Dirichlet character χ1183(729,⋅)\chi_{1183}(729,\cdot)

• Label: 1183.729
• Modulus: $1183$
• Conductor: $169$
• Order: $13$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1183$
Conductor:	$169$
Order:	$13$
Real:	no
Primitive:	no, induced from $\chi_{169}(53,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1183.be

$\chi_{1183}(92,\cdot)$ $\chi_{1183}(183,\cdot)$ $\chi_{1183}(274,\cdot)$ $\chi_{1183}(365,\cdot)$ $\chi_{1183}(456,\cdot)$ $\chi_{1183}(547,\cdot)$ $\chi_{1183}(638,\cdot)$ $\chi_{1183}(729,\cdot)$ $\chi_{1183}(820,\cdot)$ $\chi_{1183}(911,\cdot)$ $\chi_{1183}(1002,\cdot)$ $\chi_{1183}(1093,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{13})$
Fixed field:	13.13.542800770374370512771595361.1

Values on generators

$(339,1016)$ → $(1,e\left(\frac{10}{13}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 1183 }(729, a)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$