sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4020)
sage: chi = H[59]
pari: [g,chi] = znchar(Mod(59,4020))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4020 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 22 |
| 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 | = | 4020.by |
| Orbit index | = | 51 |
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 ]
\(\chi_{4020}(59,\cdot)\) \(\chi_{4020}(359,\cdot)\) \(\chi_{4020}(1019,\cdot)\) \(\chi_{4020}(1499,\cdot)\) \(\chi_{4020}(1739,\cdot)\) \(\chi_{4020}(2099,\cdot)\) \(\chi_{4020}(2159,\cdot)\) \(\chi_{4020}(2519,\cdot)\) \(\chi_{4020}(3359,\cdot)\) \(\chi_{4020}(3479,\cdot)\)
Values on generators
\((2011,2681,3217,1141)\) → \((-1,-1,-1,e\left(\frac{6}{11}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(-1\) | \(e\left(\frac{3}{22}\right)\) | \(-1\) | \(e\left(\frac{9}{22}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{11})\) |