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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6369.ef
\(\chi_{6369}(5,\cdot)\) \(\chi_{6369}(26,\cdot)\) \(\chi_{6369}(38,\cdot)\) \(\chi_{6369}(47,\cdot)\) \(\chi_{6369}(53,\cdot)\) \(\chi_{6369}(80,\cdot)\) \(\chi_{6369}(113,\cdot)\) \(\chi_{6369}(146,\cdot)\) \(\chi_{6369}(152,\cdot)\) \(\chi_{6369}(203,\cdot)\) \(\chi_{6369}(212,\cdot)\) \(\chi_{6369}(245,\cdot)\) \(\chi_{6369}(251,\cdot)\) \(\chi_{6369}(284,\cdot)\) \(\chi_{6369}(335,\cdot)\) \(\chi_{6369}(356,\cdot)\) \(\chi_{6369}(401,\cdot)\) \(\chi_{6369}(416,\cdot)\) \(\chi_{6369}(443,\cdot)\) \(\chi_{6369}(476,\cdot)\) \(\chi_{6369}(488,\cdot)\) \(\chi_{6369}(500,\cdot)\) \(\chi_{6369}(509,\cdot)\) \(\chi_{6369}(521,\cdot)\) \(\chi_{6369}(542,\cdot)\) \(\chi_{6369}(620,\cdot)\) \(\chi_{6369}(632,\cdot)\) \(\chi_{6369}(719,\cdot)\) \(\chi_{6369}(731,\cdot)\) \(\chi_{6369}(746,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{960})$ |
| Fixed field: | Number field defined by a degree 960 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{59}{192}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 6369 }(1202, a) \) | \(1\) | \(1\) | \(e\left(\frac{359}{480}\right)\) | \(e\left(\frac{119}{240}\right)\) | \(e\left(\frac{7}{960}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{39}{160}\right)\) | \(e\left(\frac{145}{192}\right)\) | \(e\left(\frac{41}{320}\right)\) | \(e\left(\frac{49}{160}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{217}{960}\right)\) |