sage: H = DirichletGroup_conrey(97)
sage: chi = H[15]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 97 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 96 |
| 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 | = | 97.l |
| Orbit index | = | 12 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{97}(5,\cdot)\) \(\chi_{97}(7,\cdot)\) \(\chi_{97}(10,\cdot)\) \(\chi_{97}(13,\cdot)\) \(\chi_{97}(14,\cdot)\) \(\chi_{97}(15,\cdot)\) \(\chi_{97}(17,\cdot)\) \(\chi_{97}(21,\cdot)\) \(\chi_{97}(23,\cdot)\) \(\chi_{97}(26,\cdot)\) \(\chi_{97}(29,\cdot)\) \(\chi_{97}(37,\cdot)\) \(\chi_{97}(38,\cdot)\) \(\chi_{97}(39,\cdot)\) \(\chi_{97}(40,\cdot)\) \(\chi_{97}(41,\cdot)\) \(\chi_{97}(56,\cdot)\) \(\chi_{97}(57,\cdot)\) \(\chi_{97}(58,\cdot)\) \(\chi_{97}(59,\cdot)\) \(\chi_{97}(60,\cdot)\) \(\chi_{97}(68,\cdot)\) \(\chi_{97}(71,\cdot)\) \(\chi_{97}(74,\cdot)\) \(\chi_{97}(76,\cdot)\) \(\chi_{97}(80,\cdot)\) \(\chi_{97}(82,\cdot)\) \(\chi_{97}(83,\cdot)\) \(\chi_{97}(84,\cdot)\) \(\chi_{97}(87,\cdot)\) ...
Values on generators
\(5\) → \(e\left(\frac{71}{96}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{71}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{96})\) |