Dirichlet character \(\chi_{1045}(348,\cdot)\)

• Label: 1045.348
• Modulus: $1045$
• Conductor: $1045$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1045.cs

\(\chi_{1045}(17,\cdot)\) \(\chi_{1045}(28,\cdot)\) \(\chi_{1045}(62,\cdot)\) \(\chi_{1045}(63,\cdot)\) \(\chi_{1045}(73,\cdot)\) \(\chi_{1045}(112,\cdot)\) \(\chi_{1045}(118,\cdot)\) \(\chi_{1045}(123,\cdot)\) \(\chi_{1045}(138,\cdot)\) \(\chi_{1045}(233,\cdot)\) \(\chi_{1045}(237,\cdot)\) \(\chi_{1045}(272,\cdot)\) \(\chi_{1045}(282,\cdot)\) \(\chi_{1045}(283,\cdot)\) \(\chi_{1045}(327,\cdot)\) \(\chi_{1045}(332,\cdot)\) \(\chi_{1045}(347,\cdot)\) \(\chi_{1045}(348,\cdot)\) \(\chi_{1045}(358,\cdot)\) \(\chi_{1045}(403,\cdot)\) \(\chi_{1045}(442,\cdot)\) \(\chi_{1045}(453,\cdot)\) \(\chi_{1045}(492,\cdot)\) \(\chi_{1045}(503,\cdot)\) \(\chi_{1045}(557,\cdot)\) \(\chi_{1045}(567,\cdot)\) \(\chi_{1045}(568,\cdot)\) \(\chi_{1045}(612,\cdot)\) \(\chi_{1045}(613,\cdot)\) \(\chi_{1045}(633,\cdot)\) ...

Related number fields

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

Values on generators

\((837,761,496)\) → \((-i,e\left(\frac{7}{10}\right),e\left(\frac{7}{9}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\( \chi_{ 1045 }(348, a) \)	\(1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)