Basic properties
| Modulus: | \(8011\) | |
| Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(445\) | 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 8011.p
\(\chi_{8011}(5,\cdot)\) \(\chi_{8011}(25,\cdot)\) \(\chi_{8011}(29,\cdot)\) \(\chi_{8011}(30,\cdot)\) \(\chi_{8011}(31,\cdot)\) \(\chi_{8011}(64,\cdot)\) \(\chi_{8011}(88,\cdot)\) \(\chi_{8011}(121,\cdot)\) \(\chi_{8011}(125,\cdot)\) \(\chi_{8011}(150,\cdot)\) \(\chi_{8011}(155,\cdot)\) \(\chi_{8011}(174,\cdot)\) \(\chi_{8011}(180,\cdot)\) \(\chi_{8011}(186,\cdot)\) \(\chi_{8011}(226,\cdot)\) \(\chi_{8011}(268,\cdot)\) \(\chi_{8011}(297,\cdot)\) \(\chi_{8011}(320,\cdot)\) \(\chi_{8011}(323,\cdot)\) \(\chi_{8011}(356,\cdot)\) \(\chi_{8011}(376,\cdot)\) \(\chi_{8011}(384,\cdot)\) \(\chi_{8011}(440,\cdot)\) \(\chi_{8011}(517,\cdot)\) \(\chi_{8011}(518,\cdot)\) \(\chi_{8011}(528,\cdot)\) \(\chi_{8011}(537,\cdot)\) \(\chi_{8011}(543,\cdot)\) \(\chi_{8011}(571,\cdot)\) \(\chi_{8011}(605,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{445})$ |
| Fixed field: | Number field defined by a degree 445 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{324}{445}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8011 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{147}{445}\right)\) | \(e\left(\frac{33}{445}\right)\) | \(e\left(\frac{294}{445}\right)\) | \(e\left(\frac{232}{445}\right)\) | \(e\left(\frac{36}{89}\right)\) | \(e\left(\frac{177}{445}\right)\) | \(e\left(\frac{441}{445}\right)\) | \(e\left(\frac{66}{445}\right)\) | \(e\left(\frac{379}{445}\right)\) | \(e\left(\frac{243}{445}\right)\) |