Dirichlet character χ4368(1681,⋅)\chi_{4368}(1681,\cdot)

• Label: 4368.1681
• Modulus: $4368$
• Conductor: $13$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$4368$
Conductor:	$13$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{13}(4,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 4368.do

$\chi_{4368}(673,\cdot)$ $\chi_{4368}(1681,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{13})^+$

Values on generators

$(3823,1093,1457,1249,2017)$ → $(1,1,1,1,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 4368 }(1681, a)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$