Basic properties
| Modulus: | \(4027\) | |
| Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(366\) | 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 4027.l
\(\chi_{4027}(23,\cdot)\) \(\chi_{4027}(129,\cdot)\) \(\chi_{4027}(137,\cdot)\) \(\chi_{4027}(178,\cdot)\) \(\chi_{4027}(267,\cdot)\) \(\chi_{4027}(271,\cdot)\) \(\chi_{4027}(293,\cdot)\) \(\chi_{4027}(299,\cdot)\) \(\chi_{4027}(365,\cdot)\) \(\chi_{4027}(447,\cdot)\) \(\chi_{4027}(502,\cdot)\) \(\chi_{4027}(532,\cdot)\) \(\chi_{4027}(535,\cdot)\) \(\chi_{4027}(581,\cdot)\) \(\chi_{4027}(589,\cdot)\) \(\chi_{4027}(707,\cdot)\) \(\chi_{4027}(718,\cdot)\) \(\chi_{4027}(750,\cdot)\) \(\chi_{4027}(800,\cdot)\) \(\chi_{4027}(803,\cdot)\) \(\chi_{4027}(826,\cdot)\) \(\chi_{4027}(856,\cdot)\) \(\chi_{4027}(876,\cdot)\) \(\chi_{4027}(943,\cdot)\) \(\chi_{4027}(974,\cdot)\) \(\chi_{4027}(987,\cdot)\) \(\chi_{4027}(1125,\cdot)\) \(\chi_{4027}(1137,\cdot)\) \(\chi_{4027}(1177,\cdot)\) \(\chi_{4027}(1193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{183})$ |
| Fixed field: | Number field defined by a degree 366 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{43}{366}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4027 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{122}\right)\) | \(e\left(\frac{43}{366}\right)\) | \(e\left(\frac{7}{61}\right)\) | \(e\left(\frac{191}{366}\right)\) | \(e\left(\frac{32}{183}\right)\) | \(e\left(\frac{115}{122}\right)\) | \(e\left(\frac{21}{122}\right)\) | \(e\left(\frac{43}{183}\right)\) | \(e\left(\frac{106}{183}\right)\) | \(e\left(\frac{95}{366}\right)\) |