Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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.x
\(\chi_{1009}(16,\cdot)\) \(\chi_{1009}(36,\cdot)\) \(\chi_{1009}(40,\cdot)\) \(\chi_{1009}(49,\cdot)\) \(\chi_{1009}(54,\cdot)\) \(\chi_{1009}(67,\cdot)\) \(\chi_{1009}(90,\cdot)\) \(\chi_{1009}(100,\cdot)\) \(\chi_{1009}(111,\cdot)\) \(\chi_{1009}(135,\cdot)\) \(\chi_{1009}(145,\cdot)\) \(\chi_{1009}(164,\cdot)\) \(\chi_{1009}(225,\cdot)\) \(\chi_{1009}(347,\cdot)\) \(\chi_{1009}(363,\cdot)\) \(\chi_{1009}(369,\cdot)\) \(\chi_{1009}(381,\cdot)\) \(\chi_{1009}(403,\cdot)\) \(\chi_{1009}(410,\cdot)\) \(\chi_{1009}(418,\cdot)\) \(\chi_{1009}(556,\cdot)\) \(\chi_{1009}(625,\cdot)\) \(\chi_{1009}(626,\cdot)\) \(\chi_{1009}(627,\cdot)\) \(\chi_{1009}(654,\cdot)\) \(\chi_{1009}(671,\cdot)\) \(\chi_{1009}(722,\cdot)\) \(\chi_{1009}(753,\cdot)\) \(\chi_{1009}(782,\cdot)\) \(\chi_{1009}(796,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{65}{126}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{65}{126}\right)\) |