Group of Dirichlet characters

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

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

$\times$	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 47, ·)\)
\(\chi_{ 48 }(1, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 47, ·)\)
\(\chi_{ 48 }(5, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 43, ·)\)
\(\chi_{ 48 }(7, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 41, ·)\)
\(\chi_{ 48 }(11, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 37, ·)\)
\(\chi_{ 48 }(13, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 35, ·)\)
\(\chi_{ 48 }(17, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 31, ·)\)
\(\chi_{ 48 }(19, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 29, ·)\)
\(\chi_{ 48 }(23, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 25, ·)\)
\(\chi_{ 48 }(25, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 23, ·)\)
\(\chi_{ 48 }(29, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 19, ·)\)
\(\chi_{ 48 }(31, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 17, ·)\)
\(\chi_{ 48 }(35, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 13, ·)\)
\(\chi_{ 48 }(37, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 11, ·)\)
\(\chi_{ 48 }(41, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 7, ·)\)
\(\chi_{ 48 }(43, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 1, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 5, ·)\)
\(\chi_{ 48 }(47, ·)\)	\(\chi_{ 48 } ( 47, ·)\)	\(\chi_{ 48 } ( 43, ·)\)	\(\chi_{ 48 } ( 41, ·)\)	\(\chi_{ 48 } ( 37, ·)\)	\(\chi_{ 48 } ( 35, ·)\)	\(\chi_{ 48 } ( 31, ·)\)	\(\chi_{ 48 } ( 29, ·)\)	\(\chi_{ 48 } ( 25, ·)\)	\(\chi_{ 48 } ( 23, ·)\)	\(\chi_{ 48 } ( 19, ·)\)	\(\chi_{ 48 } ( 17, ·)\)	\(\chi_{ 48 } ( 13, ·)\)	\(\chi_{ 48 } ( 11, ·)\)	\(\chi_{ 48 } ( 7, ·)\)	\(\chi_{ 48 } ( 5, ·)\)	\(\chi_{ 48 } ( 1, ·)\)