Dirichlet character χ87(86,⋅)\chi_{87}(86,\cdot)

• Label: 87.86
• Modulus: $87$
• Conductor: $87$
• Order: $2$
• Real: yes
• Primitive: yes
• Minimal: yes
• Parity: odd

Kronecker symbol representation

$\displaystyle\left(\frac{-87}{\bullet}\right)$

Basic properties

Modulus:	$87$
Conductor:	$87$
Order:	$2$
Real:	yes
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 87.d

$\chi_{87}(86,\cdot)$

Related number fields

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{-87})$

Values on generators

$(59,31)$ → $(-1,-1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 87 }(86, a)$	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum