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

$K$ is the global number field defined by \( x^{12} - x^{11} - 68 x^{10} + 3 x^{9} + 1528 x^{8} + 1135 x^{7} - 12600 x^{6} - 17100 x^{5} + \cdots - 2789 \) Copy content Toggle raw display

$\times$ \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 565, ·)\)
\(\chi_{ 629 }(1, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 565, ·)\)
\(\chi_{ 629 }(322, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 149, ·)\)
\(\chi_{ 629 }(38, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 84, ·)\)
\(\chi_{ 629 }(137, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 38, ·)\)
\(\chi_{ 629 }(174, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 186, ·)\)
\(\chi_{ 629 }(47, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 137, ·)\)
\(\chi_{ 629 }(528, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 174, ·)\)
\(\chi_{ 629 }(84, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 285, ·)\)
\(\chi_{ 629 }(149, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 528, ·)\)
\(\chi_{ 629 }(186, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 47, ·)\)
\(\chi_{ 629 }(285, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 322, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 1, ·)\)
\(\chi_{ 629 }(565, ·)\) \(\chi_{ 629 } ( 565, ·)\) \(\chi_{ 629 } ( 149, ·)\) \(\chi_{ 629 } ( 84, ·)\) \(\chi_{ 629 } ( 38, ·)\) \(\chi_{ 629 } ( 186, ·)\) \(\chi_{ 629 } ( 137, ·)\) \(\chi_{ 629 } ( 174, ·)\) \(\chi_{ 629 } ( 285, ·)\) \(\chi_{ 629 } ( 528, ·)\) \(\chi_{ 629 } ( 47, ·)\) \(\chi_{ 629 } ( 1, ·)\) \(\chi_{ 629 } ( 322, ·)\)