Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 4001 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 2000 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | no |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | even |
| Orbit label | = | 8002.w |
| Orbit index | = | 23 |
Galois orbit
\(\chi_{8002}(9,\cdot)\) \(\chi_{8002}(29,\cdot)\) \(\chi_{8002}(31,\cdot)\) \(\chi_{8002}(33,\cdot)\) \(\chi_{8002}(45,\cdot)\) \(\chi_{8002}(47,\cdot)\) \(\chi_{8002}(61,\cdot)\) \(\chi_{8002}(83,\cdot)\) \(\chi_{8002}(89,\cdot)\) \(\chi_{8002}(97,\cdot)\) \(\chi_{8002}(111,\cdot)\) \(\chi_{8002}(117,\cdot)\) \(\chi_{8002}(137,\cdot)\) \(\chi_{8002}(145,\cdot)\) \(\chi_{8002}(149,\cdot)\) \(\chi_{8002}(155,\cdot)\) \(\chi_{8002}(165,\cdot)\) \(\chi_{8002}(171,\cdot)\) \(\chi_{8002}(197,\cdot)\) \(\chi_{8002}(203,\cdot)\) \(\chi_{8002}(225,\cdot)\) \(\chi_{8002}(231,\cdot)\) \(\chi_{8002}(235,\cdot)\) \(\chi_{8002}(253,\cdot)\) \(\chi_{8002}(257,\cdot)\) \(\chi_{8002}(269,\cdot)\) \(\chi_{8002}(289,\cdot)\) \(\chi_{8002}(305,\cdot)\) \(\chi_{8002}(339,\cdot)\) \(\chi_{8002}(377,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{191}{2000}\right)\)
Values
| -1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
| \(1\) | \(1\) | \(e\left(\frac{191}{2000}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{387}{500}\right)\) | \(e\left(\frac{191}{1000}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{331}{500}\right)\) | \(e\left(\frac{1571}{2000}\right)\) | \(e\left(\frac{1321}{2000}\right)\) | \(e\left(\frac{371}{500}\right)\) | \(e\left(\frac{1739}{2000}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{2000})\) |