Dirichlet character orbit 9576.rq

• Label: 9576.rq
• Modulus: $9576$
• Conductor: $1368$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$9576$
Conductor:	$1368$
Order:	$18$
Real:	no
Primitive:	no, induced from 1368.eb
Minimal:	yes
Parity:	even

Related number fields

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

Characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{9576}(491,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$-1$	$e\left(\frac{1}{18}\right)$
$\chi_{9576}(1163,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$
$\chi_{9576}(1499,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$-1$	$e\left(\frac{7}{18}\right)$
$\chi_{9576}(3179,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$-1$	$e\left(\frac{17}{18}\right)$
$\chi_{9576}(6203,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$-1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$-1$	$e\left(\frac{11}{18}\right)$
$\chi_{9576}(8555,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$