sage: H = DirichletGroup_conrey(199)
sage: chi = H[9]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 199 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 99 |
| 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 | = | 199.k |
| Orbit index | = | 11 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{199}(2,\cdot)\) \(\chi_{199}(4,\cdot)\) \(\chi_{199}(7,\cdot)\) \(\chi_{199}(9,\cdot)\) \(\chi_{199}(10,\cdot)\) \(\chi_{199}(13,\cdot)\) \(\chi_{199}(14,\cdot)\) \(\chi_{199}(16,\cdot)\) \(\chi_{199}(20,\cdot)\) \(\chi_{199}(23,\cdot)\) \(\chi_{199}(26,\cdot)\) \(\chi_{199}(29,\cdot)\) \(\chi_{199}(31,\cdot)\) \(\chi_{199}(32,\cdot)\) \(\chi_{199}(33,\cdot)\) \(\chi_{199}(35,\cdot)\) \(\chi_{199}(36,\cdot)\) \(\chi_{199}(45,\cdot)\) \(\chi_{199}(46,\cdot)\) \(\chi_{199}(47,\cdot)\) \(\chi_{199}(49,\cdot)\) \(\chi_{199}(50,\cdot)\) \(\chi_{199}(51,\cdot)\) \(\chi_{199}(53,\cdot)\) \(\chi_{199}(56,\cdot)\) \(\chi_{199}(57,\cdot)\) \(\chi_{199}(65,\cdot)\) \(\chi_{199}(66,\cdot)\) \(\chi_{199}(70,\cdot)\) \(\chi_{199}(72,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{1}{99}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{99})\) |