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^{28} - x^{27} + 14 x^{26} - 11 x^{25} + 115 x^{24} - 79 x^{23} + 617 x^{22} - 353 x^{21} + 2421 x^{20} - 1188 x^{19} + 7015 x^{18} - 2803 x^{17} + 15415 x^{16} - 5107 x^{15} + 25195 x^{14} - 6334 x^{13} + 30532 x^{12} - 6088 x^{11} + 26057 x^{10} - 3239 x^{9} + 15207 x^{8} - 1590 x^{7} + 5362 x^{6} - 70 x^{5} + 1050 x^{4} - 84 x^{3} + 77 x^{2} + 7 x + 1 $

$\times$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 65, ·)$
$\chi_{ 87 }(1, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 65, ·)$
$\chi_{ 87 }(64, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 71, ·)$
$\chi_{ 87 }(86, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 22, ·)$
$\chi_{ 87 }(67, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 5, ·)$
$\chi_{ 87 }(4, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 86, ·)$
$\chi_{ 87 }(5, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 64, ·)$
$\chi_{ 87 }(7, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 20, ·)$
$\chi_{ 87 }(74, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 25, ·)$
$\chi_{ 87 }(13, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 62, ·)$
$\chi_{ 87 }(16, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 83, ·)$
$\chi_{ 87 }(82, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 23, ·)$
$\chi_{ 87 }(83, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 1, ·)$
$\chi_{ 87 }(20, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 82, ·)$
$\chi_{ 87 }(22, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 38, ·)$
$\chi_{ 87 }(23, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 16, ·)$
$\chi_{ 87 }(25, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 59, ·)$
$\chi_{ 87 }(28, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 80, ·)$
$\chi_{ 87 }(80, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 67, ·)$
$\chi_{ 87 }(34, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 35, ·)$
$\chi_{ 87 }(35, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 13, ·)$
$\chi_{ 87 }(38, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 34, ·)$
$\chi_{ 87 }(71, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 4, ·)$
$\chi_{ 87 }(49, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 53, ·)$
$\chi_{ 87 }(52, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 74, ·)$
$\chi_{ 87 }(53, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 52, ·)$
$\chi_{ 87 }(59, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 7, ·)$
$\chi_{ 87 }(62, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 49, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 28, ·)$
$\chi_{ 87 }(65, ·)$	$\chi_{ 87 } ( 65, ·)$	$\chi_{ 87 } ( 71, ·)$	$\chi_{ 87 } ( 22, ·)$	$\chi_{ 87 } ( 5, ·)$	$\chi_{ 87 } ( 86, ·)$	$\chi_{ 87 } ( 64, ·)$	$\chi_{ 87 } ( 20, ·)$	$\chi_{ 87 } ( 25, ·)$	$\chi_{ 87 } ( 62, ·)$	$\chi_{ 87 } ( 83, ·)$	$\chi_{ 87 } ( 23, ·)$	$\chi_{ 87 } ( 1, ·)$	$\chi_{ 87 } ( 82, ·)$	$\chi_{ 87 } ( 38, ·)$	$\chi_{ 87 } ( 16, ·)$	$\chi_{ 87 } ( 59, ·)$	$\chi_{ 87 } ( 80, ·)$	$\chi_{ 87 } ( 67, ·)$	$\chi_{ 87 } ( 35, ·)$	$\chi_{ 87 } ( 13, ·)$	$\chi_{ 87 } ( 34, ·)$	$\chi_{ 87 } ( 4, ·)$	$\chi_{ 87 } ( 53, ·)$	$\chi_{ 87 } ( 74, ·)$	$\chi_{ 87 } ( 52, ·)$	$\chi_{ 87 } ( 7, ·)$	$\chi_{ 87 } ( 28, ·)$	$\chi_{ 87 } ( 49, ·)$

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 $\F_{q}$

$\times$	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 65, ·)\)
\(\chi_{ 87 }(1, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 65, ·)\)
\(\chi_{ 87 }(64, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 71, ·)\)
\(\chi_{ 87 }(86, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 22, ·)\)
\(\chi_{ 87 }(67, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 5, ·)\)
\(\chi_{ 87 }(4, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 86, ·)\)
\(\chi_{ 87 }(5, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 64, ·)\)
\(\chi_{ 87 }(7, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 20, ·)\)
\(\chi_{ 87 }(74, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 25, ·)\)
\(\chi_{ 87 }(13, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 62, ·)\)
\(\chi_{ 87 }(16, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 83, ·)\)
\(\chi_{ 87 }(82, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 23, ·)\)
\(\chi_{ 87 }(83, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 1, ·)\)
\(\chi_{ 87 }(20, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 82, ·)\)
\(\chi_{ 87 }(22, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 38, ·)\)
\(\chi_{ 87 }(23, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 16, ·)\)
\(\chi_{ 87 }(25, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 59, ·)\)
\(\chi_{ 87 }(28, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 80, ·)\)
\(\chi_{ 87 }(80, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 67, ·)\)
\(\chi_{ 87 }(34, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 35, ·)\)
\(\chi_{ 87 }(35, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 13, ·)\)
\(\chi_{ 87 }(38, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 34, ·)\)
\(\chi_{ 87 }(71, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 4, ·)\)
\(\chi_{ 87 }(49, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 53, ·)\)
\(\chi_{ 87 }(52, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 74, ·)\)
\(\chi_{ 87 }(53, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 52, ·)\)
\(\chi_{ 87 }(59, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 7, ·)\)
\(\chi_{ 87 }(62, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 49, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 28, ·)\)
\(\chi_{ 87 }(65, ·)\)	\(\chi_{ 87 } ( 65, ·)\)	\(\chi_{ 87 } ( 71, ·)\)	\(\chi_{ 87 } ( 22, ·)\)	\(\chi_{ 87 } ( 5, ·)\)	\(\chi_{ 87 } ( 86, ·)\)	\(\chi_{ 87 } ( 64, ·)\)	\(\chi_{ 87 } ( 20, ·)\)	\(\chi_{ 87 } ( 25, ·)\)	\(\chi_{ 87 } ( 62, ·)\)	\(\chi_{ 87 } ( 83, ·)\)	\(\chi_{ 87 } ( 23, ·)\)	\(\chi_{ 87 } ( 1, ·)\)	\(\chi_{ 87 } ( 82, ·)\)	\(\chi_{ 87 } ( 38, ·)\)	\(\chi_{ 87 } ( 16, ·)\)	\(\chi_{ 87 } ( 59, ·)\)	\(\chi_{ 87 } ( 80, ·)\)	\(\chi_{ 87 } ( 67, ·)\)	\(\chi_{ 87 } ( 35, ·)\)	\(\chi_{ 87 } ( 13, ·)\)	\(\chi_{ 87 } ( 34, ·)\)	\(\chi_{ 87 } ( 4, ·)\)	\(\chi_{ 87 } ( 53, ·)\)	\(\chi_{ 87 } ( 74, ·)\)	\(\chi_{ 87 } ( 52, ·)\)	\(\chi_{ 87 } ( 7, ·)\)	\(\chi_{ 87 } ( 28, ·)\)	\(\chi_{ 87 } ( 49, ·)\)

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.