Dirichlet character χ85(48,⋅)\chi_{85}(48,\cdot)

• Label: 85.48
• Modulus: $85$
• Conductor: $85$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$85$
Conductor:	$85$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 85.o

$\chi_{85}(3,\cdot)$ $\chi_{85}(7,\cdot)$ $\chi_{85}(27,\cdot)$ $\chi_{85}(48,\cdot)$ $\chi_{85}(57,\cdot)$ $\chi_{85}(62,\cdot)$ $\chi_{85}(63,\cdot)$ $\chi_{85}(73,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.698833752810013621337890625.2

Values on generators

$(52,71)$ → $(-i,e\left(\frac{9}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 85 }(48, a)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum