Dirichlet character \(\chi_{1045}(42,\cdot)\)

• Label: 1045.42
• Modulus: $1045$
• Conductor: $1045$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1045\)
Conductor:	\(1045\)
Order:	\(180\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1045.ct

\(\chi_{1045}(42,\cdot)\) \(\chi_{1045}(47,\cdot)\) \(\chi_{1045}(82,\cdot)\) \(\chi_{1045}(92,\cdot)\) \(\chi_{1045}(93,\cdot)\) \(\chi_{1045}(137,\cdot)\) \(\chi_{1045}(157,\cdot)\) \(\chi_{1045}(158,\cdot)\) \(\chi_{1045}(168,\cdot)\) \(\chi_{1045}(207,\cdot)\) \(\chi_{1045}(213,\cdot)\) \(\chi_{1045}(218,\cdot)\) \(\chi_{1045}(302,\cdot)\) \(\chi_{1045}(313,\cdot)\) \(\chi_{1045}(328,\cdot)\) \(\chi_{1045}(367,\cdot)\) \(\chi_{1045}(377,\cdot)\) \(\chi_{1045}(378,\cdot)\) \(\chi_{1045}(422,\cdot)\) \(\chi_{1045}(423,\cdot)\) \(\chi_{1045}(427,\cdot)\) \(\chi_{1045}(443,\cdot)\) \(\chi_{1045}(498,\cdot)\) \(\chi_{1045}(522,\cdot)\) \(\chi_{1045}(537,\cdot)\) \(\chi_{1045}(548,\cdot)\) \(\chi_{1045}(587,\cdot)\) \(\chi_{1045}(598,\cdot)\) \(\chi_{1045}(632,\cdot)\) \(\chi_{1045}(643,\cdot)\) ...

Related number fields

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

Values on generators

\((837,761,496)\) → \((i,e\left(\frac{3}{5}\right),e\left(\frac{1}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1045 }(42, a) \)	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)