Dirichlet character χ1309(180,⋅)\chi_{1309}(180,\cdot)

• Label: 1309.180
• Modulus: $1309$
• Conductor: $1309$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1309$
Conductor:	$1309$
Order:	$240$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1309.da

$\chi_{1309}(3,\cdot)$ $\chi_{1309}(5,\cdot)$ $\chi_{1309}(31,\cdot)$ $\chi_{1309}(75,\cdot)$ $\chi_{1309}(80,\cdot)$ $\chi_{1309}(82,\cdot)$ $\chi_{1309}(108,\cdot)$ $\chi_{1309}(124,\cdot)$ $\chi_{1309}(159,\cdot)$ $\chi_{1309}(180,\cdot)$ $\chi_{1309}(192,\cdot)$ $\chi_{1309}(201,\cdot)$ $\chi_{1309}(262,\cdot)$ $\chi_{1309}(269,\cdot)$ $\chi_{1309}(278,\cdot)$ $\chi_{1309}(311,\cdot)$ $\chi_{1309}(313,\cdot)$ $\chi_{1309}(334,\cdot)$ $\chi_{1309}(346,\cdot)$ $\chi_{1309}(367,\cdot)$ $\chi_{1309}(388,\cdot)$ $\chi_{1309}(411,\cdot)$ $\chi_{1309}(432,\cdot)$ $\chi_{1309}(465,\cdot)$ $\chi_{1309}(488,\cdot)$ $\chi_{1309}(500,\cdot)$ $\chi_{1309}(521,\cdot)$ $\chi_{1309}(537,\cdot)$ $\chi_{1309}(598,\cdot)$ $\chi_{1309}(619,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

Values on generators

$(1123,596,309)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right),e\left(\frac{3}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{ 1309 }(180, a)$	$1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{9}{20}\right)$