Basic properties
| Modulus: | \(8032\) | |
| Conductor: | \(4016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4016}(1027,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8032.cf
\(\chi_{8032}(7,\cdot)\) \(\chi_{8032}(23,\cdot)\) \(\chi_{8032}(39,\cdot)\) \(\chi_{8032}(103,\cdot)\) \(\chi_{8032}(119,\cdot)\) \(\chi_{8032}(135,\cdot)\) \(\chi_{8032}(263,\cdot)\) \(\chi_{8032}(279,\cdot)\) \(\chi_{8032}(311,\cdot)\) \(\chi_{8032}(343,\cdot)\) \(\chi_{8032}(359,\cdot)\) \(\chi_{8032}(375,\cdot)\) \(\chi_{8032}(391,\cdot)\) \(\chi_{8032}(407,\cdot)\) \(\chi_{8032}(519,\cdot)\) \(\chi_{8032}(551,\cdot)\) \(\chi_{8032}(567,\cdot)\) \(\chi_{8032}(583,\cdot)\) \(\chi_{8032}(663,\cdot)\) \(\chi_{8032}(711,\cdot)\) \(\chi_{8032}(727,\cdot)\) \(\chi_{8032}(775,\cdot)\) \(\chi_{8032}(791,\cdot)\) \(\chi_{8032}(839,\cdot)\) \(\chi_{8032}(871,\cdot)\) \(\chi_{8032}(951,\cdot)\) \(\chi_{8032}(967,\cdot)\) \(\chi_{8032}(1031,\cdot)\) \(\chi_{8032}(1079,\cdot)\) \(\chi_{8032}(1159,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((-1,-i,e\left(\frac{12}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8032 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{143}{500}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{143}{250}\right)\) | \(e\left(\frac{253}{500}\right)\) | \(e\left(\frac{361}{500}\right)\) | \(e\left(\frac{129}{250}\right)\) | \(e\left(\frac{13}{125}\right)\) | \(e\left(\frac{199}{500}\right)\) | \(e\left(\frac{47}{500}\right)\) |