Basic properties
| Modulus: | \(3089\) | |
| Conductor: | \(3089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3088\) | 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 3089.j
\(\chi_{3089}(3,\cdot)\) \(\chi_{3089}(6,\cdot)\) \(\chi_{3089}(12,\cdot)\) \(\chi_{3089}(13,\cdot)\) \(\chi_{3089}(15,\cdot)\) \(\chi_{3089}(17,\cdot)\) \(\chi_{3089}(21,\cdot)\) \(\chi_{3089}(23,\cdot)\) \(\chi_{3089}(24,\cdot)\) \(\chi_{3089}(26,\cdot)\) \(\chi_{3089}(27,\cdot)\) \(\chi_{3089}(29,\cdot)\) \(\chi_{3089}(30,\cdot)\) \(\chi_{3089}(33,\cdot)\) \(\chi_{3089}(34,\cdot)\) \(\chi_{3089}(37,\cdot)\) \(\chi_{3089}(41,\cdot)\) \(\chi_{3089}(42,\cdot)\) \(\chi_{3089}(46,\cdot)\) \(\chi_{3089}(48,\cdot)\) \(\chi_{3089}(52,\cdot)\) \(\chi_{3089}(54,\cdot)\) \(\chi_{3089}(57,\cdot)\) \(\chi_{3089}(58,\cdot)\) \(\chi_{3089}(60,\cdot)\) \(\chi_{3089}(65,\cdot)\) \(\chi_{3089}(66,\cdot)\) \(\chi_{3089}(67,\cdot)\) \(\chi_{3089}(68,\cdot)\) \(\chi_{3089}(74,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3088})$ |
| Fixed field: | Number field defined by a degree 3088 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1261}{3088}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3089 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{407}{772}\right)\) | \(e\left(\frac{1261}{3088}\right)\) | \(e\left(\frac{21}{386}\right)\) | \(e\left(\frac{269}{1544}\right)\) | \(e\left(\frac{2889}{3088}\right)\) | \(e\left(\frac{623}{1544}\right)\) | \(e\left(\frac{449}{772}\right)\) | \(e\left(\frac{1261}{1544}\right)\) | \(e\left(\frac{1083}{1544}\right)\) | \(e\left(\frac{243}{1544}\right)\) |