Properties

Conductor 1021
Order 510
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1021.w

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[141]
 
pari: [g,chi] = znchar(Mod(141,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 510
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1021.w
Orbit index = 23

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 ]
 

\(\chi_{1021}(15,\cdot)\) \(\chi_{1021}(17,\cdot)\) \(\chi_{1021}(20,\cdot)\) \(\chi_{1021}(29,\cdot)\) \(\chi_{1021}(33,\cdot)\) \(\chi_{1021}(38,\cdot)\) \(\chi_{1021}(44,\cdot)\) \(\chi_{1021}(61,\cdot)\) \(\chi_{1021}(69,\cdot)\) \(\chi_{1021}(74,\cdot)\) \(\chi_{1021}(75,\cdot)\) \(\chi_{1021}(92,\cdot)\) \(\chi_{1021}(100,\cdot)\) \(\chi_{1021}(106,\cdot)\) \(\chi_{1021}(130,\cdot)\) \(\chi_{1021}(135,\cdot)\) \(\chi_{1021}(141,\cdot)\) \(\chi_{1021}(149,\cdot)\) \(\chi_{1021}(153,\cdot)\) \(\chi_{1021}(163,\cdot)\) \(\chi_{1021}(165,\cdot)\) \(\chi_{1021}(179,\cdot)\) \(\chi_{1021}(180,\cdot)\) \(\chi_{1021}(188,\cdot)\) \(\chi_{1021}(190,\cdot)\) \(\chi_{1021}(194,\cdot)\) \(\chi_{1021}(201,\cdot)\) \(\chi_{1021}(204,\cdot)\) \(\chi_{1021}(205,\cdot)\) \(\chi_{1021}(210,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{253}{510}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{33}{170}\right)\)\(e\left(\frac{16}{17}\right)\)\(e\left(\frac{33}{85}\right)\)\(e\left(\frac{77}{255}\right)\)\(e\left(\frac{23}{170}\right)\)\(e\left(\frac{93}{170}\right)\)\(e\left(\frac{99}{170}\right)\)\(e\left(\frac{15}{17}\right)\)\(e\left(\frac{253}{510}\right)\)\(e\left(\frac{239}{255}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{255})\)