Conductor 2009
Order 14
Real no
Primitive no
Minimal yes
Parity even
Orbit label

Related objects

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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[778]
pari: [g,chi] = znchar(Mod(778,6027))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2009
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 14
Real = no
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = no
Minimal = yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = even
Orbit label =
Orbit index = 38

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 ]

\(\chi_{6027}(778,\cdot)\) \(\chi_{6027}(1639,\cdot)\) \(\chi_{6027}(3361,\cdot)\) \(\chi_{6027}(4222,\cdot)\) \(\chi_{6027}(5083,\cdot)\) \(\chi_{6027}(5944,\cdot)\)

Values on generators

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


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{7})\)