Dirichlet character χ224(181,⋅)\chi_{224}(181,\cdot)

• Label: 224.181
• Modulus: $224$
• Conductor: $224$
• Order: $8$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$224$
Conductor:	$224$
Order:	$8$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 224.v

$\chi_{224}(13,\cdot)$ $\chi_{224}(69,\cdot)$ $\chi_{224}(125,\cdot)$ $\chi_{224}(181,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.0.5156108238848.1

Values on generators

$(127,197,129)$ → $(1,e\left(\frac{5}{8}\right),-1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 224 }(181, a)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$

Gauss sum

Jacobi sum

Kloosterman sum