Dirichlet character \(\chi_{1620}(643,\cdot)\)

• Label: 1620.643
• Modulus: $1620$
• Conductor: $1620$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1620\)
Conductor:	\(1620\)
Order:	\(108\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1620.bv

\(\chi_{1620}(7,\cdot)\) \(\chi_{1620}(43,\cdot)\) \(\chi_{1620}(67,\cdot)\) \(\chi_{1620}(103,\cdot)\) \(\chi_{1620}(187,\cdot)\) \(\chi_{1620}(223,\cdot)\) \(\chi_{1620}(247,\cdot)\) \(\chi_{1620}(283,\cdot)\) \(\chi_{1620}(367,\cdot)\) \(\chi_{1620}(403,\cdot)\) \(\chi_{1620}(427,\cdot)\) \(\chi_{1620}(463,\cdot)\) \(\chi_{1620}(547,\cdot)\) \(\chi_{1620}(583,\cdot)\) \(\chi_{1620}(607,\cdot)\) \(\chi_{1620}(643,\cdot)\) \(\chi_{1620}(727,\cdot)\) \(\chi_{1620}(763,\cdot)\) \(\chi_{1620}(787,\cdot)\) \(\chi_{1620}(823,\cdot)\) \(\chi_{1620}(907,\cdot)\) \(\chi_{1620}(943,\cdot)\) \(\chi_{1620}(967,\cdot)\) \(\chi_{1620}(1003,\cdot)\) \(\chi_{1620}(1087,\cdot)\) \(\chi_{1620}(1123,\cdot)\) \(\chi_{1620}(1147,\cdot)\) \(\chi_{1620}(1183,\cdot)\) \(\chi_{1620}(1267,\cdot)\) \(\chi_{1620}(1303,\cdot)\) ...

Related number fields

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

Values on generators

\((811,1541,1297)\) → \((-1,e\left(\frac{25}{27}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 1620 }(643, a) \)	\(1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{27}\right)\)