Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 167 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 83 |
| 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 | = | 167.c |
| Orbit index | = | 3 |
Galois orbit
\(\chi_{167}(2,\cdot)\) \(\chi_{167}(3,\cdot)\) \(\chi_{167}(4,\cdot)\) \(\chi_{167}(6,\cdot)\) \(\chi_{167}(7,\cdot)\) \(\chi_{167}(8,\cdot)\) \(\chi_{167}(9,\cdot)\) \(\chi_{167}(11,\cdot)\) \(\chi_{167}(12,\cdot)\) \(\chi_{167}(14,\cdot)\) \(\chi_{167}(16,\cdot)\) \(\chi_{167}(18,\cdot)\) \(\chi_{167}(19,\cdot)\) \(\chi_{167}(21,\cdot)\) \(\chi_{167}(22,\cdot)\) \(\chi_{167}(24,\cdot)\) \(\chi_{167}(25,\cdot)\) \(\chi_{167}(27,\cdot)\) \(\chi_{167}(28,\cdot)\) \(\chi_{167}(29,\cdot)\) \(\chi_{167}(31,\cdot)\) \(\chi_{167}(32,\cdot)\) \(\chi_{167}(33,\cdot)\) \(\chi_{167}(36,\cdot)\) \(\chi_{167}(38,\cdot)\) \(\chi_{167}(42,\cdot)\) \(\chi_{167}(44,\cdot)\) \(\chi_{167}(47,\cdot)\) \(\chi_{167}(48,\cdot)\) \(\chi_{167}(49,\cdot)\) ...
Values on generators
\(5\) → \(e\left(\frac{66}{83}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{67}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{51}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{46}{83}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{41}{83}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{22}{83}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{83})\) |