Dirichlet character χ9576(1357,⋅)\chi_{9576}(1357,\cdot)

• Label: 9576.1357
• Modulus: $9576$
• Conductor: $9576$
• Order: $6$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$9576$
Conductor:	$9576$
Order:	$6$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 9576.qt

$\chi_{9576}(1357,\cdot)$ $\chi_{9576}(8581,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	Number field defined by a degree 6 polynomial

Values on generators

$(7183,4789,5321,4105,1009)$ → $(1,-1,e\left(\frac{2}{3}\right),-1,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 9576 }(1357, a)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$