Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 569 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 142 |
| 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 | = | 569.f |
| Orbit index | = | 6 |
Galois orbit
\(\chi_{569}(4,\cdot)\) \(\chi_{569}(14,\cdot)\) \(\chi_{569}(20,\cdot)\) \(\chi_{569}(26,\cdot)\) \(\chi_{569}(34,\cdot)\) \(\chi_{569}(41,\cdot)\) \(\chi_{569}(43,\cdot)\) \(\chi_{569}(49,\cdot)\) \(\chi_{569}(64,\cdot)\) \(\chi_{569}(70,\cdot)\) \(\chi_{569}(72,\cdot)\) \(\chi_{569}(81,\cdot)\) \(\chi_{569}(87,\cdot)\) \(\chi_{569}(91,\cdot)\) \(\chi_{569}(93,\cdot)\) \(\chi_{569}(100,\cdot)\) \(\chi_{569}(119,\cdot)\) \(\chi_{569}(122,\cdot)\) \(\chi_{569}(130,\cdot)\) \(\chi_{569}(132,\cdot)\) \(\chi_{569}(158,\cdot)\) \(\chi_{569}(169,\cdot)\) \(\chi_{569}(170,\cdot)\) \(\chi_{569}(197,\cdot)\) \(\chi_{569}(205,\cdot)\) \(\chi_{569}(215,\cdot)\) \(\chi_{569}(221,\cdot)\) \(\chi_{569}(224,\cdot)\) \(\chi_{569}(242,\cdot)\) \(\chi_{569}(245,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{53}{142}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{25}{71}\right)\) | \(e\left(\frac{53}{142}\right)\) | \(e\left(\frac{50}{71}\right)\) | \(e\left(\frac{34}{71}\right)\) | \(e\left(\frac{103}{142}\right)\) | \(e\left(\frac{61}{71}\right)\) | \(e\left(\frac{4}{71}\right)\) | \(e\left(\frac{53}{71}\right)\) | \(e\left(\frac{59}{71}\right)\) | \(e\left(\frac{69}{142}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{71})\) |