Basic properties
Modulus: | \(1049\) | |
Conductor: | \(1049\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(524\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1049.g
\(\chi_{1049}(5,\cdot)\) \(\chi_{1049}(9,\cdot)\) \(\chi_{1049}(10,\cdot)\) \(\chi_{1049}(11,\cdot)\) \(\chi_{1049}(18,\cdot)\) \(\chi_{1049}(20,\cdot)\) \(\chi_{1049}(22,\cdot)\) \(\chi_{1049}(36,\cdot)\) \(\chi_{1049}(40,\cdot)\) \(\chi_{1049}(44,\cdot)\) \(\chi_{1049}(49,\cdot)\) \(\chi_{1049}(51,\cdot)\) \(\chi_{1049}(59,\cdot)\) \(\chi_{1049}(65,\cdot)\) \(\chi_{1049}(72,\cdot)\) \(\chi_{1049}(79,\cdot)\) \(\chi_{1049}(80,\cdot)\) \(\chi_{1049}(88,\cdot)\) \(\chi_{1049}(93,\cdot)\) \(\chi_{1049}(95,\cdot)\) \(\chi_{1049}(98,\cdot)\) \(\chi_{1049}(102,\cdot)\) \(\chi_{1049}(103,\cdot)\) \(\chi_{1049}(105,\cdot)\) \(\chi_{1049}(107,\cdot)\) \(\chi_{1049}(111,\cdot)\) \(\chi_{1049}(113,\cdot)\) \(\chi_{1049}(117,\cdot)\) \(\chi_{1049}(118,\cdot)\) \(\chi_{1049}(123,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{524})$ |
Fixed field: | Number field defined by a degree 524 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{49}{524}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1049 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{96}{131}\right)\) | \(e\left(\frac{49}{524}\right)\) | \(e\left(\frac{61}{131}\right)\) | \(e\left(\frac{43}{262}\right)\) | \(e\left(\frac{433}{524}\right)\) | \(e\left(\frac{443}{524}\right)\) | \(e\left(\frac{26}{131}\right)\) | \(e\left(\frac{49}{262}\right)\) | \(e\left(\frac{235}{262}\right)\) | \(e\left(\frac{23}{262}\right)\) |