Group of Dirichlet characters of modulus 5

• Modulus: $5$
• Structure: $C_{4}$
• Order: $4$

Character group

Order	=	4
Structure	=	$C_{4}$
Generators	=	$\chi_{5}(2,\cdot)$

Characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$
$\chi_{5}(1,\cdot)$	5.a	1	no	$1$	$1$	$1$	$1$
$\chi_{5}(2,\cdot)$	5.c	4	yes	$-1$	$1$	$i$	$-i$
$\chi_{5}(3,\cdot)$	5.c	4	yes	$-1$	$1$	$-i$	$i$
$\chi_{5}(4,\cdot)$	5.b	2	yes	$1$	$1$	$-1$	$-1$