Basic properties
Modulus: | \(1009\) | |
Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(504\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1009.bc
\(\chi_{1009}(2,\cdot)\) \(\chi_{1009}(5,\cdot)\) \(\chi_{1009}(12,\cdot)\) \(\chi_{1009}(18,\cdot)\) \(\chi_{1009}(21,\cdot)\) \(\chi_{1009}(29,\cdot)\) \(\chi_{1009}(30,\cdot)\) \(\chi_{1009}(32,\cdot)\) \(\chi_{1009}(45,\cdot)\) \(\chi_{1009}(48,\cdot)\) \(\chi_{1009}(56,\cdot)\) \(\chi_{1009}(71,\cdot)\) \(\chi_{1009}(75,\cdot)\) \(\chi_{1009}(80,\cdot)\) \(\chi_{1009}(84,\cdot)\) \(\chi_{1009}(98,\cdot)\) \(\chi_{1009}(108,\cdot)\) \(\chi_{1009}(120,\cdot)\) \(\chi_{1009}(121,\cdot)\) \(\chi_{1009}(123,\cdot)\) \(\chi_{1009}(127,\cdot)\) \(\chi_{1009}(137,\cdot)\) \(\chi_{1009}(140,\cdot)\) \(\chi_{1009}(143,\cdot)\) \(\chi_{1009}(147,\cdot)\) \(\chi_{1009}(148,\cdot)\) \(\chi_{1009}(151,\cdot)\) \(\chi_{1009}(162,\cdot)\) \(\chi_{1009}(174,\cdot)\) \(\chi_{1009}(187,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{504})$ |
Fixed field: | Number field defined by a degree 504 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{191}{504}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1009 }(1007, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{252}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{1}{252}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{191}{504}\right)\) |