Basic properties
| Modulus: | \(3017\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1290\) | 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.bf
\(\chi_{3017}(37,\cdot)\) \(\chi_{3017}(39,\cdot)\) \(\chi_{3017}(51,\cdot)\) \(\chi_{3017}(65,\cdot)\) \(\chi_{3017}(67,\cdot)\) \(\chi_{3017}(74,\cdot)\) \(\chi_{3017}(79,\cdot)\) \(\chi_{3017}(86,\cdot)\) \(\chi_{3017}(93,\cdot)\) \(\chi_{3017}(102,\cdot)\) \(\chi_{3017}(130,\cdot)\) \(\chi_{3017}(137,\cdot)\) \(\chi_{3017}(142,\cdot)\) \(\chi_{3017}(156,\cdot)\) \(\chi_{3017}(158,\cdot)\) \(\chi_{3017}(170,\cdot)\) \(\chi_{3017}(172,\cdot)\) \(\chi_{3017}(191,\cdot)\) \(\chi_{3017}(193,\cdot)\) \(\chi_{3017}(219,\cdot)\) \(\chi_{3017}(226,\cdot)\) \(\chi_{3017}(233,\cdot)\) \(\chi_{3017}(235,\cdot)\) \(\chi_{3017}(247,\cdot)\) \(\chi_{3017}(249,\cdot)\) \(\chi_{3017}(254,\cdot)\) \(\chi_{3017}(268,\cdot)\) \(\chi_{3017}(284,\cdot)\) \(\chi_{3017}(296,\cdot)\) \(\chi_{3017}(310,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{67}{430}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 3017 }(284, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{129}\right)\) | \(e\left(\frac{38}{129}\right)\) | \(e\left(\frac{29}{129}\right)\) | \(e\left(\frac{401}{645}\right)\) | \(e\left(\frac{39}{43}\right)\) | \(e\left(\frac{36}{43}\right)\) | \(e\left(\frac{76}{129}\right)\) | \(e\left(\frac{151}{645}\right)\) | \(e\left(\frac{514}{645}\right)\) | \(e\left(\frac{67}{129}\right)\) |