Dirichlet character χ85(19,⋅)\chi_{85}(19,\cdot)

• Label: 85.19
• Modulus: $85$
• Conductor: $85$
• Order: $8$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$85$
Conductor:	$85$
Order:	$8$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 85.m

$\chi_{85}(9,\cdot)$ $\chi_{85}(19,\cdot)$ $\chi_{85}(49,\cdot)$ $\chi_{85}(59,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.256461670625.1

Values on generators

$(52,71)$ → $(-1,e\left(\frac{7}{8}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 85 }(19, a)$	$1$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum