Dirichlet character χ2888(1689,⋅)\chi_{2888}(1689,\cdot)

• Label: 2888.1689
• Modulus: $2888$
• Conductor: $19$
• Order: $9$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$2888$
Conductor:	$19$
Order:	$9$
Real:	no
Primitive:	no, induced from $\chi_{19}(17,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 2888.q

$\chi_{2888}(1137,\cdot)$ $\chi_{2888}(1145,\cdot)$ $\chi_{2888}(1689,\cdot)$ $\chi_{2888}(1833,\cdot)$ $\chi_{2888}(2265,\cdot)$ $\chi_{2888}(2761,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{9})$
Fixed field:	$\Q(\zeta_{19})^+$

Values on generators

$(2167,1445,2529)$ → $(1,1,e\left(\frac{5}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{ 2888 }(1689, a)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$