Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | 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.r
\(\chi_{4001}(16,\cdot)\) \(\chi_{4001}(65,\cdot)\) \(\chi_{4001}(95,\cdot)\) \(\chi_{4001}(100,\cdot)\) \(\chi_{4001}(107,\cdot)\) \(\chi_{4001}(158,\cdot)\) \(\chi_{4001}(162,\cdot)\) \(\chi_{4001}(204,\cdot)\) \(\chi_{4001}(211,\cdot)\) \(\chi_{4001}(246,\cdot)\) \(\chi_{4001}(279,\cdot)\) \(\chi_{4001}(364,\cdot)\) \(\chi_{4001}(416,\cdot)\) \(\chi_{4001}(438,\cdot)\) \(\chi_{4001}(490,\cdot)\) \(\chi_{4001}(532,\cdot)\) \(\chi_{4001}(554,\cdot)\) \(\chi_{4001}(557,\cdot)\) \(\chi_{4001}(560,\cdot)\) \(\chi_{4001}(608,\cdot)\) \(\chi_{4001}(640,\cdot)\) \(\chi_{4001}(737,\cdot)\) \(\chi_{4001}(967,\cdot)\) \(\chi_{4001}(994,\cdot)\) \(\chi_{4001}(1047,\cdot)\) \(\chi_{4001}(1062,\cdot)\) \(\chi_{4001}(1136,\cdot)\) \(\chi_{4001}(1142,\cdot)\) \(\chi_{4001}(1145,\cdot)\) \(\chi_{4001}(1146,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{23}{250}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{58}{125}\right)\) | \(e\left(\frac{23}{250}\right)\) | \(e\left(\frac{116}{125}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{139}{250}\right)\) | \(e\left(\frac{122}{125}\right)\) | \(e\left(\frac{49}{125}\right)\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{1}{10}\right)\) |