Dirichlet character χ1071(613,⋅)\chi_{1071}(613,\cdot)

• Label: 1071.613
• Modulus: $1071$
• Conductor: $7$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1071$
Conductor:	$7$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{7}(4,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1071.i

$\chi_{1071}(613,\cdot)$ $\chi_{1071}(919,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{7})^+$

Values on generators

$(596,766,190)$ → $(1,e\left(\frac{2}{3}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{ 1071 }(613, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$