Basic properties
| Modulus: | \(6037\) | |
| Conductor: | \(6037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1509\) | 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 6037.i
\(\chi_{6037}(9,\cdot)\) \(\chi_{6037}(12,\cdot)\) \(\chi_{6037}(26,\cdot)\) \(\chi_{6037}(29,\cdot)\) \(\chi_{6037}(33,\cdot)\) \(\chi_{6037}(35,\cdot)\) \(\chi_{6037}(40,\cdot)\) \(\chi_{6037}(41,\cdot)\) \(\chi_{6037}(47,\cdot)\) \(\chi_{6037}(51,\cdot)\) \(\chi_{6037}(59,\cdot)\) \(\chi_{6037}(68,\cdot)\) \(\chi_{6037}(74,\cdot)\) \(\chi_{6037}(75,\cdot)\) \(\chi_{6037}(81,\cdot)\) \(\chi_{6037}(95,\cdot)\) \(\chi_{6037}(100,\cdot)\) \(\chi_{6037}(101,\cdot)\) \(\chi_{6037}(103,\cdot)\) \(\chi_{6037}(106,\cdot)\) \(\chi_{6037}(110,\cdot)\) \(\chi_{6037}(122,\cdot)\) \(\chi_{6037}(126,\cdot)\) \(\chi_{6037}(134,\cdot)\) \(\chi_{6037}(138,\cdot)\) \(\chi_{6037}(144,\cdot)\) \(\chi_{6037}(147,\cdot)\) \(\chi_{6037}(161,\cdot)\) \(\chi_{6037}(168,\cdot)\) \(\chi_{6037}(172,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1509})$ |
| Fixed field: | Number field defined by a degree 1509 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{133}{1509}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6037 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{445}{503}\right)\) | \(e\left(\frac{671}{1509}\right)\) | \(e\left(\frac{387}{503}\right)\) | \(e\left(\frac{133}{1509}\right)\) | \(e\left(\frac{497}{1509}\right)\) | \(e\left(\frac{74}{503}\right)\) | \(e\left(\frac{329}{503}\right)\) | \(e\left(\frac{1342}{1509}\right)\) | \(e\left(\frac{1468}{1509}\right)\) | \(e\left(\frac{455}{503}\right)\) |