Basic properties
Modulus: | \(1021\) | |
Conductor: | \(1021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1020\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 1021.x
\(\chi_{1021}(10,\cdot)\) \(\chi_{1021}(22,\cdot)\) \(\chi_{1021}(30,\cdot)\) \(\chi_{1021}(31,\cdot)\) \(\chi_{1021}(34,\cdot)\) \(\chi_{1021}(35,\cdot)\) \(\chi_{1021}(37,\cdot)\) \(\chi_{1021}(40,\cdot)\) \(\chi_{1021}(43,\cdot)\) \(\chi_{1021}(46,\cdot)\) \(\chi_{1021}(50,\cdot)\) \(\chi_{1021}(53,\cdot)\) \(\chi_{1021}(59,\cdot)\) \(\chi_{1021}(65,\cdot)\) \(\chi_{1021}(66,\cdot)\) \(\chi_{1021}(76,\cdot)\) \(\chi_{1021}(77,\cdot)\) \(\chi_{1021}(82,\cdot)\) \(\chi_{1021}(90,\cdot)\) \(\chi_{1021}(93,\cdot)\) \(\chi_{1021}(94,\cdot)\) \(\chi_{1021}(95,\cdot)\) \(\chi_{1021}(102,\cdot)\) \(\chi_{1021}(103,\cdot)\) \(\chi_{1021}(105,\cdot)\) \(\chi_{1021}(109,\cdot)\) \(\chi_{1021}(111,\cdot)\) \(\chi_{1021}(119,\cdot)\) \(\chi_{1021}(120,\cdot)\) \(\chi_{1021}(122,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1020})$ |
Fixed field: | Number field defined by a degree 1020 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{689}{1020}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1021 }(50, a) \) | \(-1\) | \(1\) | \(e\left(\frac{319}{340}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{149}{170}\right)\) | \(e\left(\frac{188}{255}\right)\) | \(e\left(\frac{109}{340}\right)\) | \(e\left(\frac{49}{340}\right)\) | \(e\left(\frac{277}{340}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{689}{1020}\right)\) | \(e\left(\frac{206}{255}\right)\) |