Basic properties
Modulus: | \(4889\) | |
Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2444\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4889.o
\(\chi_{4889}(2,\cdot)\) \(\chi_{4889}(8,\cdot)\) \(\chi_{4889}(9,\cdot)\) \(\chi_{4889}(10,\cdot)\) \(\chi_{4889}(11,\cdot)\) \(\chi_{4889}(13,\cdot)\) \(\chi_{4889}(21,\cdot)\) \(\chi_{4889}(32,\cdot)\) \(\chi_{4889}(38,\cdot)\) \(\chi_{4889}(40,\cdot)\) \(\chi_{4889}(44,\cdot)\) \(\chi_{4889}(45,\cdot)\) \(\chi_{4889}(46,\cdot)\) \(\chi_{4889}(49,\cdot)\) \(\chi_{4889}(50,\cdot)\) \(\chi_{4889}(51,\cdot)\) \(\chi_{4889}(52,\cdot)\) \(\chi_{4889}(53,\cdot)\) \(\chi_{4889}(55,\cdot)\) \(\chi_{4889}(61,\cdot)\) \(\chi_{4889}(65,\cdot)\) \(\chi_{4889}(83,\cdot)\) \(\chi_{4889}(84,\cdot)\) \(\chi_{4889}(87,\cdot)\) \(\chi_{4889}(94,\cdot)\) \(\chi_{4889}(105,\cdot)\) \(\chi_{4889}(109,\cdot)\) \(\chi_{4889}(111,\cdot)\) \(\chi_{4889}(118,\cdot)\) \(\chi_{4889}(128,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2444})$ |
Fixed field: | Number field defined by a degree 2444 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{445}{2444}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4889 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{837}{1222}\right)\) | \(e\left(\frac{445}{2444}\right)\) | \(e\left(\frac{226}{611}\right)\) | \(e\left(\frac{424}{611}\right)\) | \(e\left(\frac{163}{188}\right)\) | \(e\left(\frac{2121}{2444}\right)\) | \(e\left(\frac{67}{1222}\right)\) | \(e\left(\frac{445}{1222}\right)\) | \(e\left(\frac{463}{1222}\right)\) | \(e\left(\frac{603}{1222}\right)\) |