Dirichlet character χ5733(4436,⋅)\chi_{5733}(4436,\cdot)

• Label: 5733.4436
• Modulus: $5733$
• Conductor: $1911$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$1911$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{1911}(614,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5733.kq

$\chi_{5733}(269,\cdot)$ $\chi_{5733}(341,\cdot)$ $\chi_{5733}(1088,\cdot)$ $\chi_{5733}(1160,\cdot)$ $\chi_{5733}(1907,\cdot)$ $\chi_{5733}(2798,\cdot)$ $\chi_{5733}(3545,\cdot)$ $\chi_{5733}(3617,\cdot)$ $\chi_{5733}(4364,\cdot)$ $\chi_{5733}(4436,\cdot)$ $\chi_{5733}(5183,\cdot)$ $\chi_{5733}(5255,\cdot)$

Related number fields

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

Values on generators

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

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(4436, a)$	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{20}{21}\right)$