Basic properties
| Modulus: | \(1849\) | |
| Conductor: | \(1849\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(602\) | 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.n
\(\chi_{1849}(2,\cdot)\) \(\chi_{1849}(8,\cdot)\) \(\chi_{1849}(22,\cdot)\) \(\chi_{1849}(27,\cdot)\) \(\chi_{1849}(32,\cdot)\) \(\chi_{1849}(39,\cdot)\) \(\chi_{1849}(45,\cdot)\) \(\chi_{1849}(51,\cdot)\) \(\chi_{1849}(65,\cdot)\) \(\chi_{1849}(70,\cdot)\) \(\chi_{1849}(82,\cdot)\) \(\chi_{1849}(88,\cdot)\) \(\chi_{1849}(94,\cdot)\) \(\chi_{1849}(108,\cdot)\) \(\chi_{1849}(113,\cdot)\) \(\chi_{1849}(118,\cdot)\) \(\chi_{1849}(125,\cdot)\) \(\chi_{1849}(131,\cdot)\) \(\chi_{1849}(137,\cdot)\) \(\chi_{1849}(151,\cdot)\) \(\chi_{1849}(156,\cdot)\) \(\chi_{1849}(161,\cdot)\) \(\chi_{1849}(168,\cdot)\) \(\chi_{1849}(174,\cdot)\) \(\chi_{1849}(180,\cdot)\) \(\chi_{1849}(194,\cdot)\) \(\chi_{1849}(199,\cdot)\) \(\chi_{1849}(204,\cdot)\) \(\chi_{1849}(211,\cdot)\) \(\chi_{1849}(217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{301})$ |
| Fixed field: | Number field defined by a degree 602 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{335}{602}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1849 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{253}{602}\right)\) | \(e\left(\frac{335}{602}\right)\) | \(e\left(\frac{253}{301}\right)\) | \(e\left(\frac{241}{602}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{29}{86}\right)\) | \(e\left(\frac{157}{602}\right)\) | \(e\left(\frac{34}{301}\right)\) | \(e\left(\frac{247}{301}\right)\) | \(e\left(\frac{104}{301}\right)\) |