LMFDB - Group of Dirichlet characters

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

$K$ is the global number field defined by $ x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $

$\times$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 67, ·)$
$\chi_{ 68 }(1, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 67, ·)$
$\chi_{ 68 }(3, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 65, ·)$
$\chi_{ 68 }(5, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 63, ·)$
$\chi_{ 68 }(7, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 61, ·)$
$\chi_{ 68 }(9, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 59, ·)$
$\chi_{ 68 }(11, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 57, ·)$
$\chi_{ 68 }(13, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 55, ·)$
$\chi_{ 68 }(15, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 53, ·)$
$\chi_{ 68 }(19, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 49, ·)$
$\chi_{ 68 }(21, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 47, ·)$
$\chi_{ 68 }(23, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 45, ·)$
$\chi_{ 68 }(25, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 43, ·)$
$\chi_{ 68 }(27, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 41, ·)$
$\chi_{ 68 }(29, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 39, ·)$
$\chi_{ 68 }(31, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 37, ·)$
$\chi_{ 68 }(33, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 35, ·)$
$\chi_{ 68 }(35, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 33, ·)$
$\chi_{ 68 }(37, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 31, ·)$
$\chi_{ 68 }(39, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 29, ·)$
$\chi_{ 68 }(41, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 27, ·)$
$\chi_{ 68 }(43, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 25, ·)$
$\chi_{ 68 }(45, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 23, ·)$
$\chi_{ 68 }(47, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 21, ·)$
$\chi_{ 68 }(49, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 19, ·)$
$\chi_{ 68 }(53, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 15, ·)$
$\chi_{ 68 }(55, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 13, ·)$
$\chi_{ 68 }(57, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 11, ·)$
$\chi_{ 68 }(59, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 9, ·)$
$\chi_{ 68 }(61, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 7, ·)$
$\chi_{ 68 }(63, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 5, ·)$
$\chi_{ 68 }(65, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 1, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 3, ·)$
$\chi_{ 68 }(67, ·)$	$\chi_{ 68 } ( 67, ·)$	$\chi_{ 68 } ( 65, ·)$	$\chi_{ 68 } ( 63, ·)$	$\chi_{ 68 } ( 61, ·)$	$\chi_{ 68 } ( 59, ·)$	$\chi_{ 68 } ( 57, ·)$	$\chi_{ 68 } ( 55, ·)$	$\chi_{ 68 } ( 53, ·)$	$\chi_{ 68 } ( 49, ·)$	$\chi_{ 68 } ( 47, ·)$	$\chi_{ 68 } ( 45, ·)$	$\chi_{ 68 } ( 43, ·)$	$\chi_{ 68 } ( 41, ·)$	$\chi_{ 68 } ( 39, ·)$	$\chi_{ 68 } ( 37, ·)$	$\chi_{ 68 } ( 35, ·)$	$\chi_{ 68 } ( 33, ·)$	$\chi_{ 68 } ( 31, ·)$	$\chi_{ 68 } ( 29, ·)$	$\chi_{ 68 } ( 27, ·)$	$\chi_{ 68 } ( 25, ·)$	$\chi_{ 68 } ( 23, ·)$	$\chi_{ 68 } ( 21, ·)$	$\chi_{ 68 } ( 19, ·)$	$\chi_{ 68 } ( 15, ·)$	$\chi_{ 68 } ( 13, ·)$	$\chi_{ 68 } ( 11, ·)$	$\chi_{ 68 } ( 9, ·)$	$\chi_{ 68 } ( 7, ·)$	$\chi_{ 68 } ( 5, ·)$	$\chi_{ 68 } ( 3, ·)$	$\chi_{ 68 } ( 1, ·)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

$\times$	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 67, ·)\)
\(\chi_{ 68 }(1, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 67, ·)\)
\(\chi_{ 68 }(3, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 65, ·)\)
\(\chi_{ 68 }(5, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 63, ·)\)
\(\chi_{ 68 }(7, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 61, ·)\)
\(\chi_{ 68 }(9, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 59, ·)\)
\(\chi_{ 68 }(11, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 57, ·)\)
\(\chi_{ 68 }(13, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 55, ·)\)
\(\chi_{ 68 }(15, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 53, ·)\)
\(\chi_{ 68 }(19, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 49, ·)\)
\(\chi_{ 68 }(21, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 47, ·)\)
\(\chi_{ 68 }(23, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 45, ·)\)
\(\chi_{ 68 }(25, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 43, ·)\)
\(\chi_{ 68 }(27, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 41, ·)\)
\(\chi_{ 68 }(29, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 39, ·)\)
\(\chi_{ 68 }(31, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 37, ·)\)
\(\chi_{ 68 }(33, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 35, ·)\)
\(\chi_{ 68 }(35, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 33, ·)\)
\(\chi_{ 68 }(37, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 31, ·)\)
\(\chi_{ 68 }(39, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 29, ·)\)
\(\chi_{ 68 }(41, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 27, ·)\)
\(\chi_{ 68 }(43, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 25, ·)\)
\(\chi_{ 68 }(45, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 23, ·)\)
\(\chi_{ 68 }(47, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 21, ·)\)
\(\chi_{ 68 }(49, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 19, ·)\)
\(\chi_{ 68 }(53, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 15, ·)\)
\(\chi_{ 68 }(55, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 13, ·)\)
\(\chi_{ 68 }(57, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 11, ·)\)
\(\chi_{ 68 }(59, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 9, ·)\)
\(\chi_{ 68 }(61, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 7, ·)\)
\(\chi_{ 68 }(63, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 5, ·)\)
\(\chi_{ 68 }(65, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 1, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 3, ·)\)
\(\chi_{ 68 }(67, ·)\)	\(\chi_{ 68 } ( 67, ·)\)	\(\chi_{ 68 } ( 65, ·)\)	\(\chi_{ 68 } ( 63, ·)\)	\(\chi_{ 68 } ( 61, ·)\)	\(\chi_{ 68 } ( 59, ·)\)	\(\chi_{ 68 } ( 57, ·)\)	\(\chi_{ 68 } ( 55, ·)\)	\(\chi_{ 68 } ( 53, ·)\)	\(\chi_{ 68 } ( 49, ·)\)	\(\chi_{ 68 } ( 47, ·)\)	\(\chi_{ 68 } ( 45, ·)\)	\(\chi_{ 68 } ( 43, ·)\)	\(\chi_{ 68 } ( 41, ·)\)	\(\chi_{ 68 } ( 39, ·)\)	\(\chi_{ 68 } ( 37, ·)\)	\(\chi_{ 68 } ( 35, ·)\)	\(\chi_{ 68 } ( 33, ·)\)	\(\chi_{ 68 } ( 31, ·)\)	\(\chi_{ 68 } ( 29, ·)\)	\(\chi_{ 68 } ( 27, ·)\)	\(\chi_{ 68 } ( 25, ·)\)	\(\chi_{ 68 } ( 23, ·)\)	\(\chi_{ 68 } ( 21, ·)\)	\(\chi_{ 68 } ( 19, ·)\)	\(\chi_{ 68 } ( 15, ·)\)	\(\chi_{ 68 } ( 13, ·)\)	\(\chi_{ 68 } ( 11, ·)\)	\(\chi_{ 68 } ( 9, ·)\)	\(\chi_{ 68 } ( 7, ·)\)	\(\chi_{ 68 } ( 5, ·)\)	\(\chi_{ 68 } ( 3, ·)\)	\(\chi_{ 68 } ( 1, ·)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.