Basic properties
| Modulus: | \(6043\) | |
| Conductor: | \(6043\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(6042\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 6043.p
\(\chi_{6043}(5,\cdot)\) \(\chi_{6043}(7,\cdot)\) \(\chi_{6043}(12,\cdot)\) \(\chi_{6043}(13,\cdot)\) \(\chi_{6043}(18,\cdot)\) \(\chi_{6043}(19,\cdot)\) \(\chi_{6043}(28,\cdot)\) \(\chi_{6043}(29,\cdot)\) \(\chi_{6043}(30,\cdot)\) \(\chi_{6043}(43,\cdot)\) \(\chi_{6043}(45,\cdot)\) \(\chi_{6043}(46,\cdot)\) \(\chi_{6043}(47,\cdot)\) \(\chi_{6043}(48,\cdot)\) \(\chi_{6043}(51,\cdot)\) \(\chi_{6043}(52,\cdot)\) \(\chi_{6043}(59,\cdot)\) \(\chi_{6043}(62,\cdot)\) \(\chi_{6043}(63,\cdot)\) \(\chi_{6043}(66,\cdot)\) \(\chi_{6043}(70,\cdot)\) \(\chi_{6043}(74,\cdot)\) \(\chi_{6043}(75,\cdot)\) \(\chi_{6043}(76,\cdot)\) \(\chi_{6043}(80,\cdot)\) \(\chi_{6043}(82,\cdot)\) \(\chi_{6043}(93,\cdot)\) \(\chi_{6043}(97,\cdot)\) \(\chi_{6043}(98,\cdot)\) \(\chi_{6043}(99,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3021})$ |
| Fixed field: | Number field defined by a degree 6042 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1621}{6042}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6043 }(52, a) \) | \(-1\) | \(1\) | \(e\left(\frac{277}{318}\right)\) | \(e\left(\frac{1941}{2014}\right)\) | \(e\left(\frac{118}{159}\right)\) | \(e\left(\frac{1621}{6042}\right)\) | \(e\left(\frac{2522}{3021}\right)\) | \(e\left(\frac{131}{6042}\right)\) | \(e\left(\frac{65}{106}\right)\) | \(e\left(\frac{934}{1007}\right)\) | \(e\left(\frac{421}{3021}\right)\) | \(e\left(\frac{35}{114}\right)\) |