sage: H = DirichletGroup_conrey(349)
sage: chi = H[14]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 349 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 87 |
| 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 | = | 349.i |
| Orbit index | = | 9 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{349}(9,\cdot)\) \(\chi_{349}(12,\cdot)\) \(\chi_{349}(14,\cdot)\) \(\chi_{349}(15,\cdot)\) \(\chi_{349}(16,\cdot)\) \(\chi_{349}(19,\cdot)\) \(\chi_{349}(20,\cdot)\) \(\chi_{349}(23,\cdot)\) \(\chi_{349}(25,\cdot)\) \(\chi_{349}(26,\cdot)\) \(\chi_{349}(51,\cdot)\) \(\chi_{349}(68,\cdot)\) \(\chi_{349}(77,\cdot)\) \(\chi_{349}(81,\cdot)\) \(\chi_{349}(85,\cdot)\) \(\chi_{349}(87,\cdot)\) \(\chi_{349}(94,\cdot)\) \(\chi_{349}(106,\cdot)\) \(\chi_{349}(108,\cdot)\) \(\chi_{349}(111,\cdot)\) \(\chi_{349}(116,\cdot)\) \(\chi_{349}(135,\cdot)\) \(\chi_{349}(143,\cdot)\) \(\chi_{349}(144,\cdot)\) \(\chi_{349}(145,\cdot)\) \(\chi_{349}(147,\cdot)\) \(\chi_{349}(148,\cdot)\) \(\chi_{349}(151,\cdot)\) \(\chi_{349}(158,\cdot)\) \(\chi_{349}(180,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{17}{87}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{17}{87}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{34}{87}\right)\) | \(e\left(\frac{31}{87}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{8}{87}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{14}{87}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{87})\) |