Basic properties
| Modulus: | \(1027\) | |
| Conductor: | \(1027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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 1027.bj
\(\chi_{1027}(22,\cdot)\) \(\chi_{1027}(87,\cdot)\) \(\chi_{1027}(100,\cdot)\) \(\chi_{1027}(146,\cdot)\) \(\chi_{1027}(204,\cdot)\) \(\chi_{1027}(289,\cdot)\) \(\chi_{1027}(302,\cdot)\) \(\chi_{1027}(334,\cdot)\) \(\chi_{1027}(354,\cdot)\) \(\chi_{1027}(380,\cdot)\) \(\chi_{1027}(484,\cdot)\) \(\chi_{1027}(536,\cdot)\) \(\chi_{1027}(575,\cdot)\) \(\chi_{1027}(620,\cdot)\) \(\chi_{1027}(640,\cdot)\) \(\chi_{1027}(653,\cdot)\) \(\chi_{1027}(757,\cdot)\) \(\chi_{1027}(763,\cdot)\) \(\chi_{1027}(776,\cdot)\) \(\chi_{1027}(828,\cdot)\) \(\chi_{1027}(854,\cdot)\) \(\chi_{1027}(887,\cdot)\) \(\chi_{1027}(958,\cdot)\) \(\chi_{1027}(1010,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((80,872)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{6}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(828, a) \) | \(1\) | \(1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) |