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 \(\chi_{2003}(7,\cdot)\) | 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
\((4007,2008)\) → \((1,e\left(\frac{123}{2002}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6009 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{286}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{123}{2002}\right)\) | \(e\left(\frac{1115}{2002}\right)\) | \(e\left(\frac{123}{286}\right)\) | \(e\left(\frac{205}{1001}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{790}{1001}\right)\) | \(e\left(\frac{701}{1001}\right)\) | \(e\left(\frac{82}{143}\right)\) |