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.hv
\(\chi_{6031}(18,\cdot)\) \(\chi_{6031}(89,\cdot)\) \(\chi_{6031}(124,\cdot)\) \(\chi_{6031}(165,\cdot)\) \(\chi_{6031}(239,\cdot)\) \(\chi_{6031}(279,\cdot)\) \(\chi_{6031}(346,\cdot)\) \(\chi_{6031}(368,\cdot)\) \(\chi_{6031}(389,\cdot)\) \(\chi_{6031}(664,\cdot)\) \(\chi_{6031}(684,\cdot)\) \(\chi_{6031}(772,\cdot)\) \(\chi_{6031}(833,\cdot)\) \(\chi_{6031}(1060,\cdot)\) \(\chi_{6031}(1086,\cdot)\) \(\chi_{6031}(1108,\cdot)\) \(\chi_{6031}(1152,\cdot)\) \(\chi_{6031}(1160,\cdot)\) \(\chi_{6031}(1290,\cdot)\) \(\chi_{6031}(1300,\cdot)\) \(\chi_{6031}(1349,\cdot)\) \(\chi_{6031}(1356,\cdot)\) \(\chi_{6031}(1499,\cdot)\) \(\chi_{6031}(1535,\cdot)\) \(\chi_{6031}(1539,\cdot)\) \(\chi_{6031}(1559,\cdot)\) \(\chi_{6031}(1576,\cdot)\) \(\chi_{6031}(1615,\cdot)\) \(\chi_{6031}(1633,\cdot)\) \(\chi_{6031}(1737,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{17}{36}\right),e\left(\frac{41}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{235}{324}\right)\) | \(e\left(\frac{68}{81}\right)\) | \(e\left(\frac{73}{162}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{95}{162}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{55}{81}\right)\) | \(e\left(\frac{31}{81}\right)\) | \(e\left(\frac{5}{81}\right)\) |