Basic properties
| Modulus: | \(6047\) | |
| Conductor: | \(6047\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3023\) | 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 6047.c
\(\chi_{6047}(2,\cdot)\) \(\chi_{6047}(3,\cdot)\) \(\chi_{6047}(4,\cdot)\) \(\chi_{6047}(6,\cdot)\) \(\chi_{6047}(7,\cdot)\) \(\chi_{6047}(8,\cdot)\) \(\chi_{6047}(9,\cdot)\) \(\chi_{6047}(11,\cdot)\) \(\chi_{6047}(12,\cdot)\) \(\chi_{6047}(14,\cdot)\) \(\chi_{6047}(16,\cdot)\) \(\chi_{6047}(18,\cdot)\) \(\chi_{6047}(21,\cdot)\) \(\chi_{6047}(22,\cdot)\) \(\chi_{6047}(23,\cdot)\) \(\chi_{6047}(24,\cdot)\) \(\chi_{6047}(25,\cdot)\) \(\chi_{6047}(27,\cdot)\) \(\chi_{6047}(28,\cdot)\) \(\chi_{6047}(32,\cdot)\) \(\chi_{6047}(33,\cdot)\) \(\chi_{6047}(36,\cdot)\) \(\chi_{6047}(37,\cdot)\) \(\chi_{6047}(41,\cdot)\) \(\chi_{6047}(42,\cdot)\) \(\chi_{6047}(43,\cdot)\) \(\chi_{6047}(44,\cdot)\) \(\chi_{6047}(46,\cdot)\) \(\chi_{6047}(47,\cdot)\) \(\chi_{6047}(48,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3023})$ |
| Fixed field: | Number field defined by a degree 3023 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{2821}{3023}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6047 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{609}{3023}\right)\) | \(e\left(\frac{200}{3023}\right)\) | \(e\left(\frac{1218}{3023}\right)\) | \(e\left(\frac{2821}{3023}\right)\) | \(e\left(\frac{809}{3023}\right)\) | \(e\left(\frac{2401}{3023}\right)\) | \(e\left(\frac{1827}{3023}\right)\) | \(e\left(\frac{400}{3023}\right)\) | \(e\left(\frac{407}{3023}\right)\) | \(e\left(\frac{1509}{3023}\right)\) |