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 \(\chi_{1339}(124,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.eg
\(\chi_{4017}(124,\cdot)\) \(\chi_{4017}(202,\cdot)\) \(\chi_{4017}(292,\cdot)\) \(\chi_{4017}(397,\cdot)\) \(\chi_{4017}(418,\cdot)\) \(\chi_{4017}(466,\cdot)\) \(\chi_{4017}(496,\cdot)\) \(\chi_{4017}(526,\cdot)\) \(\chi_{4017}(535,\cdot)\) \(\chi_{4017}(661,\cdot)\) \(\chi_{4017}(769,\cdot)\) \(\chi_{4017}(808,\cdot)\) \(\chi_{4017}(877,\cdot)\) \(\chi_{4017}(886,\cdot)\) \(\chi_{4017}(925,\cdot)\) \(\chi_{4017}(994,\cdot)\) \(\chi_{4017}(1012,\cdot)\) \(\chi_{4017}(1138,\cdot)\) \(\chi_{4017}(1168,\cdot)\) \(\chi_{4017}(1207,\cdot)\) \(\chi_{4017}(1306,\cdot)\) \(\chi_{4017}(1384,\cdot)\) \(\chi_{4017}(1393,\cdot)\) \(\chi_{4017}(1519,\cdot)\) \(\chi_{4017}(1528,\cdot)\) \(\chi_{4017}(1588,\cdot)\) \(\chi_{4017}(1762,\cdot)\) \(\chi_{4017}(1939,\cdot)\) \(\chi_{4017}(1969,\cdot)\) \(\chi_{4017}(2008,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{43}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(124, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{204}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{137}{204}\right)\) | \(e\left(\frac{157}{204}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{35}{102}\right)\) |