Basic properties
| Modulus: | \(4889\) | |
| Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4888\) | 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 4889.p
\(\chi_{4889}(3,\cdot)\) \(\chi_{4889}(7,\cdot)\) \(\chi_{4889}(12,\cdot)\) \(\chi_{4889}(14,\cdot)\) \(\chi_{4889}(15,\cdot)\) \(\chi_{4889}(17,\cdot)\) \(\chi_{4889}(24,\cdot)\) \(\chi_{4889}(27,\cdot)\) \(\chi_{4889}(28,\cdot)\) \(\chi_{4889}(29,\cdot)\) \(\chi_{4889}(30,\cdot)\) \(\chi_{4889}(31,\cdot)\) \(\chi_{4889}(34,\cdot)\) \(\chi_{4889}(35,\cdot)\) \(\chi_{4889}(37,\cdot)\) \(\chi_{4889}(39,\cdot)\) \(\chi_{4889}(43,\cdot)\) \(\chi_{4889}(48,\cdot)\) \(\chi_{4889}(54,\cdot)\) \(\chi_{4889}(56,\cdot)\) \(\chi_{4889}(58,\cdot)\) \(\chi_{4889}(60,\cdot)\) \(\chi_{4889}(63,\cdot)\) \(\chi_{4889}(66,\cdot)\) \(\chi_{4889}(68,\cdot)\) \(\chi_{4889}(69,\cdot)\) \(\chi_{4889}(70,\cdot)\) \(\chi_{4889}(71,\cdot)\) \(\chi_{4889}(74,\cdot)\) \(\chi_{4889}(75,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4888})$ |
| Fixed field: | Number field defined by a degree 4888 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{2469}{4888}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4889 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{761}{2444}\right)\) | \(e\left(\frac{2469}{4888}\right)\) | \(e\left(\frac{761}{1222}\right)\) | \(e\left(\frac{1033}{1222}\right)\) | \(e\left(\frac{307}{376}\right)\) | \(e\left(\frac{229}{4888}\right)\) | \(e\left(\frac{2283}{2444}\right)\) | \(e\left(\frac{25}{2444}\right)\) | \(e\left(\frac{383}{2444}\right)\) | \(e\left(\frac{995}{2444}\right)\) |