Dirichlet character χ1600(1311,⋅)\chi_{1600}(1311,\cdot)

• Label: 1600.1311
• Modulus: $1600$
• Conductor: $200$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1600$
Conductor:	$200$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{200}(11,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1600.bd

$\chi_{1600}(31,\cdot)$ $\chi_{1600}(671,\cdot)$ $\chi_{1600}(991,\cdot)$ $\chi_{1600}(1311,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.0.5000000000000000.1

Values on generators

$(1151,901,577)$ → $(-1,-1,e\left(\frac{4}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 1600 }(1311, a)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$