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.fk
\(\chi_{28900}(39,\cdot)\) \(\chi_{28900}(79,\cdot)\) \(\chi_{28900}(139,\cdot)\) \(\chi_{28900}(159,\cdot)\) \(\chi_{28900}(279,\cdot)\) \(\chi_{28900}(379,\cdot)\) \(\chi_{28900}(419,\cdot)\) \(\chi_{28900}(439,\cdot)\) \(\chi_{28900}(479,\cdot)\) \(\chi_{28900}(539,\cdot)\) \(\chi_{28900}(619,\cdot)\) \(\chi_{28900}(639,\cdot)\) \(\chi_{28900}(719,\cdot)\) \(\chi_{28900}(759,\cdot)\) \(\chi_{28900}(779,\cdot)\) \(\chi_{28900}(819,\cdot)\) \(\chi_{28900}(839,\cdot)\) \(\chi_{28900}(879,\cdot)\) \(\chi_{28900}(959,\cdot)\) \(\chi_{28900}(979,\cdot)\) \(\chi_{28900}(1059,\cdot)\) \(\chi_{28900}(1119,\cdot)\) \(\chi_{28900}(1159,\cdot)\) \(\chi_{28900}(1179,\cdot)\) \(\chi_{28900}(1219,\cdot)\) \(\chi_{28900}(1319,\cdot)\) \(\chi_{28900}(1439,\cdot)\) \(\chi_{28900}(1459,\cdot)\) \(\chi_{28900}(1519,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1360})$ |
| Fixed field: | Number field defined by a degree 1360 polynomial (not computed) |
Values on generators
\((14451,24277,23701)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{55}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 28900 }(1439, a) \) | \(1\) | \(1\) | \(e\left(\frac{1091}{1360}\right)\) | \(e\left(\frac{93}{272}\right)\) | \(e\left(\frac{411}{680}\right)\) | \(e\left(\frac{1293}{1360}\right)\) | \(e\left(\frac{113}{340}\right)\) | \(e\left(\frac{497}{680}\right)\) | \(e\left(\frac{49}{340}\right)\) | \(e\left(\frac{1213}{1360}\right)\) | \(e\left(\frac{553}{1360}\right)\) | \(e\left(\frac{1191}{1360}\right)\) |