Basic properties
| Modulus: | \(6031\) | |
| Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6031.gl
\(\chi_{6031}(41,\cdot)\) \(\chi_{6031}(95,\cdot)\) \(\chi_{6031}(189,\cdot)\) \(\chi_{6031}(373,\cdot)\) \(\chi_{6031}(469,\cdot)\) \(\chi_{6031}(691,\cdot)\) \(\chi_{6031}(946,\cdot)\) \(\chi_{6031}(1027,\cdot)\) \(\chi_{6031}(1040,\cdot)\) \(\chi_{6031}(1138,\cdot)\) \(\chi_{6031}(1151,\cdot)\) \(\chi_{6031}(1187,\cdot)\) \(\chi_{6031}(1212,\cdot)\) \(\chi_{6031}(1224,\cdot)\) \(\chi_{6031}(1471,\cdot)\) \(\chi_{6031}(1521,\cdot)\) \(\chi_{6031}(1558,\cdot)\) \(\chi_{6031}(1612,\cdot)\) \(\chi_{6031}(1619,\cdot)\) \(\chi_{6031}(1764,\cdot)\) \(\chi_{6031}(1853,\cdot)\) \(\chi_{6031}(2056,\cdot)\) \(\chi_{6031}(2112,\cdot)\) \(\chi_{6031}(2134,\cdot)\) \(\chi_{6031}(2393,\cdot)\) \(\chi_{6031}(2689,\cdot)\) \(\chi_{6031}(2805,\cdot)\) \(\chi_{6031}(2840,\cdot)\) \(\chi_{6031}(2889,\cdot)\) \(\chi_{6031}(2990,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{76}{81}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(691, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{80}{81}\right)\) | \(e\left(\frac{35}{81}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{31}{81}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{79}{81}\right)\) | \(e\left(\frac{55}{81}\right)\) | \(e\left(\frac{35}{81}\right)\) |