Basic properties
Modulus: | \(1049\) | |
Conductor: | \(1049\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1048\) | 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 1049.h
\(\chi_{1049}(3,\cdot)\) \(\chi_{1049}(6,\cdot)\) \(\chi_{1049}(7,\cdot)\) \(\chi_{1049}(12,\cdot)\) \(\chi_{1049}(14,\cdot)\) \(\chi_{1049}(15,\cdot)\) \(\chi_{1049}(17,\cdot)\) \(\chi_{1049}(23,\cdot)\) \(\chi_{1049}(24,\cdot)\) \(\chi_{1049}(27,\cdot)\) \(\chi_{1049}(28,\cdot)\) \(\chi_{1049}(30,\cdot)\) \(\chi_{1049}(31,\cdot)\) \(\chi_{1049}(33,\cdot)\) \(\chi_{1049}(34,\cdot)\) \(\chi_{1049}(35,\cdot)\) \(\chi_{1049}(37,\cdot)\) \(\chi_{1049}(39,\cdot)\) \(\chi_{1049}(41,\cdot)\) \(\chi_{1049}(46,\cdot)\) \(\chi_{1049}(47,\cdot)\) \(\chi_{1049}(48,\cdot)\) \(\chi_{1049}(54,\cdot)\) \(\chi_{1049}(56,\cdot)\) \(\chi_{1049}(57,\cdot)\) \(\chi_{1049}(60,\cdot)\) \(\chi_{1049}(62,\cdot)\) \(\chi_{1049}(63,\cdot)\) \(\chi_{1049}(66,\cdot)\) \(\chi_{1049}(67,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1048})$ |
Fixed field: | Number field defined by a degree 1048 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{1048}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1049 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{262}\right)\) | \(e\left(\frac{1}{1048}\right)\) | \(e\left(\frac{18}{131}\right)\) | \(e\left(\frac{49}{524}\right)\) | \(e\left(\frac{597}{1048}\right)\) | \(e\left(\frac{255}{1048}\right)\) | \(e\left(\frac{185}{262}\right)\) | \(e\left(\frac{1}{524}\right)\) | \(e\left(\frac{347}{524}\right)\) | \(e\left(\frac{209}{524}\right)\) |