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.r
\(\chi_{6145}(7,\cdot)\) \(\chi_{6145}(22,\cdot)\) \(\chi_{6145}(42,\cdot)\) \(\chi_{6145}(43,\cdot)\) \(\chi_{6145}(57,\cdot)\) \(\chi_{6145}(58,\cdot)\) \(\chi_{6145}(73,\cdot)\) \(\chi_{6145}(97,\cdot)\) \(\chi_{6145}(107,\cdot)\) \(\chi_{6145}(112,\cdot)\) \(\chi_{6145}(113,\cdot)\) \(\chi_{6145}(132,\cdot)\) \(\chi_{6145}(142,\cdot)\) \(\chi_{6145}(152,\cdot)\) \(\chi_{6145}(157,\cdot)\) \(\chi_{6145}(182,\cdot)\) \(\chi_{6145}(188,\cdot)\) \(\chi_{6145}(197,\cdot)\) \(\chi_{6145}(212,\cdot)\) \(\chi_{6145}(217,\cdot)\) \(\chi_{6145}(233,\cdot)\) \(\chi_{6145}(238,\cdot)\) \(\chi_{6145}(247,\cdot)\) \(\chi_{6145}(252,\cdot)\) \(\chi_{6145}(253,\cdot)\) \(\chi_{6145}(258,\cdot)\) \(\chi_{6145}(262,\cdot)\) \(\chi_{6145}(268,\cdot)\) \(\chi_{6145}(277,\cdot)\) \(\chi_{6145}(283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((-i,e\left(\frac{531}{614}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(1063, a) \) | \(-1\) | \(1\) | \(e\left(\frac{755}{1228}\right)\) | \(e\left(\frac{905}{1228}\right)\) | \(e\left(\frac{141}{614}\right)\) | \(e\left(\frac{108}{307}\right)\) | \(e\left(\frac{881}{1228}\right)\) | \(e\left(\frac{1037}{1228}\right)\) | \(e\left(\frac{291}{614}\right)\) | \(e\left(\frac{37}{614}\right)\) | \(e\left(\frac{1187}{1228}\right)\) | \(e\left(\frac{1009}{1228}\right)\) |