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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8032.cj
\(\chi_{8032}(11,\cdot)\) \(\chi_{8032}(19,\cdot)\) \(\chi_{8032}(43,\cdot)\) \(\chi_{8032}(59,\cdot)\) \(\chi_{8032}(99,\cdot)\) \(\chi_{8032}(107,\cdot)\) \(\chi_{8032}(139,\cdot)\) \(\chi_{8032}(163,\cdot)\) \(\chi_{8032}(203,\cdot)\) \(\chi_{8032}(275,\cdot)\) \(\chi_{8032}(307,\cdot)\) \(\chi_{8032}(323,\cdot)\) \(\chi_{8032}(347,\cdot)\) \(\chi_{8032}(355,\cdot)\) \(\chi_{8032}(371,\cdot)\) \(\chi_{8032}(387,\cdot)\) \(\chi_{8032}(419,\cdot)\) \(\chi_{8032}(427,\cdot)\) \(\chi_{8032}(435,\cdot)\) \(\chi_{8032}(467,\cdot)\) \(\chi_{8032}(475,\cdot)\) \(\chi_{8032}(499,\cdot)\) \(\chi_{8032}(531,\cdot)\) \(\chi_{8032}(539,\cdot)\) \(\chi_{8032}(555,\cdot)\) \(\chi_{8032}(563,\cdot)\) \(\chi_{8032}(579,\cdot)\) \(\chi_{8032}(611,\cdot)\) \(\chi_{8032}(635,\cdot)\) \(\chi_{8032}(643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1000})$ |
| Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{51}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8032 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{1000}\right)\) | \(e\left(\frac{129}{200}\right)\) | \(e\left(\frac{171}{500}\right)\) | \(e\left(\frac{139}{500}\right)\) | \(e\left(\frac{169}{1000}\right)\) | \(e\left(\frac{3}{1000}\right)\) | \(e\left(\frac{98}{125}\right)\) | \(e\left(\frac{149}{250}\right)\) | \(e\left(\frac{627}{1000}\right)\) | \(e\left(\frac{481}{1000}\right)\) |