Dirichlet character χ243675(7,⋅)\chi_{243675}(7,\cdot)

• Label: 243675.7
• 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 $\chi_{48735}(7,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 243675.yj

$\chi_{243675}(7,\cdot)$ $\chi_{243675}(2443,\cdot)$ $\chi_{243675}(2743,\cdot)$ $\chi_{243675}(3982,\cdot)$ $\chi_{243675}(4282,\cdot)$ $\chi_{243675}(6718,\cdot)$ $\chi_{243675}(7018,\cdot)$ $\chi_{243675}(8257,\cdot)$ $\chi_{243675}(8557,\cdot)$ $\chi_{243675}(10993,\cdot)$ $\chi_{243675}(11293,\cdot)$ $\chi_{243675}(12532,\cdot)$ $\chi_{243675}(12832,\cdot)$ $\chi_{243675}(15268,\cdot)$ $\chi_{243675}(15568,\cdot)$ $\chi_{243675}(16807,\cdot)$ $\chi_{243675}(17107,\cdot)$ $\chi_{243675}(19543,\cdot)$ $\chi_{243675}(19843,\cdot)$ $\chi_{243675}(21082,\cdot)$ $\chi_{243675}(21382,\cdot)$ $\chi_{243675}(23818,\cdot)$ $\chi_{243675}(25357,\cdot)$ $\chi_{243675}(25657,\cdot)$ $\chi_{243675}(28093,\cdot)$ $\chi_{243675}(28393,\cdot)$ $\chi_{243675}(29632,\cdot)$ $\chi_{243675}(29932,\cdot)$ $\chi_{243675}(32368,\cdot)$ $\chi_{243675}(32668,\cdot)$ ...

Related number fields

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

Values on generators

$(36101,77977,129601)$ → $(e\left(\frac{8}{9}\right),i,e\left(\frac{25}{57}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{ 243675 }(7, a)$	$-1$	$1$	$e\left(\frac{395}{684}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{179}{684}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{595}{684}\right)$