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.gs
\(\chi_{6031}(4,\cdot)\) \(\chi_{6031}(152,\cdot)\) \(\chi_{6031}(210,\cdot)\) \(\chi_{6031}(361,\cdot)\) \(\chi_{6031}(632,\cdot)\) \(\chi_{6031}(854,\cdot)\) \(\chi_{6031}(1024,\cdot)\) \(\chi_{6031}(1029,\cdot)\) \(\chi_{6031}(1061,\cdot)\) \(\chi_{6031}(1066,\cdot)\) \(\chi_{6031}(1373,\cdot)\) \(\chi_{6031}(1399,\cdot)\) \(\chi_{6031}(1501,\cdot)\) \(\chi_{6031}(1508,\cdot)\) \(\chi_{6031}(1656,\cdot)\) \(\chi_{6031}(1686,\cdot)\) \(\chi_{6031}(1690,\cdot)\) \(\chi_{6031}(1927,\cdot)\) \(\chi_{6031}(1949,\cdot)\) \(\chi_{6031}(2250,\cdot)\) \(\chi_{6031}(2297,\cdot)\) \(\chi_{6031}(2315,\cdot)\) \(\chi_{6031}(2372,\cdot)\) \(\chi_{6031}(2507,\cdot)\) \(\chi_{6031}(2556,\cdot)\) \(\chi_{6031}(2618,\cdot)\) \(\chi_{6031}(2726,\cdot)\) \(\chi_{6031}(2759,\cdot)\) \(\chi_{6031}(2852,\cdot)\) \(\chi_{6031}(2916,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{1}{81}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{162}\right)\) | \(e\left(\frac{56}{81}\right)\) | \(e\left(\frac{11}{81}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{55}{81}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{31}{81}\right)\) | \(e\left(\frac{43}{81}\right)\) | \(e\left(\frac{20}{81}\right)\) |