sage: H = DirichletGroup_conrey(173)
sage: chi = H[132]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 173 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 43 |
| 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 | = | 173.d |
| Orbit index | = | 4 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{173}(6,\cdot)\) \(\chi_{173}(10,\cdot)\) \(\chi_{173}(14,\cdot)\) \(\chi_{173}(16,\cdot)\) \(\chi_{173}(22,\cdot)\) \(\chi_{173}(23,\cdot)\) \(\chi_{173}(29,\cdot)\) \(\chi_{173}(36,\cdot)\) \(\chi_{173}(43,\cdot)\) \(\chi_{173}(47,\cdot)\) \(\chi_{173}(51,\cdot)\) \(\chi_{173}(52,\cdot)\) \(\chi_{173}(57,\cdot)\) \(\chi_{173}(60,\cdot)\) \(\chi_{173}(81,\cdot)\) \(\chi_{173}(83,\cdot)\) \(\chi_{173}(84,\cdot)\) \(\chi_{173}(85,\cdot)\) \(\chi_{173}(95,\cdot)\) \(\chi_{173}(96,\cdot)\) \(\chi_{173}(100,\cdot)\) \(\chi_{173}(106,\cdot)\) \(\chi_{173}(109,\cdot)\) \(\chi_{173}(117,\cdot)\) \(\chi_{173}(118,\cdot)\) \(\chi_{173}(119,\cdot)\) \(\chi_{173}(124,\cdot)\) \(\chi_{173}(132,\cdot)\) \(\chi_{173}(133,\cdot)\) \(\chi_{173}(135,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{13}{43}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{13}{43}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{26}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{20}{43}\right)\) | \(e\left(\frac{31}{43}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{4}{43}\right)\) | \(e\left(\frac{41}{43}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{43})\) |