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.du
\(\chi_{6400}(29,\cdot)\) \(\chi_{6400}(69,\cdot)\) \(\chi_{6400}(109,\cdot)\) \(\chi_{6400}(189,\cdot)\) \(\chi_{6400}(229,\cdot)\) \(\chi_{6400}(269,\cdot)\) \(\chi_{6400}(309,\cdot)\) \(\chi_{6400}(389,\cdot)\) \(\chi_{6400}(429,\cdot)\) \(\chi_{6400}(469,\cdot)\) \(\chi_{6400}(509,\cdot)\) \(\chi_{6400}(589,\cdot)\) \(\chi_{6400}(629,\cdot)\) \(\chi_{6400}(669,\cdot)\) \(\chi_{6400}(709,\cdot)\) \(\chi_{6400}(789,\cdot)\) \(\chi_{6400}(829,\cdot)\) \(\chi_{6400}(869,\cdot)\) \(\chi_{6400}(909,\cdot)\) \(\chi_{6400}(989,\cdot)\) \(\chi_{6400}(1029,\cdot)\) \(\chi_{6400}(1069,\cdot)\) \(\chi_{6400}(1109,\cdot)\) \(\chi_{6400}(1189,\cdot)\) \(\chi_{6400}(1229,\cdot)\) \(\chi_{6400}(1269,\cdot)\) \(\chi_{6400}(1309,\cdot)\) \(\chi_{6400}(1389,\cdot)\) \(\chi_{6400}(1429,\cdot)\) \(\chi_{6400}(1469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{59}{64}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{309}{320}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{149}{160}\right)\) | \(e\left(\frac{307}{320}\right)\) | \(e\left(\frac{73}{320}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{1}{320}\right)\) | \(e\left(\frac{219}{320}\right)\) | \(e\left(\frac{1}{160}\right)\) | \(e\left(\frac{287}{320}\right)\) |