Basic properties
| Modulus: | \(4023\) | |
| Conductor: | \(4023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(333\) | 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 4023.bc
\(\chi_{4023}(16,\cdot)\) \(\chi_{4023}(25,\cdot)\) \(\chi_{4023}(31,\cdot)\) \(\chi_{4023}(49,\cdot)\) \(\chi_{4023}(67,\cdot)\) \(\chi_{4023}(85,\cdot)\) \(\chi_{4023}(88,\cdot)\) \(\chi_{4023}(142,\cdot)\) \(\chi_{4023}(166,\cdot)\) \(\chi_{4023}(178,\cdot)\) \(\chi_{4023}(229,\cdot)\) \(\chi_{4023}(256,\cdot)\) \(\chi_{4023}(274,\cdot)\) \(\chi_{4023}(304,\cdot)\) \(\chi_{4023}(328,\cdot)\) \(\chi_{4023}(331,\cdot)\) \(\chi_{4023}(337,\cdot)\) \(\chi_{4023}(394,\cdot)\) \(\chi_{4023}(400,\cdot)\) \(\chi_{4023}(412,\cdot)\) \(\chi_{4023}(421,\cdot)\) \(\chi_{4023}(427,\cdot)\) \(\chi_{4023}(463,\cdot)\) \(\chi_{4023}(466,\cdot)\) \(\chi_{4023}(472,\cdot)\) \(\chi_{4023}(475,\cdot)\) \(\chi_{4023}(484,\cdot)\) \(\chi_{4023}(493,\cdot)\) \(\chi_{4023}(520,\cdot)\) \(\chi_{4023}(535,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{333})$ |
| Fixed field: | Number field defined by a degree 333 polynomial (not computed) |
Values on generators
\((299,3727)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{33}{37}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4023 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{333}\right)\) | \(e\left(\frac{2}{333}\right)\) | \(e\left(\frac{104}{333}\right)\) | \(e\left(\frac{142}{333}\right)\) | \(e\left(\frac{1}{111}\right)\) | \(e\left(\frac{35}{111}\right)\) | \(e\left(\frac{220}{333}\right)\) | \(e\left(\frac{53}{333}\right)\) | \(e\left(\frac{143}{333}\right)\) | \(e\left(\frac{4}{333}\right)\) |