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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1280.by
\(\chi_{1280}(43,\cdot)\) \(\chi_{1280}(67,\cdot)\) \(\chi_{1280}(123,\cdot)\) \(\chi_{1280}(147,\cdot)\) \(\chi_{1280}(203,\cdot)\) \(\chi_{1280}(227,\cdot)\) \(\chi_{1280}(283,\cdot)\) \(\chi_{1280}(307,\cdot)\) \(\chi_{1280}(363,\cdot)\) \(\chi_{1280}(387,\cdot)\) \(\chi_{1280}(443,\cdot)\) \(\chi_{1280}(467,\cdot)\) \(\chi_{1280}(523,\cdot)\) \(\chi_{1280}(547,\cdot)\) \(\chi_{1280}(603,\cdot)\) \(\chi_{1280}(627,\cdot)\) \(\chi_{1280}(683,\cdot)\) \(\chi_{1280}(707,\cdot)\) \(\chi_{1280}(763,\cdot)\) \(\chi_{1280}(787,\cdot)\) \(\chi_{1280}(843,\cdot)\) \(\chi_{1280}(867,\cdot)\) \(\chi_{1280}(923,\cdot)\) \(\chi_{1280}(947,\cdot)\) \(\chi_{1280}(1003,\cdot)\) \(\chi_{1280}(1027,\cdot)\) \(\chi_{1280}(1083,\cdot)\) \(\chi_{1280}(1107,\cdot)\) \(\chi_{1280}(1163,\cdot)\) \(\chi_{1280}(1187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((-1,e\left(\frac{61}{64}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1280 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{21}{64}\right)\) |