Basic properties
Modulus: | \(8047\) | |
Conductor: | \(8047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(618\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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
\((3096,4954)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{116}{309}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8047 }(361, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{206}\right)\) | \(e\left(\frac{151}{309}\right)\) | \(e\left(\frac{43}{103}\right)\) | \(e\left(\frac{391}{618}\right)\) | \(e\left(\frac{431}{618}\right)\) | \(e\left(\frac{159}{206}\right)\) | \(e\left(\frac{129}{206}\right)\) | \(e\left(\frac{302}{309}\right)\) | \(e\left(\frac{260}{309}\right)\) | \(e\left(\frac{53}{206}\right)\) |