Dirichlet character χ1215(164,⋅)\chi_{1215}(164,\cdot)

• Label: 1215.164
• Modulus: $1215$
• Conductor: $1215$
• Order: $162$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1215$
Conductor:	$1215$
Order:	$162$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1215.bb

$\chi_{1215}(14,\cdot)$ $\chi_{1215}(29,\cdot)$ $\chi_{1215}(59,\cdot)$ $\chi_{1215}(74,\cdot)$ $\chi_{1215}(104,\cdot)$ $\chi_{1215}(119,\cdot)$ $\chi_{1215}(149,\cdot)$ $\chi_{1215}(164,\cdot)$ $\chi_{1215}(194,\cdot)$ $\chi_{1215}(209,\cdot)$ $\chi_{1215}(239,\cdot)$ $\chi_{1215}(254,\cdot)$ $\chi_{1215}(284,\cdot)$ $\chi_{1215}(299,\cdot)$ $\chi_{1215}(329,\cdot)$ $\chi_{1215}(344,\cdot)$ $\chi_{1215}(374,\cdot)$ $\chi_{1215}(389,\cdot)$ $\chi_{1215}(419,\cdot)$ $\chi_{1215}(434,\cdot)$ $\chi_{1215}(464,\cdot)$ $\chi_{1215}(479,\cdot)$ $\chi_{1215}(509,\cdot)$ $\chi_{1215}(524,\cdot)$ $\chi_{1215}(554,\cdot)$ $\chi_{1215}(569,\cdot)$ $\chi_{1215}(599,\cdot)$ $\chi_{1215}(614,\cdot)$ $\chi_{1215}(644,\cdot)$ $\chi_{1215}(659,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 162 polynomial (not computed)

Values on generators

$(731,487)$ → $(e\left(\frac{55}{162}\right),-1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 1215 }(164, a)$	$-1$	$1$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{26}{27}\right)$