Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 569 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 568 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | odd |
| Orbit label | = | 569.h |
| Orbit index | = | 8 |
Galois orbit
\(\chi_{569}(3,\cdot)\) \(\chi_{569}(6,\cdot)\) \(\chi_{569}(11,\cdot)\) \(\chi_{569}(12,\cdot)\) \(\chi_{569}(15,\cdot)\) \(\chi_{569}(19,\cdot)\) \(\chi_{569}(21,\cdot)\) \(\chi_{569}(22,\cdot)\) \(\chi_{569}(23,\cdot)\) \(\chi_{569}(24,\cdot)\) \(\chi_{569}(27,\cdot)\) \(\chi_{569}(29,\cdot)\) \(\chi_{569}(30,\cdot)\) \(\chi_{569}(31,\cdot)\) \(\chi_{569}(37,\cdot)\) \(\chi_{569}(38,\cdot)\) \(\chi_{569}(39,\cdot)\) \(\chi_{569}(42,\cdot)\) \(\chi_{569}(44,\cdot)\) \(\chi_{569}(46,\cdot)\) \(\chi_{569}(47,\cdot)\) \(\chi_{569}(48,\cdot)\) \(\chi_{569}(51,\cdot)\) \(\chi_{569}(53,\cdot)\) \(\chi_{569}(54,\cdot)\) \(\chi_{569}(55,\cdot)\) \(\chi_{569}(58,\cdot)\) \(\chi_{569}(59,\cdot)\) \(\chi_{569}(60,\cdot)\) \(\chi_{569}(62,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{127}{568}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{9}{284}\right)\) | \(e\left(\frac{127}{568}\right)\) | \(e\left(\frac{9}{142}\right)\) | \(e\left(\frac{13}{71}\right)\) | \(e\left(\frac{145}{568}\right)\) | \(e\left(\frac{181}{284}\right)\) | \(e\left(\frac{27}{284}\right)\) | \(e\left(\frac{127}{284}\right)\) | \(e\left(\frac{61}{284}\right)\) | \(e\left(\frac{377}{568}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{568})\) |