Dirichlet character χ507(80,⋅)\chi_{507}(80,\cdot)

• Label: 507.80
• Modulus: $507$
• Conductor: $39$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$507$
Conductor:	$39$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{39}(2,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 507.k

$\chi_{507}(80,\cdot)$ $\chi_{507}(89,\cdot)$ $\chi_{507}(188,\cdot)$ $\chi_{507}(488,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	$\Q(\zeta_{39})^+$

Values on generators

$(170,340)$ → $(-1,e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 507 }(80, a)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum