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

$K$ is the global number field defined by \( x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display

$\times$ \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 18, ·)\)
\(\chi_{ 19 }(1, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 18, ·)\)
\(\chi_{ 19 }(2, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 17, ·)\)
\(\chi_{ 19 }(3, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 16, ·)\)
\(\chi_{ 19 }(4, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 15, ·)\)
\(\chi_{ 19 }(5, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 14, ·)\)
\(\chi_{ 19 }(6, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 13, ·)\)
\(\chi_{ 19 }(7, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 12, ·)\)
\(\chi_{ 19 }(8, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 11, ·)\)
\(\chi_{ 19 }(9, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 10, ·)\)
\(\chi_{ 19 }(10, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 9, ·)\)
\(\chi_{ 19 }(11, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 8, ·)\)
\(\chi_{ 19 }(12, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 7, ·)\)
\(\chi_{ 19 }(13, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 6, ·)\)
\(\chi_{ 19 }(14, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 5, ·)\)
\(\chi_{ 19 }(15, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 4, ·)\)
\(\chi_{ 19 }(16, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 3, ·)\)
\(\chi_{ 19 }(17, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 1, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 2, ·)\)
\(\chi_{ 19 }(18, ·)\) \(\chi_{ 19 } ( 18, ·)\) \(\chi_{ 19 } ( 17, ·)\) \(\chi_{ 19 } ( 16, ·)\) \(\chi_{ 19 } ( 15, ·)\) \(\chi_{ 19 } ( 14, ·)\) \(\chi_{ 19 } ( 13, ·)\) \(\chi_{ 19 } ( 12, ·)\) \(\chi_{ 19 } ( 11, ·)\) \(\chi_{ 19 } ( 10, ·)\) \(\chi_{ 19 } ( 9, ·)\) \(\chi_{ 19 } ( 8, ·)\) \(\chi_{ 19 } ( 7, ·)\) \(\chi_{ 19 } ( 6, ·)\) \(\chi_{ 19 } ( 5, ·)\) \(\chi_{ 19 } ( 4, ·)\) \(\chi_{ 19 } ( 3, ·)\) \(\chi_{ 19 } ( 2, ·)\) \(\chi_{ 19 } ( 1, ·)\)