Basic properties
| Modulus: | \(1093\) | |
| Conductor: | \(1093\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1092\) | 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 1093.x
\(\chi_{1093}(5,\cdot)\) \(\chi_{1093}(14,\cdot)\) \(\chi_{1093}(15,\cdot)\) \(\chi_{1093}(19,\cdot)\) \(\chi_{1093}(20,\cdot)\) \(\chi_{1093}(26,\cdot)\) \(\chi_{1093}(41,\cdot)\) \(\chi_{1093}(42,\cdot)\) \(\chi_{1093}(43,\cdot)\) \(\chi_{1093}(45,\cdot)\) \(\chi_{1093}(53,\cdot)\) \(\chi_{1093}(55,\cdot)\) \(\chi_{1093}(57,\cdot)\) \(\chi_{1093}(58,\cdot)\) \(\chi_{1093}(60,\cdot)\) \(\chi_{1093}(65,\cdot)\) \(\chi_{1093}(68,\cdot)\) \(\chi_{1093}(71,\cdot)\) \(\chi_{1093}(76,\cdot)\) \(\chi_{1093}(78,\cdot)\) \(\chi_{1093}(79,\cdot)\) \(\chi_{1093}(80,\cdot)\) \(\chi_{1093}(83,\cdot)\) \(\chi_{1093}(97,\cdot)\) \(\chi_{1093}(98,\cdot)\) \(\chi_{1093}(104,\cdot)\) \(\chi_{1093}(113,\cdot)\) \(\chi_{1093}(115,\cdot)\) \(\chi_{1093}(122,\cdot)\) \(\chi_{1093}(123,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1092})$ |
| Fixed field: | Number field defined by a degree 1092 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{1092}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1093 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{229}{364}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{47}{182}\right)\) | \(e\left(\frac{1}{1092}\right)\) | \(e\left(\frac{73}{364}\right)\) | \(e\left(\frac{155}{273}\right)\) | \(e\left(\frac{323}{364}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{172}{273}\right)\) | \(e\left(\frac{4}{13}\right)\) |