Dirichlet character χ216000(13,⋅)\chi_{216000}(13,\cdot)

• Label: 216000.13
• Modulus: $216000$
• Conductor: $216000$
• Order: $3600$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 216000.yv

$\chi_{216000}(13,\cdot)$ $\chi_{216000}(277,\cdot)$ $\chi_{216000}(517,\cdot)$ $\chi_{216000}(733,\cdot)$ $\chi_{216000}(997,\cdot)$ $\chi_{216000}(1213,\cdot)$ $\chi_{216000}(1237,\cdot)$ $\chi_{216000}(1453,\cdot)$

Related number fields

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

Values on generators

$(114751,202501,136001,29377)$ → $(1,e\left(\frac{15}{16}\right),e\left(\frac{4}{9}\right),e\left(\frac{39}{100}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(13, a)$	$-1$	$1$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{379}{3600}\right)$	$e\left(\frac{2981}{3600}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{1099}{1200}\right)$	$e\left(\frac{187}{1800}\right)$	$e\left(\frac{3373}{3600}\right)$	$e\left(\frac{49}{450}\right)$	$e\left(\frac{497}{1200}\right)$	$e\left(\frac{1513}{1800}\right)$