Dirichlet character χ1216(577,⋅)\chi_{1216}(577,\cdot)

• Label: 1216.577
• Modulus: $1216$
• Conductor: $19$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$1216$
Conductor:	$19$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{19}(7,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 1216.i

$\chi_{1216}(577,\cdot)$ $\chi_{1216}(961,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	3.3.361.1

Values on generators

$(191,837,705)$ → $(1,1,e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{ 1216 }(577, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$