Dirichlet character χ729(28,⋅)\chi_{729}(28,\cdot)

• Label: 729.28
• Modulus: $729$
• Conductor: $81$
• Order: $27$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$729$
Conductor:	$81$
Order:	$27$
Real:	no
Primitive:	no, induced from $\chi_{81}(67,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 729.g

$\chi_{729}(28,\cdot)$ $\chi_{729}(55,\cdot)$ $\chi_{729}(109,\cdot)$ $\chi_{729}(136,\cdot)$ $\chi_{729}(190,\cdot)$ $\chi_{729}(217,\cdot)$ $\chi_{729}(271,\cdot)$ $\chi_{729}(298,\cdot)$ $\chi_{729}(352,\cdot)$ $\chi_{729}(379,\cdot)$ $\chi_{729}(433,\cdot)$ $\chi_{729}(460,\cdot)$ $\chi_{729}(514,\cdot)$ $\chi_{729}(541,\cdot)$ $\chi_{729}(595,\cdot)$ $\chi_{729}(622,\cdot)$ $\chi_{729}(676,\cdot)$ $\chi_{729}(703,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{27})$
Fixed field:	Number field defined by a degree 27 polynomial

Values on generators

$2$ → $e\left(\frac{22}{27}\right)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 729 }(28, a)$	$1$	$1$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{27}\right)$

Gauss sum

Jacobi sum

Kloosterman sum