Dirichlet character χ86400(1579,⋅)\chi_{86400}(1579,\cdot)

• Label: 86400.1579
• Modulus: $86400$
• Conductor: $86400$
• Order: $1440$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$86400$
Conductor:	$86400$
Order:	$1440$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 86400.uh

$\chi_{86400}(139,\cdot)$ $\chi_{86400}(259,\cdot)$ $\chi_{86400}(619,\cdot)$ $\chi_{86400}(859,\cdot)$ $\chi_{86400}(979,\cdot)$ $\chi_{86400}(1219,\cdot)$ $\chi_{86400}(1339,\cdot)$ $\chi_{86400}(1579,\cdot)$ $\chi_{86400}(1939,\cdot)$ $\chi_{86400}(2059,\cdot)$ $\chi_{86400}(2419,\cdot)$ $\chi_{86400}(2659,\cdot)$ $\chi_{86400}(2779,\cdot)$ $\chi_{86400}(3019,\cdot)$ $\chi_{86400}(3139,\cdot)$ $\chi_{86400}(3379,\cdot)$ $\chi_{86400}(3739,\cdot)$ $\chi_{86400}(3859,\cdot)$ $\chi_{86400}(4219,\cdot)$ $\chi_{86400}(4459,\cdot)$ $\chi_{86400}(4579,\cdot)$ $\chi_{86400}(4819,\cdot)$ $\chi_{86400}(4939,\cdot)$ $\chi_{86400}(5179,\cdot)$ $\chi_{86400}(5539,\cdot)$ $\chi_{86400}(5659,\cdot)$ $\chi_{86400}(6019,\cdot)$ $\chi_{86400}(6259,\cdot)$ $\chi_{86400}(6379,\cdot)$ $\chi_{86400}(6619,\cdot)$ ...

Related number fields

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

Values on generators

$(71551,29701,6401,72577)$ → $(-1,e\left(\frac{29}{32}\right),e\left(\frac{4}{9}\right),e\left(\frac{1}{10}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 86400 }(1579, a)$	$-1$	$1$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{1309}{1440}\right)$	$e\left(\frac{71}{1440}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{229}{480}\right)$	$e\left(\frac{127}{720}\right)$	$e\left(\frac{163}{1440}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{107}{480}\right)$	$e\left(\frac{103}{720}\right)$