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 \(\chi_{3013}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.bf
\(\chi_{6026}(5,\cdot)\) \(\chi_{6026}(7,\cdot)\) \(\chi_{6026}(11,\cdot)\) \(\chi_{6026}(15,\cdot)\) \(\chi_{6026}(21,\cdot)\) \(\chi_{6026}(33,\cdot)\) \(\chi_{6026}(43,\cdot)\) \(\chi_{6026}(65,\cdot)\) \(\chi_{6026}(109,\cdot)\) \(\chi_{6026}(125,\cdot)\) \(\chi_{6026}(129,\cdot)\) \(\chi_{6026}(135,\cdot)\) \(\chi_{6026}(143,\cdot)\) \(\chi_{6026}(159,\cdot)\) \(\chi_{6026}(175,\cdot)\) \(\chi_{6026}(195,\cdot)\) \(\chi_{6026}(205,\cdot)\) \(\chi_{6026}(245,\cdot)\) \(\chi_{6026}(267,\cdot)\) \(\chi_{6026}(273,\cdot)\) \(\chi_{6026}(283,\cdot)\) \(\chi_{6026}(287,\cdot)\) \(\chi_{6026}(295,\cdot)\) \(\chi_{6026}(297,\cdot)\) \(\chi_{6026}(327,\cdot)\) \(\chi_{6026}(337,\cdot)\) \(\chi_{6026}(339,\cdot)\) \(\chi_{6026}(343,\cdot)\) \(\chi_{6026}(379,\cdot)\) \(\chi_{6026}(383,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{715})$ |
| Fixed field: | Number field defined by a degree 1430 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{1}{22}\right),e\left(\frac{23}{65}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6026 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{146}{715}\right)\) | \(e\left(\frac{461}{1430}\right)\) | \(e\left(\frac{1191}{1430}\right)\) | \(e\left(\frac{292}{715}\right)\) | \(e\left(\frac{321}{1430}\right)\) | \(e\left(\frac{4}{715}\right)\) | \(e\left(\frac{753}{1430}\right)\) | \(e\left(\frac{763}{1430}\right)\) | \(e\left(\frac{19}{286}\right)\) | \(e\left(\frac{53}{1430}\right)\) |