Dirichlet character χ117(14,⋅)\chi_{117}(14,\cdot)

• Label: 117.14
• Modulus: $117$
• Conductor: $9$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$117$
Conductor:	$9$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{9}(5,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 117.s

$\chi_{117}(14,\cdot)$ $\chi_{117}(92,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{9})$

Values on generators

$(92,28)$ → $(e\left(\frac{5}{6}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 117 }(14, a)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum