Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.eq
\(\chi_{6027}(2,\cdot)\) \(\chi_{6027}(74,\cdot)\) \(\chi_{6027}(200,\cdot)\) \(\chi_{6027}(254,\cdot)\) \(\chi_{6027}(326,\cdot)\) \(\chi_{6027}(389,\cdot)\) \(\chi_{6027}(431,\cdot)\) \(\chi_{6027}(443,\cdot)\) \(\chi_{6027}(494,\cdot)\) \(\chi_{6027}(620,\cdot)\) \(\chi_{6027}(695,\cdot)\) \(\chi_{6027}(746,\cdot)\) \(\chi_{6027}(758,\cdot)\) \(\chi_{6027}(800,\cdot)\) \(\chi_{6027}(935,\cdot)\) \(\chi_{6027}(989,\cdot)\) \(\chi_{6027}(1061,\cdot)\) \(\chi_{6027}(1115,\cdot)\) \(\chi_{6027}(1187,\cdot)\) \(\chi_{6027}(1250,\cdot)\) \(\chi_{6027}(1355,\cdot)\) \(\chi_{6027}(1430,\cdot)\) \(\chi_{6027}(1481,\cdot)\) \(\chi_{6027}(1556,\cdot)\) \(\chi_{6027}(1607,\cdot)\) \(\chi_{6027}(1619,\cdot)\) \(\chi_{6027}(1661,\cdot)\) \(\chi_{6027}(1724,\cdot)\) \(\chi_{6027}(1796,\cdot)\) \(\chi_{6027}(1850,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{13}{21}\right),e\left(\frac{13}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{179}{420}\right)\) | \(e\left(\frac{31}{60}\right)\) |