Dirichlet character χ729(10,⋅)\chi_{729}(10,\cdot)

• Label: 729.10
• Modulus: $729$
• Conductor: $243$
• Order: $81$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$729$
Conductor:	$243$
Order:	$81$
Real:	no
Primitive:	no, induced from $\chi_{243}(13,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 729.i

$\chi_{729}(10,\cdot)$ $\chi_{729}(19,\cdot)$ $\chi_{729}(37,\cdot)$ $\chi_{729}(46,\cdot)$ $\chi_{729}(64,\cdot)$ $\chi_{729}(73,\cdot)$ $\chi_{729}(91,\cdot)$ $\chi_{729}(100,\cdot)$ $\chi_{729}(118,\cdot)$ $\chi_{729}(127,\cdot)$ $\chi_{729}(145,\cdot)$ $\chi_{729}(154,\cdot)$ $\chi_{729}(172,\cdot)$ $\chi_{729}(181,\cdot)$ $\chi_{729}(199,\cdot)$ $\chi_{729}(208,\cdot)$ $\chi_{729}(226,\cdot)$ $\chi_{729}(235,\cdot)$ $\chi_{729}(253,\cdot)$ $\chi_{729}(262,\cdot)$ $\chi_{729}(280,\cdot)$ $\chi_{729}(289,\cdot)$ $\chi_{729}(307,\cdot)$ $\chi_{729}(316,\cdot)$ $\chi_{729}(334,\cdot)$ $\chi_{729}(343,\cdot)$ $\chi_{729}(361,\cdot)$ $\chi_{729}(370,\cdot)$ $\chi_{729}(388,\cdot)$ $\chi_{729}(397,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 81 polynomial

Values on generators

$2$ → $e\left(\frac{4}{81}\right)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 729 }(10, a)$	$1$	$1$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{16}{81}\right)$

Gauss sum

Jacobi sum

Kloosterman sum