Dirichlet character χ5733(1759,⋅)\chi_{5733}(1759,\cdot)

• Label: 5733.1759
• 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.if

$\chi_{5733}(88,\cdot)$ $\chi_{5733}(121,\cdot)$ $\chi_{5733}(907,\cdot)$ $\chi_{5733}(940,\cdot)$ $\chi_{5733}(1726,\cdot)$ $\chi_{5733}(1759,\cdot)$ $\chi_{5733}(2545,\cdot)$ $\chi_{5733}(3364,\cdot)$ $\chi_{5733}(3397,\cdot)$ $\chi_{5733}(4216,\cdot)$ $\chi_{5733}(5002,\cdot)$ $\chi_{5733}(5035,\cdot)$

Related number fields

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

Values on generators

$(2549,1522,5293)$ → $(e\left(\frac{1}{3}\right),e\left(\frac{4}{21}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(1759, a)$	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{21}\right)$	$-1$	$e\left(\frac{25}{42}\right)$