Basic properties
| Modulus: | \(4889\) | |
| Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(611\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.m
\(\chi_{4889}(16,\cdot)\) \(\chi_{4889}(22,\cdot)\) \(\chi_{4889}(23,\cdot)\) \(\chi_{4889}(25,\cdot)\) \(\chi_{4889}(72,\cdot)\) \(\chi_{4889}(73,\cdot)\) \(\chi_{4889}(76,\cdot)\) \(\chi_{4889}(90,\cdot)\) \(\chi_{4889}(93,\cdot)\) \(\chi_{4889}(95,\cdot)\) \(\chi_{4889}(99,\cdot)\) \(\chi_{4889}(102,\cdot)\) \(\chi_{4889}(104,\cdot)\) \(\chi_{4889}(113,\cdot)\) \(\chi_{4889}(130,\cdot)\) \(\chi_{4889}(143,\cdot)\) \(\chi_{4889}(164,\cdot)\) \(\chi_{4889}(168,\cdot)\) \(\chi_{4889}(179,\cdot)\) \(\chi_{4889}(188,\cdot)\) \(\chi_{4889}(193,\cdot)\) \(\chi_{4889}(205,\cdot)\) \(\chi_{4889}(210,\cdot)\) \(\chi_{4889}(222,\cdot)\) \(\chi_{4889}(231,\cdot)\) \(\chi_{4889}(235,\cdot)\) \(\chi_{4889}(236,\cdot)\) \(\chi_{4889}(238,\cdot)\) \(\chi_{4889}(256,\cdot)\) \(\chi_{4889}(278,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{611})$ |
| Fixed field: | Number field defined by a degree 611 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{42}{611}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4889 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{504}{611}\right)\) | \(e\left(\frac{42}{611}\right)\) | \(e\left(\frac{397}{611}\right)\) | \(e\left(\frac{123}{611}\right)\) | \(e\left(\frac{42}{47}\right)\) | \(e\left(\frac{67}{611}\right)\) | \(e\left(\frac{290}{611}\right)\) | \(e\left(\frac{84}{611}\right)\) | \(e\left(\frac{16}{611}\right)\) | \(e\left(\frac{166}{611}\right)\) |