Dirichlet character χ4032(1819,⋅)\chi_{4032}(1819,\cdot)

• Label: 4032.1819
• Modulus: $4032$
• Conductor: $448$
• Order: $16$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4032$
Conductor:	$448$
Order:	$16$
Real:	no
Primitive:	no, induced from $\chi_{448}(27,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4032.fb

$\chi_{4032}(307,\cdot)$ $\chi_{4032}(811,\cdot)$ $\chi_{4032}(1315,\cdot)$ $\chi_{4032}(1819,\cdot)$ $\chi_{4032}(2323,\cdot)$ $\chi_{4032}(2827,\cdot)$ $\chi_{4032}(3331,\cdot)$ $\chi_{4032}(3835,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.3484608386920116940487669055488.4

Values on generators

$(127,3781,1793,577)$ → $(-1,e\left(\frac{9}{16}\right),1,-1)$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 4032 }(1819, a)$	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{1}{16}\right)$