Dirichlet character χ5733(1717,⋅)\chi_{5733}(1717,\cdot)

• Label: 5733.1717
• Modulus: $5733$
• Conductor: $441$
• Order: $21$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$441$
Order:	$21$
Real:	no
Primitive:	no, induced from $\chi_{441}(394,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5733.gy

$\chi_{5733}(898,\cdot)$ $\chi_{5733}(1327,\cdot)$ $\chi_{5733}(1717,\cdot)$ $\chi_{5733}(2146,\cdot)$ $\chi_{5733}(2536,\cdot)$ $\chi_{5733}(2965,\cdot)$ $\chi_{5733}(3355,\cdot)$ $\chi_{5733}(3784,\cdot)$ $\chi_{5733}(4174,\cdot)$ $\chi_{5733}(4603,\cdot)$ $\chi_{5733}(4993,\cdot)$ $\chi_{5733}(5422,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 21 polynomial

Values on generators

$(2549,1522,5293)$ → $(e\left(\frac{2}{3}\right),e\left(\frac{13}{21}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(1717, a)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$