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.gn
\(\chi_{6031}(250,\cdot)\) \(\chi_{6031}(284,\cdot)\) \(\chi_{6031}(324,\cdot)\) \(\chi_{6031}(410,\cdot)\) \(\chi_{6031}(546,\cdot)\) \(\chi_{6031}(633,\cdot)\) \(\chi_{6031}(687,\cdot)\) \(\chi_{6031}(707,\cdot)\) \(\chi_{6031}(765,\cdot)\) \(\chi_{6031}(987,\cdot)\) \(\chi_{6031}(992,\cdot)\) \(\chi_{6031}(1002,\cdot)\) \(\chi_{6031}(1320,\cdot)\) \(\chi_{6031}(1447,\cdot)\) \(\chi_{6031}(1510,\cdot)\) \(\chi_{6031}(1669,\cdot)\) \(\chi_{6031}(1834,\cdot)\) \(\chi_{6031}(1890,\cdot)\) \(\chi_{6031}(1912,\cdot)\) \(\chi_{6031}(1982,\cdot)\) \(\chi_{6031}(2655,\cdot)\) \(\chi_{6031}(2657,\cdot)\) \(\chi_{6031}(2742,\cdot)\) \(\chi_{6031}(2768,\cdot)\) \(\chi_{6031}(2833,\cdot)\) \(\chi_{6031}(2842,\cdot)\) \(\chi_{6031}(2944,\cdot)\) \(\chi_{6031}(3101,\cdot)\) \(\chi_{6031}(3112,\cdot)\) \(\chi_{6031}(3148,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{23}{81}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(250, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{19}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{77}{81}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{38}{81}\right)\) | \(e\left(\frac{17}{81}\right)\) | \(e\left(\frac{55}{81}\right)\) |