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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.en
\(\chi_{4017}(50,\cdot)\) \(\chi_{4017}(59,\cdot)\) \(\chi_{4017}(266,\cdot)\) \(\chi_{4017}(401,\cdot)\) \(\chi_{4017}(461,\cdot)\) \(\chi_{4017}(470,\cdot)\) \(\chi_{4017}(548,\cdot)\) \(\chi_{4017}(635,\cdot)\) \(\chi_{4017}(644,\cdot)\) \(\chi_{4017}(860,\cdot)\) \(\chi_{4017}(929,\cdot)\) \(\chi_{4017}(956,\cdot)\) \(\chi_{4017}(968,\cdot)\) \(\chi_{4017}(977,\cdot)\) \(\chi_{4017}(995,\cdot)\) \(\chi_{4017}(1025,\cdot)\) \(\chi_{4017}(1046,\cdot)\) \(\chi_{4017}(1085,\cdot)\) \(\chi_{4017}(1151,\cdot)\) \(\chi_{4017}(1319,\cdot)\) \(\chi_{4017}(1328,\cdot)\) \(\chi_{4017}(1358,\cdot)\) \(\chi_{4017}(1436,\cdot)\) \(\chi_{4017}(1502,\cdot)\) \(\chi_{4017}(1562,\cdot)\) \(\chi_{4017}(1697,\cdot)\) \(\chi_{4017}(1766,\cdot)\) \(\chi_{4017}(1952,\cdot)\) \(\chi_{4017}(1961,\cdot)\) \(\chi_{4017}(1982,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{41}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(2741, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{113}{204}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) |