Dirichlet character χ216000(11971,⋅)\chi_{216000}(11971,\cdot)

• Label: 216000.11971
• Modulus: $216000$
• Conductor: $72000$
• Order: $1200$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$216000$
Conductor:	$72000$
Order:	$1200$
Real:	no
Primitive:	no, induced from $\chi_{72000}(59971,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 216000.xj

$\chi_{216000}(91,\cdot)$ $\chi_{216000}(1171,\cdot)$ $\chi_{216000}(1531,\cdot)$ $\chi_{216000}(2611,\cdot)$ $\chi_{216000}(3331,\cdot)$ $\chi_{216000}(3691,\cdot)$ $\chi_{216000}(4411,\cdot)$ $\chi_{216000}(4771,\cdot)$ $\chi_{216000}(5491,\cdot)$ $\chi_{216000}(6571,\cdot)$ $\chi_{216000}(6931,\cdot)$ $\chi_{216000}(8011,\cdot)$ $\chi_{216000}(8731,\cdot)$ $\chi_{216000}(9091,\cdot)$ $\chi_{216000}(9811,\cdot)$ $\chi_{216000}(10171,\cdot)$ $\chi_{216000}(10891,\cdot)$ $\chi_{216000}(11971,\cdot)$ $\chi_{216000}(12331,\cdot)$ $\chi_{216000}(13411,\cdot)$ $\chi_{216000}(14131,\cdot)$ $\chi_{216000}(14491,\cdot)$ $\chi_{216000}(15211,\cdot)$ $\chi_{216000}(15571,\cdot)$ $\chi_{216000}(16291,\cdot)$ $\chi_{216000}(17371,\cdot)$ $\chi_{216000}(17731,\cdot)$ $\chi_{216000}(18811,\cdot)$ $\chi_{216000}(19531,\cdot)$ $\chi_{216000}(19891,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1200})$
Fixed field:	Number field defined by a degree 1200 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(-1,e\left(\frac{3}{16}\right),e\left(\frac{1}{3}\right),e\left(\frac{3}{25}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(11971, a)$	$-1$	$1$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1069}{1200}\right)$	$e\left(\frac{191}{1200}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{307}{600}\right)$	$e\left(\frac{1003}{1200}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{67}{400}\right)$	$e\left(\frac{343}{600}\right)$