Basic properties
| Modulus: | \(1849\) | |
| Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1806\) | 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 1849.p
\(\chi_{1849}(3,\cdot)\) \(\chi_{1849}(5,\cdot)\) \(\chi_{1849}(12,\cdot)\) \(\chi_{1849}(18,\cdot)\) \(\chi_{1849}(20,\cdot)\) \(\chi_{1849}(26,\cdot)\) \(\chi_{1849}(28,\cdot)\) \(\chi_{1849}(29,\cdot)\) \(\chi_{1849}(30,\cdot)\) \(\chi_{1849}(33,\cdot)\) \(\chi_{1849}(34,\cdot)\) \(\chi_{1849}(46,\cdot)\) \(\chi_{1849}(48,\cdot)\) \(\chi_{1849}(55,\cdot)\) \(\chi_{1849}(61,\cdot)\) \(\chi_{1849}(62,\cdot)\) \(\chi_{1849}(63,\cdot)\) \(\chi_{1849}(69,\cdot)\) \(\chi_{1849}(71,\cdot)\) \(\chi_{1849}(72,\cdot)\) \(\chi_{1849}(73,\cdot)\) \(\chi_{1849}(76,\cdot)\) \(\chi_{1849}(77,\cdot)\) \(\chi_{1849}(89,\cdot)\) \(\chi_{1849}(91,\cdot)\) \(\chi_{1849}(98,\cdot)\) \(\chi_{1849}(104,\cdot)\) \(\chi_{1849}(105,\cdot)\) \(\chi_{1849}(106,\cdot)\) \(\chi_{1849}(112,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{903})$ |
| Fixed field: | Number field defined by a degree 1806 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{1806}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1849 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{513}{602}\right)\) | \(e\left(\frac{1}{1806}\right)\) | \(e\left(\frac{212}{301}\right)\) | \(e\left(\frac{193}{1806}\right)\) | \(e\left(\frac{110}{129}\right)\) | \(e\left(\frac{35}{258}\right)\) | \(e\left(\frac{335}{602}\right)\) | \(e\left(\frac{1}{903}\right)\) | \(e\left(\frac{866}{903}\right)\) | \(e\left(\frac{243}{301}\right)\) |