Basic properties
Modulus: | \(4021\) | |
Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1005\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4021.u
\(\chi_{4021}(3,\cdot)\) \(\chi_{4021}(5,\cdot)\) \(\chi_{4021}(9,\cdot)\) \(\chi_{4021}(14,\cdot)\) \(\chi_{4021}(15,\cdot)\) \(\chi_{4021}(16,\cdot)\) \(\chi_{4021}(25,\cdot)\) \(\chi_{4021}(46,\cdot)\) \(\chi_{4021}(52,\cdot)\) \(\chi_{4021}(68,\cdot)\) \(\chi_{4021}(81,\cdot)\) \(\chi_{4021}(82,\cdot)\) \(\chi_{4021}(111,\cdot)\) \(\chi_{4021}(114,\cdot)\) \(\chi_{4021}(126,\cdot)\) \(\chi_{4021}(135,\cdot)\) \(\chi_{4021}(138,\cdot)\) \(\chi_{4021}(144,\cdot)\) \(\chi_{4021}(156,\cdot)\) \(\chi_{4021}(185,\cdot)\) \(\chi_{4021}(190,\cdot)\) \(\chi_{4021}(191,\cdot)\) \(\chi_{4021}(196,\cdot)\) \(\chi_{4021}(201,\cdot)\) \(\chi_{4021}(203,\cdot)\) \(\chi_{4021}(204,\cdot)\) \(\chi_{4021}(210,\cdot)\) \(\chi_{4021}(212,\cdot)\) \(\chi_{4021}(217,\cdot)\) \(\chi_{4021}(223,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1005})$ |
Fixed field: | Number field defined by a degree 1005 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{746}{1005}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4021 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{746}{1005}\right)\) | \(e\left(\frac{994}{1005}\right)\) | \(e\left(\frac{487}{1005}\right)\) | \(e\left(\frac{964}{1005}\right)\) | \(e\left(\frac{49}{67}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{76}{335}\right)\) | \(e\left(\frac{983}{1005}\right)\) | \(e\left(\frac{47}{67}\right)\) | \(e\left(\frac{32}{1005}\right)\) |