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

$K$ is the global number field defined by \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)  Toggle raw display

$\times$ \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 24, ·)\)
\(\chi_{ 25 }(1, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 24, ·)\)
\(\chi_{ 25 }(2, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 23, ·)\)
\(\chi_{ 25 }(3, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 22, ·)\)
\(\chi_{ 25 }(4, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 21, ·)\)
\(\chi_{ 25 }(6, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 19, ·)\)
\(\chi_{ 25 }(7, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 18, ·)\)
\(\chi_{ 25 }(8, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 17, ·)\)
\(\chi_{ 25 }(9, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 16, ·)\)
\(\chi_{ 25 }(11, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 14, ·)\)
\(\chi_{ 25 }(12, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 13, ·)\)
\(\chi_{ 25 }(13, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 12, ·)\)
\(\chi_{ 25 }(14, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 11, ·)\)
\(\chi_{ 25 }(16, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 9, ·)\)
\(\chi_{ 25 }(17, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 8, ·)\)
\(\chi_{ 25 }(18, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 7, ·)\)
\(\chi_{ 25 }(19, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 6, ·)\)
\(\chi_{ 25 }(21, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 4, ·)\)
\(\chi_{ 25 }(22, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 3, ·)\)
\(\chi_{ 25 }(23, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 1, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 2, ·)\)
\(\chi_{ 25 }(24, ·)\) \(\chi_{ 25 } ( 24, ·)\) \(\chi_{ 25 } ( 23, ·)\) \(\chi_{ 25 } ( 22, ·)\) \(\chi_{ 25 } ( 21, ·)\) \(\chi_{ 25 } ( 19, ·)\) \(\chi_{ 25 } ( 18, ·)\) \(\chi_{ 25 } ( 17, ·)\) \(\chi_{ 25 } ( 16, ·)\) \(\chi_{ 25 } ( 14, ·)\) \(\chi_{ 25 } ( 13, ·)\) \(\chi_{ 25 } ( 12, ·)\) \(\chi_{ 25 } ( 11, ·)\) \(\chi_{ 25 } ( 9, ·)\) \(\chi_{ 25 } ( 8, ·)\) \(\chi_{ 25 } ( 7, ·)\) \(\chi_{ 25 } ( 6, ·)\) \(\chi_{ 25 } ( 4, ·)\) \(\chi_{ 25 } ( 3, ·)\) \(\chi_{ 25 } ( 2, ·)\) \(\chi_{ 25 } ( 1, ·)\)