Dirichlet character orbit 4160.ds

• Label: 4160.ds
• Modulus: $4160$
• Conductor: $416$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$4160$
Conductor:	$416$
Order:	$8$
Real:	no
Primitive:	no, induced from 416.bg
Minimal:	no
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.61334280470528.1

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{4160}(441,\cdot)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{4160}(1481,\cdot)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4160}(2521,\cdot)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{4160}(3561,\cdot)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$