Dirichlet character χ8048(27,⋅)\chi_{8048}(27,\cdot)

• Label: 8048.27
• Modulus: $8048$
• Conductor: $8048$
• Order: $1004$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$8048$
Conductor:	$8048$
Order:	$1004$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 8048.v

$\chi_{8048}(3,\cdot)$ $\chi_{8048}(11,\cdot)$ $\chi_{8048}(27,\cdot)$ $\chi_{8048}(43,\cdot)$ $\chi_{8048}(59,\cdot)$ $\chi_{8048}(67,\cdot)$ $\chi_{8048}(75,\cdot)$ $\chi_{8048}(83,\cdot)$ $\chi_{8048}(91,\cdot)$ $\chi_{8048}(99,\cdot)$ $\chi_{8048}(131,\cdot)$ $\chi_{8048}(147,\cdot)$ $\chi_{8048}(155,\cdot)$ $\chi_{8048}(219,\cdot)$ $\chi_{8048}(243,\cdot)$ $\chi_{8048}(275,\cdot)$ $\chi_{8048}(283,\cdot)$ $\chi_{8048}(291,\cdot)$ $\chi_{8048}(299,\cdot)$ $\chi_{8048}(323,\cdot)$ $\chi_{8048}(339,\cdot)$ $\chi_{8048}(355,\cdot)$ $\chi_{8048}(363,\cdot)$ $\chi_{8048}(379,\cdot)$ $\chi_{8048}(387,\cdot)$ $\chi_{8048}(427,\cdot)$ $\chi_{8048}(435,\cdot)$ $\chi_{8048}(443,\cdot)$ $\chi_{8048}(483,\cdot)$ $\chi_{8048}(507,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1004})$
Fixed field:	Number field defined by a degree 1004 polynomial (not computed)

Values on generators

$(1007,6037,2017)$ → $(-1,i,e\left(\frac{234}{251}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 8048 }(27, a)$	$-1$	$1$	$e\left(\frac{687}{1004}\right)$	$e\left(\frac{183}{1004}\right)$	$e\left(\frac{44}{251}\right)$	$e\left(\frac{185}{502}\right)$	$e\left(\frac{909}{1004}\right)$	$e\left(\frac{353}{1004}\right)$	$e\left(\frac{435}{502}\right)$	$e\left(\frac{123}{251}\right)$	$e\left(\frac{199}{1004}\right)$	$e\left(\frac{863}{1004}\right)$