Dirichlet character χ5733(503,⋅)\chi_{5733}(503,\cdot)

• Label: 5733.503
• 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 $\chi_{1911}(503,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5733.hz

$\chi_{5733}(503,\cdot)$ $\chi_{5733}(692,\cdot)$ $\chi_{5733}(1511,\cdot)$ $\chi_{5733}(2141,\cdot)$ $\chi_{5733}(2330,\cdot)$ $\chi_{5733}(2960,\cdot)$ $\chi_{5733}(3149,\cdot)$ $\chi_{5733}(3779,\cdot)$ $\chi_{5733}(4598,\cdot)$ $\chi_{5733}(4787,\cdot)$ $\chi_{5733}(5417,\cdot)$ $\chi_{5733}(5606,\cdot)$

Related number fields

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

Values on generators

$(2549,1522,5293)$ → $(-1,e\left(\frac{11}{14}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 5733 }(503, a)$	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$