Basic properties
| Modulus: | \(28900\) | |
| Conductor: | \(7225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1360\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{7225}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 28900.fl
\(\chi_{28900}(29,\cdot)\) \(\chi_{28900}(109,\cdot)\) \(\chi_{28900}(129,\cdot)\) \(\chi_{28900}(209,\cdot)\) \(\chi_{28900}(269,\cdot)\) \(\chi_{28900}(309,\cdot)\) \(\chi_{28900}(369,\cdot)\) \(\chi_{28900}(469,\cdot)\) \(\chi_{28900}(589,\cdot)\) \(\chi_{28900}(609,\cdot)\) \(\chi_{28900}(669,\cdot)\) \(\chi_{28900}(789,\cdot)\) \(\chi_{28900}(809,\cdot)\) \(\chi_{28900}(889,\cdot)\) \(\chi_{28900}(929,\cdot)\) \(\chi_{28900}(989,\cdot)\) \(\chi_{28900}(1009,\cdot)\) \(\chi_{28900}(1129,\cdot)\) \(\chi_{28900}(1229,\cdot)\) \(\chi_{28900}(1269,\cdot)\) \(\chi_{28900}(1289,\cdot)\) \(\chi_{28900}(1329,\cdot)\) \(\chi_{28900}(1389,\cdot)\) \(\chi_{28900}(1469,\cdot)\) \(\chi_{28900}(1489,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1360})$ |
| Fixed field: | Number field defined by a degree 1360 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{125}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{217}{1360}\right)\) | \(e\left(\frac{199}{272}\right)\) | \(e\left(\frac{217}{680}\right)\) | \(e\left(\frac{231}{1360}\right)\) | \(e\left(\frac{331}{340}\right)\) | \(e\left(\frac{159}{680}\right)\) | \(e\left(\frac{303}{340}\right)\) | \(e\left(\frac{791}{1360}\right)\) | \(e\left(\frac{651}{1360}\right)\) | \(e\left(\frac{877}{1360}\right)\) |