Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 2011 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 2010 |
| 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 | = | 2011.p |
| Orbit index | = | 16 |
Galois orbit
\(\chi_{2011}(3,\cdot)\) \(\chi_{2011}(7,\cdot)\) \(\chi_{2011}(11,\cdot)\) \(\chi_{2011}(12,\cdot)\) \(\chi_{2011}(17,\cdot)\) \(\chi_{2011}(18,\cdot)\) \(\chi_{2011}(19,\cdot)\) \(\chi_{2011}(26,\cdot)\) \(\chi_{2011}(28,\cdot)\) \(\chi_{2011}(29,\cdot)\) \(\chi_{2011}(35,\cdot)\) \(\chi_{2011}(39,\cdot)\) \(\chi_{2011}(40,\cdot)\) \(\chi_{2011}(42,\cdot)\) \(\chi_{2011}(50,\cdot)\) \(\chi_{2011}(61,\cdot)\) \(\chi_{2011}(62,\cdot)\) \(\chi_{2011}(66,\cdot)\) \(\chi_{2011}(69,\cdot)\) \(\chi_{2011}(73,\cdot)\) \(\chi_{2011}(79,\cdot)\) \(\chi_{2011}(82,\cdot)\) \(\chi_{2011}(86,\cdot)\) \(\chi_{2011}(90,\cdot)\) \(\chi_{2011}(93,\cdot)\) \(\chi_{2011}(98,\cdot)\) \(\chi_{2011}(99,\cdot)\) \(\chi_{2011}(102,\cdot)\) \(\chi_{2011}(107,\cdot)\) \(\chi_{2011}(108,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{493}{2010}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{37}{402}\right)\) | \(e\left(\frac{493}{2010}\right)\) | \(e\left(\frac{37}{201}\right)\) | \(e\left(\frac{161}{1005}\right)\) | \(e\left(\frac{113}{335}\right)\) | \(e\left(\frac{421}{2010}\right)\) | \(e\left(\frac{37}{134}\right)\) | \(e\left(\frac{493}{1005}\right)\) | \(e\left(\frac{169}{670}\right)\) | \(e\left(\frac{701}{2010}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{1005})\) |