Dirichlet character χ1053(137,⋅)\chi_{1053}(137,\cdot)

• Label: 1053.137
• 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.cm

$\chi_{1053}(20,\cdot)$ $\chi_{1053}(41,\cdot)$ $\chi_{1053}(50,\cdot)$ $\chi_{1053}(110,\cdot)$ $\chi_{1053}(137,\cdot)$ $\chi_{1053}(158,\cdot)$ $\chi_{1053}(167,\cdot)$ $\chi_{1053}(227,\cdot)$ $\chi_{1053}(254,\cdot)$ $\chi_{1053}(275,\cdot)$ $\chi_{1053}(284,\cdot)$ $\chi_{1053}(344,\cdot)$ $\chi_{1053}(371,\cdot)$ $\chi_{1053}(392,\cdot)$ $\chi_{1053}(401,\cdot)$ $\chi_{1053}(461,\cdot)$ $\chi_{1053}(488,\cdot)$ $\chi_{1053}(509,\cdot)$ $\chi_{1053}(518,\cdot)$ $\chi_{1053}(578,\cdot)$ $\chi_{1053}(605,\cdot)$ $\chi_{1053}(626,\cdot)$ $\chi_{1053}(635,\cdot)$ $\chi_{1053}(695,\cdot)$ $\chi_{1053}(722,\cdot)$ $\chi_{1053}(743,\cdot)$ $\chi_{1053}(752,\cdot)$ $\chi_{1053}(812,\cdot)$ $\chi_{1053}(839,\cdot)$ $\chi_{1053}(860,\cdot)$ ...

Related number fields

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

Values on generators

$(326,730)$ → $(e\left(\frac{19}{54}\right),e\left(\frac{11}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 1053 }(137, a)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{4}{9}\right)$