Basic properties
| Modulus: | \(6369\) | |
| Conductor: | \(6369\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6369.dw
\(\chi_{6369}(29,\cdot)\) \(\chi_{6369}(35,\cdot)\) \(\chi_{6369}(68,\cdot)\) \(\chi_{6369}(74,\cdot)\) \(\chi_{6369}(173,\cdot)\) \(\chi_{6369}(182,\cdot)\) \(\chi_{6369}(206,\cdot)\) \(\chi_{6369}(281,\cdot)\) \(\chi_{6369}(299,\cdot)\) \(\chi_{6369}(326,\cdot)\) \(\chi_{6369}(347,\cdot)\) \(\chi_{6369}(425,\cdot)\) \(\chi_{6369}(446,\cdot)\) \(\chi_{6369}(491,\cdot)\) \(\chi_{6369}(503,\cdot)\) \(\chi_{6369}(590,\cdot)\) \(\chi_{6369}(668,\cdot)\) \(\chi_{6369}(701,\cdot)\) \(\chi_{6369}(743,\cdot)\) \(\chi_{6369}(761,\cdot)\) \(\chi_{6369}(860,\cdot)\) \(\chi_{6369}(866,\cdot)\) \(\chi_{6369}(926,\cdot)\) \(\chi_{6369}(932,\cdot)\) \(\chi_{6369}(998,\cdot)\) \(\chi_{6369}(1025,\cdot)\) \(\chi_{6369}(1052,\cdot)\) \(\chi_{6369}(1064,\cdot)\) \(\chi_{6369}(1229,\cdot)\) \(\chi_{6369}(1262,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{320})$ |
| Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{3}{64}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(1316, a) \) | \(-1\) | \(1\) | \(e\left(\frac{127}{160}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{111}{320}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{61}{160}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{99}{320}\right)\) | \(e\left(\frac{91}{160}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{81}{320}\right)\) |