Basic properties
| Modulus: | \(1039\) | |
| Conductor: | \(1039\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1038\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1039.h
\(\chi_{1039}(3,\cdot)\) \(\chi_{1039}(6,\cdot)\) \(\chi_{1039}(11,\cdot)\) \(\chi_{1039}(15,\cdot)\) \(\chi_{1039}(22,\cdot)\) \(\chi_{1039}(24,\cdot)\) \(\chi_{1039}(30,\cdot)\) \(\chi_{1039}(31,\cdot)\) \(\chi_{1039}(42,\cdot)\) \(\chi_{1039}(46,\cdot)\) \(\chi_{1039}(48,\cdot)\) \(\chi_{1039}(51,\cdot)\) \(\chi_{1039}(53,\cdot)\) \(\chi_{1039}(54,\cdot)\) \(\chi_{1039}(55,\cdot)\) \(\chi_{1039}(57,\cdot)\) \(\chi_{1039}(71,\cdot)\) \(\chi_{1039}(73,\cdot)\) \(\chi_{1039}(75,\cdot)\) \(\chi_{1039}(78,\cdot)\) \(\chi_{1039}(82,\cdot)\) \(\chi_{1039}(84,\cdot)\) \(\chi_{1039}(88,\cdot)\) \(\chi_{1039}(89,\cdot)\) \(\chi_{1039}(92,\cdot)\) \(\chi_{1039}(101,\cdot)\) \(\chi_{1039}(103,\cdot)\) \(\chi_{1039}(106,\cdot)\) \(\chi_{1039}(107,\cdot)\) \(\chi_{1039}(108,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{519})$ |
| Fixed field: | Number field defined by a degree 1038 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{751}{1038}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1039 }(1037, a) \) | \(-1\) | \(1\) | \(e\left(\frac{443}{519}\right)\) | \(e\left(\frac{751}{1038}\right)\) | \(e\left(\frac{367}{519}\right)\) | \(e\left(\frac{54}{173}\right)\) | \(e\left(\frac{599}{1038}\right)\) | \(e\left(\frac{163}{519}\right)\) | \(e\left(\frac{97}{173}\right)\) | \(e\left(\frac{232}{519}\right)\) | \(e\left(\frac{86}{519}\right)\) | \(e\left(\frac{535}{1038}\right)\) |