Basic properties
| Modulus: | \(8047\) | |
| Conductor: | \(8047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1236\) | 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.cb
\(\chi_{8047}(59,\cdot)\) \(\chi_{8047}(84,\cdot)\) \(\chi_{8047}(85,\cdot)\) \(\chi_{8047}(97,\cdot)\) \(\chi_{8047}(106,\cdot)\) \(\chi_{8047}(119,\cdot)\) \(\chi_{8047}(123,\cdot)\) \(\chi_{8047}(137,\cdot)\) \(\chi_{8047}(162,\cdot)\) \(\chi_{8047}(171,\cdot)\) \(\chi_{8047}(214,\cdot)\) \(\chi_{8047}(215,\cdot)\) \(\chi_{8047}(254,\cdot)\) \(\chi_{8047}(262,\cdot)\) \(\chi_{8047}(271,\cdot)\) \(\chi_{8047}(288,\cdot)\) \(\chi_{8047}(301,\cdot)\) \(\chi_{8047}(310,\cdot)\) \(\chi_{8047}(314,\cdot)\) \(\chi_{8047}(327,\cdot)\) \(\chi_{8047}(349,\cdot)\) \(\chi_{8047}(353,\cdot)\) \(\chi_{8047}(370,\cdot)\) \(\chi_{8047}(409,\cdot)\) \(\chi_{8047}(414,\cdot)\) \(\chi_{8047}(422,\cdot)\) \(\chi_{8047}(453,\cdot)\) \(\chi_{8047}(462,\cdot)\) \(\chi_{8047}(475,\cdot)\) \(\chi_{8047}(479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1236})$ |
| Fixed field: | Number field defined by a degree 1236 polynomial (not computed) |
Values on generators
\((3096,4954)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{283}{618}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8047 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{463}{1236}\right)\) | \(e\left(\frac{7}{618}\right)\) | \(e\left(\frac{463}{618}\right)\) | \(e\left(\frac{557}{1236}\right)\) | \(e\left(\frac{159}{412}\right)\) | \(e\left(\frac{179}{1236}\right)\) | \(e\left(\frac{51}{412}\right)\) | \(e\left(\frac{7}{309}\right)\) | \(e\left(\frac{85}{103}\right)\) | \(e\left(\frac{1021}{1236}\right)\) |