Basic properties
| Modulus: | \(8009\) | |
| Conductor: | \(8009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8009.bc
\(\chi_{8009}(15,\cdot)\) \(\chi_{8009}(21,\cdot)\) \(\chi_{8009}(24,\cdot)\) \(\chi_{8009}(76,\cdot)\) \(\chi_{8009}(87,\cdot)\) \(\chi_{8009}(94,\cdot)\) \(\chi_{8009}(108,\cdot)\) \(\chi_{8009}(109,\cdot)\) \(\chi_{8009}(131,\cdot)\) \(\chi_{8009}(132,\cdot)\) \(\chi_{8009}(151,\cdot)\) \(\chi_{8009}(158,\cdot)\) \(\chi_{8009}(194,\cdot)\) \(\chi_{8009}(195,\cdot)\) \(\chi_{8009}(197,\cdot)\) \(\chi_{8009}(205,\cdot)\) \(\chi_{8009}(258,\cdot)\) \(\chi_{8009}(273,\cdot)\) \(\chi_{8009}(287,\cdot)\) \(\chi_{8009}(312,\cdot)\) \(\chi_{8009}(379,\cdot)\) \(\chi_{8009}(418,\cdot)\) \(\chi_{8009}(423,\cdot)\) \(\chi_{8009}(426,\cdot)\) \(\chi_{8009}(449,\cdot)\) \(\chi_{8009}(458,\cdot)\) \(\chi_{8009}(459,\cdot)\) \(\chi_{8009}(486,\cdot)\) \(\chi_{8009}(487,\cdot)\) \(\chi_{8009}(489,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1144})$ |
| Fixed field: | Number field defined by a degree 1144 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1005}{1144}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8009 }(24, a) \) | \(-1\) | \(1\) | \(e\left(\frac{447}{572}\right)\) | \(e\left(\frac{1005}{1144}\right)\) | \(e\left(\frac{161}{286}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{755}{1144}\right)\) | \(e\left(\frac{47}{143}\right)\) | \(e\left(\frac{197}{572}\right)\) | \(e\left(\frac{433}{572}\right)\) | \(e\left(\frac{87}{286}\right)\) | \(e\left(\frac{19}{572}\right)\) |