sage: H = DirichletGroup_conrey(101)
sage: chi = H[51]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 101 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 100 |
| 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 | = | Odd |
| Orbit label | = | 101.i |
| Orbit index | = | 9 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{101}(2,\cdot)\) \(\chi_{101}(3,\cdot)\) \(\chi_{101}(7,\cdot)\) \(\chi_{101}(8,\cdot)\) \(\chi_{101}(11,\cdot)\) \(\chi_{101}(12,\cdot)\) \(\chi_{101}(15,\cdot)\) \(\chi_{101}(18,\cdot)\) \(\chi_{101}(26,\cdot)\) \(\chi_{101}(27,\cdot)\) \(\chi_{101}(28,\cdot)\) \(\chi_{101}(29,\cdot)\) \(\chi_{101}(34,\cdot)\) \(\chi_{101}(35,\cdot)\) \(\chi_{101}(38,\cdot)\) \(\chi_{101}(40,\cdot)\) \(\chi_{101}(42,\cdot)\) \(\chi_{101}(46,\cdot)\) \(\chi_{101}(48,\cdot)\) \(\chi_{101}(50,\cdot)\) \(\chi_{101}(51,\cdot)\) \(\chi_{101}(53,\cdot)\) \(\chi_{101}(55,\cdot)\) \(\chi_{101}(59,\cdot)\) \(\chi_{101}(61,\cdot)\) \(\chi_{101}(63,\cdot)\) \(\chi_{101}(66,\cdot)\) \(\chi_{101}(67,\cdot)\) \(\chi_{101}(72,\cdot)\) \(\chi_{101}(73,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{99}{100}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(-i\) | \(e\left(\frac{87}{100}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{100})\) |