Properties

Conductor 80
Order 4
Real No
Primitive No
Parity Odd
Orbit Label 4000.i

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(4000)
 
sage: chi = H[57]
 
pari: [g,chi] = znchar(Mod(57,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 80
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 = Odd
Orbit label = 4000.i
Orbit index = 9

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 ]
 

\(\chi_{4000}(57,\cdot)\) \(\chi_{4000}(1193,\cdot)\)

Inducing primitive character

\(\chi_{80}(37,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((1,i,i)\)

Values

-1137911131719212327
\(-1\)\(1\)\(-1\)\(-i\)\(1\)\(i\)\(-1\)\(i\)\(i\)\(i\)\(i\)\(-1\)
value at  e.g. 2

Related number fields

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