Dirichlet character χ507(22,⋅)\chi_{507}(22,\cdot)

• Label: 507.22
• Modulus: $507$
• Conductor: $13$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$507$
Conductor:	$13$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{13}(9,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 507.e

$\chi_{507}(22,\cdot)$ $\chi_{507}(484,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	3.3.169.1

Values on generators

$(170,340)$ → $(1,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 507 }(22, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum