Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 193 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 64 |
| 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 | = | odd |
| Orbit label | = | 193.l |
| Orbit index | = | 12 |
Galois orbit
\(\chi_{193}(11,\cdot)\) \(\chi_{193}(13,\cdot)\) \(\chi_{193}(20,\cdot)\) \(\chi_{193}(29,\cdot)\) \(\chi_{193}(33,\cdot)\) \(\chi_{193}(35,\cdot)\) \(\chi_{193}(39,\cdot)\) \(\chi_{193}(60,\cdot)\) \(\chi_{193}(68,\cdot)\) \(\chi_{193}(71,\cdot)\) \(\chi_{193}(74,\cdot)\) \(\chi_{193}(76,\cdot)\) \(\chi_{193}(87,\cdot)\) \(\chi_{193}(88,\cdot)\) \(\chi_{193}(89,\cdot)\) \(\chi_{193}(94,\cdot)\) \(\chi_{193}(99,\cdot)\) \(\chi_{193}(104,\cdot)\) \(\chi_{193}(105,\cdot)\) \(\chi_{193}(106,\cdot)\) \(\chi_{193}(117,\cdot)\) \(\chi_{193}(119,\cdot)\) \(\chi_{193}(122,\cdot)\) \(\chi_{193}(125,\cdot)\) \(\chi_{193}(133,\cdot)\) \(\chi_{193}(154,\cdot)\) \(\chi_{193}(158,\cdot)\) \(\chi_{193}(160,\cdot)\) \(\chi_{193}(164,\cdot)\) \(\chi_{193}(173,\cdot)\) ...
Values on generators
\(5\) → \(e\left(\frac{55}{64}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{17}{64}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{64})\) |