Basic properties
| Modulus: | \(4021\) | |
| Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2010\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4021.w
\(\chi_{4021}(4,\cdot)\) \(\chi_{4021}(12,\cdot)\) \(\chi_{4021}(20,\cdot)\) \(\chi_{4021}(22,\cdot)\) \(\chi_{4021}(39,\cdot)\) \(\chi_{4021}(51,\cdot)\) \(\chi_{4021}(58,\cdot)\) \(\chi_{4021}(59,\cdot)\) \(\chi_{4021}(61,\cdot)\) \(\chi_{4021}(62,\cdot)\) \(\chi_{4021}(65,\cdot)\) \(\chi_{4021}(66,\cdot)\) \(\chi_{4021}(83,\cdot)\) \(\chi_{4021}(85,\cdot)\) \(\chi_{4021}(89,\cdot)\) \(\chi_{4021}(97,\cdot)\) \(\chi_{4021}(108,\cdot)\) \(\chi_{4021}(109,\cdot)\) \(\chi_{4021}(117,\cdot)\) \(\chi_{4021}(121,\cdot)\) \(\chi_{4021}(131,\cdot)\) \(\chi_{4021}(133,\cdot)\) \(\chi_{4021}(148,\cdot)\) \(\chi_{4021}(152,\cdot)\) \(\chi_{4021}(158,\cdot)\) \(\chi_{4021}(159,\cdot)\) \(\chi_{4021}(161,\cdot)\) \(\chi_{4021}(177,\cdot)\) \(\chi_{4021}(180,\cdot)\) \(\chi_{4021}(182,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1005})$ |
| Fixed field: | Number field defined by a degree 2010 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{263}{2010}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4021 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{263}{2010}\right)\) | \(e\left(\frac{446}{1005}\right)\) | \(e\left(\frac{263}{1005}\right)\) | \(e\left(\frac{566}{1005}\right)\) | \(e\left(\frac{77}{134}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{263}{670}\right)\) | \(e\left(\frac{892}{1005}\right)\) | \(e\left(\frac{93}{134}\right)\) | \(e\left(\frac{1151}{2010}\right)\) |