Dirichlet character χ547(137,⋅)\chi_{547}(137,\cdot)

• Label: 547.137
• Modulus: $547$
• Conductor: $547$
• Order: $273$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$547$
Conductor:	$547$
Order:	$273$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 547.o

$\chi_{547}(4,\cdot)$ $\chi_{547}(6,\cdot)$ $\chi_{547}(15,\cdot)$ $\chi_{547}(16,\cdot)$ $\chi_{547}(19,\cdot)$ $\chi_{547}(25,\cdot)$ $\chi_{547}(34,\cdot)$ $\chi_{547}(36,\cdot)$ $\chi_{547}(49,\cdot)$ $\chi_{547}(51,\cdot)$ $\chi_{547}(53,\cdot)$ $\chi_{547}(56,\cdot)$ $\chi_{547}(60,\cdot)$ $\chi_{547}(62,\cdot)$ $\chi_{547}(66,\cdot)$ $\chi_{547}(67,\cdot)$ $\chi_{547}(69,\cdot)$ $\chi_{547}(73,\cdot)$ $\chi_{547}(74,\cdot)$ $\chi_{547}(76,\cdot)$ $\chi_{547}(78,\cdot)$ $\chi_{547}(82,\cdot)$ $\chi_{547}(86,\cdot)$ $\chi_{547}(97,\cdot)$ $\chi_{547}(99,\cdot)$ $\chi_{547}(110,\cdot)$ $\chi_{547}(111,\cdot)$ $\chi_{547}(113,\cdot)$ $\chi_{547}(115,\cdot)$ $\chi_{547}(116,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{273})$
Fixed field:	Number field defined by a degree 273 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{272}{273}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 547 }(137, a)$	$1$	$1$	$e\left(\frac{272}{273}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{271}{273}\right)$	$e\left(\frac{94}{273}\right)$	$e\left(\frac{116}{273}\right)$	$e\left(\frac{170}{273}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{29}{39}\right)$

Gauss sum

Jacobi sum

Kloosterman sum