Basic properties
| Modulus: | \(1033\) | |
| Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1032\) | 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.p
\(\chi_{1033}(5,\cdot)\) \(\chi_{1033}(10,\cdot)\) \(\chi_{1033}(11,\cdot)\) \(\chi_{1033}(13,\cdot)\) \(\chi_{1033}(22,\cdot)\) \(\chi_{1033}(23,\cdot)\) \(\chi_{1033}(26,\cdot)\) \(\chi_{1033}(29,\cdot)\) \(\chi_{1033}(30,\cdot)\) \(\chi_{1033}(35,\cdot)\) \(\chi_{1033}(40,\cdot)\) \(\chi_{1033}(45,\cdot)\) \(\chi_{1033}(47,\cdot)\) \(\chi_{1033}(58,\cdot)\) \(\chi_{1033}(59,\cdot)\) \(\chi_{1033}(60,\cdot)\) \(\chi_{1033}(66,\cdot)\) \(\chi_{1033}(67,\cdot)\) \(\chi_{1033}(69,\cdot)\) \(\chi_{1033}(70,\cdot)\) \(\chi_{1033}(71,\cdot)\) \(\chi_{1033}(77,\cdot)\) \(\chi_{1033}(78,\cdot)\) \(\chi_{1033}(79,\cdot)\) \(\chi_{1033}(80,\cdot)\) \(\chi_{1033}(88,\cdot)\) \(\chi_{1033}(91,\cdot)\) \(\chi_{1033}(92,\cdot)\) \(\chi_{1033}(94,\cdot)\) \(\chi_{1033}(97,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1032})$ |
| Fixed field: | Number field defined by a degree 1032 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{365}{1032}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1033 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{258}\right)\) | \(e\left(\frac{491}{516}\right)\) | \(e\left(\frac{62}{129}\right)\) | \(e\left(\frac{365}{1032}\right)\) | \(e\left(\frac{119}{172}\right)\) | \(e\left(\frac{59}{172}\right)\) | \(e\left(\frac{19}{86}\right)\) | \(e\left(\frac{233}{258}\right)\) | \(e\left(\frac{97}{1032}\right)\) | \(e\left(\frac{857}{1032}\right)\) |