Dirichlet character χ253(160,⋅)\chi_{253}(160,\cdot)

• Label: 253.160
• Modulus: $253$
• Conductor: $253$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$253$
Conductor:	$253$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 253.h

$\chi_{253}(68,\cdot)$ $\chi_{253}(160,\cdot)$ $\chi_{253}(183,\cdot)$ $\chi_{253}(206,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.10.15176560115334013.1

Values on generators

$(24,166)$ → $(e\left(\frac{9}{10}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 253 }(160, a)$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum