Dirichlet character χ243(13,⋅)\chi_{243}(13,\cdot)

• Label: 243.13
• Modulus: $243$
• Conductor: $243$
• Order: $81$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$243$
Conductor:	$243$
Order:	$81$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 243.i

$\chi_{243}(4,\cdot)$ $\chi_{243}(7,\cdot)$ $\chi_{243}(13,\cdot)$ $\chi_{243}(16,\cdot)$ $\chi_{243}(22,\cdot)$ $\chi_{243}(25,\cdot)$ $\chi_{243}(31,\cdot)$ $\chi_{243}(34,\cdot)$ $\chi_{243}(40,\cdot)$ $\chi_{243}(43,\cdot)$ $\chi_{243}(49,\cdot)$ $\chi_{243}(52,\cdot)$ $\chi_{243}(58,\cdot)$ $\chi_{243}(61,\cdot)$ $\chi_{243}(67,\cdot)$ $\chi_{243}(70,\cdot)$ $\chi_{243}(76,\cdot)$ $\chi_{243}(79,\cdot)$ $\chi_{243}(85,\cdot)$ $\chi_{243}(88,\cdot)$ $\chi_{243}(94,\cdot)$ $\chi_{243}(97,\cdot)$ $\chi_{243}(103,\cdot)$ $\chi_{243}(106,\cdot)$ $\chi_{243}(112,\cdot)$ $\chi_{243}(115,\cdot)$ $\chi_{243}(121,\cdot)$ $\chi_{243}(124,\cdot)$ $\chi_{243}(130,\cdot)$ $\chi_{243}(133,\cdot)$ ...

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

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 243 }(13, a)$	$1$	$1$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{16}{81}\right)$

Gauss sum

Jacobi sum

Kloosterman sum