Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | 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.o
\(\chi_{4001}(26,\cdot)\) \(\chi_{4001}(35,\cdot)\) \(\chi_{4001}(38,\cdot)\) \(\chi_{4001}(40,\cdot)\) \(\chi_{4001}(71,\cdot)\) \(\chi_{4001}(224,\cdot)\) \(\chi_{4001}(250,\cdot)\) \(\chi_{4001}(256,\cdot)\) \(\chi_{4001}(405,\cdot)\) \(\chi_{4001}(417,\cdot)\) \(\chi_{4001}(458,\cdot)\) \(\chi_{4001}(463,\cdot)\) \(\chi_{4001}(501,\cdot)\) \(\chi_{4001}(510,\cdot)\) \(\chi_{4001}(615,\cdot)\) \(\chi_{4001}(674,\cdot)\) \(\chi_{4001}(676,\cdot)\) \(\chi_{4001}(785,\cdot)\) \(\chi_{4001}(862,\cdot)\) \(\chi_{4001}(865,\cdot)\) \(\chi_{4001}(910,\cdot)\) \(\chi_{4001}(958,\cdot)\) \(\chi_{4001}(988,\cdot)\) \(\chi_{4001}(1013,\cdot)\) \(\chi_{4001}(1023,\cdot)\) \(\chi_{4001}(1040,\cdot)\) \(\chi_{4001}(1095,\cdot)\) \(\chi_{4001}(1219,\cdot)\) \(\chi_{4001}(1225,\cdot)\) \(\chi_{4001}(1330,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{44}{125}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{48}{125}\right)\) | \(e\left(\frac{44}{125}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{92}{125}\right)\) | \(e\left(\frac{32}{125}\right)\) | \(e\left(\frac{19}{125}\right)\) | \(e\left(\frac{88}{125}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{3}{5}\right)\) |