Basic properties
| Modulus: | \(4016\) | |
| Conductor: | \(1004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1004}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4016.bn
\(\chi_{4016}(15,\cdot)\) \(\chi_{4016}(31,\cdot)\) \(\chi_{4016}(79,\cdot)\) \(\chi_{4016}(175,\cdot)\) \(\chi_{4016}(207,\cdot)\) \(\chi_{4016}(287,\cdot)\) \(\chi_{4016}(303,\cdot)\) \(\chi_{4016}(319,\cdot)\) \(\chi_{4016}(335,\cdot)\) \(\chi_{4016}(415,\cdot)\) \(\chi_{4016}(431,\cdot)\) \(\chi_{4016}(447,\cdot)\) \(\chi_{4016}(511,\cdot)\) \(\chi_{4016}(543,\cdot)\) \(\chi_{4016}(575,\cdot)\) \(\chi_{4016}(591,\cdot)\) \(\chi_{4016}(607,\cdot)\) \(\chi_{4016}(623,\cdot)\) \(\chi_{4016}(655,\cdot)\) \(\chi_{4016}(671,\cdot)\) \(\chi_{4016}(719,\cdot)\) \(\chi_{4016}(735,\cdot)\) \(\chi_{4016}(863,\cdot)\) \(\chi_{4016}(895,\cdot)\) \(\chi_{4016}(927,\cdot)\) \(\chi_{4016}(943,\cdot)\) \(\chi_{4016}(975,\cdot)\) \(\chi_{4016}(1007,\cdot)\) \(\chi_{4016}(1039,\cdot)\) \(\chi_{4016}(1071,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((-1,1,e\left(\frac{93}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{250}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{121}{250}\right)\) | \(e\left(\frac{51}{125}\right)\) | \(e\left(\frac{31}{250}\right)\) | \(e\left(\frac{7}{125}\right)\) | \(e\left(\frac{193}{250}\right)\) | \(e\left(\frac{52}{125}\right)\) |