Properties

Conductor 1021
Order 340
Real No
Primitive Yes
Parity Odd
Orbit Label 1021.v

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[24]
 
pari: [g,chi] = znchar(Mod(24,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 340
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.v
Orbit index = 22

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 ]
 

\(\chi_{1021}(2,\cdot)\) \(\chi_{1021}(6,\cdot)\) \(\chi_{1021}(7,\cdot)\) \(\chi_{1021}(8,\cdot)\) \(\chi_{1021}(18,\cdot)\) \(\chi_{1021}(21,\cdot)\) \(\chi_{1021}(24,\cdot)\) \(\chi_{1021}(28,\cdot)\) \(\chi_{1021}(52,\cdot)\) \(\chi_{1021}(54,\cdot)\) \(\chi_{1021}(63,\cdot)\) \(\chi_{1021}(72,\cdot)\) \(\chi_{1021}(84,\cdot)\) \(\chi_{1021}(98,\cdot)\) \(\chi_{1021}(128,\cdot)\) \(\chi_{1021}(131,\cdot)\) \(\chi_{1021}(139,\cdot)\) \(\chi_{1021}(142,\cdot)\) \(\chi_{1021}(146,\cdot)\) \(\chi_{1021}(151,\cdot)\) \(\chi_{1021}(156,\cdot)\) \(\chi_{1021}(158,\cdot)\) \(\chi_{1021}(162,\cdot)\) \(\chi_{1021}(170,\cdot)\) \(\chi_{1021}(182,\cdot)\) \(\chi_{1021}(189,\cdot)\) \(\chi_{1021}(191,\cdot)\) \(\chi_{1021}(208,\cdot)\) \(\chi_{1021}(216,\cdot)\) \(\chi_{1021}(230,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{83}{340}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{99}{340}\right)\)\(e\left(\frac{31}{34}\right)\)\(e\left(\frac{99}{170}\right)\)\(e\left(\frac{81}{85}\right)\)\(e\left(\frac{69}{340}\right)\)\(e\left(\frac{109}{340}\right)\)\(e\left(\frac{297}{340}\right)\)\(e\left(\frac{14}{17}\right)\)\(e\left(\frac{83}{340}\right)\)\(e\left(\frac{77}{85}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{340})\)