Basic properties
| Modulus: | \(8038\) | |
| Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4018\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4019}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8038.l
\(\chi_{8038}(7,\cdot)\) \(\chi_{8038}(11,\cdot)\) \(\chi_{8038}(13,\cdot)\) \(\chi_{8038}(17,\cdot)\) \(\chi_{8038}(21,\cdot)\) \(\chi_{8038}(29,\cdot)\) \(\chi_{8038}(31,\cdot)\) \(\chi_{8038}(33,\cdot)\) \(\chi_{8038}(35,\cdot)\) \(\chi_{8038}(37,\cdot)\) \(\chi_{8038}(39,\cdot)\) \(\chi_{8038}(47,\cdot)\) \(\chi_{8038}(51,\cdot)\) \(\chi_{8038}(59,\cdot)\) \(\chi_{8038}(61,\cdot)\) \(\chi_{8038}(63,\cdot)\) \(\chi_{8038}(65,\cdot)\) \(\chi_{8038}(71,\cdot)\) \(\chi_{8038}(85,\cdot)\) \(\chi_{8038}(93,\cdot)\) \(\chi_{8038}(99,\cdot)\) \(\chi_{8038}(103,\cdot)\) \(\chi_{8038}(105,\cdot)\) \(\chi_{8038}(109,\cdot)\) \(\chi_{8038}(111,\cdot)\) \(\chi_{8038}(127,\cdot)\) \(\chi_{8038}(131,\cdot)\) \(\chi_{8038}(133,\cdot)\) \(\chi_{8038}(137,\cdot)\) \(\chi_{8038}(139,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2009})$ |
| Fixed field: | Number field defined by a degree 4018 polynomial (not computed) |
Values on generators
\(4021\) → \(e\left(\frac{473}{4018}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8038 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{1417}{2009}\right)\) | \(e\left(\frac{2763}{4018}\right)\) | \(e\left(\frac{16}{49}\right)\) | \(e\left(\frac{2913}{4018}\right)\) | \(e\left(\frac{2895}{4018}\right)\) | \(e\left(\frac{1745}{2009}\right)\) | \(e\left(\frac{1375}{4018}\right)\) | \(e\left(\frac{411}{2009}\right)\) | \(e\left(\frac{3419}{4018}\right)\) |