Basic properties
| Modulus: | \(6009\) | |
| Conductor: | \(6009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(286\) | 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 6009.bb
\(\chi_{6009}(2,\cdot)\) \(\chi_{6009}(8,\cdot)\) \(\chi_{6009}(11,\cdot)\) \(\chi_{6009}(23,\cdot)\) \(\chi_{6009}(32,\cdot)\) \(\chi_{6009}(44,\cdot)\) \(\chi_{6009}(71,\cdot)\) \(\chi_{6009}(92,\cdot)\) \(\chi_{6009}(128,\cdot)\) \(\chi_{6009}(149,\cdot)\) \(\chi_{6009}(176,\cdot)\) \(\chi_{6009}(239,\cdot)\) \(\chi_{6009}(242,\cdot)\) \(\chi_{6009}(284,\cdot)\) \(\chi_{6009}(368,\cdot)\) \(\chi_{6009}(377,\cdot)\) \(\chi_{6009}(380,\cdot)\) \(\chi_{6009}(506,\cdot)\) \(\chi_{6009}(512,\cdot)\) \(\chi_{6009}(563,\cdot)\) \(\chi_{6009}(704,\cdot)\) \(\chi_{6009}(845,\cdot)\) \(\chi_{6009}(956,\cdot)\) \(\chi_{6009}(968,\cdot)\) \(\chi_{6009}(1046,\cdot)\) \(\chi_{6009}(1058,\cdot)\) \(\chi_{6009}(1079,\cdot)\) \(\chi_{6009}(1094,\cdot)\) \(\chi_{6009}(1136,\cdot)\) \(\chi_{6009}(1241,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((-1,e\left(\frac{1}{286}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6009 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{143}\right)\) | \(e\left(\frac{50}{143}\right)\) | \(e\left(\frac{72}{143}\right)\) | \(e\left(\frac{123}{286}\right)\) | \(e\left(\frac{75}{143}\right)\) | \(e\left(\frac{97}{143}\right)\) | \(e\left(\frac{96}{143}\right)\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{173}{286}\right)\) | \(e\left(\frac{100}{143}\right)\) |