Dirichlet character χ287(251,⋅)\chi_{287}(251,\cdot)

• Label: 287.251
• Modulus: $287$
• Conductor: $287$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$287$
Conductor:	$287$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 287.t

$\chi_{287}(20,\cdot)$ $\chi_{287}(62,\cdot)$ $\chi_{287}(90,\cdot)$ $\chi_{287}(118,\cdot)$ $\chi_{287}(125,\cdot)$ $\chi_{287}(244,\cdot)$ $\chi_{287}(251,\cdot)$ $\chi_{287}(279,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.0.1241291203716901419760482976136252014889.1

Values on generators

$(206,211)$ → $(-1,e\left(\frac{11}{20}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 287 }(251, a)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$

Gauss sum

Jacobi sum

Kloosterman sum