Basic properties
| Modulus: | \(86400\) | |
| Conductor: | \(86400\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1440\) | 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 86400.uh
\(\chi_{86400}(139,\cdot)\) \(\chi_{86400}(259,\cdot)\) \(\chi_{86400}(619,\cdot)\) \(\chi_{86400}(859,\cdot)\) \(\chi_{86400}(979,\cdot)\) \(\chi_{86400}(1219,\cdot)\) \(\chi_{86400}(1339,\cdot)\) \(\chi_{86400}(1579,\cdot)\) \(\chi_{86400}(1939,\cdot)\) \(\chi_{86400}(2059,\cdot)\) \(\chi_{86400}(2419,\cdot)\) \(\chi_{86400}(2659,\cdot)\) \(\chi_{86400}(2779,\cdot)\) \(\chi_{86400}(3019,\cdot)\) \(\chi_{86400}(3139,\cdot)\) \(\chi_{86400}(3379,\cdot)\) \(\chi_{86400}(3739,\cdot)\) \(\chi_{86400}(3859,\cdot)\) \(\chi_{86400}(4219,\cdot)\) \(\chi_{86400}(4459,\cdot)\) \(\chi_{86400}(4579,\cdot)\) \(\chi_{86400}(4819,\cdot)\) \(\chi_{86400}(4939,\cdot)\) \(\chi_{86400}(5179,\cdot)\) \(\chi_{86400}(5539,\cdot)\) \(\chi_{86400}(5659,\cdot)\) \(\chi_{86400}(6019,\cdot)\) \(\chi_{86400}(6259,\cdot)\) \(\chi_{86400}(6379,\cdot)\) \(\chi_{86400}(6619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1440})$ |
| Fixed field: | Number field defined by a degree 1440 polynomial (not computed) |
Values on generators
\((71551,29701,6401,72577)\) → \((-1,e\left(\frac{29}{32}\right),e\left(\frac{4}{9}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 86400 }(1579, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{144}\right)\) | \(e\left(\frac{1309}{1440}\right)\) | \(e\left(\frac{71}{1440}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{229}{480}\right)\) | \(e\left(\frac{127}{720}\right)\) | \(e\left(\frac{163}{1440}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{107}{480}\right)\) | \(e\left(\frac{103}{720}\right)\) |