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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6145.p
\(\chi_{6145}(14,\cdot)\) \(\chi_{6145}(19,\cdot)\) \(\chi_{6145}(29,\cdot)\) \(\chi_{6145}(44,\cdot)\) \(\chi_{6145}(84,\cdot)\) \(\chi_{6145}(94,\cdot)\) \(\chi_{6145}(99,\cdot)\) \(\chi_{6145}(109,\cdot)\) \(\chi_{6145}(114,\cdot)\) \(\chi_{6145}(119,\cdot)\) \(\chi_{6145}(129,\cdot)\) \(\chi_{6145}(134,\cdot)\) \(\chi_{6145}(159,\cdot)\) \(\chi_{6145}(174,\cdot)\) \(\chi_{6145}(189,\cdot)\) \(\chi_{6145}(194,\cdot)\) \(\chi_{6145}(214,\cdot)\) \(\chi_{6145}(219,\cdot)\) \(\chi_{6145}(224,\cdot)\) \(\chi_{6145}(229,\cdot)\) \(\chi_{6145}(259,\cdot)\) \(\chi_{6145}(264,\cdot)\) \(\chi_{6145}(269,\cdot)\) \(\chi_{6145}(274,\cdot)\) \(\chi_{6145}(284,\cdot)\) \(\chi_{6145}(304,\cdot)\) \(\chi_{6145}(314,\cdot)\) \(\chi_{6145}(339,\cdot)\) \(\chi_{6145}(344,\cdot)\) \(\chi_{6145}(349,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((-1,e\left(\frac{83}{1228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(1134, a) \) | \(-1\) | \(1\) | \(e\left(\frac{697}{1228}\right)\) | \(e\left(\frac{315}{1228}\right)\) | \(e\left(\frac{83}{614}\right)\) | \(e\left(\frac{253}{307}\right)\) | \(e\left(\frac{5}{307}\right)\) | \(e\left(\frac{863}{1228}\right)\) | \(e\left(\frac{315}{614}\right)\) | \(e\left(\frac{1191}{1228}\right)\) | \(e\left(\frac{481}{1228}\right)\) | \(e\left(\frac{263}{1228}\right)\) |