Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 3021 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 468 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | No |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Odd |
| Orbit label | = | 6042.cs |
| Orbit index | = | 71 |
Galois orbit
\(\chi_{6042}(41,\cdot)\) \(\chi_{6042}(71,\cdot)\) \(\chi_{6042}(167,\cdot)\) \(\chi_{6042}(173,\cdot)\) \(\chi_{6042}(185,\cdot)\) \(\chi_{6042}(257,\cdot)\) \(\chi_{6042}(287,\cdot)\) \(\chi_{6042}(299,\cdot)\) \(\chi_{6042}(383,\cdot)\) \(\chi_{6042}(485,\cdot)\) \(\chi_{6042}(497,\cdot)\) \(\chi_{6042}(509,\cdot)\) \(\chi_{6042}(527,\cdot)\) \(\chi_{6042}(641,\cdot)\) \(\chi_{6042}(737,\cdot)\) \(\chi_{6042}(773,\cdot)\) \(\chi_{6042}(827,\cdot)\) \(\chi_{6042}(851,\cdot)\) \(\chi_{6042}(869,\cdot)\) \(\chi_{6042}(887,\cdot)\) \(\chi_{6042}(1055,\cdot)\) \(\chi_{6042}(1079,\cdot)\) \(\chi_{6042}(1115,\cdot)\) \(\chi_{6042}(1169,\cdot)\) \(\chi_{6042}(1193,\cdot)\) \(\chi_{6042}(1199,\cdot)\) \(\chi_{6042}(1211,\cdot)\) \(\chi_{6042}(1307,\cdot)\) \(\chi_{6042}(1313,\cdot)\) \(\chi_{6042}(1343,\cdot)\) ...
Inducing primitive character
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{45}{52}\right))\)
Values
| -1 | 1 | 5 | 7 | 11 | 13 | 17 | 23 | 25 | 29 | 31 | 35 |
| \(-1\) | \(1\) | \(e\left(\frac{341}{468}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{83}{468}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{468})\) |