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 \(\chi_{1339}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4017.em
\(\chi_{4017}(19,\cdot)\) \(\chi_{4017}(97,\cdot)\) \(\chi_{4017}(163,\cdot)\) \(\chi_{4017}(223,\cdot)\) \(\chi_{4017}(358,\cdot)\) \(\chi_{4017}(427,\cdot)\) \(\chi_{4017}(613,\cdot)\) \(\chi_{4017}(622,\cdot)\) \(\chi_{4017}(643,\cdot)\) \(\chi_{4017}(700,\cdot)\) \(\chi_{4017}(826,\cdot)\) \(\chi_{4017}(856,\cdot)\) \(\chi_{4017}(865,\cdot)\) \(\chi_{4017}(934,\cdot)\) \(\chi_{4017}(943,\cdot)\) \(\chi_{4017}(955,\cdot)\) \(\chi_{4017}(982,\cdot)\) \(\chi_{4017}(1216,\cdot)\) \(\chi_{4017}(1255,\cdot)\) \(\chi_{4017}(1333,\cdot)\) \(\chi_{4017}(1354,\cdot)\) \(\chi_{4017}(1402,\cdot)\) \(\chi_{4017}(1480,\cdot)\) \(\chi_{4017}(1501,\cdot)\) \(\chi_{4017}(1549,\cdot)\) \(\chi_{4017}(1597,\cdot)\) \(\chi_{4017}(1627,\cdot)\) \(\chi_{4017}(1636,\cdot)\) \(\chi_{4017}(1783,\cdot)\) \(\chi_{4017}(1861,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1340,1237,1756)\) → \((1,e\left(\frac{5}{12}\right),e\left(\frac{40}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 4017 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{109}{204}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) |