Properties

Conductor 1001
Order 2
Real Yes
Primitive Yes
Parity Even
Orbit Label 1001.g

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(1001)
 
sage: chi = H[1000]
 
pari: [g,chi] = znchar(Mod(1000,1001))
 

Kronecker symbol representation

sage: kronecker_character(1001)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{1001}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1001
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 1001.g
Orbit index = 7

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 ]
 

\(\chi_{1001}(1000,\cdot)\)

Values on generators

\((430,365,925)\) → \((-1,-1,-1)\)

Values

-112345689101215
\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(-1\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)