Basic properties
| Modulus: | \(6369\) | |
| Conductor: | \(6369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(960\) | 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.eg
\(\chi_{6369}(17,\cdot)\) \(\chi_{6369}(41,\cdot)\) \(\chi_{6369}(116,\cdot)\) \(\chi_{6369}(140,\cdot)\) \(\chi_{6369}(149,\cdot)\) \(\chi_{6369}(167,\cdot)\) \(\chi_{6369}(215,\cdot)\) \(\chi_{6369}(227,\cdot)\) \(\chi_{6369}(233,\cdot)\) \(\chi_{6369}(266,\cdot)\) \(\chi_{6369}(272,\cdot)\) \(\chi_{6369}(371,\cdot)\) \(\chi_{6369}(431,\cdot)\) \(\chi_{6369}(437,\cdot)\) \(\chi_{6369}(464,\cdot)\) \(\chi_{6369}(497,\cdot)\) \(\chi_{6369}(545,\cdot)\) \(\chi_{6369}(557,\cdot)\) \(\chi_{6369}(569,\cdot)\) \(\chi_{6369}(596,\cdot)\) \(\chi_{6369}(623,\cdot)\) \(\chi_{6369}(656,\cdot)\) \(\chi_{6369}(695,\cdot)\) \(\chi_{6369}(728,\cdot)\) \(\chi_{6369}(734,\cdot)\) \(\chi_{6369}(755,\cdot)\) \(\chi_{6369}(767,\cdot)\) \(\chi_{6369}(794,\cdot)\) \(\chi_{6369}(809,\cdot)\) \(\chi_{6369}(833,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{960})$ |
| Fixed field: | Number field defined by a degree 960 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{179}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(1196, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{480}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{607}{960}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{79}{160}\right)\) | \(e\left(\frac{25}{192}\right)\) | \(e\left(\frac{241}{320}\right)\) | \(e\left(\frac{89}{160}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{97}{960}\right)\) |