sage: H = DirichletGroup_conrey(191)
sage: chi = H[27]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 191 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 95 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Even |
| Orbit label | = | 191.g |
| Orbit index | = | 7 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{191}(2,\cdot)\) \(\chi_{191}(3,\cdot)\) \(\chi_{191}(4,\cdot)\) \(\chi_{191}(8,\cdot)\) \(\chi_{191}(9,\cdot)\) \(\chi_{191}(10,\cdot)\) \(\chi_{191}(12,\cdot)\) \(\chi_{191}(13,\cdot)\) \(\chi_{191}(15,\cdot)\) \(\chi_{191}(16,\cdot)\) \(\chi_{191}(17,\cdot)\) \(\chi_{191}(18,\cdot)\) \(\chi_{191}(20,\cdot)\) \(\chi_{191}(23,\cdot)\) \(\chi_{191}(24,\cdot)\) \(\chi_{191}(26,\cdot)\) \(\chi_{191}(27,\cdot)\) \(\chi_{191}(34,\cdot)\) \(\chi_{191}(40,\cdot)\) \(\chi_{191}(43,\cdot)\) \(\chi_{191}(45,\cdot)\) \(\chi_{191}(46,\cdot)\) \(\chi_{191}(48,\cdot)\) \(\chi_{191}(50,\cdot)\) \(\chi_{191}(51,\cdot)\) \(\chi_{191}(54,\cdot)\) \(\chi_{191}(59,\cdot)\) \(\chi_{191}(60,\cdot)\) \(\chi_{191}(64,\cdot)\) \(\chi_{191}(65,\cdot)\) ...
Values on generators
\(19\) → \(e\left(\frac{79}{95}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{56}{95}\right)\) | \(e\left(\frac{44}{95}\right)\) | \(e\left(\frac{17}{95}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{73}{95}\right)\) | \(e\left(\frac{88}{95}\right)\) | \(e\left(\frac{16}{95}\right)\) | \(e\left(\frac{13}{19}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{95})\) |