Basic properties
| Modulus: | \(6009\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2002\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6009.be
\(\chi_{6009}(7,\cdot)\) \(\chi_{6009}(28,\cdot)\) \(\chi_{6009}(31,\cdot)\) \(\chi_{6009}(37,\cdot)\) \(\chi_{6009}(43,\cdot)\) \(\chi_{6009}(61,\cdot)\) \(\chi_{6009}(70,\cdot)\) \(\chi_{6009}(94,\cdot)\) \(\chi_{6009}(97,\cdot)\) \(\chi_{6009}(103,\cdot)\) \(\chi_{6009}(106,\cdot)\) \(\chi_{6009}(109,\cdot)\) \(\chi_{6009}(112,\cdot)\) \(\chi_{6009}(118,\cdot)\) \(\chi_{6009}(127,\cdot)\) \(\chi_{6009}(133,\cdot)\) \(\chi_{6009}(139,\cdot)\) \(\chi_{6009}(148,\cdot)\) \(\chi_{6009}(151,\cdot)\) \(\chi_{6009}(154,\cdot)\) \(\chi_{6009}(157,\cdot)\) \(\chi_{6009}(163,\cdot)\) \(\chi_{6009}(172,\cdot)\) \(\chi_{6009}(175,\cdot)\) \(\chi_{6009}(193,\cdot)\) \(\chi_{6009}(202,\cdot)\) \(\chi_{6009}(235,\cdot)\) \(\chi_{6009}(238,\cdot)\) \(\chi_{6009}(244,\cdot)\) \(\chi_{6009}(265,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((1,e\left(\frac{1255}{2002}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6009 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{286}\right)\) | \(e\left(\frac{37}{143}\right)\) | \(e\left(\frac{1255}{2002}\right)\) | \(e\left(\frac{211}{2002}\right)\) | \(e\left(\frac{111}{286}\right)\) | \(e\left(\frac{757}{1001}\right)\) | \(e\left(\frac{205}{286}\right)\) | \(e\left(\frac{549}{1001}\right)\) | \(e\left(\frac{235}{1001}\right)\) | \(e\left(\frac{74}{143}\right)\) |