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.t
\(\chi_{6145}(17,\cdot)\) \(\chi_{6145}(23,\cdot)\) \(\chi_{6145}(68,\cdot)\) \(\chi_{6145}(77,\cdot)\) \(\chi_{6145}(82,\cdot)\) \(\chi_{6145}(92,\cdot)\) \(\chi_{6145}(98,\cdot)\) \(\chi_{6145}(102,\cdot)\) \(\chi_{6145}(103,\cdot)\) \(\chi_{6145}(123,\cdot)\) \(\chi_{6145}(127,\cdot)\) \(\chi_{6145}(133,\cdot)\) \(\chi_{6145}(138,\cdot)\) \(\chi_{6145}(147,\cdot)\) \(\chi_{6145}(153,\cdot)\) \(\chi_{6145}(158,\cdot)\) \(\chi_{6145}(167,\cdot)\) \(\chi_{6145}(178,\cdot)\) \(\chi_{6145}(207,\cdot)\) \(\chi_{6145}(237,\cdot)\) \(\chi_{6145}(242,\cdot)\) \(\chi_{6145}(257,\cdot)\) \(\chi_{6145}(263,\cdot)\) \(\chi_{6145}(267,\cdot)\) \(\chi_{6145}(272,\cdot)\) \(\chi_{6145}(278,\cdot)\) \(\chi_{6145}(298,\cdot)\) \(\chi_{6145}(308,\cdot)\) \(\chi_{6145}(328,\cdot)\) \(\chi_{6145}(337,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1228})$ |
| Fixed field: | Number field defined by a degree 1228 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((-i,e\left(\frac{689}{1228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(178, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{614}\right)\) | \(e\left(\frac{355}{614}\right)\) | \(e\left(\frac{191}{307}\right)\) | \(e\left(\frac{273}{307}\right)\) | \(e\left(\frac{547}{1228}\right)\) | \(e\left(\frac{573}{614}\right)\) | \(e\left(\frac{48}{307}\right)\) | \(e\left(\frac{477}{1228}\right)\) | \(e\left(\frac{123}{614}\right)\) | \(e\left(\frac{43}{614}\right)\) |