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.br
\(\chi_{1027}(17,\cdot)\) \(\chi_{1027}(69,\cdot)\) \(\chi_{1027}(140,\cdot)\) \(\chi_{1027}(173,\cdot)\) \(\chi_{1027}(199,\cdot)\) \(\chi_{1027}(251,\cdot)\) \(\chi_{1027}(264,\cdot)\) \(\chi_{1027}(270,\cdot)\) \(\chi_{1027}(374,\cdot)\) \(\chi_{1027}(387,\cdot)\) \(\chi_{1027}(407,\cdot)\) \(\chi_{1027}(452,\cdot)\) \(\chi_{1027}(491,\cdot)\) \(\chi_{1027}(543,\cdot)\) \(\chi_{1027}(647,\cdot)\) \(\chi_{1027}(673,\cdot)\) \(\chi_{1027}(693,\cdot)\) \(\chi_{1027}(725,\cdot)\) \(\chi_{1027}(738,\cdot)\) \(\chi_{1027}(823,\cdot)\) \(\chi_{1027}(881,\cdot)\) \(\chi_{1027}(927,\cdot)\) \(\chi_{1027}(940,\cdot)\) \(\chi_{1027}(1005,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((80,872)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{11}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(1005, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) |