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.bv
\(\chi_{1027}(61,\cdot)\) \(\chi_{1027}(94,\cdot)\) \(\chi_{1027}(120,\cdot)\) \(\chi_{1027}(172,\cdot)\) \(\chi_{1027}(185,\cdot)\) \(\chi_{1027}(191,\cdot)\) \(\chi_{1027}(295,\cdot)\) \(\chi_{1027}(308,\cdot)\) \(\chi_{1027}(328,\cdot)\) \(\chi_{1027}(373,\cdot)\) \(\chi_{1027}(412,\cdot)\) \(\chi_{1027}(464,\cdot)\) \(\chi_{1027}(568,\cdot)\) \(\chi_{1027}(594,\cdot)\) \(\chi_{1027}(614,\cdot)\) \(\chi_{1027}(646,\cdot)\) \(\chi_{1027}(659,\cdot)\) \(\chi_{1027}(744,\cdot)\) \(\chi_{1027}(802,\cdot)\) \(\chi_{1027}(848,\cdot)\) \(\chi_{1027}(861,\cdot)\) \(\chi_{1027}(926,\cdot)\) \(\chi_{1027}(965,\cdot)\) \(\chi_{1027}(1017,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((80,872)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(1017, a) \) | \(-1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) |