Dirichlet character χ720(23,⋅)\chi_{720}(23,\cdot)

• Label: 720.23
• Modulus: $720$
• Conductor: $360$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$720$
Conductor:	$360$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{360}(203,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 720.cv

$\chi_{720}(23,\cdot)$ $\chi_{720}(167,\cdot)$ $\chi_{720}(263,\cdot)$ $\chi_{720}(407,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.198359290368000000000.1

Values on generators

$(271,181,641,577)$ → $(-1,-1,e\left(\frac{5}{6}\right),-i)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 720 }(23, a)$	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum