Basic properties
Modulus: | \(729\) | |
Conductor: | \(729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(486\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 729.l
\(\chi_{729}(2,\cdot)\) \(\chi_{729}(5,\cdot)\) \(\chi_{729}(11,\cdot)\) \(\chi_{729}(14,\cdot)\) \(\chi_{729}(20,\cdot)\) \(\chi_{729}(23,\cdot)\) \(\chi_{729}(29,\cdot)\) \(\chi_{729}(32,\cdot)\) \(\chi_{729}(38,\cdot)\) \(\chi_{729}(41,\cdot)\) \(\chi_{729}(47,\cdot)\) \(\chi_{729}(50,\cdot)\) \(\chi_{729}(56,\cdot)\) \(\chi_{729}(59,\cdot)\) \(\chi_{729}(65,\cdot)\) \(\chi_{729}(68,\cdot)\) \(\chi_{729}(74,\cdot)\) \(\chi_{729}(77,\cdot)\) \(\chi_{729}(83,\cdot)\) \(\chi_{729}(86,\cdot)\) \(\chi_{729}(92,\cdot)\) \(\chi_{729}(95,\cdot)\) \(\chi_{729}(101,\cdot)\) \(\chi_{729}(104,\cdot)\) \(\chi_{729}(110,\cdot)\) \(\chi_{729}(113,\cdot)\) \(\chi_{729}(119,\cdot)\) \(\chi_{729}(122,\cdot)\) \(\chi_{729}(128,\cdot)\) \(\chi_{729}(131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{243})$ |
Fixed field: | Number field defined by a degree 486 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{486}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 729 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{486}\right)\) | \(e\left(\frac{1}{243}\right)\) | \(e\left(\frac{23}{486}\right)\) | \(e\left(\frac{197}{243}\right)\) | \(e\left(\frac{1}{162}\right)\) | \(e\left(\frac{4}{81}\right)\) | \(e\left(\frac{283}{486}\right)\) | \(e\left(\frac{166}{243}\right)\) | \(e\left(\frac{395}{486}\right)\) | \(e\left(\frac{2}{243}\right)\) |