Dirichlet character orbit 5733.gf

• Label: 5733.gf
• Modulus: $5733$
• Conductor: $819$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$819$
Order:	$12$
Real:	no
Primitive:	no, induced from 819.ge
Minimal:	no
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.4002614648521196621698550493.3

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{5733}(275,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{5733}(2039,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{5733}(4232,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{5733}(4673,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$-i$