sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4020)
sage: chi = H[101]
pari: [g,chi] = znchar(Mod(101,4020))
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 201 |
| 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.da |
| Orbit index | = | 79 |
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 ]
\(\chi_{4020}(41,\cdot)\) \(\chi_{4020}(101,\cdot)\) \(\chi_{4020}(221,\cdot)\) \(\chi_{4020}(281,\cdot)\) \(\chi_{4020}(701,\cdot)\) \(\chi_{4020}(1001,\cdot)\) \(\chi_{4020}(1301,\cdot)\) \(\chi_{4020}(1481,\cdot)\) \(\chi_{4020}(1721,\cdot)\) \(\chi_{4020}(1841,\cdot)\) \(\chi_{4020}(1961,\cdot)\) \(\chi_{4020}(2021,\cdot)\) \(\chi_{4020}(2201,\cdot)\) \(\chi_{4020}(2261,\cdot)\) \(\chi_{4020}(2741,\cdot)\) \(\chi_{4020}(3161,\cdot)\) \(\chi_{4020}(3401,\cdot)\) \(\chi_{4020}(3461,\cdot)\) \(\chi_{4020}(3821,\cdot)\) \(\chi_{4020}(4001,\cdot)\)
Inducing primitive character
Values on generators
\((2011,2681,3217,1141)\) → \((1,-1,1,e\left(\frac{65}{66}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(1\) | \(1\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{33}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{33})\) |