Basic properties
| Modulus: | \(8032\) | |
| Conductor: | \(8032\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8032.ci
\(\chi_{8032}(3,\cdot)\) \(\chi_{8032}(27,\cdot)\) \(\chi_{8032}(35,\cdot)\) \(\chi_{8032}(67,\cdot)\) \(\chi_{8032}(75,\cdot)\) \(\chi_{8032}(83,\cdot)\) \(\chi_{8032}(115,\cdot)\) \(\chi_{8032}(131,\cdot)\) \(\chi_{8032}(147,\cdot)\) \(\chi_{8032}(155,\cdot)\) \(\chi_{8032}(179,\cdot)\) \(\chi_{8032}(195,\cdot)\) \(\chi_{8032}(227,\cdot)\) \(\chi_{8032}(299,\cdot)\) \(\chi_{8032}(339,\cdot)\) \(\chi_{8032}(363,\cdot)\) \(\chi_{8032}(395,\cdot)\) \(\chi_{8032}(403,\cdot)\) \(\chi_{8032}(443,\cdot)\) \(\chi_{8032}(459,\cdot)\) \(\chi_{8032}(483,\cdot)\) \(\chi_{8032}(491,\cdot)\) \(\chi_{8032}(515,\cdot)\) \(\chi_{8032}(523,\cdot)\) \(\chi_{8032}(547,\cdot)\) \(\chi_{8032}(587,\cdot)\) \(\chi_{8032}(595,\cdot)\) \(\chi_{8032}(603,\cdot)\) \(\chi_{8032}(619,\cdot)\) \(\chi_{8032}(675,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1000})$ |
| Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{8}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8032 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{649}{1000}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{61}{500}\right)\) | \(e\left(\frac{149}{500}\right)\) | \(e\left(\frac{879}{1000}\right)\) | \(e\left(\frac{273}{1000}\right)\) | \(e\left(\frac{43}{125}\right)\) | \(e\left(\frac{59}{250}\right)\) | \(e\left(\frac{557}{1000}\right)\) | \(e\left(\frac{771}{1000}\right)\) |