Basic properties
| Modulus: | \(512\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | 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 512.o
\(\chi_{512}(5,\cdot)\) \(\chi_{512}(13,\cdot)\) \(\chi_{512}(21,\cdot)\) \(\chi_{512}(29,\cdot)\) \(\chi_{512}(37,\cdot)\) \(\chi_{512}(45,\cdot)\) \(\chi_{512}(53,\cdot)\) \(\chi_{512}(61,\cdot)\) \(\chi_{512}(69,\cdot)\) \(\chi_{512}(77,\cdot)\) \(\chi_{512}(85,\cdot)\) \(\chi_{512}(93,\cdot)\) \(\chi_{512}(101,\cdot)\) \(\chi_{512}(109,\cdot)\) \(\chi_{512}(117,\cdot)\) \(\chi_{512}(125,\cdot)\) \(\chi_{512}(133,\cdot)\) \(\chi_{512}(141,\cdot)\) \(\chi_{512}(149,\cdot)\) \(\chi_{512}(157,\cdot)\) \(\chi_{512}(165,\cdot)\) \(\chi_{512}(173,\cdot)\) \(\chi_{512}(181,\cdot)\) \(\chi_{512}(189,\cdot)\) \(\chi_{512}(197,\cdot)\) \(\chi_{512}(205,\cdot)\) \(\chi_{512}(213,\cdot)\) \(\chi_{512}(221,\cdot)\) \(\chi_{512}(229,\cdot)\) \(\chi_{512}(237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((511,5)\) → \((1,e\left(\frac{5}{128}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 512 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{128}\right)\) | \(e\left(\frac{5}{128}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{41}{128}\right)\) | \(e\left(\frac{43}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{115}{128}\right)\) | \(e\left(\frac{33}{128}\right)\) |