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.hs
\(\chi_{6031}(29,\cdot)\) \(\chi_{6031}(66,\cdot)\) \(\chi_{6031}(82,\cdot)\) \(\chi_{6031}(208,\cdot)\) \(\chi_{6031}(310,\cdot)\) \(\chi_{6031}(378,\cdot)\) \(\chi_{6031}(393,\cdot)\) \(\chi_{6031}(399,\cdot)\) \(\chi_{6031}(569,\cdot)\) \(\chi_{6031}(578,\cdot)\) \(\chi_{6031}(606,\cdot)\) \(\chi_{6031}(637,\cdot)\) \(\chi_{6031}(643,\cdot)\) \(\chi_{6031}(865,\cdot)\) \(\chi_{6031}(954,\cdot)\) \(\chi_{6031}(985,\cdot)\) \(\chi_{6031}(1007,\cdot)\) \(\chi_{6031}(1022,\cdot)\) \(\chi_{6031}(1044,\cdot)\) \(\chi_{6031}(1050,\cdot)\) \(\chi_{6031}(1087,\cdot)\) \(\chi_{6031}(1102,\cdot)\) \(\chi_{6031}(1244,\cdot)\) \(\chi_{6031}(1324,\cdot)\) \(\chi_{6031}(1346,\cdot)\) \(\chi_{6031}(1377,\cdot)\) \(\chi_{6031}(1398,\cdot)\) \(\chi_{6031}(1420,\cdot)\) \(\chi_{6031}(1457,\cdot)\) \(\chi_{6031}(1546,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{107}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{324}\right)\) | \(e\left(\frac{71}{81}\right)\) | \(e\left(\frac{79}{162}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{143}{162}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{61}{81}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{44}{81}\right)\) |