ·)\) \(\chi_{ 408 } ( 1, ·)\)