Basic properties
Modulus: | \(8011\) | |
Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(4005\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8011.w
\(\chi_{8011}(7,\cdot)\) \(\chi_{8011}(13,\cdot)\) \(\chi_{8011}(17,\cdot)\) \(\chi_{8011}(23,\cdot)\) \(\chi_{8011}(28,\cdot)\) \(\chi_{8011}(35,\cdot)\) \(\chi_{8011}(41,\cdot)\) \(\chi_{8011}(42,\cdot)\) \(\chi_{8011}(49,\cdot)\) \(\chi_{8011}(61,\cdot)\) \(\chi_{8011}(63,\cdot)\) \(\chi_{8011}(65,\cdot)\) \(\chi_{8011}(68,\cdot)\) \(\chi_{8011}(73,\cdot)\) \(\chi_{8011}(74,\cdot)\) \(\chi_{8011}(76,\cdot)\) \(\chi_{8011}(78,\cdot)\) \(\chi_{8011}(83,\cdot)\) \(\chi_{8011}(86,\cdot)\) \(\chi_{8011}(92,\cdot)\) \(\chi_{8011}(95,\cdot)\) \(\chi_{8011}(102,\cdot)\) \(\chi_{8011}(106,\cdot)\) \(\chi_{8011}(107,\cdot)\) \(\chi_{8011}(111,\cdot)\) \(\chi_{8011}(115,\cdot)\) \(\chi_{8011}(117,\cdot)\) \(\chi_{8011}(127,\cdot)\) \(\chi_{8011}(129,\cdot)\) \(\chi_{8011}(137,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4005})$ |
Fixed field: | Number field defined by a degree 4005 polynomial (not computed) |
Values on generators
\(14\) → \(e\left(\frac{2969}{4005}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{1019}{1335}\right)\) | \(e\left(\frac{256}{1335}\right)\) | \(e\left(\frac{703}{1335}\right)\) | \(e\left(\frac{83}{445}\right)\) | \(e\left(\frac{85}{89}\right)\) | \(e\left(\frac{3917}{4005}\right)\) | \(e\left(\frac{129}{445}\right)\) | \(e\left(\frac{512}{1335}\right)\) | \(e\left(\frac{1268}{1335}\right)\) | \(e\left(\frac{62}{445}\right)\) |