Basic properties
| Modulus: | \(6400\) | |
| Conductor: | \(6400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(320\) | 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 6400.ds
\(\chi_{6400}(67,\cdot)\) \(\chi_{6400}(123,\cdot)\) \(\chi_{6400}(147,\cdot)\) \(\chi_{6400}(203,\cdot)\) \(\chi_{6400}(227,\cdot)\) \(\chi_{6400}(283,\cdot)\) \(\chi_{6400}(363,\cdot)\) \(\chi_{6400}(387,\cdot)\) \(\chi_{6400}(467,\cdot)\) \(\chi_{6400}(523,\cdot)\) \(\chi_{6400}(547,\cdot)\) \(\chi_{6400}(603,\cdot)\) \(\chi_{6400}(627,\cdot)\) \(\chi_{6400}(683,\cdot)\) \(\chi_{6400}(763,\cdot)\) \(\chi_{6400}(787,\cdot)\) \(\chi_{6400}(867,\cdot)\) \(\chi_{6400}(923,\cdot)\) \(\chi_{6400}(947,\cdot)\) \(\chi_{6400}(1003,\cdot)\) \(\chi_{6400}(1027,\cdot)\) \(\chi_{6400}(1083,\cdot)\) \(\chi_{6400}(1163,\cdot)\) \(\chi_{6400}(1187,\cdot)\) \(\chi_{6400}(1267,\cdot)\) \(\chi_{6400}(1323,\cdot)\) \(\chi_{6400}(1347,\cdot)\) \(\chi_{6400}(1403,\cdot)\) \(\chi_{6400}(1427,\cdot)\) \(\chi_{6400}(1483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((-1,e\left(\frac{51}{64}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{301}{320}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{203}{320}\right)\) | \(e\left(\frac{257}{320}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{169}{320}\right)\) | \(e\left(\frac{211}{320}\right)\) | \(e\left(\frac{129}{160}\right)\) | \(e\left(\frac{263}{320}\right)\) |