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

$K$ is the global number field defined by \( x^{16} - x^{15} + 5 x^{14} - 14 x^{13} + 14 x^{12} + 31 x^{11} - 30 x^{10} + 434 x^{9} - 1059 x^{8} + 2170 x^{7} - 750 x^{6} + 3875 x^{5} + 8750 x^{4} - 43750 x^{3} + 78125 x^{2} - 78125 x + 390625 \)

$\times$ \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 191, ·)\)
\(\chi_{ 285 }(1, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 191, ·)\)
\(\chi_{ 285 }(134, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 229, ·)\)
\(\chi_{ 285 }(77, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 172, ·)\)
\(\chi_{ 285 }(208, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 113, ·)\)
\(\chi_{ 285 }(248, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 58, ·)\)
\(\chi_{ 285 }(151, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 56, ·)\)
\(\chi_{ 285 }(284, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 94, ·)\)
\(\chi_{ 285 }(94, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 284, ·)\)
\(\chi_{ 285 }(37, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 227, ·)\)
\(\chi_{ 285 }(227, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 37, ·)\)
\(\chi_{ 285 }(229, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 134, ·)\)
\(\chi_{ 285 }(172, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 77, ·)\)
\(\chi_{ 285 }(113, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 208, ·)\)
\(\chi_{ 285 }(56, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 151, ·)\)
\(\chi_{ 285 }(58, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 1, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 248, ·)\)
\(\chi_{ 285 }(191, ·)\) \(\chi_{ 285 } ( 191, ·)\) \(\chi_{ 285 } ( 229, ·)\) \(\chi_{ 285 } ( 172, ·)\) \(\chi_{ 285 } ( 113, ·)\) \(\chi_{ 285 } ( 58, ·)\) \(\chi_{ 285 } ( 56, ·)\) \(\chi_{ 285 } ( 94, ·)\) \(\chi_{ 285 } ( 284, ·)\) \(\chi_{ 285 } ( 227, ·)\) \(\chi_{ 285 } ( 37, ·)\) \(\chi_{ 285 } ( 134, ·)\) \(\chi_{ 285 } ( 77, ·)\) \(\chi_{ 285 } ( 208, ·)\) \(\chi_{ 285 } ( 151, ·)\) \(\chi_{ 285 } ( 248, ·)\) \(\chi_{ 285 } ( 1, ·)\)