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^{31} + x^{29} - x^{28} + x^{26} - x^{25} + x^{23} - x^{22} + x^{20} - x^{19} + x^{17} - x^{16} + x^{15} - x^{13} + x^{12} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $

$\times$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 50, ·)$
$\chi_{ 51 }(1, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 50, ·)$
$\chi_{ 51 }(2, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 49, ·)$
$\chi_{ 51 }(4, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 47, ·)$
$\chi_{ 51 }(5, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 46, ·)$
$\chi_{ 51 }(7, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 44, ·)$
$\chi_{ 51 }(8, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 43, ·)$
$\chi_{ 51 }(10, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 41, ·)$
$\chi_{ 51 }(11, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 40, ·)$
$\chi_{ 51 }(13, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 38, ·)$
$\chi_{ 51 }(14, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 37, ·)$
$\chi_{ 51 }(16, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 35, ·)$
$\chi_{ 51 }(19, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 32, ·)$
$\chi_{ 51 }(20, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 31, ·)$
$\chi_{ 51 }(22, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 29, ·)$
$\chi_{ 51 }(23, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 28, ·)$
$\chi_{ 51 }(25, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 26, ·)$
$\chi_{ 51 }(26, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 25, ·)$
$\chi_{ 51 }(28, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 23, ·)$
$\chi_{ 51 }(29, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 22, ·)$
$\chi_{ 51 }(31, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 20, ·)$
$\chi_{ 51 }(32, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 19, ·)$
$\chi_{ 51 }(35, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 16, ·)$
$\chi_{ 51 }(37, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 14, ·)$
$\chi_{ 51 }(38, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 13, ·)$
$\chi_{ 51 }(40, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 11, ·)$
$\chi_{ 51 }(41, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 10, ·)$
$\chi_{ 51 }(43, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 8, ·)$
$\chi_{ 51 }(44, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 7, ·)$
$\chi_{ 51 }(46, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 5, ·)$
$\chi_{ 51 }(47, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 4, ·)$
$\chi_{ 51 }(49, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 1, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 2, ·)$
$\chi_{ 51 }(50, ·)$	$\chi_{ 51 } ( 50, ·)$	$\chi_{ 51 } ( 49, ·)$	$\chi_{ 51 } ( 47, ·)$	$\chi_{ 51 } ( 46, ·)$	$\chi_{ 51 } ( 44, ·)$	$\chi_{ 51 } ( 43, ·)$	$\chi_{ 51 } ( 41, ·)$	$\chi_{ 51 } ( 40, ·)$	$\chi_{ 51 } ( 38, ·)$	$\chi_{ 51 } ( 37, ·)$	$\chi_{ 51 } ( 35, ·)$	$\chi_{ 51 } ( 32, ·)$	$\chi_{ 51 } ( 31, ·)$	$\chi_{ 51 } ( 29, ·)$	$\chi_{ 51 } ( 28, ·)$	$\chi_{ 51 } ( 26, ·)$	$\chi_{ 51 } ( 25, ·)$	$\chi_{ 51 } ( 23, ·)$	$\chi_{ 51 } ( 22, ·)$	$\chi_{ 51 } ( 20, ·)$	$\chi_{ 51 } ( 19, ·)$	$\chi_{ 51 } ( 16, ·)$	$\chi_{ 51 } ( 14, ·)$	$\chi_{ 51 } ( 13, ·)$	$\chi_{ 51 } ( 11, ·)$	$\chi_{ 51 } ( 10, ·)$	$\chi_{ 51 } ( 8, ·)$	$\chi_{ 51 } ( 7, ·)$	$\chi_{ 51 } ( 5, ·)$	$\chi_{ 51 } ( 4, ·)$	$\chi_{ 51 } ( 2, ·)$	$\chi_{ 51 } ( 1, ·)$

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 $\F_{q}$

$\times$	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 50, ·)\)
\(\chi_{ 51 }(1, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 50, ·)\)
\(\chi_{ 51 }(2, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 49, ·)\)
\(\chi_{ 51 }(4, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 47, ·)\)
\(\chi_{ 51 }(5, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 46, ·)\)
\(\chi_{ 51 }(7, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 44, ·)\)
\(\chi_{ 51 }(8, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 43, ·)\)
\(\chi_{ 51 }(10, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 41, ·)\)
\(\chi_{ 51 }(11, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 40, ·)\)
\(\chi_{ 51 }(13, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 38, ·)\)
\(\chi_{ 51 }(14, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 37, ·)\)
\(\chi_{ 51 }(16, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 35, ·)\)
\(\chi_{ 51 }(19, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 32, ·)\)
\(\chi_{ 51 }(20, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 31, ·)\)
\(\chi_{ 51 }(22, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 29, ·)\)
\(\chi_{ 51 }(23, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 28, ·)\)
\(\chi_{ 51 }(25, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 26, ·)\)
\(\chi_{ 51 }(26, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 25, ·)\)
\(\chi_{ 51 }(28, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 23, ·)\)
\(\chi_{ 51 }(29, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 22, ·)\)
\(\chi_{ 51 }(31, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 20, ·)\)
\(\chi_{ 51 }(32, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 19, ·)\)
\(\chi_{ 51 }(35, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 16, ·)\)
\(\chi_{ 51 }(37, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 14, ·)\)
\(\chi_{ 51 }(38, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 13, ·)\)
\(\chi_{ 51 }(40, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 11, ·)\)
\(\chi_{ 51 }(41, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 10, ·)\)
\(\chi_{ 51 }(43, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 8, ·)\)
\(\chi_{ 51 }(44, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 7, ·)\)
\(\chi_{ 51 }(46, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 5, ·)\)
\(\chi_{ 51 }(47, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 4, ·)\)
\(\chi_{ 51 }(49, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 1, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 2, ·)\)
\(\chi_{ 51 }(50, ·)\)	\(\chi_{ 51 } ( 50, ·)\)	\(\chi_{ 51 } ( 49, ·)\)	\(\chi_{ 51 } ( 47, ·)\)	\(\chi_{ 51 } ( 46, ·)\)	\(\chi_{ 51 } ( 44, ·)\)	\(\chi_{ 51 } ( 43, ·)\)	\(\chi_{ 51 } ( 41, ·)\)	\(\chi_{ 51 } ( 40, ·)\)	\(\chi_{ 51 } ( 38, ·)\)	\(\chi_{ 51 } ( 37, ·)\)	\(\chi_{ 51 } ( 35, ·)\)	\(\chi_{ 51 } ( 32, ·)\)	\(\chi_{ 51 } ( 31, ·)\)	\(\chi_{ 51 } ( 29, ·)\)	\(\chi_{ 51 } ( 28, ·)\)	\(\chi_{ 51 } ( 26, ·)\)	\(\chi_{ 51 } ( 25, ·)\)	\(\chi_{ 51 } ( 23, ·)\)	\(\chi_{ 51 } ( 22, ·)\)	\(\chi_{ 51 } ( 20, ·)\)	\(\chi_{ 51 } ( 19, ·)\)	\(\chi_{ 51 } ( 16, ·)\)	\(\chi_{ 51 } ( 14, ·)\)	\(\chi_{ 51 } ( 13, ·)\)	\(\chi_{ 51 } ( 11, ·)\)	\(\chi_{ 51 } ( 10, ·)\)	\(\chi_{ 51 } ( 8, ·)\)	\(\chi_{ 51 } ( 7, ·)\)	\(\chi_{ 51 } ( 5, ·)\)	\(\chi_{ 51 } ( 4, ·)\)	\(\chi_{ 51 } ( 2, ·)\)	\(\chi_{ 51 } ( 1, ·)\)

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.