Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(6027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.ek
\(\chi_{6027}(23,\cdot)\) \(\chi_{6027}(86,\cdot)\) \(\chi_{6027}(107,\cdot)\) \(\chi_{6027}(359,\cdot)\) \(\chi_{6027}(515,\cdot)\) \(\chi_{6027}(578,\cdot)\) \(\chi_{6027}(599,\cdot)\) \(\chi_{6027}(884,\cdot)\) \(\chi_{6027}(947,\cdot)\) \(\chi_{6027}(968,\cdot)\) \(\chi_{6027}(1220,\cdot)\) \(\chi_{6027}(1376,\cdot)\) \(\chi_{6027}(1460,\cdot)\) \(\chi_{6027}(1712,\cdot)\) \(\chi_{6027}(1808,\cdot)\) \(\chi_{6027}(1829,\cdot)\) \(\chi_{6027}(2081,\cdot)\) \(\chi_{6027}(2237,\cdot)\) \(\chi_{6027}(2300,\cdot)\) \(\chi_{6027}(2573,\cdot)\) \(\chi_{6027}(2606,\cdot)\) \(\chi_{6027}(2669,\cdot)\) \(\chi_{6027}(2690,\cdot)\) \(\chi_{6027}(2942,\cdot)\) \(\chi_{6027}(3098,\cdot)\) \(\chi_{6027}(3161,\cdot)\) \(\chi_{6027}(3182,\cdot)\) \(\chi_{6027}(3434,\cdot)\) \(\chi_{6027}(3467,\cdot)\) \(\chi_{6027}(3530,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{19}{21}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{23}{30}\right)\) |