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.ca
\(\chi_{1027}(2,\cdot)\) \(\chi_{1027}(19,\cdot)\) \(\chi_{1027}(32,\cdot)\) \(\chi_{1027}(72,\cdot)\) \(\chi_{1027}(76,\cdot)\) \(\chi_{1027}(84,\cdot)\) \(\chi_{1027}(98,\cdot)\) \(\chi_{1027}(110,\cdot)\) \(\chi_{1027}(111,\cdot)\) \(\chi_{1027}(115,\cdot)\) \(\chi_{1027}(128,\cdot)\) \(\chi_{1027}(162,\cdot)\) \(\chi_{1027}(163,\cdot)\) \(\chi_{1027}(171,\cdot)\) \(\chi_{1027}(189,\cdot)\) \(\chi_{1027}(241,\cdot)\) \(\chi_{1027}(262,\cdot)\) \(\chi_{1027}(288,\cdot)\) \(\chi_{1027}(336,\cdot)\) \(\chi_{1027}(392,\cdot)\) \(\chi_{1027}(431,\cdot)\) \(\chi_{1027}(435,\cdot)\) \(\chi_{1027}(440,\cdot)\) \(\chi_{1027}(444,\cdot)\) \(\chi_{1027}(500,\cdot)\) \(\chi_{1027}(514,\cdot)\) \(\chi_{1027}(518,\cdot)\) \(\chi_{1027}(579,\cdot)\) \(\chi_{1027}(643,\cdot)\) \(\chi_{1027}(648,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((80,872)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{31}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1027 }(163, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{73}{156}\right)\) |