Dirichlet character χ319(173,⋅)\chi_{319}(173,\cdot)

• Label: 319.173
• Modulus: $319$
• Conductor: $319$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$319$
Conductor:	$319$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 319.i

$\chi_{319}(28,\cdot)$ $\chi_{319}(57,\cdot)$ $\chi_{319}(173,\cdot)$ $\chi_{319}(260,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.0.48364216424306959.3

Values on generators

$(233,89)$ → $(e\left(\frac{3}{10}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 319 }(173, a)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum