Basic properties
Modulus: | \(8011\) | |
Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1335\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8011.t
\(\chi_{8011}(4,\cdot)\) \(\chi_{8011}(9,\cdot)\) \(\chi_{8011}(16,\cdot)\) \(\chi_{8011}(20,\cdot)\) \(\chi_{8011}(24,\cdot)\) \(\chi_{8011}(33,\cdot)\) \(\chi_{8011}(45,\cdot)\) \(\chi_{8011}(54,\cdot)\) \(\chi_{8011}(67,\cdot)\) \(\chi_{8011}(71,\cdot)\) \(\chi_{8011}(81,\cdot)\) \(\chi_{8011}(91,\cdot)\) \(\chi_{8011}(96,\cdot)\) \(\chi_{8011}(100,\cdot)\) \(\chi_{8011}(110,\cdot)\) \(\chi_{8011}(116,\cdot)\) \(\chi_{8011}(120,\cdot)\) \(\chi_{8011}(133,\cdot)\) \(\chi_{8011}(141,\cdot)\) \(\chi_{8011}(144,\cdot)\) \(\chi_{8011}(165,\cdot)\) \(\chi_{8011}(198,\cdot)\) \(\chi_{8011}(241,\cdot)\) \(\chi_{8011}(256,\cdot)\) \(\chi_{8011}(257,\cdot)\) \(\chi_{8011}(261,\cdot)\) \(\chi_{8011}(270,\cdot)\) \(\chi_{8011}(277,\cdot)\) \(\chi_{8011}(279,\cdot)\) \(\chi_{8011}(284,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1335})$ |
Fixed field: | Number field defined by a degree 1335 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{691}{1335}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{441}{445}\right)\) | \(e\left(\frac{99}{445}\right)\) | \(e\left(\frac{437}{445}\right)\) | \(e\left(\frac{251}{445}\right)\) | \(e\left(\frac{19}{89}\right)\) | \(e\left(\frac{703}{1335}\right)\) | \(e\left(\frac{433}{445}\right)\) | \(e\left(\frac{198}{445}\right)\) | \(e\left(\frac{247}{445}\right)\) | \(e\left(\frac{284}{445}\right)\) |