Dirichlet character χ2783(1015,⋅)\chi_{2783}(1015,\cdot)

• Label: 2783.1015
• Modulus: $2783$
• Conductor: $2783$
• Order: $55$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2783$
Conductor:	$2783$
Order:	$55$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2783.cp

$\chi_{2783}(48,\cdot)$ $\chi_{2783}(58,\cdot)$ $\chi_{2783}(141,\cdot)$ $\chi_{2783}(257,\cdot)$ $\chi_{2783}(302,\cdot)$ $\chi_{2783}(400,\cdot)$ $\chi_{2783}(427,\cdot)$ $\chi_{2783}(515,\cdot)$ $\chi_{2783}(581,\cdot)$ $\chi_{2783}(740,\cdot)$ $\chi_{2783}(785,\cdot)$ $\chi_{2783}(818,\cdot)$ $\chi_{2783}(840,\cdot)$ $\chi_{2783}(1015,\cdot)$ $\chi_{2783}(1037,\cdot)$ $\chi_{2783}(1076,\cdot)$ $\chi_{2783}(1131,\cdot)$ $\chi_{2783}(1175,\cdot)$ $\chi_{2783}(1182,\cdot)$ $\chi_{2783}(1202,\cdot)$ $\chi_{2783}(1204,\cdot)$ $\chi_{2783}(1214,\cdot)$ $\chi_{2783}(1235,\cdot)$ $\chi_{2783}(1369,\cdot)$ $\chi_{2783}(1411,\cdot)$ $\chi_{2783}(1434,\cdot)$ $\chi_{2783}(1478,\cdot)$ $\chi_{2783}(1501,\cdot)$ $\chi_{2783}(1554,\cdot)$ $\chi_{2783}(1589,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 55 polynomial

Values on generators

$(2301,1937)$ → $(e\left(\frac{49}{55}\right),e\left(\frac{8}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 2783 }(1015, a)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$1$	$e\left(\frac{8}{11}\right)$