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

$K$ is the global number field defined by \( x^{16} + 16 x^{14} + 105 x^{12} + 364 x^{10} + 714 x^{8} + 784 x^{6} + 440 x^{4} + 96 x^{2} + 1 \)

$\times$ \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 119, ·)\)
\(\chi_{ 120 }(1, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 119, ·)\)
\(\chi_{ 120 }(7, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 113, ·)\)
\(\chi_{ 120 }(13, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 107, ·)\)
\(\chi_{ 120 }(17, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 103, ·)\)
\(\chi_{ 120 }(19, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 101, ·)\)
\(\chi_{ 120 }(71, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 49, ·)\)
\(\chi_{ 120 }(103, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 17, ·)\)
\(\chi_{ 120 }(29, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 91, ·)\)
\(\chi_{ 120 }(101, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 19, ·)\)
\(\chi_{ 120 }(91, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 29, ·)\)
\(\chi_{ 120 }(37, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 83, ·)\)
\(\chi_{ 120 }(49, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 71, ·)\)
\(\chi_{ 120 }(107, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 13, ·)\)
\(\chi_{ 120 }(113, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 7, ·)\)
\(\chi_{ 120 }(83, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 37, ·)\)
\(\chi_{ 120 }(119, ·)\) \(\chi_{ 120 } ( 119, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 71, ·)\) \(\chi_{ 120 } ( 13, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 37, ·)\) \(\chi_{ 120 } ( 1, ·)\)