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

$K$ is the global number field defined by \( x^{4} - 28 x^{2} + 98 \)

$\times$ \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 57, ·)\)
\(\chi_{ 112 }(1, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 57, ·)\)
\(\chi_{ 112 }(83, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 27, ·)\)
\(\chi_{ 112 }(27, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 83, ·)\)
\(\chi_{ 112 }(57, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 1, ·)\)