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