Basic properties
| Modulus: | \(1747\) | |
| Conductor: | \(1747\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1746\) | 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 1747.l
\(\chi_{1747}(2,\cdot)\) \(\chi_{1747}(3,\cdot)\) \(\chi_{1747}(5,\cdot)\) \(\chi_{1747}(7,\cdot)\) \(\chi_{1747}(12,\cdot)\) \(\chi_{1747}(13,\cdot)\) \(\chi_{1747}(18,\cdot)\) \(\chi_{1747}(20,\cdot)\) \(\chi_{1747}(30,\cdot)\) \(\chi_{1747}(32,\cdot)\) \(\chi_{1747}(37,\cdot)\) \(\chi_{1747}(38,\cdot)\) \(\chi_{1747}(42,\cdot)\) \(\chi_{1747}(44,\cdot)\) \(\chi_{1747}(46,\cdot)\) \(\chi_{1747}(47,\cdot)\) \(\chi_{1747}(50,\cdot)\) \(\chi_{1747}(51,\cdot)\) \(\chi_{1747}(53,\cdot)\) \(\chi_{1747}(57,\cdot)\) \(\chi_{1747}(58,\cdot)\) \(\chi_{1747}(59,\cdot)\) \(\chi_{1747}(63,\cdot)\) \(\chi_{1747}(70,\cdot)\) \(\chi_{1747}(71,\cdot)\) \(\chi_{1747}(72,\cdot)\) \(\chi_{1747}(78,\cdot)\) \(\chi_{1747}(82,\cdot)\) \(\chi_{1747}(83,\cdot)\) \(\chi_{1747}(85,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{873})$ |
| Fixed field: | Number field defined by a degree 1746 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{221}{1746}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1747 }(175, a) \) | \(-1\) | \(1\) | \(e\left(\frac{221}{1746}\right)\) | \(e\left(\frac{1147}{1746}\right)\) | \(e\left(\frac{221}{873}\right)\) | \(e\left(\frac{973}{1746}\right)\) | \(e\left(\frac{76}{97}\right)\) | \(e\left(\frac{1499}{1746}\right)\) | \(e\left(\frac{221}{582}\right)\) | \(e\left(\frac{274}{873}\right)\) | \(e\left(\frac{199}{291}\right)\) | \(e\left(\frac{385}{582}\right)\) |