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 \(\chi_{2008}(1011,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4016.bp
\(\chi_{4016}(7,\cdot)\) \(\chi_{4016}(23,\cdot)\) \(\chi_{4016}(39,\cdot)\) \(\chi_{4016}(103,\cdot)\) \(\chi_{4016}(119,\cdot)\) \(\chi_{4016}(135,\cdot)\) \(\chi_{4016}(263,\cdot)\) \(\chi_{4016}(279,\cdot)\) \(\chi_{4016}(311,\cdot)\) \(\chi_{4016}(343,\cdot)\) \(\chi_{4016}(359,\cdot)\) \(\chi_{4016}(375,\cdot)\) \(\chi_{4016}(391,\cdot)\) \(\chi_{4016}(407,\cdot)\) \(\chi_{4016}(519,\cdot)\) \(\chi_{4016}(551,\cdot)\) \(\chi_{4016}(567,\cdot)\) \(\chi_{4016}(583,\cdot)\) \(\chi_{4016}(663,\cdot)\) \(\chi_{4016}(711,\cdot)\) \(\chi_{4016}(727,\cdot)\) \(\chi_{4016}(775,\cdot)\) \(\chi_{4016}(791,\cdot)\) \(\chi_{4016}(839,\cdot)\) \(\chi_{4016}(871,\cdot)\) \(\chi_{4016}(951,\cdot)\) \(\chi_{4016}(967,\cdot)\) \(\chi_{4016}(1031,\cdot)\) \(\chi_{4016}(1079,\cdot)\) \(\chi_{4016}(1159,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((-1,-1,e\left(\frac{124}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{129}{250}\right)\) | \(e\left(\frac{93}{125}\right)\) | \(e\left(\frac{39}{125}\right)\) | \(e\left(\frac{11}{250}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{51}{125}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{97}{250}\right)\) |