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 \(\chi_{2009}(1276,\cdot)\) | 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
\((4019,493,2794)\) → \((1,e\left(\frac{13}{21}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(1276, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{263}{420}\right)\) | \(e\left(\frac{37}{60}\right)\) |