Properties

Conductor 6027
Order 210
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6027.ej

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[3050]
 
pari: [g,chi] = znchar(Mod(3050,6027))
 

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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6027.ej
Orbit index = 114

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 ]
 

\(\chi_{6027}(59,\cdot)\) \(\chi_{6027}(467,\cdot)\) \(\chi_{6027}(488,\cdot)\) \(\chi_{6027}(551,\cdot)\) \(\chi_{6027}(584,\cdot)\) \(\chi_{6027}(836,\cdot)\) \(\chi_{6027}(857,\cdot)\) \(\chi_{6027}(920,\cdot)\) \(\chi_{6027}(1076,\cdot)\) \(\chi_{6027}(1328,\cdot)\) \(\chi_{6027}(1349,\cdot)\) \(\chi_{6027}(1412,\cdot)\) \(\chi_{6027}(1445,\cdot)\) \(\chi_{6027}(1718,\cdot)\) \(\chi_{6027}(1781,\cdot)\) \(\chi_{6027}(1937,\cdot)\) \(\chi_{6027}(2189,\cdot)\) \(\chi_{6027}(2210,\cdot)\) \(\chi_{6027}(2306,\cdot)\) \(\chi_{6027}(2558,\cdot)\) \(\chi_{6027}(2642,\cdot)\) \(\chi_{6027}(2798,\cdot)\) \(\chi_{6027}(3050,\cdot)\) \(\chi_{6027}(3071,\cdot)\) \(\chi_{6027}(3134,\cdot)\) \(\chi_{6027}(3419,\cdot)\) \(\chi_{6027}(3440,\cdot)\) \(\chi_{6027}(3503,\cdot)\) \(\chi_{6027}(3659,\cdot)\) \(\chi_{6027}(3911,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{11}{42}\right),e\left(\frac{3}{5}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{191}{210}\right)\)\(e\left(\frac{86}{105}\right)\)\(e\left(\frac{31}{105}\right)\)\(e\left(\frac{51}{70}\right)\)\(e\left(\frac{43}{210}\right)\)\(e\left(\frac{163}{210}\right)\)\(e\left(\frac{17}{70}\right)\)\(e\left(\frac{67}{105}\right)\)\(e\left(\frac{89}{105}\right)\)\(e\left(\frac{17}{30}\right)\)
value at  e.g. 2

Related number fields

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