sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1003)
sage: chi = H[1]
pari: [g,chi] = znchar(Mod(1,1003))
Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
Conductor | = | 1 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
Order | = | 1 |
Real | = | Yes |
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 | = | 1003.a |
Orbit index | = | 1 |
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 ]
Inducing primitive character
Values on generators
\((768,120)\) → \((1,1)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
Related number fields
Field of values | \(\Q\) |