Basic properties
| Modulus: | \(1033\) | |
| Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(86\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1033.j
\(\chi_{1033}(8,\cdot)\) \(\chi_{1033}(36,\cdot)\) \(\chi_{1033}(37,\cdot)\) \(\chi_{1033}(38,\cdot)\) \(\chi_{1033}(42,\cdot)\) \(\chi_{1033}(49,\cdot)\) \(\chi_{1033}(123,\cdot)\) \(\chi_{1033}(162,\cdot)\) \(\chi_{1033}(171,\cdot)\) \(\chi_{1033}(189,\cdot)\) \(\chi_{1033}(204,\cdot)\) \(\chi_{1033}(238,\cdot)\) \(\chi_{1033}(253,\cdot)\) \(\chi_{1033}(302,\cdot)\) \(\chi_{1033}(326,\cdot)\) \(\chi_{1033}(334,\cdot)\) \(\chi_{1033}(366,\cdot)\) \(\chi_{1033}(372,\cdot)\) \(\chi_{1033}(427,\cdot)\) \(\chi_{1033}(434,\cdot)\) \(\chi_{1033}(470,\cdot)\) \(\chi_{1033}(491,\cdot)\) \(\chi_{1033}(512,\cdot)\) \(\chi_{1033}(554,\cdot)\) \(\chi_{1033}(614,\cdot)\) \(\chi_{1033}(622,\cdot)\) \(\chi_{1033}(641,\cdot)\) \(\chi_{1033}(660,\cdot)\) \(\chi_{1033}(683,\cdot)\) \(\chi_{1033}(697,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 86 polynomial |
Values on generators
\(5\) → \(e\left(\frac{5}{86}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1033 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{14}{43}\right)\) | \(e\left(\frac{5}{86}\right)\) | \(e\left(\frac{42}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{21}{43}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{19}{86}\right)\) | \(e\left(\frac{73}{86}\right)\) |