Basic properties
Modulus: | \(8011\) | |
Conductor: | \(8011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(445\) | 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.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
\(14\) → \(e\left(\frac{298}{445}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8011 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{94}{445}\right)\) | \(e\left(\frac{121}{445}\right)\) | \(e\left(\frac{188}{445}\right)\) | \(e\left(\frac{109}{445}\right)\) | \(e\left(\frac{43}{89}\right)\) | \(e\left(\frac{204}{445}\right)\) | \(e\left(\frac{282}{445}\right)\) | \(e\left(\frac{242}{445}\right)\) | \(e\left(\frac{203}{445}\right)\) | \(e\left(\frac{1}{445}\right)\) |