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.eb
\(\chi_{4017}(5,\cdot)\) \(\chi_{4017}(44,\cdot)\) \(\chi_{4017}(86,\cdot)\) \(\chi_{4017}(281,\cdot)\) \(\chi_{4017}(320,\cdot)\) \(\chi_{4017}(395,\cdot)\) \(\chi_{4017}(590,\cdot)\) \(\chi_{4017}(593,\cdot)\) \(\chi_{4017}(629,\cdot)\) \(\chi_{4017}(671,\cdot)\) \(\chi_{4017}(788,\cdot)\) \(\chi_{4017}(902,\cdot)\) \(\chi_{4017}(980,\cdot)\) \(\chi_{4017}(1097,\cdot)\) \(\chi_{4017}(1100,\cdot)\) \(\chi_{4017}(1139,\cdot)\) \(\chi_{4017}(1178,\cdot)\) \(\chi_{4017}(1217,\cdot)\) \(\chi_{4017}(1256,\cdot)\) \(\chi_{4017}(1409,\cdot)\) \(\chi_{4017}(1448,\cdot)\) \(\chi_{4017}(1487,\cdot)\) \(\chi_{4017}(1490,\cdot)\) \(\chi_{4017}(1526,\cdot)\) \(\chi_{4017}(1529,\cdot)\) \(\chi_{4017}(1565,\cdot)\) \(\chi_{4017}(1607,\cdot)\) \(\chi_{4017}(1646,\cdot)\) \(\chi_{4017}(1763,\cdot)\) \(\chi_{4017}(1799,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,-i,e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{53}{204}\right)\) | \(e\left(\frac{59}{204}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{71}{204}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) |