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

$K$ is the global number field defined by \( x^{16} - 9 x^{12} + 81 x^{8} - 729 x^{4} + 6561 \)

$\times$ \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(1, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 59, ·)\)
\(\chi_{ 120 }(7, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 53, ·)\)
\(\chi_{ 120 }(73, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 107, ·)\)
\(\chi_{ 120 }(11, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 49, ·)\)
\(\chi_{ 120 }(77, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 103, ·)\)
\(\chi_{ 120 }(79, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 101, ·)\)
\(\chi_{ 120 }(83, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 97, ·)\)
\(\chi_{ 120 }(29, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 31, ·)\)
\(\chi_{ 120 }(31, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 29, ·)\)
\(\chi_{ 120 }(97, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 83, ·)\)
\(\chi_{ 120 }(101, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 79, ·)\)
\(\chi_{ 120 }(103, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 77, ·)\)
\(\chi_{ 120 }(107, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 73, ·)\)
\(\chi_{ 120 }(49, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 11, ·)\)
\(\chi_{ 120 }(53, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 1, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 7, ·)\)
\(\chi_{ 120 }(59, ·)\) \(\chi_{ 120 } ( 59, ·)\) \(\chi_{ 120 } ( 53, ·)\) \(\chi_{ 120 } ( 107, ·)\) \(\chi_{ 120 } ( 49, ·)\) \(\chi_{ 120 } ( 103, ·)\) \(\chi_{ 120 } ( 101, ·)\) \(\chi_{ 120 } ( 97, ·)\) \(\chi_{ 120 } ( 31, ·)\) \(\chi_{ 120 } ( 29, ·)\) \(\chi_{ 120 } ( 83, ·)\) \(\chi_{ 120 } ( 79, ·)\) \(\chi_{ 120 } ( 77, ·)\) \(\chi_{ 120 } ( 73, ·)\) \(\chi_{ 120 } ( 11, ·)\) \(\chi_{ 120 } ( 7, ·)\) \(\chi_{ 120 } ( 1, ·)\)