Basic properties
Modulus: | \(4889\) | |
Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4888\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4889.p
\(\chi_{4889}(3,\cdot)\) \(\chi_{4889}(7,\cdot)\) \(\chi_{4889}(12,\cdot)\) \(\chi_{4889}(14,\cdot)\) \(\chi_{4889}(15,\cdot)\) \(\chi_{4889}(17,\cdot)\) \(\chi_{4889}(24,\cdot)\) \(\chi_{4889}(27,\cdot)\) \(\chi_{4889}(28,\cdot)\) \(\chi_{4889}(29,\cdot)\) \(\chi_{4889}(30,\cdot)\) \(\chi_{4889}(31,\cdot)\) \(\chi_{4889}(34,\cdot)\) \(\chi_{4889}(35,\cdot)\) \(\chi_{4889}(37,\cdot)\) \(\chi_{4889}(39,\cdot)\) \(\chi_{4889}(43,\cdot)\) \(\chi_{4889}(48,\cdot)\) \(\chi_{4889}(54,\cdot)\) \(\chi_{4889}(56,\cdot)\) \(\chi_{4889}(58,\cdot)\) \(\chi_{4889}(60,\cdot)\) \(\chi_{4889}(63,\cdot)\) \(\chi_{4889}(66,\cdot)\) \(\chi_{4889}(68,\cdot)\) \(\chi_{4889}(69,\cdot)\) \(\chi_{4889}(70,\cdot)\) \(\chi_{4889}(71,\cdot)\) \(\chi_{4889}(74,\cdot)\) \(\chi_{4889}(75,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4888})$ |
Fixed field: | Number field defined by a degree 4888 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{2345}{4888}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4889 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{2444}\right)\) | \(e\left(\frac{2345}{4888}\right)\) | \(e\left(\frac{17}{1222}\right)\) | \(e\left(\frac{113}{1222}\right)\) | \(e\left(\frac{183}{376}\right)\) | \(e\left(\frac{2417}{4888}\right)\) | \(e\left(\frac{51}{2444}\right)\) | \(e\left(\frac{2345}{2444}\right)\) | \(e\left(\frac{243}{2444}\right)\) | \(e\left(\frac{459}{2444}\right)\) |