Basic properties
Modulus: | \(6009\) | |
Conductor: | \(6009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2002\) | 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)
|
Galois orbit 6009.bd
\(\chi_{6009}(14,\cdot)\) \(\chi_{6009}(35,\cdot)\) \(\chi_{6009}(47,\cdot)\) \(\chi_{6009}(59,\cdot)\) \(\chi_{6009}(62,\cdot)\) \(\chi_{6009}(74,\cdot)\) \(\chi_{6009}(77,\cdot)\) \(\chi_{6009}(86,\cdot)\) \(\chi_{6009}(101,\cdot)\) \(\chi_{6009}(107,\cdot)\) \(\chi_{6009}(119,\cdot)\) \(\chi_{6009}(122,\cdot)\) \(\chi_{6009}(140,\cdot)\) \(\chi_{6009}(161,\cdot)\) \(\chi_{6009}(167,\cdot)\) \(\chi_{6009}(173,\cdot)\) \(\chi_{6009}(179,\cdot)\) \(\chi_{6009}(188,\cdot)\) \(\chi_{6009}(194,\cdot)\) \(\chi_{6009}(197,\cdot)\) \(\chi_{6009}(203,\cdot)\) \(\chi_{6009}(206,\cdot)\) \(\chi_{6009}(212,\cdot)\) \(\chi_{6009}(215,\cdot)\) \(\chi_{6009}(218,\cdot)\) \(\chi_{6009}(224,\cdot)\) \(\chi_{6009}(227,\cdot)\) \(\chi_{6009}(248,\cdot)\) \(\chi_{6009}(251,\cdot)\) \(\chi_{6009}(254,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1001})$ |
Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((-1,e\left(\frac{62}{1001}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6009 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{286}\right)\) | \(e\left(\frac{89}{143}\right)\) | \(e\left(\frac{1125}{2002}\right)\) | \(e\left(\frac{619}{1001}\right)\) | \(e\left(\frac{267}{286}\right)\) | \(e\left(\frac{874}{1001}\right)\) | \(e\left(\frac{153}{286}\right)\) | \(e\left(\frac{536}{1001}\right)\) | \(e\left(\frac{1861}{2002}\right)\) | \(e\left(\frac{35}{143}\right)\) |