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^{20} - x^{19} - 19 x^{18} + 18 x^{17} + 153 x^{16} - 136 x^{15} - 680 x^{14} + 560 x^{13} + 1820 x^{12} + \cdots + 1 $ x^20 - x^19 - 19*x^18 + 18*x^17 + 153*x^16 - 136*x^15 - 680*x^14 + 560*x^13 + 1820*x^12 - 1365*x^11 - 3003*x^10 + 2002*x^9 + 3003*x^8 - 1716*x^7 - 1716*x^6 + 792*x^5 + 495*x^4 - 165*x^3 - 55*x^2 + 10*x + 1

$\times$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 40, ·)$
$\chi_{ 41 }(1, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 40, ·)$
$\chi_{ 41 }(2, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 39, ·)$
$\chi_{ 41 }(4, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 37, ·)$
$\chi_{ 41 }(5, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 36, ·)$
$\chi_{ 41 }(8, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 33, ·)$
$\chi_{ 41 }(9, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 32, ·)$
$\chi_{ 41 }(10, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 31, ·)$
$\chi_{ 41 }(16, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 25, ·)$
$\chi_{ 41 }(18, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 23, ·)$
$\chi_{ 41 }(20, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 21, ·)$
$\chi_{ 41 }(21, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 20, ·)$
$\chi_{ 41 }(23, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 18, ·)$
$\chi_{ 41 }(25, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 16, ·)$
$\chi_{ 41 }(31, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 10, ·)$
$\chi_{ 41 }(32, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 9, ·)$
$\chi_{ 41 }(33, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 8, ·)$
$\chi_{ 41 }(36, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 5, ·)$
$\chi_{ 41 }(37, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 4, ·)$
$\chi_{ 41 }(39, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 1, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 2, ·)$
$\chi_{ 41 }(40, ·)$	$\chi_{ 41 } ( 40, ·)$	$\chi_{ 41 } ( 39, ·)$	$\chi_{ 41 } ( 37, ·)$	$\chi_{ 41 } ( 36, ·)$	$\chi_{ 41 } ( 33, ·)$	$\chi_{ 41 } ( 32, ·)$	$\chi_{ 41 } ( 31, ·)$	$\chi_{ 41 } ( 25, ·)$	$\chi_{ 41 } ( 23, ·)$	$\chi_{ 41 } ( 21, ·)$	$\chi_{ 41 } ( 20, ·)$	$\chi_{ 41 } ( 18, ·)$	$\chi_{ 41 } ( 16, ·)$	$\chi_{ 41 } ( 10, ·)$	$\chi_{ 41 } ( 9, ·)$	$\chi_{ 41 } ( 8, ·)$	$\chi_{ 41 } ( 5, ·)$	$\chi_{ 41 } ( 4, ·)$	$\chi_{ 41 } ( 2, ·)$	$\chi_{ 41 } ( 1, ·)$

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 $\F_{q}$

$\times$	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 40, ·)\)
\(\chi_{ 41 }(1, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 40, ·)\)
\(\chi_{ 41 }(2, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 39, ·)\)
\(\chi_{ 41 }(4, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 37, ·)\)
\(\chi_{ 41 }(5, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 36, ·)\)
\(\chi_{ 41 }(8, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 33, ·)\)
\(\chi_{ 41 }(9, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 32, ·)\)
\(\chi_{ 41 }(10, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 31, ·)\)
\(\chi_{ 41 }(16, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 25, ·)\)
\(\chi_{ 41 }(18, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 23, ·)\)
\(\chi_{ 41 }(20, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 21, ·)\)
\(\chi_{ 41 }(21, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 20, ·)\)
\(\chi_{ 41 }(23, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 18, ·)\)
\(\chi_{ 41 }(25, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 16, ·)\)
\(\chi_{ 41 }(31, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 10, ·)\)
\(\chi_{ 41 }(32, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 9, ·)\)
\(\chi_{ 41 }(33, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 8, ·)\)
\(\chi_{ 41 }(36, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 5, ·)\)
\(\chi_{ 41 }(37, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 4, ·)\)
\(\chi_{ 41 }(39, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 1, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 2, ·)\)
\(\chi_{ 41 }(40, ·)\)	\(\chi_{ 41 } ( 40, ·)\)	\(\chi_{ 41 } ( 39, ·)\)	\(\chi_{ 41 } ( 37, ·)\)	\(\chi_{ 41 } ( 36, ·)\)	\(\chi_{ 41 } ( 33, ·)\)	\(\chi_{ 41 } ( 32, ·)\)	\(\chi_{ 41 } ( 31, ·)\)	\(\chi_{ 41 } ( 25, ·)\)	\(\chi_{ 41 } ( 23, ·)\)	\(\chi_{ 41 } ( 21, ·)\)	\(\chi_{ 41 } ( 20, ·)\)	\(\chi_{ 41 } ( 18, ·)\)	\(\chi_{ 41 } ( 16, ·)\)	\(\chi_{ 41 } ( 10, ·)\)	\(\chi_{ 41 } ( 9, ·)\)	\(\chi_{ 41 } ( 8, ·)\)	\(\chi_{ 41 } ( 5, ·)\)	\(\chi_{ 41 } ( 4, ·)\)	\(\chi_{ 41 } ( 2, ·)\)	\(\chi_{ 41 } ( 1, ·)\)

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.