Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4033 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 108 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | odd |
| Orbit label | = | 4033.js |
| Orbit index | = | 253 |
Galois orbit
\(\chi_{4033}(15,\cdot)\) \(\chi_{4033}(187,\cdot)\) \(\chi_{4033}(198,\cdot)\) \(\chi_{4033}(315,\cdot)\) \(\chi_{4033}(348,\cdot)\) \(\chi_{4033}(405,\cdot)\) \(\chi_{4033}(439,\cdot)\) \(\chi_{4033}(461,\cdot)\) \(\chi_{4033}(836,\cdot)\) \(\chi_{4033}(1016,\cdot)\) \(\chi_{4033}(1112,\cdot)\) \(\chi_{4033}(1171,\cdot)\) \(\chi_{4033}(1313,\cdot)\) \(\chi_{4033}(1330,\cdot)\) \(\chi_{4033}(1356,\cdot)\) \(\chi_{4033}(1424,\cdot)\) \(\chi_{4033}(1615,\cdot)\) \(\chi_{4033}(1650,\cdot)\) \(\chi_{4033}(1793,\cdot)\) \(\chi_{4033}(1983,\cdot)\) \(\chi_{4033}(2151,\cdot)\) \(\chi_{4033}(2314,\cdot)\) \(\chi_{4033}(2386,\cdot)\) \(\chi_{4033}(2407,\cdot)\) \(\chi_{4033}(2625,\cdot)\) \(\chi_{4033}(2696,\cdot)\) \(\chi_{4033}(2869,\cdot)\) \(\chi_{4033}(3187,\cdot)\) \(\chi_{4033}(3234,\cdot)\) \(\chi_{4033}(3275,\cdot)\) ...
Values on generators
\((1963,2295)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{5}{27}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(-i\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{11}{54}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{108})\) |