sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4020)
sage: chi = H[79]
pari: [g,chi] = znchar(Mod(79,4020))
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 | = | Even |
| Orbit label | = | 4020.db |
| Orbit index | = | 80 |
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 ]
\(\chi_{4020}(79,\cdot)\) \(\chi_{4020}(319,\cdot)\) \(\chi_{4020}(379,\cdot)\) \(\chi_{4020}(739,\cdot)\) \(\chi_{4020}(919,\cdot)\) \(\chi_{4020}(979,\cdot)\) \(\chi_{4020}(1039,\cdot)\) \(\chi_{4020}(1159,\cdot)\) \(\chi_{4020}(1219,\cdot)\) \(\chi_{4020}(1639,\cdot)\) \(\chi_{4020}(1939,\cdot)\) \(\chi_{4020}(2239,\cdot)\) \(\chi_{4020}(2419,\cdot)\) \(\chi_{4020}(2659,\cdot)\) \(\chi_{4020}(2779,\cdot)\) \(\chi_{4020}(2899,\cdot)\) \(\chi_{4020}(2959,\cdot)\) \(\chi_{4020}(3139,\cdot)\) \(\chi_{4020}(3199,\cdot)\) \(\chi_{4020}(3679,\cdot)\)
Inducing primitive character
Values on generators
\((2011,2681,3217,1141)\) → \((-1,1,-1,e\left(\frac{41}{66}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(1\) | \(1\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{61}{66}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{33})\) |