Dirichlet character χ5733(5185,⋅)\chi_{5733}(5185,\cdot)

• Label: 5733.5185
• Modulus: $5733$
• Conductor: $637$
• Order: $84$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$637$
Order:	$84$
Real:	no
Primitive:	no, induced from $\chi_{637}(89,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5733.mq

$\chi_{5733}(136,\cdot)$ $\chi_{5733}(145,\cdot)$ $\chi_{5733}(271,\cdot)$ $\chi_{5733}(514,\cdot)$ $\chi_{5733}(955,\cdot)$ $\chi_{5733}(964,\cdot)$ $\chi_{5733}(1090,\cdot)$ $\chi_{5733}(1333,\cdot)$ $\chi_{5733}(1774,\cdot)$ $\chi_{5733}(1909,\cdot)$ $\chi_{5733}(2152,\cdot)$ $\chi_{5733}(2593,\cdot)$ $\chi_{5733}(2602,\cdot)$ $\chi_{5733}(2728,\cdot)$ $\chi_{5733}(3421,\cdot)$ $\chi_{5733}(3790,\cdot)$ $\chi_{5733}(4231,\cdot)$ $\chi_{5733}(4240,\cdot)$ $\chi_{5733}(4366,\cdot)$ $\chi_{5733}(4609,\cdot)$ $\chi_{5733}(5050,\cdot)$ $\chi_{5733}(5059,\cdot)$ $\chi_{5733}(5185,\cdot)$ $\chi_{5733}(5428,\cdot)$

Related number fields

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

Values on generators

$(2549,1522,5293)$ → $(1,e\left(\frac{23}{42}\right),e\left(\frac{7}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(5185, a)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{65}{84}\right)$