Dirichlet character \(\chi_{1620}(23,\cdot)\)

• Label: 1620.23
• Modulus: $1620$
• Conductor: $1620$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 1620.bt

\(\chi_{1620}(23,\cdot)\) \(\chi_{1620}(47,\cdot)\) \(\chi_{1620}(83,\cdot)\) \(\chi_{1620}(167,\cdot)\) \(\chi_{1620}(203,\cdot)\) \(\chi_{1620}(227,\cdot)\) \(\chi_{1620}(263,\cdot)\) \(\chi_{1620}(347,\cdot)\) \(\chi_{1620}(383,\cdot)\) \(\chi_{1620}(407,\cdot)\) \(\chi_{1620}(443,\cdot)\) \(\chi_{1620}(527,\cdot)\) \(\chi_{1620}(563,\cdot)\) \(\chi_{1620}(587,\cdot)\) \(\chi_{1620}(623,\cdot)\) \(\chi_{1620}(707,\cdot)\) \(\chi_{1620}(743,\cdot)\) \(\chi_{1620}(767,\cdot)\) \(\chi_{1620}(803,\cdot)\) \(\chi_{1620}(887,\cdot)\) \(\chi_{1620}(923,\cdot)\) \(\chi_{1620}(947,\cdot)\) \(\chi_{1620}(983,\cdot)\) \(\chi_{1620}(1067,\cdot)\) \(\chi_{1620}(1103,\cdot)\) \(\chi_{1620}(1127,\cdot)\) \(\chi_{1620}(1163,\cdot)\) \(\chi_{1620}(1247,\cdot)\) \(\chi_{1620}(1283,\cdot)\) \(\chi_{1620}(1307,\cdot)\) ...

Related number fields

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

Values on generators

\((811,1541,1297)\) → \((-1,e\left(\frac{11}{54}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 1620 }(23, a) \)	\(-1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{43}{54}\right)\)