Dirichlet character χ720(89,⋅)\chi_{720}(89,\cdot)

• Label: 720.89
• Modulus: $720$
• Conductor: $120$
• Order: $2$
• Real: yes
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$720$
Conductor:	$120$
Order:	$2$
Real:	yes
Primitive:	no, induced from $\chi_{120}(29,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 720.i

$\chi_{720}(89,\cdot)$

Related number fields

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{-30})$

Values on generators

$(271,181,641,577)$ → $(1,-1,-1,-1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 720 }(89, a)$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum