Dirichlet character χ720(11,⋅)\chi_{720}(11,\cdot)

• Label: 720.11
• Modulus: $720$
• Conductor: $144$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$720$
Conductor:	$144$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{144}(11,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 720.cf

$\chi_{720}(11,\cdot)$ $\chi_{720}(131,\cdot)$ $\chi_{720}(371,\cdot)$ $\chi_{720}(491,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.3327916660110655488.1

Values on generators

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

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 720 }(11, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum