Dirichlet character χ1710(1229,⋅)\chi_{1710}(1229,\cdot)

• Label: 1710.1229
• Modulus: $1710$
• Conductor: $855$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1710$
Conductor:	$855$
Order:	$18$
Real:	no
Primitive:	no, induced from $\chi_{855}(374,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1710.co

$\chi_{1710}(299,\cdot)$ $\chi_{1710}(509,\cdot)$ $\chi_{1710}(599,\cdot)$ $\chi_{1710}(839,\cdot)$ $\chi_{1710}(1199,\cdot)$ $\chi_{1710}(1229,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	18.18.81623484842733584357749488935542564453125.2

Values on generators

$(191,1027,1351)$ → $(e\left(\frac{5}{6}\right),-1,e\left(\frac{5}{18}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 1710 }(1229, a)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$