Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 569 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 284 |
| 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)
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| Parity | = | even |
| Orbit label | = | 569.g |
| Orbit index | = | 7 |
Galois orbit
\(\chi_{569}(2,\cdot)\) \(\chi_{569}(7,\cdot)\) \(\chi_{569}(8,\cdot)\) \(\chi_{569}(9,\cdot)\) \(\chi_{569}(10,\cdot)\) \(\chi_{569}(13,\cdot)\) \(\chi_{569}(17,\cdot)\) \(\chi_{569}(28,\cdot)\) \(\chi_{569}(32,\cdot)\) \(\chi_{569}(35,\cdot)\) \(\chi_{569}(36,\cdot)\) \(\chi_{569}(40,\cdot)\) \(\chi_{569}(45,\cdot)\) \(\chi_{569}(50,\cdot)\) \(\chi_{569}(52,\cdot)\) \(\chi_{569}(57,\cdot)\) \(\chi_{569}(61,\cdot)\) \(\chi_{569}(65,\cdot)\) \(\chi_{569}(66,\cdot)\) \(\chi_{569}(67,\cdot)\) \(\chi_{569}(68,\cdot)\) \(\chi_{569}(71,\cdot)\) \(\chi_{569}(79,\cdot)\) \(\chi_{569}(82,\cdot)\) \(\chi_{569}(85,\cdot)\) \(\chi_{569}(98,\cdot)\) \(\chi_{569}(112,\cdot)\) \(\chi_{569}(121,\cdot)\) \(\chi_{569}(126,\cdot)\) \(\chi_{569}(127,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{269}{284}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{9}{142}\right)\) | \(e\left(\frac{269}{284}\right)\) | \(e\left(\frac{9}{71}\right)\) | \(e\left(\frac{26}{71}\right)\) | \(e\left(\frac{3}{284}\right)\) | \(e\left(\frac{39}{142}\right)\) | \(e\left(\frac{27}{142}\right)\) | \(e\left(\frac{127}{142}\right)\) | \(e\left(\frac{61}{142}\right)\) | \(e\left(\frac{235}{284}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{284})\) |