Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | 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.dt
\(\chi_{4017}(17,\cdot)\) \(\chi_{4017}(335,\cdot)\) \(\chi_{4017}(407,\cdot)\) \(\chi_{4017}(647,\cdot)\) \(\chi_{4017}(686,\cdot)\) \(\chi_{4017}(842,\cdot)\) \(\chi_{4017}(1148,\cdot)\) \(\chi_{4017}(1193,\cdot)\) \(\chi_{4017}(1343,\cdot)\) \(\chi_{4017}(1388,\cdot)\) \(\chi_{4017}(1421,\cdot)\) \(\chi_{4017}(1577,\cdot)\) \(\chi_{4017}(1655,\cdot)\) \(\chi_{4017}(1856,\cdot)\) \(\chi_{4017}(1895,\cdot)\) \(\chi_{4017}(1973,\cdot)\) \(\chi_{4017}(2012,\cdot)\) \(\chi_{4017}(2123,\cdot)\) \(\chi_{4017}(2201,\cdot)\) \(\chi_{4017}(2246,\cdot)\) \(\chi_{4017}(2285,\cdot)\) \(\chi_{4017}(2318,\cdot)\) \(\chi_{4017}(2357,\cdot)\) \(\chi_{4017}(2363,\cdot)\) \(\chi_{4017}(2909,\cdot)\) \(\chi_{4017}(2942,\cdot)\) \(\chi_{4017}(3020,\cdot)\) \(\chi_{4017}(3221,\cdot)\) \(\chi_{4017}(3332,\cdot)\) \(\chi_{4017}(3449,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{16}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(2363, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{43}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{13}{102}\right)\) |