Dirichlet character χ189(164,⋅)\chi_{189}(164,\cdot)

• Label: 189.164
• Modulus: $189$
• Conductor: $189$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$189$
Conductor:	$189$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 189.ba

$\chi_{189}(5,\cdot)$ $\chi_{189}(38,\cdot)$ $\chi_{189}(68,\cdot)$ $\chi_{189}(101,\cdot)$ $\chi_{189}(131,\cdot)$ $\chi_{189}(164,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(29,136)$ → $(e\left(\frac{1}{18}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 189 }(164, a)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum