Basic properties
| Modulus: | \(4719\) | |
| Conductor: | \(4719\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | 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 4719.do
\(\chi_{4719}(20,\cdot)\) \(\chi_{4719}(59,\cdot)\) \(\chi_{4719}(71,\cdot)\) \(\chi_{4719}(80,\cdot)\) \(\chi_{4719}(119,\cdot)\) \(\chi_{4719}(137,\cdot)\) \(\chi_{4719}(158,\cdot)\) \(\chi_{4719}(236,\cdot)\) \(\chi_{4719}(284,\cdot)\) \(\chi_{4719}(344,\cdot)\) \(\chi_{4719}(383,\cdot)\) \(\chi_{4719}(401,\cdot)\) \(\chi_{4719}(410,\cdot)\) \(\chi_{4719}(422,\cdot)\) \(\chi_{4719}(449,\cdot)\) \(\chi_{4719}(488,\cdot)\) \(\chi_{4719}(500,\cdot)\) \(\chi_{4719}(509,\cdot)\) \(\chi_{4719}(548,\cdot)\) \(\chi_{4719}(566,\cdot)\) \(\chi_{4719}(587,\cdot)\) \(\chi_{4719}(665,\cdot)\) \(\chi_{4719}(674,\cdot)\) \(\chi_{4719}(713,\cdot)\) \(\chi_{4719}(752,\cdot)\) \(\chi_{4719}(773,\cdot)\) \(\chi_{4719}(812,\cdot)\) \(\chi_{4719}(830,\cdot)\) \(\chi_{4719}(839,\cdot)\) \(\chi_{4719}(851,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((1574,3511,4357)\) → \((-1,e\left(\frac{38}{55}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4719 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{660}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{607}{660}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{71}{165}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{613}{660}\right)\) |