Properties

Conductor 6027
Order 840
Real No
Primitive Yes
Parity Even
Orbit Label 6027.eu

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[11]
 
pari: [g,chi] = znchar(Mod(11,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 840
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.eu
Orbit index = 125

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 ]
 

\(\chi_{6027}(11,\cdot)\) \(\chi_{6027}(53,\cdot)\) \(\chi_{6027}(65,\cdot)\) \(\chi_{6027}(95,\cdot)\) \(\chi_{6027}(149,\cdot)\) \(\chi_{6027}(158,\cdot)\) \(\chi_{6027}(170,\cdot)\) \(\chi_{6027}(179,\cdot)\) \(\chi_{6027}(212,\cdot)\) \(\chi_{6027}(233,\cdot)\) \(\chi_{6027}(317,\cdot)\) \(\chi_{6027}(347,\cdot)\) \(\chi_{6027}(380,\cdot)\) \(\chi_{6027}(464,\cdot)\) \(\chi_{6027}(473,\cdot)\) \(\chi_{6027}(485,\cdot)\) \(\chi_{6027}(527,\cdot)\) \(\chi_{6027}(548,\cdot)\) \(\chi_{6027}(632,\cdot)\) \(\chi_{6027}(641,\cdot)\) \(\chi_{6027}(662,\cdot)\) \(\chi_{6027}(725,\cdot)\) \(\chi_{6027}(767,\cdot)\) \(\chi_{6027}(809,\cdot)\) \(\chi_{6027}(842,\cdot)\) \(\chi_{6027}(872,\cdot)\) \(\chi_{6027}(914,\cdot)\) \(\chi_{6027}(926,\cdot)\) \(\chi_{6027}(956,\cdot)\) \(\chi_{6027}(977,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{20}{21}\right),e\left(\frac{3}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{89}{420}\right)\)\(e\left(\frac{89}{210}\right)\)\(e\left(\frac{323}{420}\right)\)\(e\left(\frac{89}{140}\right)\)\(e\left(\frac{103}{105}\right)\)\(e\left(\frac{689}{840}\right)\)\(e\left(\frac{211}{280}\right)\)\(e\left(\frac{89}{105}\right)\)\(e\left(\frac{659}{840}\right)\)\(e\left(\frac{1}{120}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{840})\)