Dirichlet character χ216000(14617,⋅)\chi_{216000}(14617,\cdot)

• Label: 216000.14617
• 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 $\chi_{36000}(22117,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 216000.uz

$\chi_{216000}(73,\cdot)$ $\chi_{216000}(2953,\cdot)$ $\chi_{216000}(3097,\cdot)$ $\chi_{216000}(5977,\cdot)$ $\chi_{216000}(7273,\cdot)$ $\chi_{216000}(7417,\cdot)$ $\chi_{216000}(8713,\cdot)$ $\chi_{216000}(10297,\cdot)$ $\chi_{216000}(11737,\cdot)$ $\chi_{216000}(13033,\cdot)$ $\chi_{216000}(14617,\cdot)$ $\chi_{216000}(15913,\cdot)$ $\chi_{216000}(17353,\cdot)$ $\chi_{216000}(18937,\cdot)$ $\chi_{216000}(20233,\cdot)$ $\chi_{216000}(20377,\cdot)$ $\chi_{216000}(21673,\cdot)$ $\chi_{216000}(24553,\cdot)$ $\chi_{216000}(24697,\cdot)$ $\chi_{216000}(27577,\cdot)$ $\chi_{216000}(28873,\cdot)$ $\chi_{216000}(29017,\cdot)$ $\chi_{216000}(30313,\cdot)$ $\chi_{216000}(31897,\cdot)$ $\chi_{216000}(33337,\cdot)$ $\chi_{216000}(34633,\cdot)$ $\chi_{216000}(36217,\cdot)$ $\chi_{216000}(37513,\cdot)$ $\chi_{216000}(38953,\cdot)$ $\chi_{216000}(40537,\cdot)$ ...

Related number fields

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

Values on generators

$(114751,202501,136001,29377)$ → $(1,e\left(\frac{1}{8}\right),e\left(\frac{1}{3}\right),e\left(\frac{53}{100}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(14617, a)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{143}{600}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{341}{600}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{221}{300}\right)$