Dirichlet character χ216000(67,⋅)\chi_{216000}(67,\cdot)

• Label: 216000.67
• Modulus: $216000$
• Conductor: $216000$
• Order: $3600$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$216000$
Conductor:	$216000$
Order:	$3600$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 216000.yu

$\chi_{216000}(67,\cdot)$ $\chi_{216000}(283,\cdot)$ $\chi_{216000}(547,\cdot)$ $\chi_{216000}(763,\cdot)$ $\chi_{216000}(787,\cdot)$ $\chi_{216000}(1003,\cdot)$ $\chi_{216000}(1267,\cdot)$ $\chi_{216000}(1483,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{3600})$
Fixed field:	Number field defined by a degree 3600 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(-1,e\left(\frac{3}{16}\right),e\left(\frac{4}{9}\right),e\left(\frac{13}{100}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(67, a)$	$1$	$1$	$e\left(\frac{193}{360}\right)$	$e\left(\frac{343}{3600}\right)$	$e\left(\frac{1577}{3600}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{583}{1200}\right)$	$e\left(\frac{79}{1800}\right)$	$e\left(\frac{2041}{3600}\right)$	$e\left(\frac{29}{225}\right)$	$e\left(\frac{149}{1200}\right)$	$e\left(\frac{1621}{1800}\right)$