Basic properties
| Modulus: | \(8011\) | |
| Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2670\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8011.v
\(\chi_{8011}(2,\cdot)\) \(\chi_{8011}(3,\cdot)\) \(\chi_{8011}(10,\cdot)\) \(\chi_{8011}(12,\cdot)\) \(\chi_{8011}(18,\cdot)\) \(\chi_{8011}(44,\cdot)\) \(\chi_{8011}(50,\cdot)\) \(\chi_{8011}(60,\cdot)\) \(\chi_{8011}(62,\cdot)\) \(\chi_{8011}(72,\cdot)\) \(\chi_{8011}(75,\cdot)\) \(\chi_{8011}(87,\cdot)\) \(\chi_{8011}(93,\cdot)\) \(\chi_{8011}(99,\cdot)\) \(\chi_{8011}(108,\cdot)\) \(\chi_{8011}(113,\cdot)\) \(\chi_{8011}(128,\cdot)\) \(\chi_{8011}(134,\cdot)\) \(\chi_{8011}(160,\cdot)\) \(\chi_{8011}(173,\cdot)\) \(\chi_{8011}(176,\cdot)\) \(\chi_{8011}(178,\cdot)\) \(\chi_{8011}(179,\cdot)\) \(\chi_{8011}(181,\cdot)\) \(\chi_{8011}(188,\cdot)\) \(\chi_{8011}(213,\cdot)\) \(\chi_{8011}(220,\cdot)\) \(\chi_{8011}(242,\cdot)\) \(\chi_{8011}(250,\cdot)\) \(\chi_{8011}(259,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1335})$ |
| Fixed field: | Number field defined by a degree 2670 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{2309}{2670}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8011 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{639}{890}\right)\) | \(e\left(\frac{761}{890}\right)\) | \(e\left(\frac{194}{445}\right)\) | \(e\left(\frac{32}{445}\right)\) | \(e\left(\frac{51}{89}\right)\) | \(e\left(\frac{196}{1335}\right)\) | \(e\left(\frac{137}{890}\right)\) | \(e\left(\frac{316}{445}\right)\) | \(e\left(\frac{703}{890}\right)\) | \(e\left(\frac{21}{890}\right)\) |