Dirichlet character χ459(208,⋅)\chi_{459}(208,\cdot)

• Label: 459.208
• Modulus: $459$
• Conductor: $153$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$459$
Conductor:	$153$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{153}(106,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 459.o

$\chi_{459}(64,\cdot)$ $\chi_{459}(208,\cdot)$ $\chi_{459}(361,\cdot)$ $\chi_{459}(370,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.5104819233548816337.1

Values on generators

$(137,190)$ → $(e\left(\frac{2}{3}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 459 }(208, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum