Dirichlet character orbit 4160.ff

• Label: 4160.ff
• Modulus: $4160$
• Conductor: $520$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4160$
Conductor:	$520$
Order:	$12$
Real:	no
Primitive:	no, induced from 520.cj
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.917586121746944000000000.1

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{4160}(353,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{4160}(1697,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{4160}(2593,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{4160}(3937,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$