Basic properties
| Modulus: | \(6400\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{256}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.cx
\(\chi_{6400}(101,\cdot)\) \(\chi_{6400}(301,\cdot)\) \(\chi_{6400}(501,\cdot)\) \(\chi_{6400}(701,\cdot)\) \(\chi_{6400}(901,\cdot)\) \(\chi_{6400}(1101,\cdot)\) \(\chi_{6400}(1301,\cdot)\) \(\chi_{6400}(1501,\cdot)\) \(\chi_{6400}(1701,\cdot)\) \(\chi_{6400}(1901,\cdot)\) \(\chi_{6400}(2101,\cdot)\) \(\chi_{6400}(2301,\cdot)\) \(\chi_{6400}(2501,\cdot)\) \(\chi_{6400}(2701,\cdot)\) \(\chi_{6400}(2901,\cdot)\) \(\chi_{6400}(3101,\cdot)\) \(\chi_{6400}(3301,\cdot)\) \(\chi_{6400}(3501,\cdot)\) \(\chi_{6400}(3701,\cdot)\) \(\chi_{6400}(3901,\cdot)\) \(\chi_{6400}(4101,\cdot)\) \(\chi_{6400}(4301,\cdot)\) \(\chi_{6400}(4501,\cdot)\) \(\chi_{6400}(4701,\cdot)\) \(\chi_{6400}(4901,\cdot)\) \(\chi_{6400}(5101,\cdot)\) \(\chi_{6400}(5301,\cdot)\) \(\chi_{6400}(5501,\cdot)\) \(\chi_{6400}(5701,\cdot)\) \(\chi_{6400}(5901,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{9}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{49}{64}\right)\) |