Basic properties
| Modulus: | \(6400\) | |
| Conductor: | \(3200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3200}(1741,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.dp
\(\chi_{6400}(41,\cdot)\) \(\chi_{6400}(121,\cdot)\) \(\chi_{6400}(281,\cdot)\) \(\chi_{6400}(361,\cdot)\) \(\chi_{6400}(441,\cdot)\) \(\chi_{6400}(521,\cdot)\) \(\chi_{6400}(681,\cdot)\) \(\chi_{6400}(761,\cdot)\) \(\chi_{6400}(841,\cdot)\) \(\chi_{6400}(921,\cdot)\) \(\chi_{6400}(1081,\cdot)\) \(\chi_{6400}(1161,\cdot)\) \(\chi_{6400}(1241,\cdot)\) \(\chi_{6400}(1321,\cdot)\) \(\chi_{6400}(1481,\cdot)\) \(\chi_{6400}(1561,\cdot)\) \(\chi_{6400}(1641,\cdot)\) \(\chi_{6400}(1721,\cdot)\) \(\chi_{6400}(1881,\cdot)\) \(\chi_{6400}(1961,\cdot)\) \(\chi_{6400}(2041,\cdot)\) \(\chi_{6400}(2121,\cdot)\) \(\chi_{6400}(2281,\cdot)\) \(\chi_{6400}(2361,\cdot)\) \(\chi_{6400}(2441,\cdot)\) \(\chi_{6400}(2521,\cdot)\) \(\chi_{6400}(2681,\cdot)\) \(\chi_{6400}(2761,\cdot)\) \(\chi_{6400}(2841,\cdot)\) \(\chi_{6400}(2921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{31}{32}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{160}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{87}{160}\right)\) | \(e\left(\frac{53}{160}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{147}{160}\right)\) |