Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4000\) | 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 4001.x
\(\chi_{4001}(3,\cdot)\) \(\chi_{4001}(6,\cdot)\) \(\chi_{4001}(15,\cdot)\) \(\chi_{4001}(17,\cdot)\) \(\chi_{4001}(21,\cdot)\) \(\chi_{4001}(22,\cdot)\) \(\chi_{4001}(23,\cdot)\) \(\chi_{4001}(24,\cdot)\) \(\chi_{4001}(27,\cdot)\) \(\chi_{4001}(30,\cdot)\) \(\chi_{4001}(34,\cdot)\) \(\chi_{4001}(37,\cdot)\) \(\chi_{4001}(41,\cdot)\) \(\chi_{4001}(42,\cdot)\) \(\chi_{4001}(43,\cdot)\) \(\chi_{4001}(44,\cdot)\) \(\chi_{4001}(46,\cdot)\) \(\chi_{4001}(48,\cdot)\) \(\chi_{4001}(67,\cdot)\) \(\chi_{4001}(75,\cdot)\) \(\chi_{4001}(77,\cdot)\) \(\chi_{4001}(78,\cdot)\) \(\chi_{4001}(84,\cdot)\) \(\chi_{4001}(85,\cdot)\) \(\chi_{4001}(86,\cdot)\) \(\chi_{4001}(87,\cdot)\) \(\chi_{4001}(88,\cdot)\) \(\chi_{4001}(92,\cdot)\) \(\chi_{4001}(93,\cdot)\) \(\chi_{4001}(96,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4000})$ |
| Fixed field: | Number field defined by a degree 4000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{3689}{4000}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{347}{1000}\right)\) | \(e\left(\frac{3689}{4000}\right)\) | \(e\left(\frac{347}{500}\right)\) | \(e\left(\frac{51}{200}\right)\) | \(e\left(\frac{1077}{4000}\right)\) | \(e\left(\frac{273}{1000}\right)\) | \(e\left(\frac{41}{1000}\right)\) | \(e\left(\frac{1689}{2000}\right)\) | \(e\left(\frac{301}{500}\right)\) | \(e\left(\frac{33}{160}\right)\) |