Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8619.eg
\(\chi_{8619}(98,\cdot)\) \(\chi_{8619}(344,\cdot)\) \(\chi_{8619}(548,\cdot)\) \(\chi_{8619}(557,\cdot)\) \(\chi_{8619}(761,\cdot)\) \(\chi_{8619}(1007,\cdot)\) \(\chi_{8619}(1211,\cdot)\) \(\chi_{8619}(1220,\cdot)\) \(\chi_{8619}(1424,\cdot)\) \(\chi_{8619}(1670,\cdot)\) \(\chi_{8619}(1874,\cdot)\) \(\chi_{8619}(1883,\cdot)\) \(\chi_{8619}(2087,\cdot)\) \(\chi_{8619}(2333,\cdot)\) \(\chi_{8619}(2537,\cdot)\) \(\chi_{8619}(2546,\cdot)\) \(\chi_{8619}(2750,\cdot)\) \(\chi_{8619}(2996,\cdot)\) \(\chi_{8619}(3200,\cdot)\) \(\chi_{8619}(3209,\cdot)\) \(\chi_{8619}(3413,\cdot)\) \(\chi_{8619}(3659,\cdot)\) \(\chi_{8619}(3863,\cdot)\) \(\chi_{8619}(3872,\cdot)\) \(\chi_{8619}(4076,\cdot)\) \(\chi_{8619}(4322,\cdot)\) \(\chi_{8619}(4526,\cdot)\) \(\chi_{8619}(4535,\cdot)\) \(\chi_{8619}(4739,\cdot)\) \(\chi_{8619}(4985,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{59}{156}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(98, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) |