Basic properties
| Modulus: | \(140659\) | |
| Conductor: | \(140659\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70329\) | 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 140659.be
\(\chi_{140659}(6,\cdot)\) \(\chi_{140659}(9,\cdot)\) \(\chi_{140659}(11,\cdot)\) \(\chi_{140659}(13,\cdot)\) \(\chi_{140659}(19,\cdot)\) \(\chi_{140659}(21,\cdot)\) \(\chi_{140659}(30,\cdot)\) \(\chi_{140659}(36,\cdot)\) \(\chi_{140659}(44,\cdot)\) \(\chi_{140659}(45,\cdot)\) \(\chi_{140659}(52,\cdot)\) \(\chi_{140659}(55,\cdot)\) \(\chi_{140659}(66,\cdot)\) \(\chi_{140659}(74,\cdot)\) \(\chi_{140659}(76,\cdot)\) \(\chi_{140659}(81,\cdot)\) \(\chi_{140659}(84,\cdot)\) \(\chi_{140659}(86,\cdot)\) \(\chi_{140659}(95,\cdot)\) \(\chi_{140659}(96,\cdot)\) \(\chi_{140659}(97,\cdot)\) \(\chi_{140659}(105,\cdot)\) \(\chi_{140659}(106,\cdot)\) \(\chi_{140659}(109,\cdot)\) \(\chi_{140659}(113,\cdot)\) \(\chi_{140659}(114,\cdot)\) \(\chi_{140659}(117,\cdot)\) \(\chi_{140659}(121,\cdot)\) \(\chi_{140659}(122,\cdot)\) \(\chi_{140659}(123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{70329})$ |
| Fixed field: | Number field defined by a degree 70329 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{56621}{70329}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 140659 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{2220}{23443}\right)\) | \(e\left(\frac{56621}{70329}\right)\) | \(e\left(\frac{4440}{23443}\right)\) | \(e\left(\frac{2749}{3349}\right)\) | \(e\left(\frac{63281}{70329}\right)\) | \(e\left(\frac{21942}{23443}\right)\) | \(e\left(\frac{6660}{23443}\right)\) | \(e\left(\frac{42913}{70329}\right)\) | \(e\left(\frac{21463}{23443}\right)\) | \(e\left(\frac{43907}{70329}\right)\) |