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 \(\chi_{3200}(723,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.dq
\(\chi_{6400}(23,\cdot)\) \(\chi_{6400}(167,\cdot)\) \(\chi_{6400}(183,\cdot)\) \(\chi_{6400}(327,\cdot)\) \(\chi_{6400}(487,\cdot)\) \(\chi_{6400}(503,\cdot)\) \(\chi_{6400}(647,\cdot)\) \(\chi_{6400}(663,\cdot)\) \(\chi_{6400}(823,\cdot)\) \(\chi_{6400}(967,\cdot)\) \(\chi_{6400}(983,\cdot)\) \(\chi_{6400}(1127,\cdot)\) \(\chi_{6400}(1287,\cdot)\) \(\chi_{6400}(1303,\cdot)\) \(\chi_{6400}(1447,\cdot)\) \(\chi_{6400}(1463,\cdot)\) \(\chi_{6400}(1623,\cdot)\) \(\chi_{6400}(1767,\cdot)\) \(\chi_{6400}(1783,\cdot)\) \(\chi_{6400}(1927,\cdot)\) \(\chi_{6400}(2087,\cdot)\) \(\chi_{6400}(2103,\cdot)\) \(\chi_{6400}(2247,\cdot)\) \(\chi_{6400}(2263,\cdot)\) \(\chi_{6400}(2423,\cdot)\) \(\chi_{6400}(2567,\cdot)\) \(\chi_{6400}(2583,\cdot)\) \(\chi_{6400}(2727,\cdot)\) \(\chi_{6400}(2887,\cdot)\) \(\chi_{6400}(2903,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,4101,5377)\) → \((-1,e\left(\frac{7}{32}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6400 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{160}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{143}{160}\right)\) | \(e\left(\frac{117}{160}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{69}{160}\right)\) | \(e\left(\frac{71}{160}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{3}{160}\right)\) |