sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4030)
sage: chi = H[1741]
pari: [g,chi] = znchar(Mod(1741,4030))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 403 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 6 |
| 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 | = | 4030.bk |
| Orbit index | = | 37 |
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 ]
\(\chi_{4030}(831,\cdot)\) \(\chi_{4030}(1741,\cdot)\)
Inducing primitive character
Values on generators
\((807,1861,2731)\) → \((1,-1,e\left(\frac{2}{3}\right))\)
Values
| -1 | 1 | 3 | 7 | 9 | 11 | 17 | 19 | 21 | 23 | 27 | 29 |
| \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Related number fields
| Field of values | \(\Q(\zeta_{3})\) |