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

$K$ is the global number field defined by \( x^{6} + 13 x^{4} + 26 x^{2} + 13 \)

$\times$ \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 29, ·)\)
\(\chi_{ 52 }(1, ·)\) \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 29, ·)\)
\(\chi_{ 52 }(51, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 29, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 23, ·)\)
\(\chi_{ 52 }(23, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 29, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 43, ·)\)
\(\chi_{ 52 }(9, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 29, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 1, ·)\)
\(\chi_{ 52 }(43, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 9, ·)\) \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 29, ·)\) \(\chi_{ 52 } ( 51, ·)\)
\(\chi_{ 52 }(29, ·)\) \(\chi_{ 52 } ( 29, ·)\) \(\chi_{ 52 } ( 23, ·)\) \(\chi_{ 52 } ( 43, ·)\) \(\chi_{ 52 } ( 1, ·)\) \(\chi_{ 52 } ( 51, ·)\) \(\chi_{ 52 } ( 9, ·)\)