Basic properties
| Modulus: | \(8047\) | |
| Conductor: | \(8047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(618\) | 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 8047.bz
\(\chi_{8047}(4,\cdot)\) \(\chi_{8047}(23,\cdot)\) \(\chi_{8047}(30,\cdot)\) \(\chi_{8047}(49,\cdot)\) \(\chi_{8047}(88,\cdot)\) \(\chi_{8047}(121,\cdot)\) \(\chi_{8047}(134,\cdot)\) \(\chi_{8047}(199,\cdot)\) \(\chi_{8047}(225,\cdot)\) \(\chi_{8047}(290,\cdot)\) \(\chi_{8047}(316,\cdot)\) \(\chi_{8047}(361,\cdot)\) \(\chi_{8047}(368,\cdot)\) \(\chi_{8047}(426,\cdot)\) \(\chi_{8047}(491,\cdot)\) \(\chi_{8047}(511,\cdot)\) \(\chi_{8047}(517,\cdot)\) \(\chi_{8047}(537,\cdot)\) \(\chi_{8047}(543,\cdot)\) \(\chi_{8047}(563,\cdot)\) \(\chi_{8047}(608,\cdot)\) \(\chi_{8047}(641,\cdot)\) \(\chi_{8047}(647,\cdot)\) \(\chi_{8047}(660,\cdot)\) \(\chi_{8047}(673,\cdot)\) \(\chi_{8047}(771,\cdot)\) \(\chi_{8047}(784,\cdot)\) \(\chi_{8047}(816,\cdot)\) \(\chi_{8047}(823,\cdot)\) \(\chi_{8047}(829,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{309})$ |
| Fixed field: | Number field defined by a degree 618 polynomial (not computed) |
Values on generators
\((3096,4954)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{309}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8047 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{206}\right)\) | \(e\left(\frac{281}{309}\right)\) | \(e\left(\frac{35}{103}\right)\) | \(e\left(\frac{347}{618}\right)\) | \(e\left(\frac{49}{618}\right)\) | \(e\left(\frac{139}{206}\right)\) | \(e\left(\frac{105}{206}\right)\) | \(e\left(\frac{253}{309}\right)\) | \(e\left(\frac{226}{309}\right)\) | \(e\left(\frac{115}{206}\right)\) |