Dirichlet character χ72(11,⋅)\chi_{72}(11,\cdot)

• Label: 72.11
• Modulus: $72$
• Conductor: $72$
• Order: $6$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$72$
Conductor:	$72$
Order:	$6$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 72.l

$\chi_{72}(11,\cdot)$ $\chi_{72}(59,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.10077696.1

Values on generators

$(55,37,65)$ → $(-1,-1,e\left(\frac{1}{6}\right))$

Values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 72 }(11, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum