Dirichlet character χ4032(19,⋅)\chi_{4032}(19,\cdot)

• Label: 4032.19
• Modulus: $4032$
• Conductor: $448$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4032$
Conductor:	$448$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{448}(19,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4032.he

$\chi_{4032}(19,\cdot)$ $\chi_{4032}(451,\cdot)$ $\chi_{4032}(523,\cdot)$ $\chi_{4032}(955,\cdot)$ $\chi_{4032}(1027,\cdot)$ $\chi_{4032}(1459,\cdot)$ $\chi_{4032}(1531,\cdot)$ $\chi_{4032}(1963,\cdot)$ $\chi_{4032}(2035,\cdot)$ $\chi_{4032}(2467,\cdot)$ $\chi_{4032}(2539,\cdot)$ $\chi_{4032}(2971,\cdot)$ $\chi_{4032}(3043,\cdot)$ $\chi_{4032}(3475,\cdot)$ $\chi_{4032}(3547,\cdot)$ $\chi_{4032}(3979,\cdot)$

Related number fields

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

Values on generators

$(127,3781,1793,577)$ → $(-1,e\left(\frac{7}{16}\right),1,e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 4032 }(19, a)$	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{48}\right)$