Basic properties
| Modulus: | \(1280\) | |
| Conductor: | \(1280\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1280.bu
\(\chi_{1280}(19,\cdot)\) \(\chi_{1280}(59,\cdot)\) \(\chi_{1280}(99,\cdot)\) \(\chi_{1280}(139,\cdot)\) \(\chi_{1280}(179,\cdot)\) \(\chi_{1280}(219,\cdot)\) \(\chi_{1280}(259,\cdot)\) \(\chi_{1280}(299,\cdot)\) \(\chi_{1280}(339,\cdot)\) \(\chi_{1280}(379,\cdot)\) \(\chi_{1280}(419,\cdot)\) \(\chi_{1280}(459,\cdot)\) \(\chi_{1280}(499,\cdot)\) \(\chi_{1280}(539,\cdot)\) \(\chi_{1280}(579,\cdot)\) \(\chi_{1280}(619,\cdot)\) \(\chi_{1280}(659,\cdot)\) \(\chi_{1280}(699,\cdot)\) \(\chi_{1280}(739,\cdot)\) \(\chi_{1280}(779,\cdot)\) \(\chi_{1280}(819,\cdot)\) \(\chi_{1280}(859,\cdot)\) \(\chi_{1280}(899,\cdot)\) \(\chi_{1280}(939,\cdot)\) \(\chi_{1280}(979,\cdot)\) \(\chi_{1280}(1019,\cdot)\) \(\chi_{1280}(1059,\cdot)\) \(\chi_{1280}(1099,\cdot)\) \(\chi_{1280}(1139,\cdot)\) \(\chi_{1280}(1179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((-1,e\left(\frac{17}{64}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1280 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{57}{64}\right)\) |