Basic properties
| Modulus: | \(4027\) | |
| Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(183\) | 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 4027.k
\(\chi_{4027}(41,\cdot)\) \(\chi_{4027}(68,\cdot)\) \(\chi_{4027}(102,\cdot)\) \(\chi_{4027}(140,\cdot)\) \(\chi_{4027}(155,\cdot)\) \(\chi_{4027}(218,\cdot)\) \(\chi_{4027}(248,\cdot)\) \(\chi_{4027}(308,\cdot)\) \(\chi_{4027}(315,\cdot)\) \(\chi_{4027}(334,\cdot)\) \(\chi_{4027}(336,\cdot)\) \(\chi_{4027}(341,\cdot)\) \(\chi_{4027}(397,\cdot)\) \(\chi_{4027}(398,\cdot)\) \(\chi_{4027}(406,\cdot)\) \(\chi_{4027}(489,\cdot)\) \(\chi_{4027}(501,\cdot)\) \(\chi_{4027}(504,\cdot)\) \(\chi_{4027}(508,\cdot)\) \(\chi_{4027}(529,\cdot)\) \(\chi_{4027}(533,\cdot)\) \(\chi_{4027}(547,\cdot)\) \(\chi_{4027}(556,\cdot)\) \(\chi_{4027}(558,\cdot)\) \(\chi_{4027}(597,\cdot)\) \(\chi_{4027}(599,\cdot)\) \(\chi_{4027}(609,\cdot)\) \(\chi_{4027}(693,\cdot)\) \(\chi_{4027}(807,\cdot)\) \(\chi_{4027}(837,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{183})$ |
| Fixed field: | Number field defined by a degree 183 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{92}{183}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4027 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{61}\right)\) | \(e\left(\frac{92}{183}\right)\) | \(e\left(\frac{3}{61}\right)\) | \(e\left(\frac{115}{183}\right)\) | \(e\left(\frac{5}{183}\right)\) | \(e\left(\frac{29}{61}\right)\) | \(e\left(\frac{35}{61}\right)\) | \(e\left(\frac{1}{183}\right)\) | \(e\left(\frac{28}{183}\right)\) | \(e\left(\frac{16}{183}\right)\) |