Dirichlet character χ216000(7,⋅)\chi_{216000}(7,\cdot)

• Label: 216000.7
• Modulus: $216000$
• Conductor: $21600$
• Order: $360$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$216000$
Conductor:	$21600$
Order:	$360$
Real:	no
Primitive:	no, induced from $\chi_{21600}(16747,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 216000.th

$\chi_{216000}(7,\cdot)$ $\chi_{216000}(2407,\cdot)$ $\chi_{216000}(2743,\cdot)$ $\chi_{216000}(5143,\cdot)$ $\chi_{216000}(7207,\cdot)$ $\chi_{216000}(9607,\cdot)$ $\chi_{216000}(12343,\cdot)$ $\chi_{216000}(14407,\cdot)$ $\chi_{216000}(17143,\cdot)$ $\chi_{216000}(19543,\cdot)$ $\chi_{216000}(21607,\cdot)$ $\chi_{216000}(24007,\cdot)$ $\chi_{216000}(24343,\cdot)$ $\chi_{216000}(26743,\cdot)$ $\chi_{216000}(31207,\cdot)$ $\chi_{216000}(31543,\cdot)$ $\chi_{216000}(36007,\cdot)$ $\chi_{216000}(38407,\cdot)$ $\chi_{216000}(38743,\cdot)$ $\chi_{216000}(41143,\cdot)$ $\chi_{216000}(43207,\cdot)$ $\chi_{216000}(45607,\cdot)$ $\chi_{216000}(48343,\cdot)$ $\chi_{216000}(50407,\cdot)$ $\chi_{216000}(53143,\cdot)$ $\chi_{216000}(55543,\cdot)$ $\chi_{216000}(57607,\cdot)$ $\chi_{216000}(60007,\cdot)$ $\chi_{216000}(60343,\cdot)$ $\chi_{216000}(62743,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{360})$
Fixed field:	Number field defined by a degree 360 polynomial (not computed)

Values on generators

$(114751,202501,136001,29377)$ → $(-1,e\left(\frac{5}{8}\right),e\left(\frac{8}{9}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 216000 }(7, a)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{281}{360}\right)$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{47}{180}\right)$