Dirichlet character \(\chi_{5160}(587,\cdot)\)

• Label: 5160.587
• Modulus: $5160$
• Conductor: $5160$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5160\)
Conductor:	\(5160\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5160.hi

\(\chi_{5160}(227,\cdot)\) \(\chi_{5160}(347,\cdot)\) \(\chi_{5160}(587,\cdot)\) \(\chi_{5160}(707,\cdot)\) \(\chi_{5160}(803,\cdot)\) \(\chi_{5160}(923,\cdot)\) \(\chi_{5160}(1187,\cdot)\) \(\chi_{5160}(1523,\cdot)\) \(\chi_{5160}(1667,\cdot)\) \(\chi_{5160}(1883,\cdot)\) \(\chi_{5160}(2843,\cdot)\) \(\chi_{5160}(2867,\cdot)\) \(\chi_{5160}(2987,\cdot)\) \(\chi_{5160}(3083,\cdot)\) \(\chi_{5160}(3323,\cdot)\) \(\chi_{5160}(3443,\cdot)\) \(\chi_{5160}(3587,\cdot)\) \(\chi_{5160}(3683,\cdot)\) \(\chi_{5160}(3803,\cdot)\) \(\chi_{5160}(3947,\cdot)\) \(\chi_{5160}(4283,\cdot)\) \(\chi_{5160}(4763,\cdot)\) \(\chi_{5160}(4907,\cdot)\) \(\chi_{5160}(5147,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((3871,2581,1721,3097,4561)\) → \((-1,-1,-1,i,e\left(\frac{5}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 5160 }(587, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{14}\right)\)