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

$K$ is the global number field defined by \( x^{16} - 31 x^{8} + 256 \)

$\times$ \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 57, ·)\)
\(\chi_{ 112 }(1, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 57, ·)\)
\(\chi_{ 112 }(69, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 13, ·)\)
\(\chi_{ 112 }(71, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 15, ·)\)
\(\chi_{ 112 }(13, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 69, ·)\)
\(\chi_{ 112 }(15, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 71, ·)\)
\(\chi_{ 112 }(83, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 27, ·)\)
\(\chi_{ 112 }(85, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 29, ·)\)
\(\chi_{ 112 }(27, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 83, ·)\)
\(\chi_{ 112 }(29, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 85, ·)\)
\(\chi_{ 112 }(97, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 41, ·)\)
\(\chi_{ 112 }(99, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 43, ·)\)
\(\chi_{ 112 }(41, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 97, ·)\)
\(\chi_{ 112 }(43, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 99, ·)\)
\(\chi_{ 112 }(111, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 55, ·)\)
\(\chi_{ 112 }(55, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 1, ·)\) \(\chi_{ 112 } ( 111, ·)\)
\(\chi_{ 112 }(57, ·)\) \(\chi_{ 112 } ( 57, ·)\) \(\chi_{ 112 } ( 13, ·)\) \(\chi_{ 112 } ( 15, ·)\) \(\chi_{ 112 } ( 69, ·)\) \(\chi_{ 112 } ( 71, ·)\) \(\chi_{ 112 } ( 27, ·)\) \(\chi_{ 112 } ( 29, ·)\) \(\chi_{ 112 } ( 83, ·)\) \(\chi_{ 112 } ( 85, ·)\) \(\chi_{ 112 } ( 41, ·)\) \(\chi_{ 112 } ( 43, ·)\) \(\chi_{ 112 } ( 97, ·)\) \(\chi_{ 112 } ( 99, ·)\) \(\chi_{ 112 } ( 55, ·)\) \(\chi_{ 112 } ( 111, ·)\) \(\chi_{ 112 } ( 1, ·)\)