Properties

Conductor 6027
Order 210
Real No
Primitive Yes
Parity Even
Orbit Label 6027.ei

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[236]
 
pari: [g,chi] = znchar(Mod(236,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
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.ei
Orbit index = 113

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 ]
 

\(\chi_{6027}(236,\cdot)\) \(\chi_{6027}(269,\cdot)\) \(\chi_{6027}(332,\cdot)\) \(\chi_{6027}(353,\cdot)\) \(\chi_{6027}(605,\cdot)\) \(\chi_{6027}(761,\cdot)\) \(\chi_{6027}(824,\cdot)\) \(\chi_{6027}(845,\cdot)\) \(\chi_{6027}(1130,\cdot)\) \(\chi_{6027}(1193,\cdot)\) \(\chi_{6027}(1214,\cdot)\) \(\chi_{6027}(1466,\cdot)\) \(\chi_{6027}(1622,\cdot)\) \(\chi_{6027}(1706,\cdot)\) \(\chi_{6027}(1958,\cdot)\) \(\chi_{6027}(2054,\cdot)\) \(\chi_{6027}(2075,\cdot)\) \(\chi_{6027}(2327,\cdot)\) \(\chi_{6027}(2483,\cdot)\) \(\chi_{6027}(2546,\cdot)\) \(\chi_{6027}(2819,\cdot)\) \(\chi_{6027}(2852,\cdot)\) \(\chi_{6027}(2915,\cdot)\) \(\chi_{6027}(2936,\cdot)\) \(\chi_{6027}(3188,\cdot)\) \(\chi_{6027}(3344,\cdot)\) \(\chi_{6027}(3407,\cdot)\) \(\chi_{6027}(3428,\cdot)\) \(\chi_{6027}(3680,\cdot)\) \(\chi_{6027}(3713,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{23}{42}\right),e\left(\frac{7}{10}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{197}{210}\right)\)\(e\left(\frac{92}{105}\right)\)\(e\left(\frac{82}{105}\right)\)\(e\left(\frac{57}{70}\right)\)\(e\left(\frac{151}{210}\right)\)\(e\left(\frac{53}{105}\right)\)\(e\left(\frac{27}{35}\right)\)\(e\left(\frac{79}{105}\right)\)\(e\left(\frac{61}{210}\right)\)\(e\left(\frac{7}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)