Basic properties
Modulus: | \(4889\) | |
Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1222\) | 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.n
\(\chi_{4889}(4,\cdot)\) \(\chi_{4889}(5,\cdot)\) \(\chi_{4889}(18,\cdot)\) \(\chi_{4889}(19,\cdot)\) \(\chi_{4889}(26,\cdot)\) \(\chi_{4889}(41,\cdot)\) \(\chi_{4889}(42,\cdot)\) \(\chi_{4889}(47,\cdot)\) \(\chi_{4889}(59,\cdot)\) \(\chi_{4889}(64,\cdot)\) \(\chi_{4889}(80,\cdot)\) \(\chi_{4889}(81,\cdot)\) \(\chi_{4889}(88,\cdot)\) \(\chi_{4889}(98,\cdot)\) \(\chi_{4889}(100,\cdot)\) \(\chi_{4889}(106,\cdot)\) \(\chi_{4889}(115,\cdot)\) \(\chi_{4889}(117,\cdot)\) \(\chi_{4889}(121,\cdot)\) \(\chi_{4889}(125,\cdot)\) \(\chi_{4889}(129,\cdot)\) \(\chi_{4889}(134,\cdot)\) \(\chi_{4889}(169,\cdot)\) \(\chi_{4889}(174,\cdot)\) \(\chi_{4889}(189,\cdot)\) \(\chi_{4889}(218,\cdot)\) \(\chi_{4889}(269,\cdot)\) \(\chi_{4889}(273,\cdot)\) \(\chi_{4889}(288,\cdot)\) \(\chi_{4889}(292,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{611})$ |
Fixed field: | Number field defined by a degree 1222 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{935}{1222}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4889 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{111}{611}\right)\) | \(e\left(\frac{935}{1222}\right)\) | \(e\left(\frac{222}{611}\right)\) | \(e\left(\frac{38}{611}\right)\) | \(e\left(\frac{89}{94}\right)\) | \(e\left(\frac{255}{1222}\right)\) | \(e\left(\frac{333}{611}\right)\) | \(e\left(\frac{324}{611}\right)\) | \(e\left(\frac{149}{611}\right)\) | \(e\left(\frac{553}{611}\right)\) |