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.dz
\(\chi_{6400}(3,\cdot)\) \(\chi_{6400}(27,\cdot)\) \(\chi_{6400}(83,\cdot)\) \(\chi_{6400}(163,\cdot)\) \(\chi_{6400}(187,\cdot)\) \(\chi_{6400}(267,\cdot)\) \(\chi_{6400}(323,\cdot)\) \(\chi_{6400}(347,\cdot)\) \(\chi_{6400}(403,\cdot)\) \(\chi_{6400}(427,\cdot)\) \(\chi_{6400}(483,\cdot)\) \(\chi_{6400}(563,\cdot)\) \(\chi_{6400}(587,\cdot)\) \(\chi_{6400}(667,\cdot)\) \(\chi_{6400}(723,\cdot)\) \(\chi_{6400}(747,\cdot)\) \(\chi_{6400}(803,\cdot)\) \(\chi_{6400}(827,\cdot)\) \(\chi_{6400}(883,\cdot)\) \(\chi_{6400}(963,\cdot)\) \(\chi_{6400}(987,\cdot)\) \(\chi_{6400}(1067,\cdot)\) \(\chi_{6400}(1123,\cdot)\) \(\chi_{6400}(1147,\cdot)\) \(\chi_{6400}(1203,\cdot)\) \(\chi_{6400}(1227,\cdot)\) \(\chi_{6400}(1283,\cdot)\) \(\chi_{6400}(1363,\cdot)\) \(\chi_{6400}(1387,\cdot)\) \(\chi_{6400}(1467,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((-1,e\left(\frac{35}{64}\right),e\left(\frac{7}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{320}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{29}{160}\right)\) | \(e\left(\frac{187}{320}\right)\) | \(e\left(\frac{113}{320}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{121}{320}\right)\) | \(e\left(\frac{259}{320}\right)\) | \(e\left(\frac{1}{160}\right)\) | \(e\left(\frac{87}{320}\right)\) |