Dirichlet character χ760(71,⋅)\chi_{760}(71,\cdot)

• Label: 760.71
• Modulus: $760$
• Conductor: $76$
• Order: $18$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$760$
Conductor:	$76$
Order:	$18$
Real:	no
Primitive:	no, induced from $\chi_{76}(71,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 760.ci

$\chi_{760}(71,\cdot)$ $\chi_{760}(231,\cdot)$ $\chi_{760}(431,\cdot)$ $\chi_{760}(471,\cdot)$ $\chi_{760}(591,\cdot)$ $\chi_{760}(751,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	$\Q(\zeta_{76})^+$

Values on generators

$(191,381,457,401)$ → $(-1,1,1,e\left(\frac{7}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 760 }(71, a)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum