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.bt
\(\chi_{1280}(3,\cdot)\) \(\chi_{1280}(27,\cdot)\) \(\chi_{1280}(83,\cdot)\) \(\chi_{1280}(107,\cdot)\) \(\chi_{1280}(163,\cdot)\) \(\chi_{1280}(187,\cdot)\) \(\chi_{1280}(243,\cdot)\) \(\chi_{1280}(267,\cdot)\) \(\chi_{1280}(323,\cdot)\) \(\chi_{1280}(347,\cdot)\) \(\chi_{1280}(403,\cdot)\) \(\chi_{1280}(427,\cdot)\) \(\chi_{1280}(483,\cdot)\) \(\chi_{1280}(507,\cdot)\) \(\chi_{1280}(563,\cdot)\) \(\chi_{1280}(587,\cdot)\) \(\chi_{1280}(643,\cdot)\) \(\chi_{1280}(667,\cdot)\) \(\chi_{1280}(723,\cdot)\) \(\chi_{1280}(747,\cdot)\) \(\chi_{1280}(803,\cdot)\) \(\chi_{1280}(827,\cdot)\) \(\chi_{1280}(883,\cdot)\) \(\chi_{1280}(907,\cdot)\) \(\chi_{1280}(963,\cdot)\) \(\chi_{1280}(987,\cdot)\) \(\chi_{1280}(1043,\cdot)\) \(\chi_{1280}(1067,\cdot)\) \(\chi_{1280}(1123,\cdot)\) \(\chi_{1280}(1147,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((-1,e\left(\frac{35}{64}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 1280 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{43}{64}\right)\) |