Dirichlet character χ63(32,⋅)\chi_{63}(32,\cdot)

• Label: 63.32
• Modulus: $63$
• Conductor: $63$
• Order: $6$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$63$
Conductor:	$63$
Order:	$6$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 63.n

$\chi_{63}(2,\cdot)$ $\chi_{63}(32,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.0.47258883.1

Values on generators

$(29,10)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 63 }(32, a)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum