Dirichlet character χ703(322,⋅)\chi_{703}(322,\cdot)

• Label: 703.322
• Modulus: $703$
• Conductor: $703$
• Order: $6$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$703$
Conductor:	$703$
Order:	$6$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 703.t

$\chi_{703}(322,\cdot)$ $\chi_{703}(417,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.0.12854870299.1

Values on generators

$(667,39)$ → $(-1,e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 703 }(322, a)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum