Basic properties
| Modulus: | \(6037\) | |
| Conductor: | \(6037\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1006\) | 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.h
\(\chi_{6037}(4,\cdot)\) \(\chi_{6037}(11,\cdot)\) \(\chi_{6037}(27,\cdot)\) \(\chi_{6037}(49,\cdot)\) \(\chi_{6037}(56,\cdot)\) \(\chi_{6037}(64,\cdot)\) \(\chi_{6037}(105,\cdot)\) \(\chi_{6037}(115,\cdot)\) \(\chi_{6037}(120,\cdot)\) \(\chi_{6037}(127,\cdot)\) \(\chi_{6037}(133,\cdot)\) \(\chi_{6037}(152,\cdot)\) \(\chi_{6037}(153,\cdot)\) \(\chi_{6037}(154,\cdot)\) \(\chi_{6037}(157,\cdot)\) \(\chi_{6037}(163,\cdot)\) \(\chi_{6037}(176,\cdot)\) \(\chi_{6037}(225,\cdot)\) \(\chi_{6037}(226,\cdot)\) \(\chi_{6037}(260,\cdot)\) \(\chi_{6037}(281,\cdot)\) \(\chi_{6037}(283,\cdot)\) \(\chi_{6037}(284,\cdot)\) \(\chi_{6037}(285,\cdot)\) \(\chi_{6037}(290,\cdot)\) \(\chi_{6037}(311,\cdot)\) \(\chi_{6037}(330,\cdot)\) \(\chi_{6037}(346,\cdot)\) \(\chi_{6037}(349,\cdot)\) \(\chi_{6037}(361,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{503})$ |
| Fixed field: | Number field defined by a degree 1006 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{263}{1006}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6037 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{227}{1006}\right)\) | \(e\left(\frac{272}{503}\right)\) | \(e\left(\frac{227}{503}\right)\) | \(e\left(\frac{263}{1006}\right)\) | \(e\left(\frac{771}{1006}\right)\) | \(e\left(\frac{647}{1006}\right)\) | \(e\left(\frac{681}{1006}\right)\) | \(e\left(\frac{41}{503}\right)\) | \(e\left(\frac{245}{503}\right)\) | \(e\left(\frac{198}{503}\right)\) |