Basic properties
| Modulus: | \(6031\) | |
| Conductor: | \(6031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(324\) | 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.hp
\(\chi_{6031}(45,\cdot)\) \(\chi_{6031}(103,\cdot)\) \(\chi_{6031}(230,\cdot)\) \(\chi_{6031}(236,\cdot)\) \(\chi_{6031}(245,\cdot)\) \(\chi_{6031}(415,\cdot)\) \(\chi_{6031}(473,\cdot)\) \(\chi_{6031}(541,\cdot)\) \(\chi_{6031}(732,\cdot)\) \(\chi_{6031}(769,\cdot)\) \(\chi_{6031}(791,\cdot)\) \(\chi_{6031}(800,\cdot)\) \(\chi_{6031}(806,\cdot)\) \(\chi_{6031}(822,\cdot)\) \(\chi_{6031}(859,\cdot)\) \(\chi_{6031}(939,\cdot)\) \(\chi_{6031}(1028,\cdot)\) \(\chi_{6031}(1081,\cdot)\) \(\chi_{6031}(1161,\cdot)\) \(\chi_{6031}(1170,\cdot)\) \(\chi_{6031}(1207,\cdot)\) \(\chi_{6031}(1213,\cdot)\) \(\chi_{6031}(1235,\cdot)\) \(\chi_{6031}(1250,\cdot)\) \(\chi_{6031}(1383,\cdot)\) \(\chi_{6031}(1451,\cdot)\) \(\chi_{6031}(1509,\cdot)\) \(\chi_{6031}(1540,\cdot)\) \(\chi_{6031}(1583,\cdot)\) \(\chi_{6031}(1620,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{55}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{324}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{137}{162}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{73}{162}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{74}{81}\right)\) | \(e\left(\frac{35}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) |