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

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

$\times$ \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 39, ·)\)
\(\chi_{ 40 }(1, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 39, ·)\)
\(\chi_{ 40 }(3, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 37, ·)\)
\(\chi_{ 40 }(7, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 33, ·)\)
\(\chi_{ 40 }(9, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 31, ·)\)
\(\chi_{ 40 }(11, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 29, ·)\)
\(\chi_{ 40 }(13, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 27, ·)\)
\(\chi_{ 40 }(17, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 23, ·)\)
\(\chi_{ 40 }(19, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 21, ·)\)
\(\chi_{ 40 }(21, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 19, ·)\)
\(\chi_{ 40 }(23, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 17, ·)\)
\(\chi_{ 40 }(27, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 13, ·)\)
\(\chi_{ 40 }(29, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 11, ·)\)
\(\chi_{ 40 }(31, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 9, ·)\)
\(\chi_{ 40 }(33, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 7, ·)\)
\(\chi_{ 40 }(37, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 1, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 3, ·)\)
\(\chi_{ 40 }(39, ·)\) \(\chi_{ 40 } ( 39, ·)\) \(\chi_{ 40 } ( 37, ·)\) \(\chi_{ 40 } ( 33, ·)\) \(\chi_{ 40 } ( 31, ·)\) \(\chi_{ 40 } ( 29, ·)\) \(\chi_{ 40 } ( 27, ·)\) \(\chi_{ 40 } ( 23, ·)\) \(\chi_{ 40 } ( 21, ·)\) \(\chi_{ 40 } ( 19, ·)\) \(\chi_{ 40 } ( 17, ·)\) \(\chi_{ 40 } ( 13, ·)\) \(\chi_{ 40 } ( 11, ·)\) \(\chi_{ 40 } ( 9, ·)\) \(\chi_{ 40 } ( 7, ·)\) \(\chi_{ 40 } ( 3, ·)\) \(\chi_{ 40 } ( 1, ·)\)