Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(1341\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(444\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1341}(904,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4023.be
\(\chi_{4023}(10,\cdot)\) \(\chi_{4023}(91,\cdot)\) \(\chi_{4023}(172,\cdot)\) \(\chi_{4023}(181,\cdot)\) \(\chi_{4023}(199,\cdot)\) \(\chi_{4023}(208,\cdot)\) \(\chi_{4023}(226,\cdot)\) \(\chi_{4023}(280,\cdot)\) \(\chi_{4023}(316,\cdot)\) \(\chi_{4023}(370,\cdot)\) \(\chi_{4023}(388,\cdot)\) \(\chi_{4023}(397,\cdot)\) \(\chi_{4023}(415,\cdot)\) \(\chi_{4023}(424,\cdot)\) \(\chi_{4023}(505,\cdot)\) \(\chi_{4023}(586,\cdot)\) \(\chi_{4023}(604,\cdot)\) \(\chi_{4023}(658,\cdot)\) \(\chi_{4023}(667,\cdot)\) \(\chi_{4023}(685,\cdot)\) \(\chi_{4023}(694,\cdot)\) \(\chi_{4023}(748,\cdot)\) \(\chi_{4023}(766,\cdot)\) \(\chi_{4023}(793,\cdot)\) \(\chi_{4023}(802,\cdot)\) \(\chi_{4023}(820,\cdot)\) \(\chi_{4023}(829,\cdot)\) \(\chi_{4023}(856,\cdot)\) \(\chi_{4023}(883,\cdot)\) \(\chi_{4023}(928,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{444})$ |
| Fixed field: | Number field defined by a degree 444 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{105}{148}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{444}\right)\) | \(e\left(\frac{19}{222}\right)\) | \(e\left(\frac{50}{111}\right)\) | \(e\left(\frac{17}{222}\right)\) | \(e\left(\frac{19}{148}\right)\) | \(e\left(\frac{73}{148}\right)\) | \(e\left(\frac{295}{444}\right)\) | \(e\left(\frac{119}{444}\right)\) | \(e\left(\frac{53}{444}\right)\) | \(e\left(\frac{19}{111}\right)\) |