sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6027)
sage: chi = H[419]
pari: [g,chi] = znchar(Mod(419,6027))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 6027 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 28 |
| Real | = | No |
| 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 | = | 6027.cd |
| Orbit index | = | 56 |
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 ]
\(\chi_{6027}(419,\cdot)\) \(\chi_{6027}(524,\cdot)\) \(\chi_{6027}(1280,\cdot)\) \(\chi_{6027}(1385,\cdot)\) \(\chi_{6027}(2141,\cdot)\) \(\chi_{6027}(2246,\cdot)\) \(\chi_{6027}(3002,\cdot)\) \(\chi_{6027}(3107,\cdot)\) \(\chi_{6027}(3863,\cdot)\) \(\chi_{6027}(4724,\cdot)\) \(\chi_{6027}(4829,\cdot)\) \(\chi_{6027}(5690,\cdot)\)
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{1}{14}\right),-i)\)
Values
| -1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
| \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(i\) |
Related number fields
| Field of values | \(\Q(\zeta_{28})\) |