Dirichlet character χ2557(89,⋅)\chi_{2557}(89,\cdot)

• Label: 2557.89
• Modulus: $2557$
• Conductor: $2557$
• Order: $2556$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2557$
Conductor:	$2557$
Order:	$2556$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2557.r

$\chi_{2557}(2,\cdot)$ $\chi_{2557}(5,\cdot)$ $\chi_{2557}(6,\cdot)$ $\chi_{2557}(15,\cdot)$ $\chi_{2557}(17,\cdot)$ $\chi_{2557}(24,\cdot)$ $\chi_{2557}(31,\cdot)$ $\chi_{2557}(32,\cdot)$ $\chi_{2557}(41,\cdot)$ $\chi_{2557}(42,\cdot)$ $\chi_{2557}(43,\cdot)$ $\chi_{2557}(47,\cdot)$ $\chi_{2557}(51,\cdot)$ $\chi_{2557}(54,\cdot)$ $\chi_{2557}(56,\cdot)$ $\chi_{2557}(60,\cdot)$ $\chi_{2557}(66,\cdot)$ $\chi_{2557}(67,\cdot)$ $\chi_{2557}(72,\cdot)$ $\chi_{2557}(78,\cdot)$ $\chi_{2557}(80,\cdot)$ $\chi_{2557}(83,\cdot)$ $\chi_{2557}(88,\cdot)$ $\chi_{2557}(89,\cdot)$ $\chi_{2557}(98,\cdot)$ $\chi_{2557}(103,\cdot)$ $\chi_{2557}(104,\cdot)$ $\chi_{2557}(105,\cdot)$ $\chi_{2557}(106,\cdot)$ $\chi_{2557}(107,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{2556})$
Fixed field:	Number field defined by a degree 2556 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{1001}{2556}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 2557 }(89, a)$	$-1$	$1$	$e\left(\frac{1001}{2556}\right)$	$e\left(\frac{47}{639}\right)$	$e\left(\frac{1001}{1278}\right)$	$e\left(\frac{1403}{2556}\right)$	$e\left(\frac{1189}{2556}\right)$	$e\left(\frac{899}{1278}\right)$	$e\left(\frac{149}{852}\right)$	$e\left(\frac{94}{639}\right)$	$e\left(\frac{601}{639}\right)$	$e\left(\frac{412}{639}\right)$