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 \(\chi_{3013}(57,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.be
\(\chi_{6026}(17,\cdot)\) \(\chi_{6026}(37,\cdot)\) \(\chi_{6026}(57,\cdot)\) \(\chi_{6026}(67,\cdot)\) \(\chi_{6026}(83,\cdot)\) \(\chi_{6026}(97,\cdot)\) \(\chi_{6026}(103,\cdot)\) \(\chi_{6026}(111,\cdot)\) \(\chi_{6026}(145,\cdot)\) \(\chi_{6026}(153,\cdot)\) \(\chi_{6026}(157,\cdot)\) \(\chi_{6026}(171,\cdot)\) \(\chi_{6026}(181,\cdot)\) \(\chi_{6026}(203,\cdot)\) \(\chi_{6026}(221,\cdot)\) \(\chi_{6026}(227,\cdot)\) \(\chi_{6026}(235,\cdot)\) \(\chi_{6026}(237,\cdot)\) \(\chi_{6026}(241,\cdot)\) \(\chi_{6026}(247,\cdot)\) \(\chi_{6026}(249,\cdot)\) \(\chi_{6026}(251,\cdot)\) \(\chi_{6026}(291,\cdot)\) \(\chi_{6026}(293,\cdot)\) \(\chi_{6026}(319,\cdot)\) \(\chi_{6026}(329,\cdot)\) \(\chi_{6026}(355,\cdot)\) \(\chi_{6026}(359,\cdot)\) \(\chi_{6026}(365,\cdot)\) \(\chi_{6026}(373,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{715})$ |
| Fixed field: | Number field defined by a degree 1430 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{9}{22}\right),e\left(\frac{107}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6026 }(57, a) \) | \(1\) | \(1\) | \(e\left(\frac{577}{715}\right)\) | \(e\left(\frac{387}{1430}\right)\) | \(e\left(\frac{1127}{1430}\right)\) | \(e\left(\frac{439}{715}\right)\) | \(e\left(\frac{1107}{1430}\right)\) | \(e\left(\frac{388}{715}\right)\) | \(e\left(\frac{111}{1430}\right)\) | \(e\left(\frac{183}{715}\right)\) | \(e\left(\frac{135}{143}\right)\) | \(e\left(\frac{851}{1430}\right)\) |