sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(9900)
sage: chi = H[4759]
pari: [g,chi] = znchar(Mod(4759,9900))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 9900 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 30 |
| 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 | = | 9900.hx |
| Orbit index | = | 206 |
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 ]
\(\chi_{9900}(79,\cdot)\) \(\chi_{9900}(1339,\cdot)\) \(\chi_{9900}(3379,\cdot)\) \(\chi_{9900}(4219,\cdot)\) \(\chi_{9900}(4639,\cdot)\) \(\chi_{9900}(4759,\cdot)\) \(\chi_{9900}(7519,\cdot)\) \(\chi_{9900}(8059,\cdot)\)
Values on generators
\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{7}{10}\right),e\left(\frac{7}{10}\right))\)
Values
| -1 | 1 | 7 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
| \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{15})\) |