Basic properties
| Modulus: | \(6011\) | |
| Conductor: | \(6011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(601\) | 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 6011.e
\(\chi_{6011}(3,\cdot)\) \(\chi_{6011}(9,\cdot)\) \(\chi_{6011}(20,\cdot)\) \(\chi_{6011}(27,\cdot)\) \(\chi_{6011}(46,\cdot)\) \(\chi_{6011}(58,\cdot)\) \(\chi_{6011}(60,\cdot)\) \(\chi_{6011}(81,\cdot)\) \(\chi_{6011}(112,\cdot)\) \(\chi_{6011}(136,\cdot)\) \(\chi_{6011}(138,\cdot)\) \(\chi_{6011}(154,\cdot)\) \(\chi_{6011}(174,\cdot)\) \(\chi_{6011}(180,\cdot)\) \(\chi_{6011}(182,\cdot)\) \(\chi_{6011}(187,\cdot)\) \(\chi_{6011}(205,\cdot)\) \(\chi_{6011}(221,\cdot)\) \(\chi_{6011}(236,\cdot)\) \(\chi_{6011}(243,\cdot)\) \(\chi_{6011}(245,\cdot)\) \(\chi_{6011}(248,\cdot)\) \(\chi_{6011}(251,\cdot)\) \(\chi_{6011}(278,\cdot)\) \(\chi_{6011}(284,\cdot)\) \(\chi_{6011}(292,\cdot)\) \(\chi_{6011}(301,\cdot)\) \(\chi_{6011}(326,\cdot)\) \(\chi_{6011}(336,\cdot)\) \(\chi_{6011}(337,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{601})$ |
| Fixed field: | Number field defined by a degree 601 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{139}{601}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6011 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{601}\right)\) | \(e\left(\frac{497}{601}\right)\) | \(e\left(\frac{278}{601}\right)\) | \(e\left(\frac{76}{601}\right)\) | \(e\left(\frac{35}{601}\right)\) | \(e\left(\frac{10}{601}\right)\) | \(e\left(\frac{417}{601}\right)\) | \(e\left(\frac{393}{601}\right)\) | \(e\left(\frac{215}{601}\right)\) | \(e\left(\frac{79}{601}\right)\) |