Basic properties
| Modulus: | \(8021\) | |
| Conductor: | \(8021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(231\) | 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 8021.dg
\(\chi_{8021}(16,\cdot)\) \(\chi_{8021}(94,\cdot)\) \(\chi_{8021}(133,\cdot)\) \(\chi_{8021}(198,\cdot)\) \(\chi_{8021}(256,\cdot)\) \(\chi_{8021}(308,\cdot)\) \(\chi_{8021}(334,\cdot)\) \(\chi_{8021}(438,\cdot)\) \(\chi_{8021}(445,\cdot)\) \(\chi_{8021}(536,\cdot)\) \(\chi_{8021}(568,\cdot)\) \(\chi_{8021}(633,\cdot)\) \(\chi_{8021}(711,\cdot)\) \(\chi_{8021}(750,\cdot)\) \(\chi_{8021}(815,\cdot)\) \(\chi_{8021}(887,\cdot)\) \(\chi_{8021}(1030,\cdot)\) \(\chi_{8021}(1062,\cdot)\) \(\chi_{8021}(1069,\cdot)\) \(\chi_{8021}(1153,\cdot)\) \(\chi_{8021}(1238,\cdot)\) \(\chi_{8021}(1368,\cdot)\) \(\chi_{8021}(1504,\cdot)\) \(\chi_{8021}(1511,\cdot)\) \(\chi_{8021}(1628,\cdot)\) \(\chi_{8021}(1641,\cdot)\) \(\chi_{8021}(1647,\cdot)\) \(\chi_{8021}(1680,\cdot)\) \(\chi_{8021}(1686,\cdot)\) \(\chi_{8021}(1784,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 231 polynomial (not computed) |
Values on generators
\((6788,2471)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{60}{77}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{38}{231}\right)\) |