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

$K$ is the global number field defined by $$x^{16} + 47 x^{8} + 1$$

$\times$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 61, ·)$$
$$\chi_{ 80 }(1, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 61, ·)$$
$$\chi_{ 80 }(69, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 49, ·)$$
$$\chi_{ 80 }(71, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 11, ·)$$
$$\chi_{ 80 }(9, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 69, ·)$$
$$\chi_{ 80 }(11, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 31, ·)$$
$$\chi_{ 80 }(79, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 19, ·)$$
$$\chi_{ 80 }(19, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 39, ·)$$
$$\chi_{ 80 }(21, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 1, ·)$$
$$\chi_{ 80 }(29, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 9, ·)$$
$$\chi_{ 80 }(31, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 51, ·)$$
$$\chi_{ 80 }(39, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 59, ·)$$
$$\chi_{ 80 }(41, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 21, ·)$$
$$\chi_{ 80 }(49, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 29, ·)$$
$$\chi_{ 80 }(51, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 71, ·)$$
$$\chi_{ 80 }(59, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 41, ·)$$ $$\chi_{ 80 } ( 79, ·)$$
$$\chi_{ 80 }(61, ·)$$ $$\chi_{ 80 } ( 61, ·)$$ $$\chi_{ 80 } ( 49, ·)$$ $$\chi_{ 80 } ( 11, ·)$$ $$\chi_{ 80 } ( 69, ·)$$ $$\chi_{ 80 } ( 31, ·)$$ $$\chi_{ 80 } ( 19, ·)$$ $$\chi_{ 80 } ( 39, ·)$$ $$\chi_{ 80 } ( 1, ·)$$ $$\chi_{ 80 } ( 9, ·)$$ $$\chi_{ 80 } ( 51, ·)$$ $$\chi_{ 80 } ( 59, ·)$$ $$\chi_{ 80 } ( 21, ·)$$ $$\chi_{ 80 } ( 29, ·)$$ $$\chi_{ 80 } ( 71, ·)$$ $$\chi_{ 80 } ( 79, ·)$$ $$\chi_{ 80 } ( 41, ·)$$