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

$K$ is the global number field defined by \( x^{16} + 5 x^{14} + 24 x^{12} + 115 x^{10} + 551 x^{8} + 115 x^{6} + 24 x^{4} + 5 x^{2} + 1 \)

$\times$ \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 253, ·)\)
\(\chi_{ 420 }(1, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 253, ·)\)
\(\chi_{ 420 }(323, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 239, ·)\)
\(\chi_{ 420 }(391, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 223, ·)\)
\(\chi_{ 420 }(139, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 307, ·)\)
\(\chi_{ 420 }(209, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 377, ·)\)
\(\chi_{ 420 }(407, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 71, ·)\)
\(\chi_{ 420 }(223, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 139, ·)\)
\(\chi_{ 420 }(293, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 209, ·)\)
\(\chi_{ 420 }(337, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 1, ·)\)
\(\chi_{ 420 }(169, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 337, ·)\)
\(\chi_{ 420 }(71, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 323, ·)\)
\(\chi_{ 420 }(239, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 407, ·)\)
\(\chi_{ 420 }(307, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 391, ·)\)
\(\chi_{ 420 }(41, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 293, ·)\)
\(\chi_{ 420 }(377, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 169, ·)\) \(\chi_{ 420 } ( 41, ·)\)
\(\chi_{ 420 }(253, ·)\) \(\chi_{ 420 } ( 253, ·)\) \(\chi_{ 420 } ( 239, ·)\) \(\chi_{ 420 } ( 223, ·)\) \(\chi_{ 420 } ( 307, ·)\) \(\chi_{ 420 } ( 377, ·)\) \(\chi_{ 420 } ( 71, ·)\) \(\chi_{ 420 } ( 139, ·)\) \(\chi_{ 420 } ( 209, ·)\) \(\chi_{ 420 } ( 1, ·)\) \(\chi_{ 420 } ( 337, ·)\) \(\chi_{ 420 } ( 323, ·)\) \(\chi_{ 420 } ( 407, ·)\) \(\chi_{ 420 } ( 391, ·)\) \(\chi_{ 420 } ( 293, ·)\) \(\chi_{ 420 } ( 41, ·)\) \(\chi_{ 420 } ( 169, ·)\)