Basic properties
| Modulus: | \(3017\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(86\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3017.t
\(\chi_{3017}(6,\cdot)\) \(\chi_{3017}(27,\cdot)\) \(\chi_{3017}(48,\cdot)\) \(\chi_{3017}(55,\cdot)\) \(\chi_{3017}(216,\cdot)\) \(\chi_{3017}(384,\cdot)\) \(\chi_{3017}(433,\cdot)\) \(\chi_{3017}(440,\cdot)\) \(\chi_{3017}(447,\cdot)\) \(\chi_{3017}(503,\cdot)\) \(\chi_{3017}(559,\cdot)\) \(\chi_{3017}(580,\cdot)\) \(\chi_{3017}(755,\cdot)\) \(\chi_{3017}(874,\cdot)\) \(\chi_{3017}(916,\cdot)\) \(\chi_{3017}(958,\cdot)\) \(\chi_{3017}(972,\cdot)\) \(\chi_{3017}(1007,\cdot)\) \(\chi_{3017}(1091,\cdot)\) \(\chi_{3017}(1105,\cdot)\) \(\chi_{3017}(1301,\cdot)\) \(\chi_{3017}(1329,\cdot)\) \(\chi_{3017}(1357,\cdot)\) \(\chi_{3017}(1455,\cdot)\) \(\chi_{3017}(1581,\cdot)\) \(\chi_{3017}(1623,\cdot)\) \(\chi_{3017}(1630,\cdot)\) \(\chi_{3017}(1728,\cdot)\) \(\chi_{3017}(1742,\cdot)\) \(\chi_{3017}(1756,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{43})$ |
| Fixed field: | Number field defined by a degree 86 polynomial |
Values on generators
\((1725,869)\) → \((-1,e\left(\frac{3}{43}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3017 }(1357, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{43}\right)\) | \(e\left(\frac{3}{86}\right)\) | \(e\left(\frac{30}{43}\right)\) | \(e\left(\frac{31}{86}\right)\) | \(e\left(\frac{33}{86}\right)\) | \(e\left(\frac{2}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{61}{86}\right)\) | \(e\left(\frac{7}{43}\right)\) | \(e\left(\frac{63}{86}\right)\) |