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

$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut 2 x^{3} \) \(\mathstrut -\mathstrut 7 x^{2} \) \(\mathstrut +\mathstrut 8 x \) \(\mathstrut +\mathstrut 1 \)

$\times$ \(\chi_{ 60 } ( 1, ·)\) \(\chi_{ 60 } ( 11, ·)\) \(\chi_{ 60 } ( 59, ·)\) \(\chi_{ 60 } ( 49, ·)\)
\(\chi_{ 60 }(1, ·)\) \(\chi_{ 60 } ( 1, ·)\) \(\chi_{ 60 } ( 11, ·)\) \(\chi_{ 60 } ( 59, ·)\) \(\chi_{ 60 } ( 49, ·)\)
\(\chi_{ 60 }(11, ·)\) \(\chi_{ 60 } ( 11, ·)\) \(\chi_{ 60 } ( 1, ·)\) \(\chi_{ 60 } ( 49, ·)\) \(\chi_{ 60 } ( 59, ·)\)
\(\chi_{ 60 }(59, ·)\) \(\chi_{ 60 } ( 59, ·)\) \(\chi_{ 60 } ( 49, ·)\) \(\chi_{ 60 } ( 1, ·)\) \(\chi_{ 60 } ( 11, ·)\)
\(\chi_{ 60 }(49, ·)\) \(\chi_{ 60 } ( 49, ·)\) \(\chi_{ 60 } ( 59, ·)\) \(\chi_{ 60 } ( 11, ·)\) \(\chi_{ 60 } ( 1, ·)\)