Dirichlet character \(\chi_{2700}(47,\cdot)\)

• Label: 2700.47
• Modulus: $2700$
• Conductor: $2700$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2700\)
Conductor:	\(2700\)
Order:	\(180\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2700.ct

\(\chi_{2700}(23,\cdot)\) \(\chi_{2700}(47,\cdot)\) \(\chi_{2700}(83,\cdot)\) \(\chi_{2700}(167,\cdot)\) \(\chi_{2700}(203,\cdot)\) \(\chi_{2700}(227,\cdot)\) \(\chi_{2700}(263,\cdot)\) \(\chi_{2700}(347,\cdot)\) \(\chi_{2700}(383,\cdot)\) \(\chi_{2700}(527,\cdot)\) \(\chi_{2700}(563,\cdot)\) \(\chi_{2700}(587,\cdot)\) \(\chi_{2700}(623,\cdot)\) \(\chi_{2700}(767,\cdot)\) \(\chi_{2700}(803,\cdot)\) \(\chi_{2700}(887,\cdot)\) \(\chi_{2700}(923,\cdot)\) \(\chi_{2700}(947,\cdot)\) \(\chi_{2700}(983,\cdot)\) \(\chi_{2700}(1067,\cdot)\) \(\chi_{2700}(1103,\cdot)\) \(\chi_{2700}(1127,\cdot)\) \(\chi_{2700}(1163,\cdot)\) \(\chi_{2700}(1247,\cdot)\) \(\chi_{2700}(1283,\cdot)\) \(\chi_{2700}(1427,\cdot)\) \(\chi_{2700}(1463,\cdot)\) \(\chi_{2700}(1487,\cdot)\) \(\chi_{2700}(1523,\cdot)\) \(\chi_{2700}(1667,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

\((1351,1001,2377)\) → \((-1,e\left(\frac{7}{18}\right),e\left(\frac{17}{20}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 2700 }(47, a) \)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)