Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 6047 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 3023 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 6047.c |
| Orbit index | = | 3 |
Galois orbit
\(\chi_{6047}(2,\cdot)\) \(\chi_{6047}(3,\cdot)\) \(\chi_{6047}(4,\cdot)\) \(\chi_{6047}(6,\cdot)\) \(\chi_{6047}(7,\cdot)\) \(\chi_{6047}(8,\cdot)\) \(\chi_{6047}(9,\cdot)\) \(\chi_{6047}(11,\cdot)\) \(\chi_{6047}(12,\cdot)\) \(\chi_{6047}(14,\cdot)\) \(\chi_{6047}(16,\cdot)\) \(\chi_{6047}(18,\cdot)\) \(\chi_{6047}(21,\cdot)\) \(\chi_{6047}(22,\cdot)\) \(\chi_{6047}(23,\cdot)\) \(\chi_{6047}(24,\cdot)\) \(\chi_{6047}(25,\cdot)\) \(\chi_{6047}(27,\cdot)\) \(\chi_{6047}(28,\cdot)\) \(\chi_{6047}(32,\cdot)\) \(\chi_{6047}(33,\cdot)\) \(\chi_{6047}(36,\cdot)\) \(\chi_{6047}(37,\cdot)\) \(\chi_{6047}(41,\cdot)\) \(\chi_{6047}(42,\cdot)\) \(\chi_{6047}(43,\cdot)\) \(\chi_{6047}(44,\cdot)\) \(\chi_{6047}(46,\cdot)\) \(\chi_{6047}(47,\cdot)\) \(\chi_{6047}(48,\cdot)\) ...
Values on generators
\(5\) → \(e\left(\frac{859}{3023}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{538}{3023}\right)\) | \(e\left(\frac{1095}{3023}\right)\) | \(e\left(\frac{1076}{3023}\right)\) | \(e\left(\frac{859}{3023}\right)\) | \(e\left(\frac{1633}{3023}\right)\) | \(e\left(\frac{71}{3023}\right)\) | \(e\left(\frac{1614}{3023}\right)\) | \(e\left(\frac{2190}{3023}\right)\) | \(e\left(\frac{1397}{3023}\right)\) | \(e\left(\frac{931}{3023}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{3023})\) |