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
\(14\) → \(e\left(\frac{1139}{2670}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(108, a) \) | \(-1\) | \(1\) | \(e\left(\frac{289}{890}\right)\) | \(e\left(\frac{301}{890}\right)\) | \(e\left(\frac{289}{445}\right)\) | \(e\left(\frac{222}{445}\right)\) | \(e\left(\frac{59}{89}\right)\) | \(e\left(\frac{136}{1335}\right)\) | \(e\left(\frac{867}{890}\right)\) | \(e\left(\frac{301}{445}\right)\) | \(e\left(\frac{733}{890}\right)\) | \(e\left(\frac{841}{890}\right)\) |