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.el
\(\chi_{4017}(83,\cdot)\) \(\chi_{4017}(122,\cdot)\) \(\chi_{4017}(161,\cdot)\) \(\chi_{4017}(200,\cdot)\) \(\chi_{4017}(239,\cdot)\) \(\chi_{4017}(242,\cdot)\) \(\chi_{4017}(359,\cdot)\) \(\chi_{4017}(437,\cdot)\) \(\chi_{4017}(551,\cdot)\) \(\chi_{4017}(668,\cdot)\) \(\chi_{4017}(710,\cdot)\) \(\chi_{4017}(746,\cdot)\) \(\chi_{4017}(749,\cdot)\) \(\chi_{4017}(944,\cdot)\) \(\chi_{4017}(1019,\cdot)\) \(\chi_{4017}(1058,\cdot)\) \(\chi_{4017}(1253,\cdot)\) \(\chi_{4017}(1295,\cdot)\) \(\chi_{4017}(1334,\cdot)\) \(\chi_{4017}(1604,\cdot)\) \(\chi_{4017}(1643,\cdot)\) \(\chi_{4017}(1880,\cdot)\) \(\chi_{4017}(2075,\cdot)\) \(\chi_{4017}(2189,\cdot)\) \(\chi_{4017}(2192,\cdot)\) \(\chi_{4017}(2231,\cdot)\) \(\chi_{4017}(2270,\cdot)\) \(\chi_{4017}(2348,\cdot)\) \(\chi_{4017}(2384,\cdot)\) \(\chi_{4017}(2387,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,-i,e\left(\frac{19}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{131}{204}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{151}{204}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{97}{204}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) |