Basic properties
| Modulus: | \(6009\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(143\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2003}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6009.s
\(\chi_{6009}(4,\cdot)\) \(\chi_{6009}(16,\cdot)\) \(\chi_{6009}(46,\cdot)\) \(\chi_{6009}(64,\cdot)\) \(\chi_{6009}(88,\cdot)\) \(\chi_{6009}(121,\cdot)\) \(\chi_{6009}(142,\cdot)\) \(\chi_{6009}(184,\cdot)\) \(\chi_{6009}(190,\cdot)\) \(\chi_{6009}(256,\cdot)\) \(\chi_{6009}(298,\cdot)\) \(\chi_{6009}(478,\cdot)\) \(\chi_{6009}(529,\cdot)\) \(\chi_{6009}(547,\cdot)\) \(\chi_{6009}(568,\cdot)\) \(\chi_{6009}(751,\cdot)\) \(\chi_{6009}(754,\cdot)\) \(\chi_{6009}(763,\cdot)\) \(\chi_{6009}(781,\cdot)\) \(\chi_{6009}(931,\cdot)\) \(\chi_{6009}(1012,\cdot)\) \(\chi_{6009}(1024,\cdot)\) \(\chi_{6009}(1045,\cdot)\) \(\chi_{6009}(1099,\cdot)\) \(\chi_{6009}(1126,\cdot)\) \(\chi_{6009}(1192,\cdot)\) \(\chi_{6009}(1291,\cdot)\) \(\chi_{6009}(1408,\cdot)\) \(\chi_{6009}(1465,\cdot)\) \(\chi_{6009}(1633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 143 polynomial (not computed) |
Values on generators
\((4007,2008)\) → \((1,e\left(\frac{125}{143}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 6009 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{143}\right)\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{74}{143}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{83}{143}\right)\) | \(e\left(\frac{119}{143}\right)\) | \(e\left(\frac{135}{143}\right)\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{118}{143}\right)\) |