Dirichlet character χ1800(1021,⋅)\chi_{1800}(1021,\cdot)

• Label: 1800.1021
• 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.cv

$\chi_{1800}(61,\cdot)$ $\chi_{1800}(421,\cdot)$ $\chi_{1800}(661,\cdot)$ $\chi_{1800}(781,\cdot)$ $\chi_{1800}(1021,\cdot)$ $\chi_{1800}(1141,\cdot)$ $\chi_{1800}(1381,\cdot)$ $\chi_{1800}(1741,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(1351,901,1001,577)$ → $(1,-1,e\left(\frac{1}{3}\right),e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1800 }(1021, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$