Properties

Conductor 6027
Order 56
Real No
Primitive Yes
Parity Even
Orbit Label 6027.cz

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[260]
 
pari: [g,chi] = znchar(Mod(260,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 56
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.cz
Orbit index = 78

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 ]
 

\(\chi_{6027}(260,\cdot)\) \(\chi_{6027}(407,\cdot)\) \(\chi_{6027}(659,\cdot)\) \(\chi_{6027}(806,\cdot)\) \(\chi_{6027}(1121,\cdot)\) \(\chi_{6027}(1268,\cdot)\) \(\chi_{6027}(1982,\cdot)\) \(\chi_{6027}(2129,\cdot)\) \(\chi_{6027}(2381,\cdot)\) \(\chi_{6027}(2528,\cdot)\) \(\chi_{6027}(3242,\cdot)\) \(\chi_{6027}(3389,\cdot)\) \(\chi_{6027}(3704,\cdot)\) \(\chi_{6027}(3851,\cdot)\) \(\chi_{6027}(4103,\cdot)\) \(\chi_{6027}(4250,\cdot)\) \(\chi_{6027}(4565,\cdot)\) \(\chi_{6027}(4712,\cdot)\) \(\chi_{6027}(4964,\cdot)\) \(\chi_{6027}(5111,\cdot)\) \(\chi_{6027}(5426,\cdot)\) \(\chi_{6027}(5573,\cdot)\) \(\chi_{6027}(5825,\cdot)\) \(\chi_{6027}(5972,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{5}{8}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{53}{56}\right)\)\(e\left(\frac{53}{56}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{55}{56}\right)\)\(e\left(\frac{5}{8}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{56})\)