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.bp
\(\chi_{1027}(77,\cdot)\) \(\chi_{1027}(116,\cdot)\) \(\chi_{1027}(142,\cdot)\) \(\chi_{1027}(233,\cdot)\) \(\chi_{1027}(272,\cdot)\) \(\chi_{1027}(285,\cdot)\) \(\chi_{1027}(311,\cdot)\) \(\chi_{1027}(350,\cdot)\) \(\chi_{1027}(363,\cdot)\) \(\chi_{1027}(376,\cdot)\) \(\chi_{1027}(402,\cdot)\) \(\chi_{1027}(454,\cdot)\) \(\chi_{1027}(480,\cdot)\) \(\chi_{1027}(623,\cdot)\) \(\chi_{1027}(662,\cdot)\) \(\chi_{1027}(675,\cdot)\) \(\chi_{1027}(714,\cdot)\) \(\chi_{1027}(740,\cdot)\) \(\chi_{1027}(779,\cdot)\) \(\chi_{1027}(818,\cdot)\) \(\chi_{1027}(844,\cdot)\) \(\chi_{1027}(922,\cdot)\) \(\chi_{1027}(935,\cdot)\) \(\chi_{1027}(987,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((80,872)\) → \((-1,e\left(\frac{19}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(116, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{5}{78}\right)\) |