Basic properties
| Modulus: | \(6400\) | |
| Conductor: | \(1280\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1280}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.da
\(\chi_{6400}(43,\cdot)\) \(\chi_{6400}(307,\cdot)\) \(\chi_{6400}(443,\cdot)\) \(\chi_{6400}(707,\cdot)\) \(\chi_{6400}(843,\cdot)\) \(\chi_{6400}(1107,\cdot)\) \(\chi_{6400}(1243,\cdot)\) \(\chi_{6400}(1507,\cdot)\) \(\chi_{6400}(1643,\cdot)\) \(\chi_{6400}(1907,\cdot)\) \(\chi_{6400}(2043,\cdot)\) \(\chi_{6400}(2307,\cdot)\) \(\chi_{6400}(2443,\cdot)\) \(\chi_{6400}(2707,\cdot)\) \(\chi_{6400}(2843,\cdot)\) \(\chi_{6400}(3107,\cdot)\) \(\chi_{6400}(3243,\cdot)\) \(\chi_{6400}(3507,\cdot)\) \(\chi_{6400}(3643,\cdot)\) \(\chi_{6400}(3907,\cdot)\) \(\chi_{6400}(4043,\cdot)\) \(\chi_{6400}(4307,\cdot)\) \(\chi_{6400}(4443,\cdot)\) \(\chi_{6400}(4707,\cdot)\) \(\chi_{6400}(4843,\cdot)\) \(\chi_{6400}(5107,\cdot)\) \(\chi_{6400}(5243,\cdot)\) \(\chi_{6400}(5507,\cdot)\) \(\chi_{6400}(5643,\cdot)\) \(\chi_{6400}(5907,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((4351,4101,5377)\) → \((-1,e\left(\frac{61}{64}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{21}{64}\right)\) |