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.bs
\(\chi_{8047}(36,\cdot)\) \(\chi_{8047}(101,\cdot)\) \(\chi_{8047}(140,\cdot)\) \(\chi_{8047}(166,\cdot)\) \(\chi_{8047}(173,\cdot)\) \(\chi_{8047}(186,\cdot)\) \(\chi_{8047}(205,\cdot)\) \(\chi_{8047}(270,\cdot)\) \(\chi_{8047}(309,\cdot)\) \(\chi_{8047}(348,\cdot)\) \(\chi_{8047}(355,\cdot)\) \(\chi_{8047}(472,\cdot)\) \(\chi_{8047}(550,\cdot)\) \(\chi_{8047}(680,\cdot)\) \(\chi_{8047}(699,\cdot)\) \(\chi_{8047}(719,\cdot)\) \(\chi_{8047}(966,\cdot)\) \(\chi_{8047}(998,\cdot)\) \(\chi_{8047}(1018,\cdot)\) \(\chi_{8047}(1050,\cdot)\) \(\chi_{8047}(1057,\cdot)\) \(\chi_{8047}(1089,\cdot)\) \(\chi_{8047}(1096,\cdot)\) \(\chi_{8047}(1206,\cdot)\) \(\chi_{8047}(1219,\cdot)\) \(\chi_{8047}(1245,\cdot)\) \(\chi_{8047}(1291,\cdot)\) \(\chi_{8047}(1362,\cdot)\) \(\chi_{8047}(1369,\cdot)\) \(\chi_{8047}(1382,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{309})$ |
| Fixed field: | Number field defined by a degree 618 polynomial (not computed) |
Values on generators
\((3096,4954)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{76}{309}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8047 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{618}\right)\) | \(e\left(\frac{241}{309}\right)\) | \(e\left(\frac{49}{309}\right)\) | \(e\left(\frac{107}{618}\right)\) | \(e\left(\frac{177}{206}\right)\) | \(e\left(\frac{71}{618}\right)\) | \(e\left(\frac{49}{206}\right)\) | \(e\left(\frac{173}{309}\right)\) | \(e\left(\frac{26}{103}\right)\) | \(e\left(\frac{367}{618}\right)\) |