Dirichlet character χ109(8,⋅)\chi_{109}(8,\cdot)

• Label: 109.8
• Modulus: $109$
• Conductor: $109$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$109$
Conductor:	$109$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 109.g

$\chi_{109}(8,\cdot)$ $\chi_{109}(41,\cdot)$ $\chi_{109}(68,\cdot)$ $\chi_{109}(101,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.25804264053054077850709.1

Values on generators

$6$ → $e\left(\frac{7}{12}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 109 }(8, a)$	$-1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$

Gauss sum

Jacobi sum

Kloosterman sum