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

$K$ is the global number field defined by \( x^{16} - 113 x^{8} + 6561 \)

$\times$ \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\)
\(\chi_{ 176 }(1, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\)
\(\chi_{ 176 }(67, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\)
\(\chi_{ 176 }(133, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\)
\(\chi_{ 176 }(65, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\)
\(\chi_{ 176 }(87, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\)
\(\chi_{ 176 }(45, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\)
\(\chi_{ 176 }(131, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\)
\(\chi_{ 176 }(21, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\)
\(\chi_{ 176 }(23, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\)
\(\chi_{ 176 }(89, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\)
\(\chi_{ 176 }(111, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\)
\(\chi_{ 176 }(155, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\)
\(\chi_{ 176 }(43, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\)
\(\chi_{ 176 }(109, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\)
\(\chi_{ 176 }(175, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 1, ·)\) \(\chi_{ 176 } ( 23, ·)\)
\(\chi_{ 176 }(153, ·)\) \(\chi_{ 176 } ( 153, ·)\) \(\chi_{ 176 } ( 43, ·)\) \(\chi_{ 176 } ( 109, ·)\) \(\chi_{ 176 } ( 89, ·)\) \(\chi_{ 176 } ( 111, ·)\) \(\chi_{ 176 } ( 21, ·)\) \(\chi_{ 176 } ( 155, ·)\) \(\chi_{ 176 } ( 45, ·)\) \(\chi_{ 176 } ( 175, ·)\) \(\chi_{ 176 } ( 65, ·)\) \(\chi_{ 176 } ( 87, ·)\) \(\chi_{ 176 } ( 131, ·)\) \(\chi_{ 176 } ( 67, ·)\) \(\chi_{ 176 } ( 133, ·)\) \(\chi_{ 176 } ( 23, ·)\) \(\chi_{ 176 } ( 1, ·)\)