Basic properties
| Modulus: | \(6043\) | |
| Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6043.h
\(\chi_{6043}(91,\cdot)\) \(\chi_{6043}(121,\cdot)\) \(\chi_{6043}(156,\cdot)\) \(\chi_{6043}(164,\cdot)\) \(\chi_{6043}(251,\cdot)\) \(\chi_{6043}(421,\cdot)\) \(\chi_{6043}(650,\cdot)\) \(\chi_{6043}(1504,\cdot)\) \(\chi_{6043}(1585,\cdot)\) \(\chi_{6043}(1589,\cdot)\) \(\chi_{6043}(1648,\cdot)\) \(\chi_{6043}(1934,\cdot)\) \(\chi_{6043}(1994,\cdot)\) \(\chi_{6043}(2110,\cdot)\) \(\chi_{6043}(2238,\cdot)\) \(\chi_{6043}(2555,\cdot)\) \(\chi_{6043}(2571,\cdot)\) \(\chi_{6043}(2597,\cdot)\) \(\chi_{6043}(2724,\cdot)\) \(\chi_{6043}(2871,\cdot)\) \(\chi_{6043}(2940,\cdot)\) \(\chi_{6043}(3869,\cdot)\) \(\chi_{6043}(3918,\cdot)\) \(\chi_{6043}(4380,\cdot)\) \(\chi_{6043}(4452,\cdot)\) \(\chi_{6043}(4906,\cdot)\) \(\chi_{6043}(4990,\cdot)\) \(\chi_{6043}(5040,\cdot)\) \(\chi_{6043}(5042,\cdot)\) \(\chi_{6043}(5307,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\(5\) → \(e\left(\frac{46}{57}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6043 }(91, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(1\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) |