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.bs
\(\chi_{1280}(53,\cdot)\) \(\chi_{1280}(77,\cdot)\) \(\chi_{1280}(133,\cdot)\) \(\chi_{1280}(157,\cdot)\) \(\chi_{1280}(213,\cdot)\) \(\chi_{1280}(237,\cdot)\) \(\chi_{1280}(293,\cdot)\) \(\chi_{1280}(317,\cdot)\) \(\chi_{1280}(373,\cdot)\) \(\chi_{1280}(397,\cdot)\) \(\chi_{1280}(453,\cdot)\) \(\chi_{1280}(477,\cdot)\) \(\chi_{1280}(533,\cdot)\) \(\chi_{1280}(557,\cdot)\) \(\chi_{1280}(613,\cdot)\) \(\chi_{1280}(637,\cdot)\) \(\chi_{1280}(693,\cdot)\) \(\chi_{1280}(717,\cdot)\) \(\chi_{1280}(773,\cdot)\) \(\chi_{1280}(797,\cdot)\) \(\chi_{1280}(853,\cdot)\) \(\chi_{1280}(877,\cdot)\) \(\chi_{1280}(933,\cdot)\) \(\chi_{1280}(957,\cdot)\) \(\chi_{1280}(1013,\cdot)\) \(\chi_{1280}(1037,\cdot)\) \(\chi_{1280}(1093,\cdot)\) \(\chi_{1280}(1117,\cdot)\) \(\chi_{1280}(1173,\cdot)\) \(\chi_{1280}(1197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((1,e\left(\frac{5}{64}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1280 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) |