Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 1021 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 85 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | even |
| Orbit label | = | 1021.q |
| Orbit index | = | 17 |
Galois orbit
\(\chi_{1021}(12,\cdot)\) \(\chi_{1021}(14,\cdot)\) \(\chi_{1021}(16,\cdot)\) \(\chi_{1021}(71,\cdot)\) \(\chi_{1021}(73,\cdot)\) \(\chi_{1021}(78,\cdot)\) \(\chi_{1021}(91,\cdot)\) \(\chi_{1021}(104,\cdot)\) \(\chi_{1021}(108,\cdot)\) \(\chi_{1021}(113,\cdot)\) \(\chi_{1021}(115,\cdot)\) \(\chi_{1021}(125,\cdot)\) \(\chi_{1021}(126,\cdot)\) \(\chi_{1021}(144,\cdot)\) \(\chi_{1021}(147,\cdot)\) \(\chi_{1021}(168,\cdot)\) \(\chi_{1021}(192,\cdot)\) \(\chi_{1021}(196,\cdot)\) \(\chi_{1021}(224,\cdot)\) \(\chi_{1021}(235,\cdot)\) \(\chi_{1021}(237,\cdot)\) \(\chi_{1021}(253,\cdot)\) \(\chi_{1021}(255,\cdot)\) \(\chi_{1021}(256,\cdot)\) \(\chi_{1021}(262,\cdot)\) \(\chi_{1021}(275,\cdot)\) \(\chi_{1021}(302,\cdot)\) \(\chi_{1021}(310,\cdot)\) \(\chi_{1021}(316,\cdot)\) \(\chi_{1021}(335,\cdot)\) ...
Values on generators
\(10\) → \(e\left(\frac{19}{85}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{37}{85}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{74}{85}\right)\) | \(e\left(\frac{67}{85}\right)\) | \(e\left(\frac{67}{85}\right)\) | \(e\left(\frac{27}{85}\right)\) | \(e\left(\frac{26}{85}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{85}\right)\) | \(e\left(\frac{49}{85}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{85})\) |