Basic properties
| Modulus: | \(4021\) | |
| Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1340\) | 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 4021.v
\(\chi_{4021}(8,\cdot)\) \(\chi_{4021}(33,\cdot)\) \(\chi_{4021}(44,\cdot)\) \(\chi_{4021}(55,\cdot)\) \(\chi_{4021}(87,\cdot)\) \(\chi_{4021}(91,\cdot)\) \(\chi_{4021}(92,\cdot)\) \(\chi_{4021}(93,\cdot)\) \(\chi_{4021}(102,\cdot)\) \(\chi_{4021}(104,\cdot)\) \(\chi_{4021}(106,\cdot)\) \(\chi_{4021}(116,\cdot)\) \(\chi_{4021}(123,\cdot)\) \(\chi_{4021}(145,\cdot)\) \(\chi_{4021}(155,\cdot)\) \(\chi_{4021}(157,\cdot)\) \(\chi_{4021}(162,\cdot)\) \(\chi_{4021}(164,\cdot)\) \(\chi_{4021}(166,\cdot)\) \(\chi_{4021}(170,\cdot)\) \(\chi_{4021}(171,\cdot)\) \(\chi_{4021}(194,\cdot)\) \(\chi_{4021}(199,\cdot)\) \(\chi_{4021}(205,\cdot)\) \(\chi_{4021}(218,\cdot)\) \(\chi_{4021}(228,\cdot)\) \(\chi_{4021}(237,\cdot)\) \(\chi_{4021}(252,\cdot)\) \(\chi_{4021}(270,\cdot)\) \(\chi_{4021}(277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1340})$ |
| Fixed field: | Number field defined by a degree 1340 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1340}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4021 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1340}\right)\) | \(e\left(\frac{76}{335}\right)\) | \(e\left(\frac{1}{670}\right)\) | \(e\left(\frac{131}{335}\right)\) | \(e\left(\frac{61}{268}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{1340}\right)\) | \(e\left(\frac{152}{335}\right)\) | \(e\left(\frac{105}{268}\right)\) | \(e\left(\frac{1217}{1340}\right)\) |