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.dx
\(\chi_{6400}(21,\cdot)\) \(\chi_{6400}(61,\cdot)\) \(\chi_{6400}(141,\cdot)\) \(\chi_{6400}(181,\cdot)\) \(\chi_{6400}(221,\cdot)\) \(\chi_{6400}(261,\cdot)\) \(\chi_{6400}(341,\cdot)\) \(\chi_{6400}(381,\cdot)\) \(\chi_{6400}(421,\cdot)\) \(\chi_{6400}(461,\cdot)\) \(\chi_{6400}(541,\cdot)\) \(\chi_{6400}(581,\cdot)\) \(\chi_{6400}(621,\cdot)\) \(\chi_{6400}(661,\cdot)\) \(\chi_{6400}(741,\cdot)\) \(\chi_{6400}(781,\cdot)\) \(\chi_{6400}(821,\cdot)\) \(\chi_{6400}(861,\cdot)\) \(\chi_{6400}(941,\cdot)\) \(\chi_{6400}(981,\cdot)\) \(\chi_{6400}(1021,\cdot)\) \(\chi_{6400}(1061,\cdot)\) \(\chi_{6400}(1141,\cdot)\) \(\chi_{6400}(1181,\cdot)\) \(\chi_{6400}(1221,\cdot)\) \(\chi_{6400}(1261,\cdot)\) \(\chi_{6400}(1341,\cdot)\) \(\chi_{6400}(1381,\cdot)\) \(\chi_{6400}(1421,\cdot)\) \(\chi_{6400}(1461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{45}{64}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{259}{320}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{99}{160}\right)\) | \(e\left(\frac{117}{320}\right)\) | \(e\left(\frac{143}{320}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{311}{320}\right)\) | \(e\left(\frac{269}{320}\right)\) | \(e\left(\frac{71}{160}\right)\) | \(e\left(\frac{137}{320}\right)\) |