Basic properties
| Modulus: | \(4017\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.eo
\(\chi_{4017}(67,\cdot)\) \(\chi_{4017}(85,\cdot)\) \(\chi_{4017}(115,\cdot)\) \(\chi_{4017}(154,\cdot)\) \(\chi_{4017}(241,\cdot)\) \(\chi_{4017}(271,\cdot)\) \(\chi_{4017}(280,\cdot)\) \(\chi_{4017}(349,\cdot)\) \(\chi_{4017}(379,\cdot)\) \(\chi_{4017}(457,\cdot)\) \(\chi_{4017}(487,\cdot)\) \(\chi_{4017}(592,\cdot)\) \(\chi_{4017}(799,\cdot)\) \(\chi_{4017}(817,\cdot)\) \(\chi_{4017}(895,\cdot)\) \(\chi_{4017}(1042,\cdot)\) \(\chi_{4017}(1051,\cdot)\) \(\chi_{4017}(1081,\cdot)\) \(\chi_{4017}(1129,\cdot)\) \(\chi_{4017}(1177,\cdot)\) \(\chi_{4017}(1198,\cdot)\) \(\chi_{4017}(1276,\cdot)\) \(\chi_{4017}(1324,\cdot)\) \(\chi_{4017}(1345,\cdot)\) \(\chi_{4017}(1423,\cdot)\) \(\chi_{4017}(1462,\cdot)\) \(\chi_{4017}(1696,\cdot)\) \(\chi_{4017}(1723,\cdot)\) \(\chi_{4017}(1735,\cdot)\) \(\chi_{4017}(1744,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{1}{12}\right),e\left(\frac{13}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{179}{204}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{73}{204}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) |