Properties

Conductor 6027
Order 84
Real No
Primitive Yes
Parity Even
Orbit Label 6027.dq

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(6027)
 
sage: chi = H[173]
 
pari: [g,chi] = znchar(Mod(173,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 84
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 = Even
Orbit label = 6027.dq
Orbit index = 95

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 ]
 

\(\chi_{6027}(173,\cdot)\) \(\chi_{6027}(278,\cdot)\) \(\chi_{6027}(542,\cdot)\) \(\chi_{6027}(647,\cdot)\) \(\chi_{6027}(1034,\cdot)\) \(\chi_{6027}(1139,\cdot)\) \(\chi_{6027}(1508,\cdot)\) \(\chi_{6027}(1895,\cdot)\) \(\chi_{6027}(2000,\cdot)\) \(\chi_{6027}(2264,\cdot)\) \(\chi_{6027}(2369,\cdot)\) \(\chi_{6027}(2756,\cdot)\) \(\chi_{6027}(3125,\cdot)\) \(\chi_{6027}(3230,\cdot)\) \(\chi_{6027}(3617,\cdot)\) \(\chi_{6027}(3722,\cdot)\) \(\chi_{6027}(3986,\cdot)\) \(\chi_{6027}(4091,\cdot)\) \(\chi_{6027}(4583,\cdot)\) \(\chi_{6027}(4847,\cdot)\) \(\chi_{6027}(4952,\cdot)\) \(\chi_{6027}(5339,\cdot)\) \(\chi_{6027}(5444,\cdot)\) \(\chi_{6027}(5708,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{17}{42}\right),-i)\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{11}{21}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{11}{42}\right)\)\(e\left(\frac{79}{84}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{31}{84}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{84})\)