Dirichlet character χ4032(3203,⋅)\chi_{4032}(3203,\cdot)

• Label: 4032.3203
• Modulus: $4032$
• Conductor: $1344$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4032$
Conductor:	$1344$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{1344}(515,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4032.gz

$\chi_{4032}(107,\cdot)$ $\chi_{4032}(179,\cdot)$ $\chi_{4032}(611,\cdot)$ $\chi_{4032}(683,\cdot)$ $\chi_{4032}(1115,\cdot)$ $\chi_{4032}(1187,\cdot)$ $\chi_{4032}(1619,\cdot)$ $\chi_{4032}(1691,\cdot)$ $\chi_{4032}(2123,\cdot)$ $\chi_{4032}(2195,\cdot)$ $\chi_{4032}(2627,\cdot)$ $\chi_{4032}(2699,\cdot)$ $\chi_{4032}(3131,\cdot)$ $\chi_{4032}(3203,\cdot)$ $\chi_{4032}(3635,\cdot)$ $\chi_{4032}(3707,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(127,3781,1793,577)$ → $(-1,e\left(\frac{3}{16}\right),-1,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 4032 }(3203, a)$	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{48}\right)$