sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4020)
sage: chi = H[19]
pari: [g,chi] = znchar(Mod(19,4020))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1340 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 66 |
| 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 | = | Odd |
| Orbit label | = | 4020.dd |
| Orbit index | = | 82 |
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 ]
\(\chi_{4020}(19,\cdot)\) \(\chi_{4020}(199,\cdot)\) \(\chi_{4020}(559,\cdot)\) \(\chi_{4020}(619,\cdot)\) \(\chi_{4020}(859,\cdot)\) \(\chi_{4020}(1279,\cdot)\) \(\chi_{4020}(1759,\cdot)\) \(\chi_{4020}(1819,\cdot)\) \(\chi_{4020}(1999,\cdot)\) \(\chi_{4020}(2059,\cdot)\) \(\chi_{4020}(2179,\cdot)\) \(\chi_{4020}(2299,\cdot)\) \(\chi_{4020}(2539,\cdot)\) \(\chi_{4020}(2719,\cdot)\) \(\chi_{4020}(3019,\cdot)\) \(\chi_{4020}(3319,\cdot)\) \(\chi_{4020}(3739,\cdot)\) \(\chi_{4020}(3799,\cdot)\) \(\chi_{4020}(3919,\cdot)\) \(\chi_{4020}(3979,\cdot)\)
Inducing primitive character
Values on generators
\((2011,2681,3217,1141)\) → \((-1,1,-1,e\left(\frac{5}{33}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(-1\) | \(1\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{33}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{33})\) |