Dirichlet character χ2557(37,⋅)\chi_{2557}(37,\cdot)

• Label: 2557.37
• Modulus: $2557$
• Conductor: $2557$
• Order: $1278$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2557$
Conductor:	$2557$
Order:	$1278$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2557.q

$\chi_{2557}(4,\cdot)$ $\chi_{2557}(7,\cdot)$ $\chi_{2557}(23,\cdot)$ $\chi_{2557}(25,\cdot)$ $\chi_{2557}(29,\cdot)$ $\chi_{2557}(34,\cdot)$ $\chi_{2557}(36,\cdot)$ $\chi_{2557}(37,\cdot)$ $\chi_{2557}(40,\cdot)$ $\chi_{2557}(44,\cdot)$ $\chi_{2557}(52,\cdot)$ $\chi_{2557}(59,\cdot)$ $\chi_{2557}(63,\cdot)$ $\chi_{2557}(70,\cdot)$ $\chi_{2557}(73,\cdot)$ $\chi_{2557}(76,\cdot)$ $\chi_{2557}(77,\cdot)$ $\chi_{2557}(86,\cdot)$ $\chi_{2557}(91,\cdot)$ $\chi_{2557}(94,\cdot)$ $\chi_{2557}(108,\cdot)$ $\chi_{2557}(120,\cdot)$ $\chi_{2557}(127,\cdot)$ $\chi_{2557}(132,\cdot)$ $\chi_{2557}(133,\cdot)$ $\chi_{2557}(156,\cdot)$ $\chi_{2557}(159,\cdot)$ $\chi_{2557}(173,\cdot)$ $\chi_{2557}(186,\cdot)$ $\chi_{2557}(189,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{639})$
Fixed field:	Number field defined by a degree 1278 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{115}{1278}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 2557 }(37, a)$	$1$	$1$	$e\left(\frac{115}{1278}\right)$	$e\left(\frac{104}{639}\right)$	$e\left(\frac{115}{639}\right)$	$e\left(\frac{451}{1278}\right)$	$e\left(\frac{323}{1278}\right)$	$e\left(\frac{478}{639}\right)$	$e\left(\frac{115}{426}\right)$	$e\left(\frac{208}{639}\right)$	$e\left(\frac{283}{639}\right)$	$e\left(\frac{463}{639}\right)$