Basic properties
| Modulus: | \(729\) | |
| Conductor: | \(729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(243\) | 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 729.k
\(\chi_{729}(4,\cdot)\) \(\chi_{729}(7,\cdot)\) \(\chi_{729}(13,\cdot)\) \(\chi_{729}(16,\cdot)\) \(\chi_{729}(22,\cdot)\) \(\chi_{729}(25,\cdot)\) \(\chi_{729}(31,\cdot)\) \(\chi_{729}(34,\cdot)\) \(\chi_{729}(40,\cdot)\) \(\chi_{729}(43,\cdot)\) \(\chi_{729}(49,\cdot)\) \(\chi_{729}(52,\cdot)\) \(\chi_{729}(58,\cdot)\) \(\chi_{729}(61,\cdot)\) \(\chi_{729}(67,\cdot)\) \(\chi_{729}(70,\cdot)\) \(\chi_{729}(76,\cdot)\) \(\chi_{729}(79,\cdot)\) \(\chi_{729}(85,\cdot)\) \(\chi_{729}(88,\cdot)\) \(\chi_{729}(94,\cdot)\) \(\chi_{729}(97,\cdot)\) \(\chi_{729}(103,\cdot)\) \(\chi_{729}(106,\cdot)\) \(\chi_{729}(112,\cdot)\) \(\chi_{729}(115,\cdot)\) \(\chi_{729}(121,\cdot)\) \(\chi_{729}(124,\cdot)\) \(\chi_{729}(130,\cdot)\) \(\chi_{729}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{243})$ |
| Fixed field: | Number field defined by a degree 243 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{166}{243}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 729 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{166}{243}\right)\) | \(e\left(\frac{89}{243}\right)\) | \(e\left(\frac{173}{243}\right)\) | \(e\left(\frac{37}{243}\right)\) | \(e\left(\frac{4}{81}\right)\) | \(e\left(\frac{32}{81}\right)\) | \(e\left(\frac{79}{243}\right)\) | \(e\left(\frac{194}{243}\right)\) | \(e\left(\frac{203}{243}\right)\) | \(e\left(\frac{178}{243}\right)\) |