Dirichlet character χ216000(21709,⋅)\chi_{216000}(21709,\cdot)

• Label: 216000.21709
• Modulus: $216000$
• Conductor: $8000$
• Order: $400$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$216000$
Conductor:	$8000$
Order:	$400$
Real:	no
Primitive:	no, induced from $\chi_{8000}(5709,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 216000.tz

$\chi_{216000}(109,\cdot)$ $\chi_{216000}(1189,\cdot)$ $\chi_{216000}(2269,\cdot)$ $\chi_{216000}(4429,\cdot)$ $\chi_{216000}(5509,\cdot)$ $\chi_{216000}(6589,\cdot)$ $\chi_{216000}(7669,\cdot)$ $\chi_{216000}(9829,\cdot)$ $\chi_{216000}(10909,\cdot)$ $\chi_{216000}(11989,\cdot)$ $\chi_{216000}(13069,\cdot)$ $\chi_{216000}(15229,\cdot)$ $\chi_{216000}(16309,\cdot)$ $\chi_{216000}(17389,\cdot)$ $\chi_{216000}(18469,\cdot)$ $\chi_{216000}(20629,\cdot)$ $\chi_{216000}(21709,\cdot)$ $\chi_{216000}(22789,\cdot)$ $\chi_{216000}(23869,\cdot)$ $\chi_{216000}(26029,\cdot)$ $\chi_{216000}(27109,\cdot)$ $\chi_{216000}(28189,\cdot)$ $\chi_{216000}(29269,\cdot)$ $\chi_{216000}(31429,\cdot)$ $\chi_{216000}(32509,\cdot)$ $\chi_{216000}(33589,\cdot)$ $\chi_{216000}(34669,\cdot)$ $\chi_{216000}(36829,\cdot)$ $\chi_{216000}(37909,\cdot)$ $\chi_{216000}(38989,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{400})$
Fixed field:	Number field defined by a degree 400 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(1,e\left(\frac{15}{16}\right),1,e\left(\frac{47}{50}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(21709, a)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{51}{400}\right)$	$e\left(\frac{289}{400}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{193}{400}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{237}{400}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{97}{200}\right)$