Dirichlet character \(\chi_{1045}(744,\cdot)\)

• Label: 1045.744
• Modulus: $1045$
• Conductor: $1045$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1045.cn

\(\chi_{1045}(29,\cdot)\) \(\chi_{1045}(79,\cdot)\) \(\chi_{1045}(129,\cdot)\) \(\chi_{1045}(184,\cdot)\) \(\chi_{1045}(204,\cdot)\) \(\chi_{1045}(249,\cdot)\) \(\chi_{1045}(299,\cdot)\) \(\chi_{1045}(314,\cdot)\) \(\chi_{1045}(409,\cdot)\) \(\chi_{1045}(414,\cdot)\) \(\chi_{1045}(459,\cdot)\) \(\chi_{1045}(469,\cdot)\) \(\chi_{1045}(534,\cdot)\) \(\chi_{1045}(629,\cdot)\) \(\chi_{1045}(679,\cdot)\) \(\chi_{1045}(699,\cdot)\) \(\chi_{1045}(744,\cdot)\) \(\chi_{1045}(754,\cdot)\) \(\chi_{1045}(789,\cdot)\) \(\chi_{1045}(794,\cdot)\) \(\chi_{1045}(849,\cdot)\) \(\chi_{1045}(964,\cdot)\) \(\chi_{1045}(1009,\cdot)\) \(\chi_{1045}(1029,\cdot)\)

Related number fields

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

Values on generators

\((837,761,496)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1045 }(744, a) \)	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)