Dirichlet character χ228(119,⋅)\chi_{228}(119,\cdot)

• Label: 228.119
• Modulus: $228$
• Conductor: $228$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$228$
Conductor:	$228$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 228.v

$\chi_{228}(23,\cdot)$ $\chi_{228}(35,\cdot)$ $\chi_{228}(47,\cdot)$ $\chi_{228}(119,\cdot)$ $\chi_{228}(131,\cdot)$ $\chi_{228}(215,\cdot)$

Related number fields

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

Values on generators

$(115,77,97)$ → $(-1,-1,e\left(\frac{8}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 228 }(119, a)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum