Dirichlet character χ1800(599,⋅)\chi_{1800}(599,\cdot)

• Label: 1800.599
• Modulus: $1800$
• Conductor: $180$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$1800$
Conductor:	$180$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{180}(59,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 1800.bc

$\chi_{1800}(599,\cdot)$ $\chi_{1800}(1199,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.157464000.1

Values on generators

$(1351,901,1001,577)$ → $(-1,1,e\left(\frac{5}{6}\right),-1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1800 }(599, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$