Dirichlet character χ1800(707,⋅)\chi_{1800}(707,\cdot)

• Label: 1800.707
• Modulus: $1800$
• Conductor: $360$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1800$
Conductor:	$360$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{360}(347,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1800.cj

$\chi_{1800}(443,\cdot)$ $\chi_{1800}(707,\cdot)$ $\chi_{1800}(1307,\cdot)$ $\chi_{1800}(1643,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.0.198359290368000000000.1

Values on generators

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

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1800 }(707, a)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$