Basic properties
| Modulus: | \(3089\) | |
| Conductor: | \(3089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1544\) | 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 3089.i
\(\chi_{3089}(5,\cdot)\) \(\chi_{3089}(7,\cdot)\) \(\chi_{3089}(9,\cdot)\) \(\chi_{3089}(10,\cdot)\) \(\chi_{3089}(11,\cdot)\) \(\chi_{3089}(14,\cdot)\) \(\chi_{3089}(18,\cdot)\) \(\chi_{3089}(19,\cdot)\) \(\chi_{3089}(20,\cdot)\) \(\chi_{3089}(22,\cdot)\) \(\chi_{3089}(28,\cdot)\) \(\chi_{3089}(31,\cdot)\) \(\chi_{3089}(36,\cdot)\) \(\chi_{3089}(38,\cdot)\) \(\chi_{3089}(40,\cdot)\) \(\chi_{3089}(44,\cdot)\) \(\chi_{3089}(51,\cdot)\) \(\chi_{3089}(53,\cdot)\) \(\chi_{3089}(56,\cdot)\) \(\chi_{3089}(62,\cdot)\) \(\chi_{3089}(71,\cdot)\) \(\chi_{3089}(72,\cdot)\) \(\chi_{3089}(76,\cdot)\) \(\chi_{3089}(80,\cdot)\) \(\chi_{3089}(87,\cdot)\) \(\chi_{3089}(88,\cdot)\) \(\chi_{3089}(102,\cdot)\) \(\chi_{3089}(106,\cdot)\) \(\chi_{3089}(112,\cdot)\) \(\chi_{3089}(123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1544})$ |
| Fixed field: | Number field defined by a degree 1544 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{105}{1544}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3089 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{265}{386}\right)\) | \(e\left(\frac{105}{1544}\right)\) | \(e\left(\frac{72}{193}\right)\) | \(e\left(\frac{233}{772}\right)\) | \(e\left(\frac{1165}{1544}\right)\) | \(e\left(\frac{399}{772}\right)\) | \(e\left(\frac{23}{386}\right)\) | \(e\left(\frac{105}{772}\right)\) | \(e\left(\frac{763}{772}\right)\) | \(e\left(\frac{199}{772}\right)\) |