Basic properties
Modulus: | \(4001\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1000\) | 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)
|
Galois orbit 4001.v
\(\chi_{4001}(2,\cdot)\) \(\chi_{4001}(7,\cdot)\) \(\chi_{4001}(8,\cdot)\) \(\chi_{4001}(13,\cdot)\) \(\chi_{4001}(19,\cdot)\) \(\chi_{4001}(20,\cdot)\) \(\chi_{4001}(28,\cdot)\) \(\chi_{4001}(50,\cdot)\) \(\chi_{4001}(52,\cdot)\) \(\chi_{4001}(76,\cdot)\) \(\chi_{4001}(80,\cdot)\) \(\chi_{4001}(81,\cdot)\) \(\chi_{4001}(98,\cdot)\) \(\chi_{4001}(102,\cdot)\) \(\chi_{4001}(112,\cdot)\) \(\chi_{4001}(123,\cdot)\) \(\chi_{4001}(128,\cdot)\) \(\chi_{4001}(130,\cdot)\) \(\chi_{4001}(142,\cdot)\) \(\chi_{4001}(157,\cdot)\) \(\chi_{4001}(173,\cdot)\) \(\chi_{4001}(175,\cdot)\) \(\chi_{4001}(182,\cdot)\) \(\chi_{4001}(190,\cdot)\) \(\chi_{4001}(200,\cdot)\) \(\chi_{4001}(208,\cdot)\) \(\chi_{4001}(219,\cdot)\) \(\chi_{4001}(229,\cdot)\) \(\chi_{4001}(245,\cdot)\) \(\chi_{4001}(255,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1000})$ |
Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{981}{1000}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4001 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{250}\right)\) | \(e\left(\frac{981}{1000}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{233}{1000}\right)\) | \(e\left(\frac{167}{250}\right)\) | \(e\left(\frac{189}{250}\right)\) | \(e\left(\frac{481}{500}\right)\) | \(e\left(\frac{104}{125}\right)\) | \(e\left(\frac{37}{40}\right)\) |