Dirichlet character χ405(109,⋅)\chi_{405}(109,\cdot)

• Label: 405.109
• Modulus: $405$
• Conductor: $45$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$405$
Conductor:	$45$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{45}(4,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 405.j

$\chi_{405}(109,\cdot)$ $\chi_{405}(379,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.820125.1

Values on generators

$(326,82)$ → $(e\left(\frac{1}{3}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(109, a)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum