Dirichlet character \(\chi_{22720}(579,\cdot)\)

• Label: 22720.579
• Modulus: $22720$
• Conductor: $22720$
• Order: $560$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(22720\)
Conductor:	\(22720\)
Order:	\(560\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 22720.kq

\(\chi_{22720}(59,\cdot)\) \(\chi_{22720}(99,\cdot)\) \(\chi_{22720}(139,\cdot)\) \(\chi_{22720}(339,\cdot)\) \(\chi_{22720}(459,\cdot)\) \(\chi_{22720}(539,\cdot)\) \(\chi_{22720}(579,\cdot)\) \(\chi_{22720}(779,\cdot)\) \(\chi_{22720}(859,\cdot)\) \(\chi_{22720}(899,\cdot)\) \(\chi_{22720}(979,\cdot)\) \(\chi_{22720}(1059,\cdot)\) \(\chi_{22720}(1259,\cdot)\) \(\chi_{22720}(1299,\cdot)\) \(\chi_{22720}(1339,\cdot)\) \(\chi_{22720}(1739,\cdot)\) \(\chi_{22720}(1819,\cdot)\) \(\chi_{22720}(1859,\cdot)\) \(\chi_{22720}(1899,\cdot)\) \(\chi_{22720}(1939,\cdot)\) \(\chi_{22720}(1979,\cdot)\) \(\chi_{22720}(2019,\cdot)\) \(\chi_{22720}(2339,\cdot)\) \(\chi_{22720}(2619,\cdot)\) \(\chi_{22720}(2899,\cdot)\) \(\chi_{22720}(2939,\cdot)\) \(\chi_{22720}(2979,\cdot)\) \(\chi_{22720}(3179,\cdot)\) \(\chi_{22720}(3299,\cdot)\) \(\chi_{22720}(3379,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{560})$
Fixed field:	Number field defined by a degree 560 polynomial (not computed)

Values on generators

\((14911,15621,18177,3841)\) → \((-1,e\left(\frac{3}{16}\right),-1,e\left(\frac{31}{70}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\( \chi_{ 22720 }(579, a) \)	\(1\)	\(1\)	\(e\left(\frac{43}{560}\right)\)	\(e\left(\frac{89}{280}\right)\)	\(e\left(\frac{43}{280}\right)\)	\(e\left(\frac{93}{560}\right)\)	\(e\left(\frac{327}{560}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{503}{560}\right)\)	\(e\left(\frac{221}{560}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{129}{560}\right)\)