Dirichlet character χ243675(31993,⋅)\chi_{243675}(31993,\cdot)

• Label: 243675.31993
• Modulus: $243675$
• Conductor: $48735$
• Order: $684$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$243675$
Conductor:	$48735$
Order:	$684$
Real:	no
Primitive:	no, induced from $\chi_{48735}(31993,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 243675.yv

$\chi_{243675}(43,\cdot)$ $\chi_{243675}(682,\cdot)$ $\chi_{243675}(1582,\cdot)$ $\chi_{243675}(6343,\cdot)$ $\chi_{243675}(7882,\cdot)$ $\chi_{243675}(8293,\cdot)$ $\chi_{243675}(8518,\cdot)$ $\chi_{243675}(9832,\cdot)$ $\chi_{243675}(10057,\cdot)$ $\chi_{243675}(10093,\cdot)$ $\chi_{243675}(11632,\cdot)$ $\chi_{243675}(11968,\cdot)$ $\chi_{243675}(12868,\cdot)$ $\chi_{243675}(13507,\cdot)$ $\chi_{243675}(14407,\cdot)$ $\chi_{243675}(19168,\cdot)$ $\chi_{243675}(20707,\cdot)$ $\chi_{243675}(21118,\cdot)$ $\chi_{243675}(21343,\cdot)$ $\chi_{243675}(22657,\cdot)$ $\chi_{243675}(22882,\cdot)$ $\chi_{243675}(22918,\cdot)$ $\chi_{243675}(24457,\cdot)$ $\chi_{243675}(26332,\cdot)$ $\chi_{243675}(27232,\cdot)$ $\chi_{243675}(31993,\cdot)$ $\chi_{243675}(33532,\cdot)$ $\chi_{243675}(33943,\cdot)$ $\chi_{243675}(35482,\cdot)$ $\chi_{243675}(35707,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{684})$
Fixed field:	Number field defined by a degree 684 polynomial (not computed)

Values on generators

$(36101,77977,129601)$ → $(e\left(\frac{5}{9}\right),-i,e\left(\frac{29}{171}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{ 243675 }(31993, a)$	$-1$	$1$	$e\left(\frac{325}{684}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{53}{684}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{335}{684}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{281}{684}\right)$	$e\left(\frac{227}{228}\right)$