Dirichlet character χ5733(5618,⋅)\chi_{5733}(5618,\cdot)

• Label: 5733.5618
• 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.mf

$\chi_{5733}(11,\cdot)$ $\chi_{5733}(149,\cdot)$ $\chi_{5733}(527,\cdot)$ $\chi_{5733}(830,\cdot)$ $\chi_{5733}(968,\cdot)$ $\chi_{5733}(1346,\cdot)$ $\chi_{5733}(1523,\cdot)$ $\chi_{5733}(1649,\cdot)$ $\chi_{5733}(1787,\cdot)$ $\chi_{5733}(2165,\cdot)$ $\chi_{5733}(2342,\cdot)$ $\chi_{5733}(2606,\cdot)$ $\chi_{5733}(2984,\cdot)$ $\chi_{5733}(3161,\cdot)$ $\chi_{5733}(3287,\cdot)$ $\chi_{5733}(3425,\cdot)$ $\chi_{5733}(3980,\cdot)$ $\chi_{5733}(4106,\cdot)$ $\chi_{5733}(4622,\cdot)$ $\chi_{5733}(4799,\cdot)$ $\chi_{5733}(4925,\cdot)$ $\chi_{5733}(5063,\cdot)$ $\chi_{5733}(5441,\cdot)$ $\chi_{5733}(5618,\cdot)$

Related number fields

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

Values on generators

$(2549,1522,5293)$ → $(e\left(\frac{1}{6}\right),e\left(\frac{2}{21}\right),e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(5618, a)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$-i$	$e\left(\frac{67}{84}\right)$