Dirichlet character χ891(82,⋅)\chi_{891}(82,\cdot)

• Label: 891.82
• Modulus: $891$
• Conductor: $11$
• Order: $5$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$891$
Conductor:	$11$
Order:	$5$
Real:	no
Primitive:	no, induced from $\chi_{11}(5,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 891.f

$\chi_{891}(82,\cdot)$ $\chi_{891}(163,\cdot)$ $\chi_{891}(487,\cdot)$ $\chi_{891}(730,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	$\Q(\zeta_{11})^+$

Values on generators

$(650,244)$ → $(1,e\left(\frac{2}{5}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 891 }(82, a)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$

Gauss sum

Jacobi sum

Kloosterman sum