Properties

Conductor 77
Order 2
Real yes
Primitive no
Minimal yes
Parity even
Orbit label 4004.e

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(4004)
 
sage: chi = H[3849]
 
pari: [g,chi] = znchar(Mod(3849,4004))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 77
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2
Real = yes
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 = 4004.e
Orbit index = 5

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 ]
 

\(\chi_{4004}(3849,\cdot)\)

Values on generators

\((2003,3433,365,925)\) → \((1,-1,-1,1)\)

Values

-1135915171923252729
\(1\)\(1\)\(-1\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)