sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4020)
sage: chi = H[109]
pari: [g,chi] = znchar(Mod(109,4020))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 335 |
| 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 | = | No |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Odd |
| Orbit label | = | 4020.cb |
| Orbit index | = | 54 |
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 ]
\(\chi_{4020}(109,\cdot)\) \(\chi_{4020}(589,\cdot)\) \(\chi_{4020}(1249,\cdot)\) \(\chi_{4020}(1549,\cdot)\) \(\chi_{4020}(2149,\cdot)\) \(\chi_{4020}(2269,\cdot)\) \(\chi_{4020}(3109,\cdot)\) \(\chi_{4020}(3469,\cdot)\) \(\chi_{4020}(3529,\cdot)\) \(\chi_{4020}(3889,\cdot)\)
Inducing primitive character
Values on generators
\((2011,2681,3217,1141)\) → \((1,1,-1,e\left(\frac{21}{22}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(-1\) | \(e\left(\frac{13}{22}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{11})\) |