Basic properties
| Modulus: | \(28900\) | |
| Conductor: | \(28900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1360\) | 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 28900.fn
\(\chi_{28900}(23,\cdot)\) \(\chi_{28900}(163,\cdot)\) \(\chi_{28900}(167,\cdot)\) \(\chi_{28900}(267,\cdot)\) \(\chi_{28900}(283,\cdot)\) \(\chi_{28900}(363,\cdot)\) \(\chi_{28900}(483,\cdot)\) \(\chi_{28900}(547,\cdot)\) \(\chi_{28900}(623,\cdot)\) \(\chi_{28900}(703,\cdot)\) \(\chi_{28900}(787,\cdot)\) \(\chi_{28900}(823,\cdot)\) \(\chi_{28900}(847,\cdot)\) \(\chi_{28900}(887,\cdot)\) \(\chi_{28900}(947,\cdot)\) \(\chi_{28900}(963,\cdot)\) \(\chi_{28900}(1127,\cdot)\) \(\chi_{28900}(1163,\cdot)\) \(\chi_{28900}(1183,\cdot)\) \(\chi_{28900}(1187,\cdot)\) \(\chi_{28900}(1227,\cdot)\) \(\chi_{28900}(1303,\cdot)\) \(\chi_{28900}(1383,\cdot)\) \(\chi_{28900}(1467,\cdot)\) \(\chi_{28900}(1503,\cdot)\) \(\chi_{28900}(1523,\cdot)\) \(\chi_{28900}(1527,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1360})$ |
| Fixed field: | Number field defined by a degree 1360 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((-1,e\left(\frac{13}{20}\right),e\left(\frac{41}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(167, a) \) | \(-1\) | \(1\) | \(e\left(\frac{273}{1360}\right)\) | \(e\left(\frac{31}{272}\right)\) | \(e\left(\frac{273}{680}\right)\) | \(e\left(\frac{499}{1360}\right)\) | \(e\left(\frac{76}{85}\right)\) | \(e\left(\frac{211}{680}\right)\) | \(e\left(\frac{107}{340}\right)\) | \(e\left(\frac{359}{1360}\right)\) | \(e\left(\frac{819}{1360}\right)\) | \(e\left(\frac{193}{1360}\right)\) |