Dirichlet character χ2736(617,⋅)\chi_{2736}(617,\cdot)

• Label: 2736.617
• Modulus: $2736$
• Conductor: $1368$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$2736$
Conductor:	$1368$
Order:	$18$
Real:	no
Primitive:	no, induced from $\chi_{1368}(1301,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 2736.gf

$\chi_{2736}(329,\cdot)$ $\chi_{2736}(617,\cdot)$ $\chi_{2736}(1049,\cdot)$ $\chi_{2736}(1145,\cdot)$ $\chi_{2736}(1289,\cdot)$ $\chi_{2736}(2297,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(1711,2053,1217,1009)$ → $(1,-1,e\left(\frac{5}{6}\right),e\left(\frac{4}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 2736 }(617, a)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$