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

$K$ is the global number field defined by \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \)

$\times$ \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 32, ·)\)
\(\chi_{ 33 }(1, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 32, ·)\)
\(\chi_{ 33 }(2, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 31, ·)\)
\(\chi_{ 33 }(4, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 29, ·)\)
\(\chi_{ 33 }(5, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 28, ·)\)
\(\chi_{ 33 }(7, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 26, ·)\)
\(\chi_{ 33 }(8, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 25, ·)\)
\(\chi_{ 33 }(10, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 23, ·)\)
\(\chi_{ 33 }(13, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 20, ·)\)
\(\chi_{ 33 }(14, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 19, ·)\)
\(\chi_{ 33 }(16, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 17, ·)\)
\(\chi_{ 33 }(17, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 16, ·)\)
\(\chi_{ 33 }(19, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 14, ·)\)
\(\chi_{ 33 }(20, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 13, ·)\)
\(\chi_{ 33 }(23, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 10, ·)\)
\(\chi_{ 33 }(25, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 8, ·)\)
\(\chi_{ 33 }(26, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 7, ·)\)
\(\chi_{ 33 }(28, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 5, ·)\)
\(\chi_{ 33 }(29, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 4, ·)\)
\(\chi_{ 33 }(31, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 1, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 2, ·)\)
\(\chi_{ 33 }(32, ·)\) \(\chi_{ 33 } ( 32, ·)\) \(\chi_{ 33 } ( 31, ·)\) \(\chi_{ 33 } ( 29, ·)\) \(\chi_{ 33 } ( 28, ·)\) \(\chi_{ 33 } ( 26, ·)\) \(\chi_{ 33 } ( 25, ·)\) \(\chi_{ 33 } ( 23, ·)\) \(\chi_{ 33 } ( 20, ·)\) \(\chi_{ 33 } ( 19, ·)\) \(\chi_{ 33 } ( 17, ·)\) \(\chi_{ 33 } ( 16, ·)\) \(\chi_{ 33 } ( 14, ·)\) \(\chi_{ 33 } ( 13, ·)\) \(\chi_{ 33 } ( 10, ·)\) \(\chi_{ 33 } ( 8, ·)\) \(\chi_{ 33 } ( 7, ·)\) \(\chi_{ 33 } ( 5, ·)\) \(\chi_{ 33 } ( 4, ·)\) \(\chi_{ 33 } ( 2, ·)\) \(\chi_{ 33 } ( 1, ·)\)