Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 163 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 81 |
| 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 | = | 163.i |
| Orbit index | = | 9 |
Galois orbit
\(\chi_{163}(4,\cdot)\) \(\chi_{163}(9,\cdot)\) \(\chi_{163}(10,\cdot)\) \(\chi_{163}(14,\cdot)\) \(\chi_{163}(15,\cdot)\) \(\chi_{163}(16,\cdot)\) \(\chi_{163}(24,\cdot)\) \(\chi_{163}(26,\cdot)\) \(\chi_{163}(33,\cdot)\) \(\chi_{163}(34,\cdot)\) \(\chi_{163}(35,\cdot)\) \(\chi_{163}(39,\cdot)\) \(\chi_{163}(41,\cdot)\) \(\chi_{163}(43,\cdot)\) \(\chi_{163}(46,\cdot)\) \(\chi_{163}(47,\cdot)\) \(\chi_{163}(49,\cdot)\) \(\chi_{163}(51,\cdot)\) \(\chi_{163}(54,\cdot)\) \(\chi_{163}(55,\cdot)\) \(\chi_{163}(56,\cdot)\) \(\chi_{163}(57,\cdot)\) \(\chi_{163}(60,\cdot)\) \(\chi_{163}(62,\cdot)\) \(\chi_{163}(69,\cdot)\) \(\chi_{163}(71,\cdot)\) \(\chi_{163}(74,\cdot)\) \(\chi_{163}(81,\cdot)\) \(\chi_{163}(83,\cdot)\) \(\chi_{163}(84,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{37}{81}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{11}{81}\right)\) | \(e\left(\frac{74}{81}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{22}{81}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{38}{81}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{81})\) |