Dirichlet character χ504(17,⋅)\chi_{504}(17,\cdot)

• Label: 504.17
• Modulus: $504$
• Conductor: $21$
• Order: $6$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$504$
Conductor:	$21$
Order:	$6$
Real:	no
Primitive:	no, induced from $\chi_{21}(17,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 504.bl

$\chi_{504}(17,\cdot)$ $\chi_{504}(89,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{21})^+$

Values on generators

$(127,253,281,73)$ → $(1,1,-1,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 504 }(17, a)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum