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

$K$ is the global number field defined by \( x^{16} + 29 x^{12} + 246 x^{8} + 524 x^{4} + 1 \)

$\times$ \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 61, ·)\)
\(\chi_{ 120 }(1, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 61, ·)\)
\(\chi_{ 120 }(77, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 17, ·)\)
\(\chi_{ 120 }(79, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 19, ·)\)
\(\chi_{ 120 }(17, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 77, ·)\)
\(\chi_{ 120 }(19, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 79, ·)\)
\(\chi_{ 120 }(23, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 83, ·)\)
\(\chi_{ 120 }(91, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 31, ·)\)
\(\chi_{ 120 }(31, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 91, ·)\)
\(\chi_{ 120 }(49, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 109, ·)\)
\(\chi_{ 120 }(107, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 47, ·)\)
\(\chi_{ 120 }(109, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 49, ·)\)
\(\chi_{ 120 }(47, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 107, ·)\)
\(\chi_{ 120 }(113, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 53, ·)\)
\(\chi_{ 120 }(83, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 23, ·)\)
\(\chi_{ 120 }(53, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 113, ·)\)
\(\chi_{ 120 }(61, ·)\) \(\chi_{ 120 } ( 61, ·)\) \(\chi_{ 120 } ( 17, ·)\) \(\chi_{ 120 } ( 19, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 91, ·)\) \(\chi_{ 120 } ( 109, ·)\) \(\chi_{ 120 } ( 47, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 23, ·)\) \(\chi_{ 120 } ( 113, ·)\) \(\chi_{ 120 } ( 1, ·)\)