Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | 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 4001.t
\(\chi_{4001}(4,\cdot)\) \(\chi_{4001}(10,\cdot)\) \(\chi_{4001}(49,\cdot)\) \(\chi_{4001}(51,\cdot)\) \(\chi_{4001}(56,\cdot)\) \(\chi_{4001}(64,\cdot)\) \(\chi_{4001}(91,\cdot)\) \(\chi_{4001}(133,\cdot)\) \(\chi_{4001}(140,\cdot)\) \(\chi_{4001}(159,\cdot)\) \(\chi_{4001}(169,\cdot)\) \(\chi_{4001}(187,\cdot)\) \(\chi_{4001}(247,\cdot)\) \(\chi_{4001}(260,\cdot)\) \(\chi_{4001}(361,\cdot)\) \(\chi_{4001}(380,\cdot)\) \(\chi_{4001}(393,\cdot)\) \(\chi_{4001}(400,\cdot)\) \(\chi_{4001}(428,\cdot)\) \(\chi_{4001}(522,\cdot)\) \(\chi_{4001}(541,\cdot)\) \(\chi_{4001}(543,\cdot)\) \(\chi_{4001}(553,\cdot)\) \(\chi_{4001}(567,\cdot)\) \(\chi_{4001}(618,\cdot)\) \(\chi_{4001}(629,\cdot)\) \(\chi_{4001}(632,\cdot)\) \(\chi_{4001}(643,\cdot)\) \(\chi_{4001}(650,\cdot)\) \(\chi_{4001}(686,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{57}{500}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{125}\right)\) | \(e\left(\frac{57}{500}\right)\) | \(e\left(\frac{122}{125}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{301}{500}\right)\) | \(e\left(\frac{124}{125}\right)\) | \(e\left(\frac{58}{125}\right)\) | \(e\left(\frac{57}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{9}{20}\right)\) |