Dirichlet character χ539(405,⋅)\chi_{539}(405,\cdot)

• Label: 539.405
• Modulus: $539$
• Conductor: $539$
• Order: $70$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$539$
Conductor:	$539$
Order:	$70$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 539.bb

$\chi_{539}(20,\cdot)$ $\chi_{539}(27,\cdot)$ $\chi_{539}(69,\cdot)$ $\chi_{539}(104,\cdot)$ $\chi_{539}(125,\cdot)$ $\chi_{539}(174,\cdot)$ $\chi_{539}(181,\cdot)$ $\chi_{539}(202,\cdot)$ $\chi_{539}(223,\cdot)$ $\chi_{539}(251,\cdot)$ $\chi_{539}(258,\cdot)$ $\chi_{539}(279,\cdot)$ $\chi_{539}(300,\cdot)$ $\chi_{539}(328,\cdot)$ $\chi_{539}(335,\cdot)$ $\chi_{539}(356,\cdot)$ $\chi_{539}(377,\cdot)$ $\chi_{539}(405,\cdot)$ $\chi_{539}(412,\cdot)$ $\chi_{539}(433,\cdot)$ $\chi_{539}(454,\cdot)$ $\chi_{539}(482,\cdot)$ $\chi_{539}(510,\cdot)$ $\chi_{539}(531,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Values on generators

$(199,442)$ → $(e\left(\frac{11}{14}\right),e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 539 }(405, a)$	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{37}{70}\right)$

Gauss sum

Jacobi sum

Kloosterman sum