Dirichlet character \(\chi_{40320}(587,\cdot)\)

• Label: 40320.587
• Modulus: $40320$
• Conductor: $40320$
• Order: $96$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(40320\)
Conductor:	\(40320\)
Order:	\(96\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 40320.bdx

\(\chi_{40320}(83,\cdot)\) \(\chi_{40320}(587,\cdot)\) \(\chi_{40320}(3443,\cdot)\) \(\chi_{40320}(3947,\cdot)\) \(\chi_{40320}(5123,\cdot)\) \(\chi_{40320}(5627,\cdot)\) \(\chi_{40320}(8483,\cdot)\) \(\chi_{40320}(8987,\cdot)\) \(\chi_{40320}(10163,\cdot)\) \(\chi_{40320}(10667,\cdot)\) \(\chi_{40320}(13523,\cdot)\) \(\chi_{40320}(14027,\cdot)\) \(\chi_{40320}(15203,\cdot)\) \(\chi_{40320}(15707,\cdot)\) \(\chi_{40320}(18563,\cdot)\) \(\chi_{40320}(19067,\cdot)\) \(\chi_{40320}(20243,\cdot)\) \(\chi_{40320}(20747,\cdot)\) \(\chi_{40320}(23603,\cdot)\) \(\chi_{40320}(24107,\cdot)\) \(\chi_{40320}(25283,\cdot)\) \(\chi_{40320}(25787,\cdot)\) \(\chi_{40320}(28643,\cdot)\) \(\chi_{40320}(29147,\cdot)\) \(\chi_{40320}(30323,\cdot)\) \(\chi_{40320}(30827,\cdot)\) \(\chi_{40320}(33683,\cdot)\) \(\chi_{40320}(34187,\cdot)\) \(\chi_{40320}(35363,\cdot)\) \(\chi_{40320}(35867,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{96})$
Fixed field:	Number field defined by a degree 96 polynomial

Values on generators

\((8191,23941,17921,32257,28801)\) → \((-1,e\left(\frac{5}{32}\right),e\left(\frac{1}{6}\right),i,-1)\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 40320 }(587, a) \)	\(1\)	\(1\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)