Basic properties
| Modulus: | \(8038\) | |
| Conductor: | \(4019\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2009\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4019}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8038.k
\(\chi_{8038}(5,\cdot)\) \(\chi_{8038}(15,\cdot)\) \(\chi_{8038}(19,\cdot)\) \(\chi_{8038}(23,\cdot)\) \(\chi_{8038}(25,\cdot)\) \(\chi_{8038}(43,\cdot)\) \(\chi_{8038}(45,\cdot)\) \(\chi_{8038}(49,\cdot)\) \(\chi_{8038}(53,\cdot)\) \(\chi_{8038}(57,\cdot)\) \(\chi_{8038}(67,\cdot)\) \(\chi_{8038}(69,\cdot)\) \(\chi_{8038}(73,\cdot)\) \(\chi_{8038}(75,\cdot)\) \(\chi_{8038}(77,\cdot)\) \(\chi_{8038}(79,\cdot)\) \(\chi_{8038}(83,\cdot)\) \(\chi_{8038}(95,\cdot)\) \(\chi_{8038}(101,\cdot)\) \(\chi_{8038}(107,\cdot)\) \(\chi_{8038}(113,\cdot)\) \(\chi_{8038}(115,\cdot)\) \(\chi_{8038}(119,\cdot)\) \(\chi_{8038}(121,\cdot)\) \(\chi_{8038}(123,\cdot)\) \(\chi_{8038}(125,\cdot)\) \(\chi_{8038}(129,\cdot)\) \(\chi_{8038}(143,\cdot)\) \(\chi_{8038}(147,\cdot)\) \(\chi_{8038}(151,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2009})$ |
| Fixed field: | Number field defined by a degree 2009 polynomial (not computed) |
Values on generators
\(4021\) → \(e\left(\frac{192}{2009}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8038 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{148}{2009}\right)\) | \(e\left(\frac{408}{2009}\right)\) | \(e\left(\frac{45}{49}\right)\) | \(e\left(\frac{1896}{2009}\right)\) | \(e\left(\frac{1396}{2009}\right)\) | \(e\left(\frac{66}{2009}\right)\) | \(e\left(\frac{1586}{2009}\right)\) | \(e\left(\frac{1404}{2009}\right)\) | \(e\left(\frac{326}{2009}\right)\) |