Basic properties
| Modulus: | \(6026\) | |
| Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1430\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3013}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.bd
\(\chi_{6026}(29,\cdot)\) \(\chi_{6026}(31,\cdot)\) \(\chi_{6026}(85,\cdot)\) \(\chi_{6026}(87,\cdot)\) \(\chi_{6026}(95,\cdot)\) \(\chi_{6026}(119,\cdot)\) \(\chi_{6026}(127,\cdot)\) \(\chi_{6026}(133,\cdot)\) \(\chi_{6026}(141,\cdot)\) \(\chi_{6026}(187,\cdot)\) \(\chi_{6026}(197,\cdot)\) \(\chi_{6026}(213,\cdot)\) \(\chi_{6026}(219,\cdot)\) \(\chi_{6026}(255,\cdot)\) \(\chi_{6026}(257,\cdot)\) \(\chi_{6026}(259,\cdot)\) \(\chi_{6026}(279,\cdot)\) \(\chi_{6026}(285,\cdot)\) \(\chi_{6026}(347,\cdot)\) \(\chi_{6026}(349,\cdot)\) \(\chi_{6026}(357,\cdot)\) \(\chi_{6026}(377,\cdot)\) \(\chi_{6026}(381,\cdot)\) \(\chi_{6026}(395,\cdot)\) \(\chi_{6026}(399,\cdot)\) \(\chi_{6026}(403,\cdot)\) \(\chi_{6026}(407,\cdot)\) \(\chi_{6026}(423,\cdot)\) \(\chi_{6026}(443,\cdot)\) \(\chi_{6026}(449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{715})$ |
| Fixed field: | Number field defined by a degree 1430 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{29}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6026 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{304}{715}\right)\) | \(e\left(\frac{382}{715}\right)\) | \(e\left(\frac{427}{715}\right)\) | \(e\left(\frac{608}{715}\right)\) | \(e\left(\frac{677}{715}\right)\) | \(e\left(\frac{596}{715}\right)\) | \(e\left(\frac{686}{715}\right)\) | \(e\left(\frac{717}{1430}\right)\) | \(e\left(\frac{257}{286}\right)\) | \(e\left(\frac{16}{715}\right)\) |