Basic properties
Modulus: | \(8011\) | |
Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(8010\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8011.x
\(\chi_{8011}(14,\cdot)\) \(\chi_{8011}(26,\cdot)\) \(\chi_{8011}(38,\cdot)\) \(\chi_{8011}(43,\cdot)\) \(\chi_{8011}(46,\cdot)\) \(\chi_{8011}(51,\cdot)\) \(\chi_{8011}(53,\cdot)\) \(\chi_{8011}(56,\cdot)\) \(\chi_{8011}(57,\cdot)\) \(\chi_{8011}(59,\cdot)\) \(\chi_{8011}(70,\cdot)\) \(\chi_{8011}(82,\cdot)\) \(\chi_{8011}(84,\cdot)\) \(\chi_{8011}(98,\cdot)\) \(\chi_{8011}(104,\cdot)\) \(\chi_{8011}(105,\cdot)\) \(\chi_{8011}(109,\cdot)\) \(\chi_{8011}(122,\cdot)\) \(\chi_{8011}(123,\cdot)\) \(\chi_{8011}(130,\cdot)\) \(\chi_{8011}(136,\cdot)\) \(\chi_{8011}(147,\cdot)\) \(\chi_{8011}(148,\cdot)\) \(\chi_{8011}(151,\cdot)\) \(\chi_{8011}(152,\cdot)\) \(\chi_{8011}(156,\cdot)\) \(\chi_{8011}(170,\cdot)\) \(\chi_{8011}(183,\cdot)\) \(\chi_{8011}(184,\cdot)\) \(\chi_{8011}(185,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4005})$ |
Fixed field: | Number field defined by a degree 8010 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{1}{8010}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{691}{2670}\right)\) | \(e\left(\frac{809}{2670}\right)\) | \(e\left(\frac{691}{1335}\right)\) | \(e\left(\frac{431}{445}\right)\) | \(e\left(\frac{50}{89}\right)\) | \(e\left(\frac{2969}{4005}\right)\) | \(e\left(\frac{691}{890}\right)\) | \(e\left(\frac{809}{1335}\right)\) | \(e\left(\frac{607}{2670}\right)\) | \(e\left(\frac{853}{890}\right)\) |