Dirichlet character χ416(289,⋅)\chi_{416}(289,\cdot)

• Label: 416.289
• Modulus: $416$
• Conductor: $13$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$416$
Conductor:	$13$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{13}(3,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 416.i

$\chi_{416}(289,\cdot)$ $\chi_{416}(321,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	3.3.169.1

Values on generators

$(287,261,353)$ → $(1,1,e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 416 }(289, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum