Basic properties
| Modulus: | \(784\) | |
| Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 784.bv
\(\chi_{784}(11,\cdot)\) \(\chi_{784}(51,\cdot)\) \(\chi_{784}(107,\cdot)\) \(\chi_{784}(123,\cdot)\) \(\chi_{784}(163,\cdot)\) \(\chi_{784}(179,\cdot)\) \(\chi_{784}(219,\cdot)\) \(\chi_{784}(235,\cdot)\) \(\chi_{784}(291,\cdot)\) \(\chi_{784}(331,\cdot)\) \(\chi_{784}(347,\cdot)\) \(\chi_{784}(387,\cdot)\) \(\chi_{784}(403,\cdot)\) \(\chi_{784}(443,\cdot)\) \(\chi_{784}(499,\cdot)\) \(\chi_{784}(515,\cdot)\) \(\chi_{784}(555,\cdot)\) \(\chi_{784}(571,\cdot)\) \(\chi_{784}(611,\cdot)\) \(\chi_{784}(627,\cdot)\) \(\chi_{784}(683,\cdot)\) \(\chi_{784}(723,\cdot)\) \(\chi_{784}(739,\cdot)\) \(\chi_{784}(779,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((687,197,689)\) → \((-1,i,e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 784 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) |