Basic properties
| Modulus: | \(259200\) | |
| Conductor: | \(86400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1440\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{86400}(9619,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 259200.zv
\(\chi_{259200}(19,\cdot)\) \(\chi_{259200}(739,\cdot)\) \(\chi_{259200}(1819,\cdot)\) \(\chi_{259200}(2179,\cdot)\) \(\chi_{259200}(3259,\cdot)\) \(\chi_{259200}(3979,\cdot)\) \(\chi_{259200}(4339,\cdot)\) \(\chi_{259200}(5059,\cdot)\) \(\chi_{259200}(5419,\cdot)\) \(\chi_{259200}(6139,\cdot)\) \(\chi_{259200}(7219,\cdot)\) \(\chi_{259200}(7579,\cdot)\) \(\chi_{259200}(8659,\cdot)\) \(\chi_{259200}(9379,\cdot)\) \(\chi_{259200}(9739,\cdot)\) \(\chi_{259200}(10459,\cdot)\) \(\chi_{259200}(10819,\cdot)\) \(\chi_{259200}(11539,\cdot)\) \(\chi_{259200}(12619,\cdot)\) \(\chi_{259200}(12979,\cdot)\) \(\chi_{259200}(14059,\cdot)\) \(\chi_{259200}(14779,\cdot)\) \(\chi_{259200}(15139,\cdot)\) \(\chi_{259200}(15859,\cdot)\) \(\chi_{259200}(16219,\cdot)\) \(\chi_{259200}(16939,\cdot)\) \(\chi_{259200}(18019,\cdot)\) \(\chi_{259200}(18379,\cdot)\) \(\chi_{259200}(19459,\cdot)\) \(\chi_{259200}(20179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1440})$ |
| Fixed field: | Number field defined by a degree 1440 polynomial (not computed) |
Values on generators
\((157951,202501,6401,72577)\) → \((-1,e\left(\frac{23}{32}\right),e\left(\frac{8}{9}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 259200 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{144}\right)\) | \(e\left(\frac{791}{1440}\right)\) | \(e\left(\frac{1429}{1440}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{431}{480}\right)\) | \(e\left(\frac{173}{720}\right)\) | \(e\left(\frac{137}{1440}\right)\) | \(e\left(\frac{41}{180}\right)\) | \(e\left(\frac{193}{480}\right)\) | \(e\left(\frac{197}{720}\right)\) |