Basic properties
| Modulus: | \(3089\) | |
| Conductor: | \(3089\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(772\) | 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 3089.h
\(\chi_{3089}(2,\cdot)\) \(\chi_{3089}(8,\cdot)\) \(\chi_{3089}(25,\cdot)\) \(\chi_{3089}(32,\cdot)\) \(\chi_{3089}(45,\cdot)\) \(\chi_{3089}(47,\cdot)\) \(\chi_{3089}(49,\cdot)\) \(\chi_{3089}(69,\cdot)\) \(\chi_{3089}(70,\cdot)\) \(\chi_{3089}(77,\cdot)\) \(\chi_{3089}(78,\cdot)\) \(\chi_{3089}(79,\cdot)\) \(\chi_{3089}(81,\cdot)\) \(\chi_{3089}(86,\cdot)\) \(\chi_{3089}(100,\cdot)\) \(\chi_{3089}(110,\cdot)\) \(\chi_{3089}(118,\cdot)\) \(\chi_{3089}(121,\cdot)\) \(\chi_{3089}(122,\cdot)\) \(\chi_{3089}(126,\cdot)\) \(\chi_{3089}(128,\cdot)\) \(\chi_{3089}(133,\cdot)\) \(\chi_{3089}(146,\cdot)\) \(\chi_{3089}(155,\cdot)\) \(\chi_{3089}(180,\cdot)\) \(\chi_{3089}(188,\cdot)\) \(\chi_{3089}(190,\cdot)\) \(\chi_{3089}(196,\cdot)\) \(\chi_{3089}(198,\cdot)\) \(\chi_{3089}(209,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{772})$ |
| Fixed field: | Number field defined by a degree 772 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{561}{772}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3089 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{120}{193}\right)\) | \(e\left(\frac{561}{772}\right)\) | \(e\left(\frac{47}{193}\right)\) | \(e\left(\frac{131}{386}\right)\) | \(e\left(\frac{269}{772}\right)\) | \(e\left(\frac{279}{386}\right)\) | \(e\left(\frac{167}{193}\right)\) | \(e\left(\frac{175}{386}\right)\) | \(e\left(\frac{371}{386}\right)\) | \(e\left(\frac{203}{386}\right)\) |