Dirichlet character \(\chi_{1045}(864,\cdot)\)

• Label: 1045.864
• Modulus: $1045$
• Conductor: $1045$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1045\)
Conductor:	\(1045\)
Order:	\(90\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1045.cp

\(\chi_{1045}(24,\cdot)\) \(\chi_{1045}(74,\cdot)\) \(\chi_{1045}(139,\cdot)\) \(\chi_{1045}(149,\cdot)\) \(\chi_{1045}(194,\cdot)\) \(\chi_{1045}(244,\cdot)\) \(\chi_{1045}(294,\cdot)\) \(\chi_{1045}(359,\cdot)\) \(\chi_{1045}(404,\cdot)\) \(\chi_{1045}(424,\cdot)\) \(\chi_{1045}(479,\cdot)\) \(\chi_{1045}(519,\cdot)\) \(\chi_{1045}(574,\cdot)\) \(\chi_{1045}(579,\cdot)\) \(\chi_{1045}(624,\cdot)\) \(\chi_{1045}(644,\cdot)\) \(\chi_{1045}(689,\cdot)\) \(\chi_{1045}(739,\cdot)\) \(\chi_{1045}(864,\cdot)\) \(\chi_{1045}(899,\cdot)\) \(\chi_{1045}(909,\cdot)\) \(\chi_{1045}(954,\cdot)\) \(\chi_{1045}(959,\cdot)\) \(\chi_{1045}(974,\cdot)\)

Related number fields

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

Values on generators

\((837,761,496)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{4}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1045 }(864, a) \)	\(-1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)