Dirichlet character χ5733(5602,⋅)\chi_{5733}(5602,\cdot)

• Label: 5733.5602
• Modulus: $5733$
• Conductor: $5733$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$5733$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5733.km

$\chi_{5733}(25,\cdot)$ $\chi_{5733}(688,\cdot)$ $\chi_{5733}(844,\cdot)$ $\chi_{5733}(1507,\cdot)$ $\chi_{5733}(1663,\cdot)$ $\chi_{5733}(2326,\cdot)$ $\chi_{5733}(2482,\cdot)$ $\chi_{5733}(3145,\cdot)$ $\chi_{5733}(3964,\cdot)$ $\chi_{5733}(4120,\cdot)$ $\chi_{5733}(4939,\cdot)$ $\chi_{5733}(5602,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(2549,1522,5293)$ → $(e\left(\frac{1}{3}\right),e\left(\frac{10}{21}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(5602, a)$	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$