Dirichlet character χ32(3,⋅)\chi_{32}(3,\cdot)

• Label: 32.3
• Modulus: $32$
• Conductor: $32$
• Order: $8$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$32$
Conductor:	$32$
Order:	$8$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 32.h

$\chi_{32}(3,\cdot)$ $\chi_{32}(11,\cdot)$ $\chi_{32}(19,\cdot)$ $\chi_{32}(27,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.0.2147483648.1

Values on generators

$(31,5)$ → $(-1,e\left(\frac{3}{8}\right))$

Values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 32 }(3, a)$	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$

Gauss sum

Jacobi sum

Kloosterman sum