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.ef
\(\chi_{4017}(137,\cdot)\) \(\chi_{4017}(167,\cdot)\) \(\chi_{4017}(215,\cdot)\) \(\chi_{4017}(236,\cdot)\) \(\chi_{4017}(323,\cdot)\) \(\chi_{4017}(332,\cdot)\) \(\chi_{4017}(488,\cdot)\) \(\chi_{4017}(587,\cdot)\) \(\chi_{4017}(596,\cdot)\) \(\chi_{4017}(626,\cdot)\) \(\chi_{4017}(734,\cdot)\) \(\chi_{4017}(782,\cdot)\) \(\chi_{4017}(800,\cdot)\) \(\chi_{4017}(821,\cdot)\) \(\chi_{4017}(890,\cdot)\) \(\chi_{4017}(917,\cdot)\) \(\chi_{4017}(1064,\cdot)\) \(\chi_{4017}(1094,\cdot)\) \(\chi_{4017}(1142,\cdot)\) \(\chi_{4017}(1163,\cdot)\) \(\chi_{4017}(1250,\cdot)\) \(\chi_{4017}(1259,\cdot)\) \(\chi_{4017}(1415,\cdot)\) \(\chi_{4017}(1514,\cdot)\) \(\chi_{4017}(1523,\cdot)\) \(\chi_{4017}(1553,\cdot)\) \(\chi_{4017}(1709,\cdot)\) \(\chi_{4017}(1727,\cdot)\) \(\chi_{4017}(1748,\cdot)\) \(\chi_{4017}(1844,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{2}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{113}{204}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{19}{204}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) |