Dirichlet character χ2303(12,⋅)\chi_{2303}(12,\cdot)

• Label: 2303.12
• Modulus: $2303$
• Conductor: $2303$
• Order: $966$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2303$
Conductor:	$2303$
Order:	$966$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2303.bf

$\chi_{2303}(3,\cdot)$ $\chi_{2303}(12,\cdot)$ $\chi_{2303}(17,\cdot)$ $\chi_{2303}(24,\cdot)$ $\chi_{2303}(54,\cdot)$ $\chi_{2303}(59,\cdot)$ $\chi_{2303}(61,\cdot)$ $\chi_{2303}(75,\cdot)$ $\chi_{2303}(89,\cdot)$ $\chi_{2303}(96,\cdot)$ $\chi_{2303}(101,\cdot)$ $\chi_{2303}(103,\cdot)$ $\chi_{2303}(108,\cdot)$ $\chi_{2303}(110,\cdot)$ $\chi_{2303}(115,\cdot)$ $\chi_{2303}(122,\cdot)$ $\chi_{2303}(131,\cdot)$ $\chi_{2303}(136,\cdot)$ $\chi_{2303}(143,\cdot)$ $\chi_{2303}(145,\cdot)$ $\chi_{2303}(150,\cdot)$ $\chi_{2303}(157,\cdot)$ $\chi_{2303}(159,\cdot)$ $\chi_{2303}(173,\cdot)$ $\chi_{2303}(192,\cdot)$ $\chi_{2303}(194,\cdot)$ $\chi_{2303}(206,\cdot)$ $\chi_{2303}(213,\cdot)$ $\chi_{2303}(220,\cdot)$ $\chi_{2303}(222,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{483})$
Fixed field:	Number field defined by a degree 966 polynomial (not computed)

Values on generators

$(2257,99)$ → $(e\left(\frac{11}{42}\right),e\left(\frac{5}{23}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 2303 }(12, a)$	$-1$	$1$	$e\left(\frac{349}{483}\right)$	$e\left(\frac{589}{966}\right)$	$e\left(\frac{215}{483}\right)$	$e\left(\frac{785}{966}\right)$	$e\left(\frac{107}{322}\right)$	$e\left(\frac{27}{161}\right)$	$e\left(\frac{106}{483}\right)$	$e\left(\frac{517}{966}\right)$	$e\left(\frac{482}{483}\right)$	$e\left(\frac{53}{966}\right)$