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

$K$ is the global number field defined by \( x^{6} - 3 x^{5} - 12 x^{4} + 27 x^{3} + 21 x^{2} - 48 x + 17 \)

$\times$ \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 79, ·)\)
\(\chi_{ 117 }(1, ·)\) \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 79, ·)\)
\(\chi_{ 117 }(64, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 79, ·)\) \(\chi_{ 117 } ( 25, ·)\)
\(\chi_{ 117 }(103, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 79, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 64, ·)\)
\(\chi_{ 117 }(40, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 79, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 1, ·)\)
\(\chi_{ 117 }(25, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 79, ·)\) \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 40, ·)\) \(\chi_{ 117 } ( 103, ·)\)
\(\chi_{ 117 }(79, ·)\) \(\chi_{ 117 } ( 79, ·)\) \(\chi_{ 117 } ( 25, ·)\) \(\chi_{ 117 } ( 64, ·)\) \(\chi_{ 117 } ( 1, ·)\) \(\chi_{ 117 } ( 103, ·)\) \(\chi_{ 117 } ( 40, ·)\)