Basic properties
| Modulus: | \(4016\) | |
| Conductor: | \(2008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2008}(1013,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4016.bq
\(\chi_{4016}(9,\cdot)\) \(\chi_{4016}(41,\cdot)\) \(\chi_{4016}(73,\cdot)\) \(\chi_{4016}(89,\cdot)\) \(\chi_{4016}(105,\cdot)\) \(\chi_{4016}(121,\cdot)\) \(\chi_{4016}(153,\cdot)\) \(\chi_{4016}(169,\cdot)\) \(\chi_{4016}(217,\cdot)\) \(\chi_{4016}(233,\cdot)\) \(\chi_{4016}(361,\cdot)\) \(\chi_{4016}(393,\cdot)\) \(\chi_{4016}(425,\cdot)\) \(\chi_{4016}(441,\cdot)\) \(\chi_{4016}(473,\cdot)\) \(\chi_{4016}(505,\cdot)\) \(\chi_{4016}(537,\cdot)\) \(\chi_{4016}(569,\cdot)\) \(\chi_{4016}(585,\cdot)\) \(\chi_{4016}(617,\cdot)\) \(\chi_{4016}(633,\cdot)\) \(\chi_{4016}(649,\cdot)\) \(\chi_{4016}(681,\cdot)\) \(\chi_{4016}(697,\cdot)\) \(\chi_{4016}(729,\cdot)\) \(\chi_{4016}(841,\cdot)\) \(\chi_{4016}(905,\cdot)\) \(\chi_{4016}(985,\cdot)\) \(\chi_{4016}(1017,\cdot)\) \(\chi_{4016}(1049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((1,-1,e\left(\frac{16}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{250}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{127}{250}\right)\) | \(e\left(\frac{199}{250}\right)\) | \(e\left(\frac{86}{125}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{91}{250}\right)\) | \(e\left(\frac{73}{250}\right)\) |