Basic properties
Modulus: | \(1027\) | |
Conductor: | \(1027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | 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.ce
\(\chi_{1027}(11,\cdot)\) \(\chi_{1027}(20,\cdot)\) \(\chi_{1027}(45,\cdot)\) \(\chi_{1027}(50,\cdot)\) \(\chi_{1027}(119,\cdot)\) \(\chi_{1027}(123,\cdot)\) \(\chi_{1027}(124,\cdot)\) \(\chi_{1027}(167,\cdot)\) \(\chi_{1027}(184,\cdot)\) \(\chi_{1027}(202,\cdot)\) \(\chi_{1027}(253,\cdot)\) \(\chi_{1027}(279,\cdot)\) \(\chi_{1027}(310,\cdot)\) \(\chi_{1027}(318,\cdot)\) \(\chi_{1027}(327,\cdot)\) \(\chi_{1027}(332,\cdot)\) \(\chi_{1027}(358,\cdot)\) \(\chi_{1027}(366,\cdot)\) \(\chi_{1027}(388,\cdot)\) \(\chi_{1027}(397,\cdot)\) \(\chi_{1027}(414,\cdot)\) \(\chi_{1027}(427,\cdot)\) \(\chi_{1027}(479,\cdot)\) \(\chi_{1027}(483,\cdot)\) \(\chi_{1027}(487,\cdot)\) \(\chi_{1027}(505,\cdot)\) \(\chi_{1027}(557,\cdot)\) \(\chi_{1027}(566,\cdot)\) \(\chi_{1027}(578,\cdot)\) \(\chi_{1027}(604,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((80,872)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{1}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1027 }(167, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{43}{52}\right)\) |