Dirichlet character χ21600(16747,⋅)\chi_{21600}(16747,\cdot)

• Label: 21600.16747
• Modulus: $21600$
• Conductor: $21600$
• Order: $360$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$21600$
Conductor:	$21600$
Order:	$360$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 21600.mm

$\chi_{21600}(187,\cdot)$ $\chi_{21600}(403,\cdot)$ $\chi_{21600}(427,\cdot)$ $\chi_{21600}(1123,\cdot)$ $\chi_{21600}(1147,\cdot)$ $\chi_{21600}(1363,\cdot)$ $\chi_{21600}(1627,\cdot)$ $\chi_{21600}(1867,\cdot)$ $\chi_{21600}(2083,\cdot)$ $\chi_{21600}(2347,\cdot)$ $\chi_{21600}(2563,\cdot)$ $\chi_{21600}(2587,\cdot)$ $\chi_{21600}(2803,\cdot)$ $\chi_{21600}(3067,\cdot)$ $\chi_{21600}(3283,\cdot)$ $\chi_{21600}(3523,\cdot)$ $\chi_{21600}(3787,\cdot)$ $\chi_{21600}(4003,\cdot)$ $\chi_{21600}(4027,\cdot)$ $\chi_{21600}(4723,\cdot)$ $\chi_{21600}(4747,\cdot)$ $\chi_{21600}(4963,\cdot)$ $\chi_{21600}(5227,\cdot)$ $\chi_{21600}(5467,\cdot)$ $\chi_{21600}(5683,\cdot)$ $\chi_{21600}(5947,\cdot)$ $\chi_{21600}(6163,\cdot)$ $\chi_{21600}(6187,\cdot)$ $\chi_{21600}(6403,\cdot)$ $\chi_{21600}(6667,\cdot)$ ...

Related number fields

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

Values on generators

$(6751,8101,6401,7777)$ → $(-1,e\left(\frac{5}{8}\right),e\left(\frac{8}{9}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 21600 }(16747, a)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{281}{360}\right)$	$e\left(\frac{229}{360}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{167}{360}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{47}{180}\right)$