Dirichlet character χ9576(575,⋅)\chi_{9576}(575,\cdot)

• Label: 9576.575
• Modulus: $9576$
• Conductor: $228$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$9576$
Conductor:	$228$
Order:	$18$
Real:	no
Primitive:	no, induced from $\chi_{228}(119,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 9576.wg

$\chi_{9576}(575,\cdot)$ $\chi_{9576}(1583,\cdot)$ $\chi_{9576}(2087,\cdot)$ $\chi_{9576}(3095,\cdot)$ $\chi_{9576}(4607,\cdot)$ $\chi_{9576}(9143,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(7183,4789,5321,4105,1009)$ → $(-1,1,-1,1,e\left(\frac{8}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 9576 }(575, a)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{18}\right)$