Dirichlet character χ5733(2182,⋅)\chi_{5733}(2182,\cdot)

• Label: 5733.2182
• Modulus: $5733$
• Conductor: $5733$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$5733$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5733.lr

$\chi_{5733}(241,\cdot)$ $\chi_{5733}(418,\cdot)$ $\chi_{5733}(544,\cdot)$ $\chi_{5733}(682,\cdot)$ $\chi_{5733}(1237,\cdot)$ $\chi_{5733}(1363,\cdot)$ $\chi_{5733}(1879,\cdot)$ $\chi_{5733}(2056,\cdot)$ $\chi_{5733}(2182,\cdot)$ $\chi_{5733}(2320,\cdot)$ $\chi_{5733}(2698,\cdot)$ $\chi_{5733}(2875,\cdot)$ $\chi_{5733}(3001,\cdot)$ $\chi_{5733}(3139,\cdot)$ $\chi_{5733}(3517,\cdot)$ $\chi_{5733}(3820,\cdot)$ $\chi_{5733}(3958,\cdot)$ $\chi_{5733}(4336,\cdot)$ $\chi_{5733}(4513,\cdot)$ $\chi_{5733}(4639,\cdot)$ $\chi_{5733}(4777,\cdot)$ $\chi_{5733}(5155,\cdot)$ $\chi_{5733}(5332,\cdot)$ $\chi_{5733}(5596,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(2549,1522,5293)$ → $(e\left(\frac{1}{3}\right),e\left(\frac{17}{42}\right),e\left(\frac{7}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(2182, a)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{15}{28}\right)$