Dirichlet character χ119(47,⋅)\chi_{119}(47,\cdot)

• Label: 119.47
• Modulus: $119$
• Conductor: $119$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$119$
Conductor:	$119$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 119.m

$\chi_{119}(38,\cdot)$ $\chi_{119}(47,\cdot)$ $\chi_{119}(89,\cdot)$ $\chi_{119}(115,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.33498139941871322753.1

Values on generators

$(52,71)$ → $(e\left(\frac{5}{6}\right),i)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 119 }(47, a)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$

Gauss sum

Jacobi sum

Kloosterman sum