Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1332\) | 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 4023.bj
\(\chi_{4023}(13,\cdot)\) \(\chi_{4023}(34,\cdot)\) \(\chi_{4023}(40,\cdot)\) \(\chi_{4023}(43,\cdot)\) \(\chi_{4023}(52,\cdot)\) \(\chi_{4023}(58,\cdot)\) \(\chi_{4023}(70,\cdot)\) \(\chi_{4023}(79,\cdot)\) \(\chi_{4023}(94,\cdot)\) \(\chi_{4023}(97,\cdot)\) \(\chi_{4023}(106,\cdot)\) \(\chi_{4023}(115,\cdot)\) \(\chi_{4023}(139,\cdot)\) \(\chi_{4023}(151,\cdot)\) \(\chi_{4023}(157,\cdot)\) \(\chi_{4023}(160,\cdot)\) \(\chi_{4023}(187,\cdot)\) \(\chi_{4023}(205,\cdot)\) \(\chi_{4023}(211,\cdot)\) \(\chi_{4023}(214,\cdot)\) \(\chi_{4023}(220,\cdot)\) \(\chi_{4023}(223,\cdot)\) \(\chi_{4023}(232,\cdot)\) \(\chi_{4023}(238,\cdot)\) \(\chi_{4023}(241,\cdot)\) \(\chi_{4023}(247,\cdot)\) \(\chi_{4023}(250,\cdot)\) \(\chi_{4023}(277,\cdot)\) \(\chi_{4023}(283,\cdot)\) \(\chi_{4023}(286,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1332})$ |
| Fixed field: | Number field defined by a degree 1332 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{53}{148}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1069}{1332}\right)\) | \(e\left(\frac{403}{666}\right)\) | \(e\left(\frac{155}{333}\right)\) | \(e\left(\frac{641}{666}\right)\) | \(e\left(\frac{181}{444}\right)\) | \(e\left(\frac{119}{444}\right)\) | \(e\left(\frac{1081}{1332}\right)\) | \(e\left(\frac{713}{1332}\right)\) | \(e\left(\frac{1019}{1332}\right)\) | \(e\left(\frac{70}{333}\right)\) |