Properties

Conductor 1021
Order 1020
Real No
Primitive Yes
Parity Odd
Orbit Label 1021.x

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(1021)
 
sage: chi = H[30]
 
pari: [g,chi] = znchar(Mod(30,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1020
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 1021.x
Orbit index = 24

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1021}(10,\cdot)\) \(\chi_{1021}(22,\cdot)\) \(\chi_{1021}(30,\cdot)\) \(\chi_{1021}(31,\cdot)\) \(\chi_{1021}(34,\cdot)\) \(\chi_{1021}(35,\cdot)\) \(\chi_{1021}(37,\cdot)\) \(\chi_{1021}(40,\cdot)\) \(\chi_{1021}(43,\cdot)\) \(\chi_{1021}(46,\cdot)\) \(\chi_{1021}(50,\cdot)\) \(\chi_{1021}(53,\cdot)\) \(\chi_{1021}(59,\cdot)\) \(\chi_{1021}(65,\cdot)\) \(\chi_{1021}(66,\cdot)\) \(\chi_{1021}(76,\cdot)\) \(\chi_{1021}(77,\cdot)\) \(\chi_{1021}(82,\cdot)\) \(\chi_{1021}(90,\cdot)\) \(\chi_{1021}(93,\cdot)\) \(\chi_{1021}(94,\cdot)\) \(\chi_{1021}(95,\cdot)\) \(\chi_{1021}(102,\cdot)\) \(\chi_{1021}(103,\cdot)\) \(\chi_{1021}(105,\cdot)\) \(\chi_{1021}(109,\cdot)\) \(\chi_{1021}(111,\cdot)\) \(\chi_{1021}(119,\cdot)\) \(\chi_{1021}(120,\cdot)\) \(\chi_{1021}(122,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{271}{1020}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{161}{340}\right)\)\(e\left(\frac{25}{34}\right)\)\(e\left(\frac{161}{170}\right)\)\(e\left(\frac{202}{255}\right)\)\(e\left(\frac{71}{340}\right)\)\(e\left(\frac{191}{340}\right)\)\(e\left(\frac{143}{340}\right)\)\(e\left(\frac{8}{17}\right)\)\(e\left(\frac{271}{1020}\right)\)\(e\left(\frac{64}{255}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1020})\)