Dirichlet character χ8512(6917,⋅)\chi_{8512}(6917,\cdot)

• Label: 8512.6917
• Modulus: $8512$
• Conductor: $64$
• Order: $16$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8512$
Conductor:	$64$
Order:	$16$
Real:	no
Primitive:	no, induced from $\chi_{64}(5,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8512.fc

$\chi_{8512}(533,\cdot)$ $\chi_{8512}(1597,\cdot)$ $\chi_{8512}(2661,\cdot)$ $\chi_{8512}(3725,\cdot)$ $\chi_{8512}(4789,\cdot)$ $\chi_{8512}(5853,\cdot)$ $\chi_{8512}(6917,\cdot)$ $\chi_{8512}(7981,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	$\Q(\zeta_{64})^+$

Values on generators

$(5055,6917,7297,3137)$ → $(1,e\left(\frac{1}{16}\right),1,1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{ 8512 }(6917, a)$	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$