Basic properties
Modulus: | \(4021\) | |
Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4020\) | 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
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4021.x
\(\chi_{4021}(2,\cdot)\) \(\chi_{4021}(11,\cdot)\) \(\chi_{4021}(18,\cdot)\) \(\chi_{4021}(19,\cdot)\) \(\chi_{4021}(21,\cdot)\) \(\chi_{4021}(23,\cdot)\) \(\chi_{4021}(24,\cdot)\) \(\chi_{4021}(26,\cdot)\) \(\chi_{4021}(30,\cdot)\) \(\chi_{4021}(31,\cdot)\) \(\chi_{4021}(34,\cdot)\) \(\chi_{4021}(35,\cdot)\) \(\chi_{4021}(40,\cdot)\) \(\chi_{4021}(41,\cdot)\) \(\chi_{4021}(43,\cdot)\) \(\chi_{4021}(50,\cdot)\) \(\chi_{4021}(54,\cdot)\) \(\chi_{4021}(63,\cdot)\) \(\chi_{4021}(72,\cdot)\) \(\chi_{4021}(76,\cdot)\) \(\chi_{4021}(79,\cdot)\) \(\chi_{4021}(84,\cdot)\) \(\chi_{4021}(90,\cdot)\) \(\chi_{4021}(96,\cdot)\) \(\chi_{4021}(98,\cdot)\) \(\chi_{4021}(105,\cdot)\) \(\chi_{4021}(112,\cdot)\) \(\chi_{4021}(120,\cdot)\) \(\chi_{4021}(122,\cdot)\) \(\chi_{4021}(128,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4020})$ |
Fixed field: | Number field defined by a degree 4020 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{3509}{4020}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4021 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3509}{4020}\right)\) | \(e\left(\frac{694}{1005}\right)\) | \(e\left(\frac{1499}{2010}\right)\) | \(e\left(\frac{394}{1005}\right)\) | \(e\left(\frac{151}{268}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{829}{1340}\right)\) | \(e\left(\frac{383}{1005}\right)\) | \(e\left(\frac{71}{268}\right)\) | \(e\left(\frac{3893}{4020}\right)\) |