Dirichlet character χ109(4,⋅)\chi_{109}(4,\cdot)

• Label: 109.4
• Modulus: $109$
• Conductor: $109$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$109$
Conductor:	$109$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 109.h

$\chi_{109}(4,\cdot)$ $\chi_{109}(34,\cdot)$ $\chi_{109}(43,\cdot)$ $\chi_{109}(71,\cdot)$ $\chi_{109}(82,\cdot)$ $\chi_{109}(93,\cdot)$

Related number fields

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

Values on generators

$6$ → $e\left(\frac{1}{18}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 109 }(4, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum