Basic properties
| Modulus: | \(6027\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(840\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(691,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6027.ex
\(\chi_{6027}(52,\cdot)\) \(\chi_{6027}(94,\cdot)\) \(\chi_{6027}(136,\cdot)\) \(\chi_{6027}(145,\cdot)\) \(\chi_{6027}(157,\cdot)\) \(\chi_{6027}(199,\cdot)\) \(\chi_{6027}(220,\cdot)\) \(\chi_{6027}(229,\cdot)\) \(\chi_{6027}(304,\cdot)\) \(\chi_{6027}(334,\cdot)\) \(\chi_{6027}(376,\cdot)\) \(\chi_{6027}(388,\cdot)\) \(\chi_{6027}(397,\cdot)\) \(\chi_{6027}(439,\cdot)\) \(\chi_{6027}(481,\cdot)\) \(\chi_{6027}(514,\cdot)\) \(\chi_{6027}(544,\cdot)\) \(\chi_{6027}(586,\cdot)\) \(\chi_{6027}(598,\cdot)\) \(\chi_{6027}(628,\cdot)\) \(\chi_{6027}(649,\cdot)\) \(\chi_{6027}(682,\cdot)\) \(\chi_{6027}(691,\cdot)\) \(\chi_{6027}(703,\cdot)\) \(\chi_{6027}(712,\cdot)\) \(\chi_{6027}(745,\cdot)\) \(\chi_{6027}(796,\cdot)\) \(\chi_{6027}(808,\cdot)\) \(\chi_{6027}(850,\cdot)\) \(\chi_{6027}(880,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((4019,493,2794)\) → \((1,e\left(\frac{29}{42}\right),e\left(\frac{21}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 6027 }(691, a) \) | \(1\) | \(1\) | \(e\left(\frac{253}{420}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{241}{420}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{163}{840}\right)\) | \(e\left(\frac{17}{280}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{493}{840}\right)\) | \(e\left(\frac{107}{120}\right)\) |