Dirichlet character χ2653(570,⋅)\chi_{2653}(570,\cdot)

• Label: 2653.570
• Modulus: $2653$
• Conductor: $2653$
• Order: $378$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2653$
Conductor:	$2653$
Order:	$378$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2653.di

$\chi_{2653}(26,\cdot)$ $\chi_{2653}(45,\cdot)$ $\chi_{2653}(80,\cdot)$ $\chi_{2653}(101,\cdot)$ $\chi_{2653}(110,\cdot)$ $\chi_{2653}(129,\cdot)$ $\chi_{2653}(136,\cdot)$ $\chi_{2653}(173,\cdot)$ $\chi_{2653}(187,\cdot)$ $\chi_{2653}(227,\cdot)$ $\chi_{2653}(248,\cdot)$ $\chi_{2653}(257,\cdot)$ $\chi_{2653}(290,\cdot)$ $\chi_{2653}(297,\cdot)$ $\chi_{2653}(341,\cdot)$ $\chi_{2653}(367,\cdot)$ $\chi_{2653}(376,\cdot)$ $\chi_{2653}(383,\cdot)$ $\chi_{2653}(388,\cdot)$ $\chi_{2653}(395,\cdot)$ $\chi_{2653}(437,\cdot)$ $\chi_{2653}(460,\cdot)$ $\chi_{2653}(493,\cdot)$ $\chi_{2653}(509,\cdot)$ $\chi_{2653}(523,\cdot)$ $\chi_{2653}(528,\cdot)$ $\chi_{2653}(570,\cdot)$ $\chi_{2653}(600,\cdot)$ $\chi_{2653}(635,\cdot)$ $\chi_{2653}(642,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{189})$
Fixed field:	Number field defined by a degree 378 polynomial (not computed)

Values on generators

$(759,2276)$ → $(e\left(\frac{1}{6}\right),e\left(\frac{68}{189}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 2653 }(570, a)$	$-1$	$1$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{173}{378}\right)$	$e\left(\frac{73}{189}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{127}{378}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{319}{378}\right)$