Basic properties
| Modulus: | \(1033\) | |
| Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(258\) | 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.m
\(\chi_{1033}(2,\cdot)\) \(\chi_{1033}(9,\cdot)\) \(\chi_{1033}(32,\cdot)\) \(\chi_{1033}(51,\cdot)\) \(\chi_{1033}(93,\cdot)\) \(\chi_{1033}(128,\cdot)\) \(\chi_{1033}(144,\cdot)\) \(\chi_{1033}(148,\cdot)\) \(\chi_{1033}(150,\cdot)\) \(\chi_{1033}(152,\cdot)\) \(\chi_{1033}(165,\cdot)\) \(\chi_{1033}(168,\cdot)\) \(\chi_{1033}(175,\cdot)\) \(\chi_{1033}(179,\cdot)\) \(\chi_{1033}(226,\cdot)\) \(\chi_{1033}(230,\cdot)\) \(\chi_{1033}(258,\cdot)\) \(\chi_{1033}(271,\cdot)\) \(\chi_{1033}(289,\cdot)\) \(\chi_{1033}(301,\cdot)\) \(\chi_{1033}(303,\cdot)\) \(\chi_{1033}(365,\cdot)\) \(\chi_{1033}(381,\cdot)\) \(\chi_{1033}(390,\cdot)\) \(\chi_{1033}(422,\cdot)\) \(\chi_{1033}(429,\cdot)\) \(\chi_{1033}(431,\cdot)\) \(\chi_{1033}(455,\cdot)\) \(\chi_{1033}(492,\cdot)\) \(\chi_{1033}(498,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{129})$ |
| Fixed field: | Number field defined by a degree 258 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{197}{258}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1033 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{129}\right)\) | \(e\left(\frac{89}{129}\right)\) | \(e\left(\frac{113}{129}\right)\) | \(e\left(\frac{197}{258}\right)\) | \(e\left(\frac{27}{43}\right)\) | \(e\left(\frac{17}{43}\right)\) | \(e\left(\frac{35}{43}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{181}{258}\right)\) | \(e\left(\frac{107}{258}\right)\) |