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.hy
\(\chi_{6031}(2,\cdot)\) \(\chi_{6031}(19,\cdot)\) \(\chi_{6031}(32,\cdot)\) \(\chi_{6031}(76,\cdot)\) \(\chi_{6031}(79,\cdot)\) \(\chi_{6031}(128,\cdot)\) \(\chi_{6031}(207,\cdot)\) \(\chi_{6031}(283,\cdot)\) \(\chi_{6031}(316,\cdot)\) \(\chi_{6031}(420,\cdot)\) \(\chi_{6031}(427,\cdot)\) \(\chi_{6031}(442,\cdot)\) \(\chi_{6031}(533,\cdot)\) \(\chi_{6031}(722,\cdot)\) \(\chi_{6031}(799,\cdot)\) \(\chi_{6031}(801,\cdot)\) \(\chi_{6031}(883,\cdot)\) \(\chi_{6031}(1041,\cdot)\) \(\chi_{6031}(1125,\cdot)\) \(\chi_{6031}(1132,\cdot)\) \(\chi_{6031}(1186,\cdot)\) \(\chi_{6031}(1216,\cdot)\) \(\chi_{6031}(1253,\cdot)\) \(\chi_{6031}(1278,\cdot)\) \(\chi_{6031}(1354,\cdot)\) \(\chi_{6031}(1426,\cdot)\) \(\chi_{6031}(1458,\cdot)\) \(\chi_{6031}(1485,\cdot)\) \(\chi_{6031}(1534,\cdot)\) \(\chi_{6031}(1641,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((816,5218)\) → \((e\left(\frac{1}{36}\right),e\left(\frac{1}{162}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6031 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{324}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{11}{162}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{55}{162}\right)\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{56}{81}\right)\) | \(e\left(\frac{62}{81}\right)\) | \(e\left(\frac{10}{81}\right)\) |