Conductor 4001
Order 20
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4001.h

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4001)
sage: chi = H[1070]
pari: [g,chi] = znchar(Mod(1070,4001))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4001
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 20
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 = 4001.h
Orbit index = 8

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 ]

\(\chi_{4001}(152,\cdot)\) \(\chi_{4001}(816,\cdot)\) \(\chi_{4001}(1070,\cdot)\) \(\chi_{4001}(1305,\cdot)\) \(\chi_{4001}(2696,\cdot)\) \(\chi_{4001}(2931,\cdot)\) \(\chi_{4001}(3185,\cdot)\) \(\chi_{4001}(3849,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{3}{20}\right)\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)