Basic properties
| Modulus: | \(4096\) | |
| Conductor: | \(4096\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1024\) | 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 4096.u
\(\chi_{4096}(5,\cdot)\) \(\chi_{4096}(13,\cdot)\) \(\chi_{4096}(21,\cdot)\) \(\chi_{4096}(29,\cdot)\) \(\chi_{4096}(37,\cdot)\) \(\chi_{4096}(45,\cdot)\) \(\chi_{4096}(53,\cdot)\) \(\chi_{4096}(61,\cdot)\) \(\chi_{4096}(69,\cdot)\) \(\chi_{4096}(77,\cdot)\) \(\chi_{4096}(85,\cdot)\) \(\chi_{4096}(93,\cdot)\) \(\chi_{4096}(101,\cdot)\) \(\chi_{4096}(109,\cdot)\) \(\chi_{4096}(117,\cdot)\) \(\chi_{4096}(125,\cdot)\) \(\chi_{4096}(133,\cdot)\) \(\chi_{4096}(141,\cdot)\) \(\chi_{4096}(149,\cdot)\) \(\chi_{4096}(157,\cdot)\) \(\chi_{4096}(165,\cdot)\) \(\chi_{4096}(173,\cdot)\) \(\chi_{4096}(181,\cdot)\) \(\chi_{4096}(189,\cdot)\) \(\chi_{4096}(197,\cdot)\) \(\chi_{4096}(205,\cdot)\) \(\chi_{4096}(213,\cdot)\) \(\chi_{4096}(221,\cdot)\) \(\chi_{4096}(229,\cdot)\) \(\chi_{4096}(237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1024})$ |
| Fixed field: | Number field defined by a degree 1024 polynomial (not computed) |
Values on generators
\((4095,5)\) → \((1,e\left(\frac{969}{1024}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4096 }(613, a) \) | \(1\) | \(1\) | \(e\left(\frac{763}{1024}\right)\) | \(e\left(\frac{969}{1024}\right)\) | \(e\left(\frac{333}{512}\right)\) | \(e\left(\frac{251}{512}\right)\) | \(e\left(\frac{573}{1024}\right)\) | \(e\left(\frac{935}{1024}\right)\) | \(e\left(\frac{177}{256}\right)\) | \(e\left(\frac{223}{256}\right)\) | \(e\left(\frac{655}{1024}\right)\) | \(e\left(\frac{405}{1024}\right)\) |