Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(504\) | 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 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
\(11\) → \(e\left(\frac{31}{504}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(108, a) \) | \(1\) | \(1\) | \(e\left(\frac{125}{252}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{173}{252}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{31}{504}\right)\) |