Basic properties
Modulus: | \(6027\) | |
Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2009}(1579,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.et
\(\chi_{6027}(46,\cdot)\) \(\chi_{6027}(121,\cdot)\) \(\chi_{6027}(172,\cdot)\) \(\chi_{6027}(184,\cdot)\) \(\chi_{6027}(289,\cdot)\) \(\chi_{6027}(415,\cdot)\) \(\chi_{6027}(487,\cdot)\) \(\chi_{6027}(541,\cdot)\) \(\chi_{6027}(613,\cdot)\) \(\chi_{6027}(676,\cdot)\) \(\chi_{6027}(718,\cdot)\) \(\chi_{6027}(730,\cdot)\) \(\chi_{6027}(781,\cdot)\) \(\chi_{6027}(856,\cdot)\) \(\chi_{6027}(907,\cdot)\) \(\chi_{6027}(982,\cdot)\) \(\chi_{6027}(1033,\cdot)\) \(\chi_{6027}(1045,\cdot)\) \(\chi_{6027}(1087,\cdot)\) \(\chi_{6027}(1150,\cdot)\) \(\chi_{6027}(1222,\cdot)\) \(\chi_{6027}(1276,\cdot)\) \(\chi_{6027}(1348,\cdot)\) \(\chi_{6027}(1474,\cdot)\) \(\chi_{6027}(1579,\cdot)\) \(\chi_{6027}(1591,\cdot)\) \(\chi_{6027}(1642,\cdot)\) \(\chi_{6027}(1717,\cdot)\) \(\chi_{6027}(1768,\cdot)\) \(\chi_{6027}(1894,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{20}{21}\right),e\left(\frac{7}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 6027 }(1579, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{151}{420}\right)\) | \(e\left(\frac{29}{60}\right)\) |