Dirichlet character χ1785(2,⋅)\chi_{1785}(2,\cdot)

• Label: 1785.2
• Modulus: $1785$
• Conductor: $1785$
• Order: $24$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1785$
Conductor:	$1785$
Order:	$24$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1785.ei

$\chi_{1785}(2,\cdot)$ $\chi_{1785}(32,\cdot)$ $\chi_{1785}(128,\cdot)$ $\chi_{1785}(263,\cdot)$ $\chi_{1785}(767,\cdot)$ $\chi_{1785}(893,\cdot)$ $\chi_{1785}(1052,\cdot)$ $\chi_{1785}(1283,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{24})$
Fixed field:	Number field defined by a degree 24 polynomial

Values on generators

$(596,1072,766,1261)$ → $(-1,i,e\left(\frac{1}{3}\right),e\left(\frac{7}{8}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{ 1785 }(2, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$