Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
$\times$ | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 24, ·)\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{ 25 }(1, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 24, ·)\) |
\(\chi_{ 25 }(2, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 23, ·)\) |
\(\chi_{ 25 }(3, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 22, ·)\) |
\(\chi_{ 25 }(4, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 21, ·)\) |
\(\chi_{ 25 }(6, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 19, ·)\) |
\(\chi_{ 25 }(7, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 18, ·)\) |
\(\chi_{ 25 }(8, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 17, ·)\) |
\(\chi_{ 25 }(9, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 16, ·)\) |
\(\chi_{ 25 }(11, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 14, ·)\) |
\(\chi_{ 25 }(12, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 13, ·)\) |
\(\chi_{ 25 }(13, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 12, ·)\) |
\(\chi_{ 25 }(14, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 11, ·)\) |
\(\chi_{ 25 }(16, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 9, ·)\) |
\(\chi_{ 25 }(17, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 8, ·)\) |
\(\chi_{ 25 }(18, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 7, ·)\) |
\(\chi_{ 25 }(19, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 6, ·)\) |
\(\chi_{ 25 }(21, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 4, ·)\) |
\(\chi_{ 25 }(22, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 3, ·)\) |
\(\chi_{ 25 }(23, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 1, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 2, ·)\) |
\(\chi_{ 25 }(24, ·)\) | \(\chi_{ 25 } ( 24, ·)\) | \(\chi_{ 25 } ( 23, ·)\) | \(\chi_{ 25 } ( 22, ·)\) | \(\chi_{ 25 } ( 21, ·)\) | \(\chi_{ 25 } ( 19, ·)\) | \(\chi_{ 25 } ( 18, ·)\) | \(\chi_{ 25 } ( 17, ·)\) | \(\chi_{ 25 } ( 16, ·)\) | \(\chi_{ 25 } ( 14, ·)\) | \(\chi_{ 25 } ( 13, ·)\) | \(\chi_{ 25 } ( 12, ·)\) | \(\chi_{ 25 } ( 11, ·)\) | \(\chi_{ 25 } ( 9, ·)\) | \(\chi_{ 25 } ( 8, ·)\) | \(\chi_{ 25 } ( 7, ·)\) | \(\chi_{ 25 } ( 6, ·)\) | \(\chi_{ 25 } ( 4, ·)\) | \(\chi_{ 25 } ( 3, ·)\) | \(\chi_{ 25 } ( 2, ·)\) | \(\chi_{ 25 } ( 1, ·)\) |