Basic properties
Modulus: | \(1009\) | |
Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1008\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1009.bd
\(\chi_{1009}(11,\cdot)\) \(\chi_{1009}(17,\cdot)\) \(\chi_{1009}(22,\cdot)\) \(\chi_{1009}(26,\cdot)\) \(\chi_{1009}(31,\cdot)\) \(\chi_{1009}(33,\cdot)\) \(\chi_{1009}(34,\cdot)\) \(\chi_{1009}(38,\cdot)\) \(\chi_{1009}(46,\cdot)\) \(\chi_{1009}(51,\cdot)\) \(\chi_{1009}(52,\cdot)\) \(\chi_{1009}(53,\cdot)\) \(\chi_{1009}(55,\cdot)\) \(\chi_{1009}(65,\cdot)\) \(\chi_{1009}(66,\cdot)\) \(\chi_{1009}(76,\cdot)\) \(\chi_{1009}(78,\cdot)\) \(\chi_{1009}(79,\cdot)\) \(\chi_{1009}(83,\cdot)\) \(\chi_{1009}(85,\cdot)\) \(\chi_{1009}(86,\cdot)\) \(\chi_{1009}(88,\cdot)\) \(\chi_{1009}(89,\cdot)\) \(\chi_{1009}(91,\cdot)\) \(\chi_{1009}(92,\cdot)\) \(\chi_{1009}(94,\cdot)\) \(\chi_{1009}(95,\cdot)\) \(\chi_{1009}(97,\cdot)\) \(\chi_{1009}(99,\cdot)\) \(\chi_{1009}(102,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1008})$ |
Fixed field: | Number field defined by a degree 1008 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{1}{1008}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1009 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{443}{504}\right)\) | \(e\left(\frac{17}{168}\right)\) | \(e\left(\frac{191}{252}\right)\) | \(e\left(\frac{347}{504}\right)\) | \(e\left(\frac{247}{252}\right)\) | \(e\left(\frac{197}{252}\right)\) | \(e\left(\frac{107}{168}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{143}{252}\right)\) | \(e\left(\frac{1}{1008}\right)\) |