sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4033)
sage: chi = H[118]
pari: [g,chi] = znchar(Mod(118,4033))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4033 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 27 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | even |
| Orbit label | = | 4033.dw |
| Orbit index | = | 101 |
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 ]
\(\chi_{4033}(118,\cdot)\) \(\chi_{4033}(1422,\cdot)\) \(\chi_{4033}(1533,\cdot)\) \(\chi_{4033}(1551,\cdot)\) \(\chi_{4033}(1825,\cdot)\) \(\chi_{4033}(1931,\cdot)\) \(\chi_{4033}(1933,\cdot)\) \(\chi_{4033}(2010,\cdot)\) \(\chi_{4033}(2106,\cdot)\) \(\chi_{4033}(2253,\cdot)\) \(\chi_{4033}(2269,\cdot)\) \(\chi_{4033}(2495,\cdot)\) \(\chi_{4033}(2856,\cdot)\) \(\chi_{4033}(2883,\cdot)\) \(\chi_{4033}(2969,\cdot)\) \(\chi_{4033}(3067,\cdot)\) \(\chi_{4033}(3400,\cdot)\) \(\chi_{4033}(3709,\cdot)\)
Values on generators
\((1963,2295)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{26}{27}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{27})\) |