Dirichlet character χ216000(20969,⋅)\chi_{216000}(20969,\cdot)

• Label: 216000.20969
• Modulus: $216000$
• Conductor: $36000$
• Order: $600$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$216000$
Conductor:	$36000$
Order:	$600$
Real:	no
Primitive:	no, induced from $\chi_{36000}(31469,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 216000.vj

$\chi_{216000}(89,\cdot)$ $\chi_{216000}(1529,\cdot)$ $\chi_{216000}(3689,\cdot)$ $\chi_{216000}(4409,\cdot)$ $\chi_{216000}(6569,\cdot)$ $\chi_{216000}(8009,\cdot)$ $\chi_{216000}(8729,\cdot)$ $\chi_{216000}(10169,\cdot)$ $\chi_{216000}(10889,\cdot)$ $\chi_{216000}(12329,\cdot)$ $\chi_{216000}(14489,\cdot)$ $\chi_{216000}(15209,\cdot)$ $\chi_{216000}(17369,\cdot)$ $\chi_{216000}(18809,\cdot)$ $\chi_{216000}(19529,\cdot)$ $\chi_{216000}(20969,\cdot)$ $\chi_{216000}(21689,\cdot)$ $\chi_{216000}(23129,\cdot)$ $\chi_{216000}(25289,\cdot)$ $\chi_{216000}(26009,\cdot)$ $\chi_{216000}(28169,\cdot)$ $\chi_{216000}(29609,\cdot)$ $\chi_{216000}(30329,\cdot)$ $\chi_{216000}(31769,\cdot)$ $\chi_{216000}(32489,\cdot)$ $\chi_{216000}(33929,\cdot)$ $\chi_{216000}(36089,\cdot)$ $\chi_{216000}(36809,\cdot)$ $\chi_{216000}(38969,\cdot)$ $\chi_{216000}(40409,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{600})$
Fixed field:	Number field defined by a degree 600 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(1,e\left(\frac{7}{8}\right),e\left(\frac{5}{6}\right),e\left(\frac{49}{50}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(20969, a)$	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{7}{600}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{161}{300}\right)$