Dirichlet character χ729(368,⋅)\chi_{729}(368,\cdot)

• Label: 729.368
• Modulus: $729$
• Conductor: $243$
• Order: $162$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$729$
Conductor:	$243$
Order:	$162$
Real:	no
Primitive:	no, induced from $\chi_{243}(86,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 729.j

$\chi_{729}(8,\cdot)$ $\chi_{729}(17,\cdot)$ $\chi_{729}(35,\cdot)$ $\chi_{729}(44,\cdot)$ $\chi_{729}(62,\cdot)$ $\chi_{729}(71,\cdot)$ $\chi_{729}(89,\cdot)$ $\chi_{729}(98,\cdot)$ $\chi_{729}(116,\cdot)$ $\chi_{729}(125,\cdot)$ $\chi_{729}(143,\cdot)$ $\chi_{729}(152,\cdot)$ $\chi_{729}(170,\cdot)$ $\chi_{729}(179,\cdot)$ $\chi_{729}(197,\cdot)$ $\chi_{729}(206,\cdot)$ $\chi_{729}(224,\cdot)$ $\chi_{729}(233,\cdot)$ $\chi_{729}(251,\cdot)$ $\chi_{729}(260,\cdot)$ $\chi_{729}(278,\cdot)$ $\chi_{729}(287,\cdot)$ $\chi_{729}(305,\cdot)$ $\chi_{729}(314,\cdot)$ $\chi_{729}(332,\cdot)$ $\chi_{729}(341,\cdot)$ $\chi_{729}(359,\cdot)$ $\chi_{729}(368,\cdot)$ $\chi_{729}(386,\cdot)$ $\chi_{729}(395,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 162 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{131}{162}\right)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 729 }(368, a)$	$-1$	$1$	$e\left(\frac{131}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{19}{81}\right)$

Gauss sum

Jacobi sum

Kloosterman sum