Basic properties
| Modulus: | \(1033\) | |
| Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(516\) | 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.o
\(\chi_{1033}(3,\cdot)\) \(\chi_{1033}(12,\cdot)\) \(\chi_{1033}(17,\cdot)\) \(\chi_{1033}(24,\cdot)\) \(\chi_{1033}(25,\cdot)\) \(\chi_{1033}(28,\cdot)\) \(\chi_{1033}(31,\cdot)\) \(\chi_{1033}(41,\cdot)\) \(\chi_{1033}(43,\cdot)\) \(\chi_{1033}(54,\cdot)\) \(\chi_{1033}(55,\cdot)\) \(\chi_{1033}(57,\cdot)\) \(\chi_{1033}(63,\cdot)\) \(\chi_{1033}(65,\cdot)\) \(\chi_{1033}(68,\cdot)\) \(\chi_{1033}(82,\cdot)\) \(\chi_{1033}(83,\cdot)\) \(\chi_{1033}(86,\cdot)\) \(\chi_{1033}(96,\cdot)\) \(\chi_{1033}(100,\cdot)\) \(\chi_{1033}(108,\cdot)\) \(\chi_{1033}(111,\cdot)\) \(\chi_{1033}(112,\cdot)\) \(\chi_{1033}(114,\cdot)\) \(\chi_{1033}(121,\cdot)\) \(\chi_{1033}(122,\cdot)\) \(\chi_{1033}(124,\cdot)\) \(\chi_{1033}(126,\cdot)\) \(\chi_{1033}(127,\cdot)\) \(\chi_{1033}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{516})$ |
| Fixed field: | Number field defined by a degree 516 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{516}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1033 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{129}\right)\) | \(e\left(\frac{7}{258}\right)\) | \(e\left(\frac{53}{129}\right)\) | \(e\left(\frac{1}{516}\right)\) | \(e\left(\frac{63}{86}\right)\) | \(e\left(\frac{11}{86}\right)\) | \(e\left(\frac{5}{43}\right)\) | \(e\left(\frac{7}{129}\right)\) | \(e\left(\frac{365}{516}\right)\) | \(e\left(\frac{49}{516}\right)\) |