Basic properties
| Modulus: | \(1283\) | |
| Conductor: | \(1283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1282\) | 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 1283.d
\(\chi_{1283}(2,\cdot)\) \(\chi_{1283}(5,\cdot)\) \(\chi_{1283}(6,\cdot)\) \(\chi_{1283}(7,\cdot)\) \(\chi_{1283}(8,\cdot)\) \(\chi_{1283}(15,\cdot)\) \(\chi_{1283}(18,\cdot)\) \(\chi_{1283}(20,\cdot)\) \(\chi_{1283}(21,\cdot)\) \(\chi_{1283}(22,\cdot)\) \(\chi_{1283}(23,\cdot)\) \(\chi_{1283}(24,\cdot)\) \(\chi_{1283}(26,\cdot)\) \(\chi_{1283}(28,\cdot)\) \(\chi_{1283}(32,\cdot)\) \(\chi_{1283}(34,\cdot)\) \(\chi_{1283}(38,\cdot)\) \(\chi_{1283}(41,\cdot)\) \(\chi_{1283}(43,\cdot)\) \(\chi_{1283}(45,\cdot)\) \(\chi_{1283}(47,\cdot)\) \(\chi_{1283}(50,\cdot)\) \(\chi_{1283}(54,\cdot)\) \(\chi_{1283}(55,\cdot)\) \(\chi_{1283}(58,\cdot)\) \(\chi_{1283}(60,\cdot)\) \(\chi_{1283}(61,\cdot)\) \(\chi_{1283}(62,\cdot)\) \(\chi_{1283}(63,\cdot)\) \(\chi_{1283}(65,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{641})$ |
| Fixed field: | Number field defined by a degree 1282 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1282}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1283 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1282}\right)\) | \(e\left(\frac{607}{641}\right)\) | \(e\left(\frac{1}{641}\right)\) | \(e\left(\frac{565}{1282}\right)\) | \(e\left(\frac{1215}{1282}\right)\) | \(e\left(\frac{1027}{1282}\right)\) | \(e\left(\frac{3}{1282}\right)\) | \(e\left(\frac{573}{641}\right)\) | \(e\left(\frac{283}{641}\right)\) | \(e\left(\frac{203}{641}\right)\) |