Dirichlet character χ760(163,⋅)\chi_{760}(163,\cdot)

• Label: 760.163
• Modulus: $760$
• Conductor: $760$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$760$
Conductor:	$760$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 760.bw

$\chi_{760}(83,\cdot)$ $\chi_{760}(163,\cdot)$ $\chi_{760}(387,\cdot)$ $\chi_{760}(467,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.8695584276992000000000.1

Values on generators

$(191,381,457,401)$ → $(-1,-1,-i,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 760 }(163, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum