Dirichlet character χ180(169,⋅)\chi_{180}(169,\cdot)

• Label: 180.169
• Modulus: $180$
• Conductor: $45$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$180$
Conductor:	$45$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{45}(34,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 180.r

$\chi_{180}(49,\cdot)$ $\chi_{180}(169,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.820125.1

Values on generators

$(91,101,37)$ → $(1,e\left(\frac{2}{3}\right),-1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 180 }(169, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum