Dirichlet character χ259200(19,⋅)\chi_{259200}(19,\cdot)

• Label: 259200.19
• Modulus: $259200$
• Conductor: $86400$
• Order: $1440$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$259200$
Conductor:	$86400$
Order:	$1440$
Real:	no
Primitive:	no, induced from $\chi_{86400}(9619,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 259200.zv

$\chi_{259200}(19,\cdot)$ $\chi_{259200}(739,\cdot)$ $\chi_{259200}(1819,\cdot)$ $\chi_{259200}(2179,\cdot)$ $\chi_{259200}(3259,\cdot)$ $\chi_{259200}(3979,\cdot)$ $\chi_{259200}(4339,\cdot)$ $\chi_{259200}(5059,\cdot)$ $\chi_{259200}(5419,\cdot)$ $\chi_{259200}(6139,\cdot)$ $\chi_{259200}(7219,\cdot)$ $\chi_{259200}(7579,\cdot)$ $\chi_{259200}(8659,\cdot)$ $\chi_{259200}(9379,\cdot)$ $\chi_{259200}(9739,\cdot)$ $\chi_{259200}(10459,\cdot)$ $\chi_{259200}(10819,\cdot)$ $\chi_{259200}(11539,\cdot)$ $\chi_{259200}(12619,\cdot)$ $\chi_{259200}(12979,\cdot)$ $\chi_{259200}(14059,\cdot)$ $\chi_{259200}(14779,\cdot)$ $\chi_{259200}(15139,\cdot)$ $\chi_{259200}(15859,\cdot)$ $\chi_{259200}(16219,\cdot)$ $\chi_{259200}(16939,\cdot)$ $\chi_{259200}(18019,\cdot)$ $\chi_{259200}(18379,\cdot)$ $\chi_{259200}(19459,\cdot)$ $\chi_{259200}(20179,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1440})$
Fixed field:	Number field defined by a degree 1440 polynomial (not computed)

Values on generators

$(157951,202501,6401,72577)$ → $(-1,e\left(\frac{23}{32}\right),e\left(\frac{8}{9}\right),e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 259200 }(19, a)$	$-1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{791}{1440}\right)$	$e\left(\frac{1429}{1440}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{431}{480}\right)$	$e\left(\frac{173}{720}\right)$	$e\left(\frac{137}{1440}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{193}{480}\right)$	$e\left(\frac{197}{720}\right)$