Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 1571 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 785 |
| 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 | = | 1571.g |
| Orbit index | = | 7 |
Galois orbit
\(\chi_{1571}(3,\cdot)\) \(\chi_{1571}(4,\cdot)\) \(\chi_{1571}(5,\cdot)\) \(\chi_{1571}(7,\cdot)\) \(\chi_{1571}(9,\cdot)\) \(\chi_{1571}(12,\cdot)\) \(\chi_{1571}(16,\cdot)\) \(\chi_{1571}(19,\cdot)\) \(\chi_{1571}(20,\cdot)\) \(\chi_{1571}(21,\cdot)\) \(\chi_{1571}(22,\cdot)\) \(\chi_{1571}(25,\cdot)\) \(\chi_{1571}(26,\cdot)\) \(\chi_{1571}(27,\cdot)\) \(\chi_{1571}(28,\cdot)\) \(\chi_{1571}(29,\cdot)\) \(\chi_{1571}(31,\cdot)\) \(\chi_{1571}(34,\cdot)\) \(\chi_{1571}(35,\cdot)\) \(\chi_{1571}(45,\cdot)\) \(\chi_{1571}(47,\cdot)\) \(\chi_{1571}(48,\cdot)\) \(\chi_{1571}(49,\cdot)\) \(\chi_{1571}(57,\cdot)\) \(\chi_{1571}(59,\cdot)\) \(\chi_{1571}(60,\cdot)\) \(\chi_{1571}(61,\cdot)\) \(\chi_{1571}(64,\cdot)\) \(\chi_{1571}(66,\cdot)\) \(\chi_{1571}(67,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{74}{785}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{74}{785}\right)\) | \(e\left(\frac{506}{785}\right)\) | \(e\left(\frac{148}{785}\right)\) | \(e\left(\frac{319}{785}\right)\) | \(e\left(\frac{116}{157}\right)\) | \(e\left(\frac{68}{785}\right)\) | \(e\left(\frac{222}{785}\right)\) | \(e\left(\frac{227}{785}\right)\) | \(e\left(\frac{393}{785}\right)\) | \(e\left(\frac{112}{785}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{785})\) |