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.bt
\(\chi_{8047}(127,\cdot)\) \(\chi_{8047}(212,\cdot)\) \(\chi_{8047}(231,\cdot)\) \(\chi_{8047}(238,\cdot)\) \(\chi_{8047}(244,\cdot)\) \(\chi_{8047}(283,\cdot)\) \(\chi_{8047}(342,\cdot)\) \(\chi_{8047}(400,\cdot)\) \(\chi_{8047}(459,\cdot)\) \(\chi_{8047}(524,\cdot)\) \(\chi_{8047}(569,\cdot)\) \(\chi_{8047}(576,\cdot)\) \(\chi_{8047}(602,\cdot)\) \(\chi_{8047}(628,\cdot)\) \(\chi_{8047}(654,\cdot)\) \(\chi_{8047}(706,\cdot)\) \(\chi_{8047}(751,\cdot)\) \(\chi_{8047}(842,\cdot)\) \(\chi_{8047}(1161,\cdot)\) \(\chi_{8047}(1258,\cdot)\) \(\chi_{8047}(1317,\cdot)\) \(\chi_{8047}(1330,\cdot)\) \(\chi_{8047}(1388,\cdot)\) \(\chi_{8047}(1434,\cdot)\) \(\chi_{8047}(1447,\cdot)\) \(\chi_{8047}(1460,\cdot)\) \(\chi_{8047}(1525,\cdot)\) \(\chi_{8047}(1531,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{309})$ |
| Fixed field: | Number field defined by a degree 618 polynomial (not computed) |
Values on generators
\((3096,4954)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{84}{103}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8047 }(1531, a) \) | \(1\) | \(1\) | \(e\left(\frac{401}{618}\right)\) | \(e\left(\frac{154}{309}\right)\) | \(e\left(\frac{92}{309}\right)\) | \(e\left(\frac{205}{206}\right)\) | \(e\left(\frac{91}{618}\right)\) | \(e\left(\frac{127}{618}\right)\) | \(e\left(\frac{195}{206}\right)\) | \(e\left(\frac{308}{309}\right)\) | \(e\left(\frac{199}{309}\right)\) | \(e\left(\frac{317}{618}\right)\) |