Dirichlet character χ729(13,⋅)\chi_{729}(13,\cdot)

• Label: 729.13
• Modulus: $729$
• Conductor: $729$
• Order: $243$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$729$
Conductor:	$729$
Order:	$243$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 729.k

$\chi_{729}(4,\cdot)$ $\chi_{729}(7,\cdot)$ $\chi_{729}(13,\cdot)$ $\chi_{729}(16,\cdot)$ $\chi_{729}(22,\cdot)$ $\chi_{729}(25,\cdot)$ $\chi_{729}(31,\cdot)$ $\chi_{729}(34,\cdot)$ $\chi_{729}(40,\cdot)$ $\chi_{729}(43,\cdot)$ $\chi_{729}(49,\cdot)$ $\chi_{729}(52,\cdot)$ $\chi_{729}(58,\cdot)$ $\chi_{729}(61,\cdot)$ $\chi_{729}(67,\cdot)$ $\chi_{729}(70,\cdot)$ $\chi_{729}(76,\cdot)$ $\chi_{729}(79,\cdot)$ $\chi_{729}(85,\cdot)$ $\chi_{729}(88,\cdot)$ $\chi_{729}(94,\cdot)$ $\chi_{729}(97,\cdot)$ $\chi_{729}(103,\cdot)$ $\chi_{729}(106,\cdot)$ $\chi_{729}(112,\cdot)$ $\chi_{729}(115,\cdot)$ $\chi_{729}(121,\cdot)$ $\chi_{729}(124,\cdot)$ $\chi_{729}(130,\cdot)$ $\chi_{729}(133,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{243})$
Fixed field:	Number field defined by a degree 243 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{166}{243}\right)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 729 }(13, a)$	$1$	$1$	$e\left(\frac{166}{243}\right)$	$e\left(\frac{89}{243}\right)$	$e\left(\frac{173}{243}\right)$	$e\left(\frac{37}{243}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{79}{243}\right)$	$e\left(\frac{194}{243}\right)$	$e\left(\frac{203}{243}\right)$	$e\left(\frac{178}{243}\right)$

Gauss sum

Jacobi sum

Kloosterman sum