Properties

Conductor 4001
Order 4
Real No
Primitive No
Parity Even
Orbit Label 8002.c

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(8002)
 
sage: chi = H[899]
 
pari: [g,chi] = znchar(Mod(899,8002))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 4
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8002.c
Orbit index = 3

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 ]
 

\(\chi_{8002}(899,\cdot)\) \(\chi_{8002}(7103,\cdot)\)

Inducing primitive character

\(\chi_{4001}(899,\cdot)\)

Values on generators

\(3\) → \(-i\)

Values

-113579111315171921
\(1\)\(1\)\(-i\)\(1\)\(1\)\(-1\)\(-i\)\(1\)\(-i\)\(i\)\(1\)\(-i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(i)\)