Dirichlet character χ1053(293,⋅)\chi_{1053}(293,\cdot)

• Label: 1053.293
• Modulus: $1053$
• Conductor: $1053$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1053$
Conductor:	$1053$
Order:	$108$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1053.cn

$\chi_{1053}(2,\cdot)$ $\chi_{1053}(11,\cdot)$ $\chi_{1053}(32,\cdot)$ $\chi_{1053}(59,\cdot)$ $\chi_{1053}(119,\cdot)$ $\chi_{1053}(128,\cdot)$ $\chi_{1053}(149,\cdot)$ $\chi_{1053}(176,\cdot)$ $\chi_{1053}(236,\cdot)$ $\chi_{1053}(245,\cdot)$ $\chi_{1053}(266,\cdot)$ $\chi_{1053}(293,\cdot)$ $\chi_{1053}(353,\cdot)$ $\chi_{1053}(362,\cdot)$ $\chi_{1053}(383,\cdot)$ $\chi_{1053}(410,\cdot)$ $\chi_{1053}(470,\cdot)$ $\chi_{1053}(479,\cdot)$ $\chi_{1053}(500,\cdot)$ $\chi_{1053}(527,\cdot)$ $\chi_{1053}(587,\cdot)$ $\chi_{1053}(596,\cdot)$ $\chi_{1053}(617,\cdot)$ $\chi_{1053}(644,\cdot)$ $\chi_{1053}(704,\cdot)$ $\chi_{1053}(713,\cdot)$ $\chi_{1053}(734,\cdot)$ $\chi_{1053}(761,\cdot)$ $\chi_{1053}(821,\cdot)$ $\chi_{1053}(830,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

Values on generators

$(326,730)$ → $(e\left(\frac{47}{54}\right),e\left(\frac{11}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 1053 }(293, a)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{5}{9}\right)$