Dirichlet character χ1800(1019,⋅)\chi_{1800}(1019,\cdot)

• Label: 1800.1019
• Modulus: $1800$
• Conductor: $1800$
• Order: $30$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1800$
Conductor:	$1800$
Order:	$30$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1800.cx

$\chi_{1800}(59,\cdot)$ $\chi_{1800}(419,\cdot)$ $\chi_{1800}(659,\cdot)$ $\chi_{1800}(779,\cdot)$ $\chi_{1800}(1019,\cdot)$ $\chi_{1800}(1139,\cdot)$ $\chi_{1800}(1379,\cdot)$ $\chi_{1800}(1739,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	30.30.46161136039856776541296875000000000000000000000000000000000000000000000.1

Values on generators

$(1351,901,1001,577)$ → $(-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1800 }(1019, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{30}\right)$