Basic properties
Modulus: | \(8009\) | |
Conductor: | \(8009\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8009.bd
\(\chi_{8009}(4,\cdot)\) \(\chi_{8009}(10,\cdot)\) \(\chi_{8009}(22,\cdot)\) \(\chi_{8009}(28,\cdot)\) \(\chi_{8009}(55,\cdot)\) \(\chi_{8009}(64,\cdot)\) \(\chi_{8009}(72,\cdot)\) \(\chi_{8009}(81,\cdot)\) \(\chi_{8009}(83,\cdot)\) \(\chi_{8009}(91,\cdot)\) \(\chi_{8009}(93,\cdot)\) \(\chi_{8009}(106,\cdot)\) \(\chi_{8009}(121,\cdot)\) \(\chi_{8009}(127,\cdot)\) \(\chi_{8009}(138,\cdot)\) \(\chi_{8009}(142,\cdot)\) \(\chi_{8009}(154,\cdot)\) \(\chi_{8009}(160,\cdot)\) \(\chi_{8009}(175,\cdot)\) \(\chi_{8009}(180,\cdot)\) \(\chi_{8009}(193,\cdot)\) \(\chi_{8009}(196,\cdot)\) \(\chi_{8009}(208,\cdot)\) \(\chi_{8009}(221,\cdot)\) \(\chi_{8009}(234,\cdot)\) \(\chi_{8009}(265,\cdot)\) \(\chi_{8009}(291,\cdot)\) \(\chi_{8009}(298,\cdot)\) \(\chi_{8009}(311,\cdot)\) \(\chi_{8009}(321,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1001})$ |
Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{673}{2002}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8009 }(221, a) \) | \(1\) | \(1\) | \(e\left(\frac{526}{1001}\right)\) | \(e\left(\frac{673}{2002}\right)\) | \(e\left(\frac{51}{1001}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{1725}{2002}\right)\) | \(e\left(\frac{171}{1001}\right)\) | \(e\left(\frac{577}{1001}\right)\) | \(e\left(\frac{673}{1001}\right)\) | \(e\left(\frac{32}{1001}\right)\) | \(e\left(\frac{15}{1001}\right)\) |