Basic properties
| Modulus: | \(1027\) | |
| Conductor: | \(1027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | 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 1027.bq
\(\chi_{1027}(30,\cdot)\) \(\chi_{1027}(43,\cdot)\) \(\chi_{1027}(75,\cdot)\) \(\chi_{1027}(82,\cdot)\) \(\chi_{1027}(127,\cdot)\) \(\chi_{1027}(153,\cdot)\) \(\chi_{1027}(186,\cdot)\) \(\chi_{1027}(205,\cdot)\) \(\chi_{1027}(212,\cdot)\) \(\chi_{1027}(218,\cdot)\) \(\chi_{1027}(244,\cdot)\) \(\chi_{1027}(303,\cdot)\) \(\chi_{1027}(322,\cdot)\) \(\chi_{1027}(465,\cdot)\) \(\chi_{1027}(472,\cdot)\) \(\chi_{1027}(511,\cdot)\) \(\chi_{1027}(537,\cdot)\) \(\chi_{1027}(582,\cdot)\) \(\chi_{1027}(621,\cdot)\) \(\chi_{1027}(667,\cdot)\) \(\chi_{1027}(745,\cdot)\) \(\chi_{1027}(764,\cdot)\) \(\chi_{1027}(829,\cdot)\) \(\chi_{1027}(849,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((80,872)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{17}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(127, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) |