Basic properties
| Modulus: | \(8011\) | |
| Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(890\) | 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.s
\(\chi_{8011}(8,\cdot)\) \(\chi_{8011}(11,\cdot)\) \(\chi_{8011}(27,\cdot)\) \(\chi_{8011}(40,\cdot)\) \(\chi_{8011}(47,\cdot)\) \(\chi_{8011}(48,\cdot)\) \(\chi_{8011}(66,\cdot)\) \(\chi_{8011}(135,\cdot)\) \(\chi_{8011}(162,\cdot)\) \(\chi_{8011}(167,\cdot)\) \(\chi_{8011}(182,\cdot)\) \(\chi_{8011}(232,\cdot)\) \(\chi_{8011}(239,\cdot)\) \(\chi_{8011}(240,\cdot)\) \(\chi_{8011}(248,\cdot)\) \(\chi_{8011}(263,\cdot)\) \(\chi_{8011}(266,\cdot)\) \(\chi_{8011}(267,\cdot)\) \(\chi_{8011}(275,\cdot)\) \(\chi_{8011}(282,\cdot)\) \(\chi_{8011}(313,\cdot)\) \(\chi_{8011}(319,\cdot)\) \(\chi_{8011}(341,\cdot)\) \(\chi_{8011}(396,\cdot)\) \(\chi_{8011}(397,\cdot)\) \(\chi_{8011}(482,\cdot)\) \(\chi_{8011}(512,\cdot)\) \(\chi_{8011}(514,\cdot)\) \(\chi_{8011}(586,\cdot)\) \(\chi_{8011}(593,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{445})$ |
| Fixed field: | Number field defined by a degree 890 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{809}{890}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8011 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{297}{890}\right)\) | \(e\left(\frac{103}{890}\right)\) | \(e\left(\frac{297}{445}\right)\) | \(e\left(\frac{416}{445}\right)\) | \(e\left(\frac{40}{89}\right)\) | \(e\left(\frac{256}{445}\right)\) | \(e\left(\frac{1}{890}\right)\) | \(e\left(\frac{103}{445}\right)\) | \(e\left(\frac{239}{890}\right)\) | \(e\left(\frac{273}{890}\right)\) |