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.q
\(\chi_{6145}(28,\cdot)\) \(\chi_{6145}(33,\cdot)\) \(\chi_{6145}(38,\cdot)\) \(\chi_{6145}(47,\cdot)\) \(\chi_{6145}(53,\cdot)\) \(\chi_{6145}(63,\cdot)\) \(\chi_{6145}(67,\cdot)\) \(\chi_{6145}(87,\cdot)\) \(\chi_{6145}(88,\cdot)\) \(\chi_{6145}(137,\cdot)\) \(\chi_{6145}(143,\cdot)\) \(\chi_{6145}(163,\cdot)\) \(\chi_{6145}(168,\cdot)\) \(\chi_{6145}(172,\cdot)\) \(\chi_{6145}(187,\cdot)\) \(\chi_{6145}(198,\cdot)\) \(\chi_{6145}(213,\cdot)\) \(\chi_{6145}(218,\cdot)\) \(\chi_{6145}(228,\cdot)\) \(\chi_{6145}(232,\cdot)\) \(\chi_{6145}(273,\cdot)\) \(\chi_{6145}(282,\cdot)\) \(\chi_{6145}(287,\cdot)\) \(\chi_{6145}(292,\cdot)\) \(\chi_{6145}(307,\cdot)\) \(\chi_{6145}(317,\cdot)\) \(\chi_{6145}(318,\cdot)\) \(\chi_{6145}(322,\cdot)\) \(\chi_{6145}(357,\cdot)\) \(\chi_{6145}(377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((i,e\left(\frac{298}{307}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(1072, a) \) | \(-1\) | \(1\) | \(e\left(\frac{271}{1228}\right)\) | \(e\left(\frac{89}{1228}\right)\) | \(e\left(\frac{271}{614}\right)\) | \(e\left(\frac{90}{307}\right)\) | \(e\left(\frac{683}{1228}\right)\) | \(e\left(\frac{813}{1228}\right)\) | \(e\left(\frac{89}{614}\right)\) | \(e\left(\frac{41}{307}\right)\) | \(e\left(\frac{631}{1228}\right)\) | \(e\left(\frac{585}{1228}\right)\) |