Dirichlet character χ729(325,⋅)\chi_{729}(325,\cdot)

• Label: 729.325
• Modulus: $729$
• Conductor: $27$
• Order: $9$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$729$
Conductor:	$27$
Order:	$9$
Real:	no
Primitive:	no, induced from $\chi_{27}(22,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 729.e

$\chi_{729}(82,\cdot)$ $\chi_{729}(163,\cdot)$ $\chi_{729}(325,\cdot)$ $\chi_{729}(406,\cdot)$ $\chi_{729}(568,\cdot)$ $\chi_{729}(649,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	$\Q(\zeta_{27})^+$

Values on generators

$2$ → $e\left(\frac{7}{9}\right)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 729 }(325, a)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum