Dirichlet character χ2856(1517,⋅)\chi_{2856}(1517,\cdot)

• Label: 2856.1517
• Modulus: $2856$
• Conductor: $2856$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2856$
Conductor:	$2856$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2856.eg

$\chi_{2856}(1109,\cdot)$ $\chi_{2856}(1517,\cdot)$ $\chi_{2856}(1781,\cdot)$ $\chi_{2856}(2189,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.6401594233356076787154812928.1

Values on generators

$(2143,1429,953,409,2689)$ → $(1,-1,-1,e\left(\frac{5}{6}\right),-i)$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 2856 }(1517, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$