Basic properties
| Modulus: | \(1033\) | |
| Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(344\) | 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 1033.n
\(\chi_{1033}(15,\cdot)\) \(\chi_{1033}(20,\cdot)\) \(\chi_{1033}(33,\cdot)\) \(\chi_{1033}(39,\cdot)\) \(\chi_{1033}(44,\cdot)\) \(\chi_{1033}(46,\cdot)\) \(\chi_{1033}(52,\cdot)\) \(\chi_{1033}(53,\cdot)\) \(\chi_{1033}(73,\cdot)\) \(\chi_{1033}(85,\cdot)\) \(\chi_{1033}(87,\cdot)\) \(\chi_{1033}(89,\cdot)\) \(\chi_{1033}(90,\cdot)\) \(\chi_{1033}(95,\cdot)\) \(\chi_{1033}(103,\cdot)\) \(\chi_{1033}(105,\cdot)\) \(\chi_{1033}(116,\cdot)\) \(\chi_{1033}(118,\cdot)\) \(\chi_{1033}(120,\cdot)\) \(\chi_{1033}(125,\cdot)\) \(\chi_{1033}(131,\cdot)\) \(\chi_{1033}(134,\cdot)\) \(\chi_{1033}(140,\cdot)\) \(\chi_{1033}(141,\cdot)\) \(\chi_{1033}(142,\cdot)\) \(\chi_{1033}(155,\cdot)\) \(\chi_{1033}(158,\cdot)\) \(\chi_{1033}(160,\cdot)\) \(\chi_{1033}(181,\cdot)\) \(\chi_{1033}(187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{344})$ |
| Fixed field: | Number field defined by a degree 344 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{243}{344}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1033 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{86}\right)\) | \(e\left(\frac{153}{172}\right)\) | \(e\left(\frac{11}{43}\right)\) | \(e\left(\frac{243}{344}\right)\) | \(e\left(\frac{3}{172}\right)\) | \(e\left(\frac{107}{172}\right)\) | \(e\left(\frac{33}{86}\right)\) | \(e\left(\frac{67}{86}\right)\) | \(e\left(\frac{287}{344}\right)\) | \(e\left(\frac{39}{344}\right)\) |