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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 28900.fj
\(\chi_{28900}(11,\cdot)\) \(\chi_{28900}(31,\cdot)\) \(\chi_{28900}(71,\cdot)\) \(\chi_{28900}(91,\cdot)\) \(\chi_{28900}(211,\cdot)\) \(\chi_{28900}(231,\cdot)\) \(\chi_{28900}(311,\cdot)\) \(\chi_{28900}(371,\cdot)\) \(\chi_{28900}(411,\cdot)\) \(\chi_{28900}(431,\cdot)\) \(\chi_{28900}(471,\cdot)\) \(\chi_{28900}(571,\cdot)\) \(\chi_{28900}(691,\cdot)\) \(\chi_{28900}(711,\cdot)\) \(\chi_{28900}(771,\cdot)\) \(\chi_{28900}(811,\cdot)\) \(\chi_{28900}(891,\cdot)\) \(\chi_{28900}(911,\cdot)\) \(\chi_{28900}(991,\cdot)\) \(\chi_{28900}(1031,\cdot)\) \(\chi_{28900}(1111,\cdot)\) \(\chi_{28900}(1331,\cdot)\) \(\chi_{28900}(1371,\cdot)\) \(\chi_{28900}(1391,\cdot)\) \(\chi_{28900}(1431,\cdot)\) \(\chi_{28900}(1491,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1360})$ |
| Fixed field: | Number field defined by a degree 1360 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{23}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{251}{1360}\right)\) | \(e\left(\frac{165}{272}\right)\) | \(e\left(\frac{251}{680}\right)\) | \(e\left(\frac{333}{1360}\right)\) | \(e\left(\frac{263}{340}\right)\) | \(e\left(\frac{57}{680}\right)\) | \(e\left(\frac{269}{340}\right)\) | \(e\left(\frac{213}{1360}\right)\) | \(e\left(\frac{753}{1360}\right)\) | \(e\left(\frac{231}{1360}\right)\) |