Dirichlet character χ703(10,⋅)\chi_{703}(10,\cdot)

• Label: 703.10
• Modulus: $703$
• Conductor: $703$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$703$
Conductor:	$703$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 703.ck

$\chi_{703}(10,\cdot)$ $\chi_{703}(174,\cdot)$ $\chi_{703}(211,\cdot)$ $\chi_{703}(470,\cdot)$ $\chi_{703}(528,\cdot)$ $\chi_{703}(602,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	18.0.36077123658233831722523486199489682113859.2

Values on generators

$(667,39)$ → $(e\left(\frac{17}{18}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 703 }(10, a)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum