Dirichlet character χ390(199,⋅)\chi_{390}(199,\cdot)

• Label: 390.199
• Modulus: $390$
• Conductor: $65$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$390$
Conductor:	$65$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{65}(4,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 390.x

$\chi_{390}(49,\cdot)$ $\chi_{390}(199,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.46411625.1

Values on generators

$(131,157,301)$ → $(1,-1,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 390 }(199, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum