Dirichlet character χ11(8,⋅)\chi_{11}(8,\cdot)

• Label: 11.8
• Modulus: $11$
• Conductor: $11$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$11$
Conductor:	$11$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 11.d

$\chi_{11}(2,\cdot)$ $\chi_{11}(6,\cdot)$ $\chi_{11}(7,\cdot)$ $\chi_{11}(8,\cdot)$

Related number fields

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

Values on generators

$2$ → $e\left(\frac{3}{10}\right)$

Values

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

Gauss sum

Jacobi sum

Kloosterman sum