Dirichlet character χ143(129,⋅)\chi_{143}(129,\cdot)

• Label: 143.129
• Modulus: $143$
• Conductor: $143$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$143$
Conductor:	$143$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 143.l

$\chi_{143}(51,\cdot)$ $\chi_{143}(90,\cdot)$ $\chi_{143}(116,\cdot)$ $\chi_{143}(129,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.0.875489472034463.1

Values on generators

$(79,67)$ → $(e\left(\frac{3}{10}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 143 }(129, a)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum