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
\((80,872)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{25}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1027 }(120, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) |