Basic properties
Modulus: | \(10009\) | |
Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(5004\) | 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 10009.w
\(\chi_{10009}(3,\cdot)\) \(\chi_{10009}(10,\cdot)\) \(\chi_{10009}(12,\cdot)\) \(\chi_{10009}(17,\cdot)\) \(\chi_{10009}(18,\cdot)\) \(\chi_{10009}(23,\cdot)\) \(\chi_{10009}(40,\cdot)\) \(\chi_{10009}(48,\cdot)\) \(\chi_{10009}(50,\cdot)\) \(\chi_{10009}(58,\cdot)\) \(\chi_{10009}(61,\cdot)\) \(\chi_{10009}(65,\cdot)\) \(\chi_{10009}(67,\cdot)\) \(\chi_{10009}(68,\cdot)\) \(\chi_{10009}(72,\cdot)\) \(\chi_{10009}(75,\cdot)\) \(\chi_{10009}(78,\cdot)\) \(\chi_{10009}(85,\cdot)\) \(\chi_{10009}(87,\cdot)\) \(\chi_{10009}(90,\cdot)\) \(\chi_{10009}(92,\cdot)\) \(\chi_{10009}(103,\cdot)\) \(\chi_{10009}(115,\cdot)\) \(\chi_{10009}(117,\cdot)\) \(\chi_{10009}(121,\cdot)\) \(\chi_{10009}(135,\cdot)\) \(\chi_{10009}(137,\cdot)\) \(\chi_{10009}(139,\cdot)\) \(\chi_{10009}(146,\cdot)\) \(\chi_{10009}(149,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{5004})$ |
Fixed field: | Number field defined by a degree 5004 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{3985}{5004}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 10009 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{797}{834}\right)\) | \(e\left(\frac{1985}{2502}\right)\) | \(e\left(\frac{380}{417}\right)\) | \(e\left(\frac{239}{1251}\right)\) | \(e\left(\frac{937}{1251}\right)\) | \(e\left(\frac{63}{556}\right)\) | \(e\left(\frac{241}{278}\right)\) | \(e\left(\frac{734}{1251}\right)\) | \(e\left(\frac{367}{2502}\right)\) | \(e\left(\frac{3985}{5004}\right)\) |