Basic properties
| Modulus: | \(6145\) | |
| Conductor: | \(6145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6145.o
\(\chi_{6145}(2,\cdot)\) \(\chi_{6145}(3,\cdot)\) \(\chi_{6145}(8,\cdot)\) \(\chi_{6145}(12,\cdot)\) \(\chi_{6145}(13,\cdot)\) \(\chi_{6145}(18,\cdot)\) \(\chi_{6145}(27,\cdot)\) \(\chi_{6145}(32,\cdot)\) \(\chi_{6145}(37,\cdot)\) \(\chi_{6145}(48,\cdot)\) \(\chi_{6145}(52,\cdot)\) \(\chi_{6145}(62,\cdot)\) \(\chi_{6145}(72,\cdot)\) \(\chi_{6145}(78,\cdot)\) \(\chi_{6145}(83,\cdot)\) \(\chi_{6145}(93,\cdot)\) \(\chi_{6145}(108,\cdot)\) \(\chi_{6145}(117,\cdot)\) \(\chi_{6145}(118,\cdot)\) \(\chi_{6145}(122,\cdot)\) \(\chi_{6145}(128,\cdot)\) \(\chi_{6145}(148,\cdot)\) \(\chi_{6145}(162,\cdot)\) \(\chi_{6145}(173,\cdot)\) \(\chi_{6145}(177,\cdot)\) \(\chi_{6145}(183,\cdot)\) \(\chi_{6145}(192,\cdot)\) \(\chi_{6145}(193,\cdot)\) \(\chi_{6145}(202,\cdot)\) \(\chi_{6145}(203,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((-i,e\left(\frac{1107}{1228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(1058, a) \) | \(1\) | \(1\) | \(e\left(\frac{200}{307}\right)\) | \(e\left(\frac{256}{307}\right)\) | \(e\left(\frac{93}{307}\right)\) | \(e\left(\frac{149}{307}\right)\) | \(e\left(\frac{411}{1228}\right)\) | \(e\left(\frac{293}{307}\right)\) | \(e\left(\frac{205}{307}\right)\) | \(e\left(\frac{483}{1228}\right)\) | \(e\left(\frac{42}{307}\right)\) | \(e\left(\frac{127}{307}\right)\) |