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

$K$ is the global number field defined by \( x^{16} + 2 x^{14} - 8 x^{10} - 16 x^{8} - 32 x^{6} + 128 x^{2} + 256 \)

$\times$ \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(1, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(67, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 113, ·)\)
\(\chi_{ 120 }(17, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 43, ·)\)
\(\chi_{ 120 }(73, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 107, ·)\)
\(\chi_{ 120 }(11, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 49, ·)\)
\(\chi_{ 120 }(43, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 17, ·)\)
\(\chi_{ 120 }(83, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 97, ·)\)
\(\chi_{ 120 }(89, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 91, ·)\)
\(\chi_{ 120 }(91, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 89, ·)\)
\(\chi_{ 120 }(97, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 83, ·)\)
\(\chi_{ 120 }(113, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 67, ·)\)
\(\chi_{ 120 }(41, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 19, ·)\)
\(\chi_{ 120 }(107, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 73, ·)\)
\(\chi_{ 120 }(49, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 11, ·)\)
\(\chi_{ 120 }(19, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 41, ·)\)
\(\chi_{ 120 }(59, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 43, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 89, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 67, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 41, ·)\) \(\chi_{ 120 } ( 1, ·)\)