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

$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut -\mathstrut 254 x^{2} \) \(\mathstrut +\mathstrut 254 x \) \(\mathstrut +\mathstrut 12751 \)

$\times$ \(\chi_{ 1015 } ( 1, ·)\) \(\chi_{ 1015 } ( 608, ·)\) \(\chi_{ 1015 } ( 202, ·)\) \(\chi_{ 1015 } ( 204, ·)\)
\(\chi_{ 1015 }(1, ·)\) \(\chi_{ 1015 } ( 1, ·)\) \(\chi_{ 1015 } ( 608, ·)\) \(\chi_{ 1015 } ( 202, ·)\) \(\chi_{ 1015 } ( 204, ·)\)
\(\chi_{ 1015 }(608, ·)\) \(\chi_{ 1015 } ( 608, ·)\) \(\chi_{ 1015 } ( 204, ·)\) \(\chi_{ 1015 } ( 1, ·)\) \(\chi_{ 1015 } ( 202, ·)\)
\(\chi_{ 1015 }(202, ·)\) \(\chi_{ 1015 } ( 202, ·)\) \(\chi_{ 1015 } ( 1, ·)\) \(\chi_{ 1015 } ( 204, ·)\) \(\chi_{ 1015 } ( 608, ·)\)
\(\chi_{ 1015 }(204, ·)\) \(\chi_{ 1015 } ( 204, ·)\) \(\chi_{ 1015 } ( 202, ·)\) \(\chi_{ 1015 } ( 608, ·)\) \(\chi_{ 1015 } ( 1, ·)\)