Basic properties
| Modulus: | \(6009\) | |
| Conductor: | \(6009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2002\) | 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.bf
\(\chi_{6009}(5,\cdot)\) \(\chi_{6009}(20,\cdot)\) \(\chi_{6009}(26,\cdot)\) \(\chi_{6009}(29,\cdot)\) \(\chi_{6009}(38,\cdot)\) \(\chi_{6009}(41,\cdot)\) \(\chi_{6009}(68,\cdot)\) \(\chi_{6009}(80,\cdot)\) \(\chi_{6009}(83,\cdot)\) \(\chi_{6009}(98,\cdot)\) \(\chi_{6009}(104,\cdot)\) \(\chi_{6009}(110,\cdot)\) \(\chi_{6009}(116,\cdot)\) \(\chi_{6009}(125,\cdot)\) \(\chi_{6009}(131,\cdot)\) \(\chi_{6009}(137,\cdot)\) \(\chi_{6009}(143,\cdot)\) \(\chi_{6009}(146,\cdot)\) \(\chi_{6009}(152,\cdot)\) \(\chi_{6009}(158,\cdot)\) \(\chi_{6009}(164,\cdot)\) \(\chi_{6009}(170,\cdot)\) \(\chi_{6009}(200,\cdot)\) \(\chi_{6009}(209,\cdot)\) \(\chi_{6009}(221,\cdot)\) \(\chi_{6009}(230,\cdot)\) \(\chi_{6009}(263,\cdot)\) \(\chi_{6009}(272,\cdot)\) \(\chi_{6009}(275,\cdot)\) \(\chi_{6009}(290,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((-1,e\left(\frac{829}{2002}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6009 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{143}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{915}{1001}\right)\) | \(e\left(\frac{1867}{2002}\right)\) | \(e\left(\frac{57}{143}\right)\) | \(e\left(\frac{47}{1001}\right)\) | \(e\left(\frac{113}{143}\right)\) | \(e\left(\frac{645}{1001}\right)\) | \(e\left(\frac{131}{2002}\right)\) | \(e\left(\frac{76}{143}\right)\) |