Dirichlet character χ369(247,⋅)\chi_{369}(247,\cdot)

• Label: 369.247
• Modulus: $369$
• Conductor: $9$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$369$
Conductor:	$9$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{9}(4,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 369.e

$\chi_{369}(124,\cdot)$ $\chi_{369}(247,\cdot)$

Related number fields

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

Values on generators

$(83,334)$ → $(e\left(\frac{1}{3}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 369 }(247, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum