Dirichlet character χ189(25,⋅)\chi_{189}(25,\cdot)

• Label: 189.25
• Modulus: $189$
• Conductor: $189$
• Order: $9$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$189$
Conductor:	$189$
Order:	$9$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 189.w

$\chi_{189}(25,\cdot)$ $\chi_{189}(58,\cdot)$ $\chi_{189}(88,\cdot)$ $\chi_{189}(121,\cdot)$ $\chi_{189}(151,\cdot)$ $\chi_{189}(184,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	9.9.3691950281939241.2

Values on generators

$(29,136)$ → $(e\left(\frac{5}{9}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 189 }(25, a)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum