Basic properties
| Modulus: | \(256\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | 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 256.m
\(\chi_{256}(5,\cdot)\) \(\chi_{256}(13,\cdot)\) \(\chi_{256}(21,\cdot)\) \(\chi_{256}(29,\cdot)\) \(\chi_{256}(37,\cdot)\) \(\chi_{256}(45,\cdot)\) \(\chi_{256}(53,\cdot)\) \(\chi_{256}(61,\cdot)\) \(\chi_{256}(69,\cdot)\) \(\chi_{256}(77,\cdot)\) \(\chi_{256}(85,\cdot)\) \(\chi_{256}(93,\cdot)\) \(\chi_{256}(101,\cdot)\) \(\chi_{256}(109,\cdot)\) \(\chi_{256}(117,\cdot)\) \(\chi_{256}(125,\cdot)\) \(\chi_{256}(133,\cdot)\) \(\chi_{256}(141,\cdot)\) \(\chi_{256}(149,\cdot)\) \(\chi_{256}(157,\cdot)\) \(\chi_{256}(165,\cdot)\) \(\chi_{256}(173,\cdot)\) \(\chi_{256}(181,\cdot)\) \(\chi_{256}(189,\cdot)\) \(\chi_{256}(197,\cdot)\) \(\chi_{256}(205,\cdot)\) \(\chi_{256}(213,\cdot)\) \(\chi_{256}(221,\cdot)\) \(\chi_{256}(229,\cdot)\) \(\chi_{256}(237,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((255,5)\) → \((1,e\left(\frac{29}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 256 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{25}{64}\right)\) |