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
\((80,872)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{37}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(119, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{5}{52}\right)\) |