Dirichlet character χ1053(745,⋅)\chi_{1053}(745,\cdot)

• Label: 1053.745
• Modulus: $1053$
• Conductor: $1053$
• Order: $54$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1053$
Conductor:	$1053$
Order:	$54$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1053.bz

$\chi_{1053}(43,\cdot)$ $\chi_{1053}(49,\cdot)$ $\chi_{1053}(160,\cdot)$ $\chi_{1053}(166,\cdot)$ $\chi_{1053}(277,\cdot)$ $\chi_{1053}(283,\cdot)$ $\chi_{1053}(394,\cdot)$ $\chi_{1053}(400,\cdot)$ $\chi_{1053}(511,\cdot)$ $\chi_{1053}(517,\cdot)$ $\chi_{1053}(628,\cdot)$ $\chi_{1053}(634,\cdot)$ $\chi_{1053}(745,\cdot)$ $\chi_{1053}(751,\cdot)$ $\chi_{1053}(862,\cdot)$ $\chi_{1053}(868,\cdot)$ $\chi_{1053}(979,\cdot)$ $\chi_{1053}(985,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{27})$
Fixed field:	Number field defined by a degree 54 polynomial

Values on generators

$(326,730)$ → $(e\left(\frac{2}{27}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 1053 }(745, a)$	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{9}\right)$