Dirichlet character χ760(309,⋅)\chi_{760}(309,\cdot)

• Label: 760.309
• Modulus: $760$
• Conductor: $760$
• Order: $18$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$760$
Conductor:	$760$
Order:	$18$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 760.cj

$\chi_{760}(149,\cdot)$ $\chi_{760}(309,\cdot)$ $\chi_{760}(389,\cdot)$ $\chi_{760}(549,\cdot)$ $\chi_{760}(669,\cdot)$ $\chi_{760}(709,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	Number field defined by a degree 18 polynomial

Values on generators

$(191,381,457,401)$ → $(1,-1,-1,e\left(\frac{8}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 760 }(309, a)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum