Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 173 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 86 |
| 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 | = | 173.e |
| Orbit index | = | 5 |
Galois orbit
\(\chi_{173}(4,\cdot)\) \(\chi_{173}(9,\cdot)\) \(\chi_{173}(13,\cdot)\) \(\chi_{173}(15,\cdot)\) \(\chi_{173}(21,\cdot)\) \(\chi_{173}(24,\cdot)\) \(\chi_{173}(25,\cdot)\) \(\chi_{173}(31,\cdot)\) \(\chi_{173}(33,\cdot)\) \(\chi_{173}(34,\cdot)\) \(\chi_{173}(35,\cdot)\) \(\chi_{173}(37,\cdot)\) \(\chi_{173}(38,\cdot)\) \(\chi_{173}(40,\cdot)\) \(\chi_{173}(41,\cdot)\) \(\chi_{173}(49,\cdot)\) \(\chi_{173}(54,\cdot)\) \(\chi_{173}(55,\cdot)\) \(\chi_{173}(56,\cdot)\) \(\chi_{173}(64,\cdot)\) \(\chi_{173}(67,\cdot)\) \(\chi_{173}(73,\cdot)\) \(\chi_{173}(77,\cdot)\) \(\chi_{173}(78,\cdot)\) \(\chi_{173}(88,\cdot)\) \(\chi_{173}(89,\cdot)\) \(\chi_{173}(90,\cdot)\) \(\chi_{173}(92,\cdot)\) \(\chi_{173}(113,\cdot)\) \(\chi_{173}(116,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{77}{86}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{77}{86}\right)\) | \(e\left(\frac{15}{86}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{79}{86}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{5}{86}\right)\) | \(e\left(\frac{59}{86}\right)\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{51}{86}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{43})\) |