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 | = | Even |
| Orbit label | = | 6042.ct |
| Orbit index | = | 72 |
Galois orbit
\(\chi_{6042}(5,\cdot)\) \(\chi_{6042}(35,\cdot)\) \(\chi_{6042}(101,\cdot)\) \(\chi_{6042}(137,\cdot)\) \(\chi_{6042}(161,\cdot)\) \(\chi_{6042}(215,\cdot)\) \(\chi_{6042}(233,\cdot)\) \(\chi_{6042}(245,\cdot)\) \(\chi_{6042}(251,\cdot)\) \(\chi_{6042}(263,\cdot)\) \(\chi_{6042}(359,\cdot)\) \(\chi_{6042}(389,\cdot)\) \(\chi_{6042}(443,\cdot)\) \(\chi_{6042}(479,\cdot)\) \(\chi_{6042}(491,\cdot)\) \(\chi_{6042}(503,\cdot)\) \(\chi_{6042}(557,\cdot)\) \(\chi_{6042}(575,\cdot)\) \(\chi_{6042}(605,\cdot)\) \(\chi_{6042}(617,\cdot)\) \(\chi_{6042}(671,\cdot)\) \(\chi_{6042}(701,\cdot)\) \(\chi_{6042}(707,\cdot)\) \(\chi_{6042}(803,\cdot)\) \(\chi_{6042}(815,\cdot)\) \(\chi_{6042}(821,\cdot)\) \(\chi_{6042}(845,\cdot)\) \(\chi_{6042}(899,\cdot)\) \(\chi_{6042}(935,\cdot)\) \(\chi_{6042}(959,\cdot)\) ...
Inducing primitive character
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{8}{9}\right),e\left(\frac{47}{52}\right))\)
Values
| -1 | 1 | 5 | 7 | 11 | 13 | 17 | 23 | 25 | 29 | 31 | 35 |
| \(1\) | \(1\) | \(e\left(\frac{95}{468}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{89}{468}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{468})\) |