Dirichlet character χ143(125,⋅)\chi_{143}(125,\cdot)

• Label: 143.125
• Modulus: $143$
• Conductor: $143$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$143$
Conductor:	$143$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 143.r

$\chi_{143}(5,\cdot)$ $\chi_{143}(31,\cdot)$ $\chi_{143}(47,\cdot)$ $\chi_{143}(60,\cdot)$ $\chi_{143}(70,\cdot)$ $\chi_{143}(86,\cdot)$ $\chi_{143}(125,\cdot)$ $\chi_{143}(135,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

$(79,67)$ → $(e\left(\frac{1}{5}\right),i)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 143 }(125, a)$	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum