Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | 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 4017.ep
\(\chi_{4017}(11,\cdot)\) \(\chi_{4017}(20,\cdot)\) \(\chi_{4017}(188,\cdot)\) \(\chi_{4017}(254,\cdot)\) \(\chi_{4017}(293,\cdot)\) \(\chi_{4017}(314,\cdot)\) \(\chi_{4017}(344,\cdot)\) \(\chi_{4017}(362,\cdot)\) \(\chi_{4017}(371,\cdot)\) \(\chi_{4017}(383,\cdot)\) \(\chi_{4017}(410,\cdot)\) \(\chi_{4017}(479,\cdot)\) \(\chi_{4017}(695,\cdot)\) \(\chi_{4017}(704,\cdot)\) \(\chi_{4017}(791,\cdot)\) \(\chi_{4017}(869,\cdot)\) \(\chi_{4017}(878,\cdot)\) \(\chi_{4017}(938,\cdot)\) \(\chi_{4017}(1073,\cdot)\) \(\chi_{4017}(1280,\cdot)\) \(\chi_{4017}(1289,\cdot)\) \(\chi_{4017}(1406,\cdot)\) \(\chi_{4017}(1424,\cdot)\) \(\chi_{4017}(1454,\cdot)\) \(\chi_{4017}(1493,\cdot)\) \(\chi_{4017}(1580,\cdot)\) \(\chi_{4017}(1610,\cdot)\) \(\chi_{4017}(1619,\cdot)\) \(\chi_{4017}(1688,\cdot)\) \(\chi_{4017}(1718,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{61}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{71}{204}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) |