Basic properties
| Modulus: | \(6043\) | |
| Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(159\) | 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.k
\(\chi_{6043}(4,\cdot)\) \(\chi_{6043}(16,\cdot)\) \(\chi_{6043}(256,\cdot)\) \(\chi_{6043}(462,\cdot)\) \(\chi_{6043}(467,\cdot)\) \(\chi_{6043}(483,\cdot)\) \(\chi_{6043}(513,\cdot)\) \(\chi_{6043}(525,\cdot)\) \(\chi_{6043}(541,\cdot)\) \(\chi_{6043}(695,\cdot)\) \(\chi_{6043}(697,\cdot)\) \(\chi_{6043}(830,\cdot)\) \(\chi_{6043}(858,\cdot)\) \(\chi_{6043}(890,\cdot)\) \(\chi_{6043}(893,\cdot)\) \(\chi_{6043}(897,\cdot)\) \(\chi_{6043}(975,\cdot)\) \(\chi_{6043}(986,\cdot)\) \(\chi_{6043}(1024,\cdot)\) \(\chi_{6043}(1221,\cdot)\) \(\chi_{6043}(1294,\cdot)\) \(\chi_{6043}(1305,\cdot)\) \(\chi_{6043}(1349,\cdot)\) \(\chi_{6043}(1407,\cdot)\) \(\chi_{6043}(1453,\cdot)\) \(\chi_{6043}(1511,\cdot)\) \(\chi_{6043}(1642,\cdot)\) \(\chi_{6043}(1646,\cdot)\) \(\chi_{6043}(1713,\cdot)\) \(\chi_{6043}(1734,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{159})$ |
| Fixed field: | Number field defined by a degree 159 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{23}{159}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6043 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{159}\right)\) | \(e\left(\frac{45}{53}\right)\) | \(e\left(\frac{34}{159}\right)\) | \(e\left(\frac{23}{159}\right)\) | \(e\left(\frac{152}{159}\right)\) | \(e\left(\frac{10}{159}\right)\) | \(e\left(\frac{17}{53}\right)\) | \(e\left(\frac{37}{53}\right)\) | \(e\left(\frac{40}{159}\right)\) | \(e\left(\frac{1}{3}\right)\) |