Dirichlet character χ4032(3481,⋅)\chi_{4032}(3481,\cdot)

• Label: 4032.3481
• Modulus: $4032$
• Conductor: $2016$
• Order: $24$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$4032$
Conductor:	$2016$
Order:	$24$
Real:	no
Primitive:	no, induced from $\chi_{2016}(709,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 4032.ga

$\chi_{4032}(457,\cdot)$ $\chi_{4032}(697,\cdot)$ $\chi_{4032}(1465,\cdot)$ $\chi_{4032}(1705,\cdot)$ $\chi_{4032}(2473,\cdot)$ $\chi_{4032}(2713,\cdot)$ $\chi_{4032}(3481,\cdot)$ $\chi_{4032}(3721,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{24})$
Fixed field:	Number field defined by a degree 24 polynomial

Values on generators

$(127,3781,1793,577)$ → $(1,e\left(\frac{1}{8}\right),e\left(\frac{2}{3}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 4032 }(3481, a)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$-i$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$