Dirichlet character χ216000(5321,⋅)\chi_{216000}(5321,\cdot)

• Label: 216000.5321
• Modulus: $216000$
• Conductor: $108000$
• Order: $1800$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$216000$
Conductor:	$108000$
Order:	$1800$
Real:	no
Primitive:	no, induced from $\chi_{108000}(45821,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 216000.ye

$\chi_{216000}(41,\cdot)$ $\chi_{216000}(281,\cdot)$ $\chi_{216000}(761,\cdot)$ $\chi_{216000}(1481,\cdot)$ $\chi_{216000}(1721,\cdot)$ $\chi_{216000}(2441,\cdot)$ $\chi_{216000}(2921,\cdot)$ $\chi_{216000}(3161,\cdot)$ $\chi_{216000}(3641,\cdot)$ $\chi_{216000}(3881,\cdot)$ $\chi_{216000}(4361,\cdot)$ $\chi_{216000}(5081,\cdot)$ $\chi_{216000}(5321,\cdot)$ $\chi_{216000}(6041,\cdot)$ $\chi_{216000}(6521,\cdot)$ $\chi_{216000}(6761,\cdot)$ $\chi_{216000}(7241,\cdot)$ $\chi_{216000}(7481,\cdot)$ $\chi_{216000}(7961,\cdot)$ $\chi_{216000}(8681,\cdot)$ $\chi_{216000}(8921,\cdot)$ $\chi_{216000}(9641,\cdot)$ $\chi_{216000}(10121,\cdot)$ $\chi_{216000}(10361,\cdot)$ $\chi_{216000}(10841,\cdot)$ $\chi_{216000}(11081,\cdot)$ $\chi_{216000}(11561,\cdot)$ $\chi_{216000}(12281,\cdot)$ $\chi_{216000}(12521,\cdot)$ $\chi_{216000}(13241,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1800})$
Fixed field:	Number field defined by a degree 1800 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(1,e\left(\frac{3}{8}\right),e\left(\frac{1}{18}\right),e\left(\frac{18}{25}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(5321, a)$	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{571}{1800}\right)$	$e\left(\frac{269}{1800}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{163}{900}\right)$	$e\left(\frac{1477}{1800}\right)$	$e\left(\frac{151}{225}\right)$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{787}{900}\right)$