Dirichlet character \(\chi_{2700}(31,\cdot)\)

• Label: 2700.31
• Modulus: $2700$
• Conductor: $2700$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2700\)
Conductor:	\(2700\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2700.co

\(\chi_{2700}(31,\cdot)\) \(\chi_{2700}(211,\cdot)\) \(\chi_{2700}(331,\cdot)\) \(\chi_{2700}(391,\cdot)\) \(\chi_{2700}(511,\cdot)\) \(\chi_{2700}(571,\cdot)\) \(\chi_{2700}(691,\cdot)\) \(\chi_{2700}(871,\cdot)\) \(\chi_{2700}(931,\cdot)\) \(\chi_{2700}(1111,\cdot)\) \(\chi_{2700}(1231,\cdot)\) \(\chi_{2700}(1291,\cdot)\) \(\chi_{2700}(1411,\cdot)\) \(\chi_{2700}(1471,\cdot)\) \(\chi_{2700}(1591,\cdot)\) \(\chi_{2700}(1771,\cdot)\) \(\chi_{2700}(1831,\cdot)\) \(\chi_{2700}(2011,\cdot)\) \(\chi_{2700}(2131,\cdot)\) \(\chi_{2700}(2191,\cdot)\) \(\chi_{2700}(2311,\cdot)\) \(\chi_{2700}(2371,\cdot)\) \(\chi_{2700}(2491,\cdot)\) \(\chi_{2700}(2671,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

\((1351,1001,2377)\) → \((-1,e\left(\frac{1}{9}\right),e\left(\frac{2}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 2700 }(31, a) \)	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)