Dirichlet character \(\chi_{40320}(9643,\cdot)\)

• Label: 40320.9643
• 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.bdo

\(\chi_{40320}(67,\cdot)\) \(\chi_{40320}(4363,\cdot)\) \(\chi_{40320}(4603,\cdot)\) \(\chi_{40320}(4867,\cdot)\) \(\chi_{40320}(5107,\cdot)\) \(\chi_{40320}(9403,\cdot)\) \(\chi_{40320}(9643,\cdot)\) \(\chi_{40320}(9907,\cdot)\) \(\chi_{40320}(10147,\cdot)\) \(\chi_{40320}(14443,\cdot)\) \(\chi_{40320}(14683,\cdot)\) \(\chi_{40320}(14947,\cdot)\) \(\chi_{40320}(15187,\cdot)\) \(\chi_{40320}(19483,\cdot)\) \(\chi_{40320}(19723,\cdot)\) \(\chi_{40320}(19987,\cdot)\) \(\chi_{40320}(20227,\cdot)\) \(\chi_{40320}(24523,\cdot)\) \(\chi_{40320}(24763,\cdot)\) \(\chi_{40320}(25027,\cdot)\) \(\chi_{40320}(25267,\cdot)\) \(\chi_{40320}(29563,\cdot)\) \(\chi_{40320}(29803,\cdot)\) \(\chi_{40320}(30067,\cdot)\) \(\chi_{40320}(30307,\cdot)\) \(\chi_{40320}(34603,\cdot)\) \(\chi_{40320}(34843,\cdot)\) \(\chi_{40320}(35107,\cdot)\) \(\chi_{40320}(35347,\cdot)\) \(\chi_{40320}(39643,\cdot)\) ...

Related number fields

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

Values on generators

\((8191,23941,17921,32257,28801)\) → \((-1,e\left(\frac{29}{32}\right),e\left(\frac{1}{3}\right),-i,e\left(\frac{2}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 40320 }(9643, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)